\setlength{\unitlength}{0.1bp}
%\addtocounter{subfigure}{1}
\begin{picture}(4000,5000)(1000,0)
\put(0,3000){\mbox{\hspace*{-0.5cm}
\subfigure[]{
\special{!
%!PS-Adobe-2.0
%%Creator: gnuplot
%%DocumentFonts: Helvetica
%%BoundingBox: 50 50 590 554
%%Pages: (atend)
%%EndComments
/gnudict 40 dict def
gnudict begin
/Color false def
/Solid false def
/gnulinewidth 5.000 def
/vshift -33 def
/dl {10 mul} def
/hpt 31.5 def
/vpt 31.5 def
/M {moveto} bind def
/L {lineto} bind def
/R {rmoveto} bind def
/V {rlineto} bind def
/vpt2 vpt 2 mul def
/hpt2 hpt 2 mul def
/Lshow { currentpoint stroke M
  0 vshift R show } def
/Rshow { currentpoint stroke M
  dup stringwidth pop neg vshift R show } def
/Cshow { currentpoint stroke M
  dup stringwidth pop -2 div vshift R show } def
/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
 {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
/BL { stroke gnulinewidth 2 mul setlinewidth } def
/AL { stroke gnulinewidth 2 div setlinewidth } def
/PL { stroke gnulinewidth setlinewidth } def
/LTb { BL [] 0 0 0 DL } def
/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def
/LT0 { PL [] 0 1 0 DL } def
/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def
/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def
/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
/P { stroke [] 0 setdash
  currentlinewidth 2 div sub M
  0 currentlinewidth V stroke } def
/D { stroke [] 0 setdash 2 copy vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath stroke
  P } def
/A { stroke [] 0 setdash vpt sub M 0 vpt2 V
  currentpoint stroke M
  hpt neg vpt neg R hpt2 0 V stroke
  } def
/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V closepath stroke
  P } def
/C { stroke [] 0 setdash exch hpt sub exch vpt add M
  hpt2 vpt2 neg V currentpoint stroke M
  hpt2 neg 0 R hpt2 vpt2 V stroke } def
/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath stroke
  P  } def
/S { 2 copy A C} def
end
%%EndProlog
}
\begin{picture}(2700,2160)(0,0)
\special{"
%%Page: 1 1
gnudict begin
gsave
50 50 translate
0.100 0.100 scale
0 setgray
/Helvetica findfont 100 scalefont setfont
newpath
-500.000000 -500.000000 translate
LTa
LTb
600 251 M
63 0 V
1854 0 R
-63 0 V
600 457 M
63 0 V
1854 0 R
-63 0 V
600 664 M
63 0 V
1854 0 R
-63 0 V
600 870 M
63 0 V
1854 0 R
-63 0 V
600 1077 M
63 0 V
1854 0 R
-63 0 V
600 1283 M
63 0 V
1854 0 R
-63 0 V
600 1490 M
63 0 V
1854 0 R
-63 0 V
600 1696 M
63 0 V
1854 0 R
-63 0 V
600 1903 M
63 0 V
1854 0 R
-63 0 V
600 2109 M
63 0 V
1854 0 R
-63 0 V
826 251 M
0 63 V
0 1795 R
0 -63 V
1107 251 M
0 63 V
0 1795 R
0 -63 V
1389 251 M
0 63 V
0 1795 R
0 -63 V
1671 251 M
0 63 V
0 1795 R
0 -63 V
1953 251 M
0 63 V
0 1795 R
0 -63 V
2235 251 M
0 63 V
0 1795 R
0 -63 V
2517 251 M
0 63 V
0 1795 R
0 -63 V
600 251 M
1917 0 V
0 1858 V
-1917 0 V
600 251 L
LT0
2214 1946 M
180 0 V
600 1576 M
19 -195 V
20 -131 V
19 -95 V
19 -73 V
20 -59 V
19 -48 V
20 -40 V
19 -35 V
19 -30 V
20 -26 V
19 -23 V
19 -21 V
20 -19 V
19 -17 V
19 -16 V
20 -14 V
19 -14 V
20 -12 V
19 -11 V
19 -11 V
20 -10 V
19 -9 V
19 -9 V
20 -8 V
19 -8 V
19 -7 V
20 -7 V
19 -7 V
20 -6 V
19 -6 V
19 -6 V
20 -5 V
19 -6 V
19 -5 V
20 -4 V
19 -5 V
19 -4 V
20 -5 V
19 -4 V
20 -4 V
19 -4 V
19 -3 V
20 -4 V
19 -3 V
19 -4 V
20 -3 V
19 -3 V
19 -3 V
20 -3 V
19 -3 V
20 -3 V
19 -2 V
19 -3 V
20 -3 V
19 -2 V
19 -3 V
20 -2 V
19 -2 V
19 -3 V
20 -2 V
19 -2 V
20 -2 V
19 -2 V
19 -2 V
20 -2 V
19 -2 V
19 -2 V
20 -1 V
19 -2 V
19 -2 V
20 -2 V
19 -1 V
20 -2 V
19 -2 V
19 -1 V
20 -2 V
19 -1 V
19 -2 V
20 -1 V
19 -2 V
19 -1 V
20 -1 V
19 -2 V
20 -1 V
19 -1 V
19 -2 V
20 -1 V
19 -1 V
19 -1 V
20 -2 V
19 -1 V
19 -1 V
20 -1 V
19 -1 V
20 -1 V
19 -1 V
19 -1 V
20 -1 V
19 -2 V
LT1
602 1669 D
602 1593 D
614 1593 D
623 1658 D
628 1460 D
634 1311 D
644 1428 D
654 1214 D
656 1072 D
681 1097 D
707 975 D
718 997 D
734 970 D
760 922 D
787 865 D
813 829 D
919 743 D
1078 629 D
1183 573 D
1342 571 D
1448 546 D
1607 495 D
1818 526 D
2030 509 D
602 1630 M
0 79 V
-31 -79 R
62 0 V
-62 79 R
62 0 V
602 1282 M
0 622 V
571 1282 M
62 0 V
-62 622 R
62 0 V
614 1292 M
0 602 V
583 1292 M
62 0 V
-62 602 R
62 0 V
623 1451 M
0 414 V
592 1451 M
62 0 V
-62 414 R
62 0 V
628 1361 M
0 197 V
597 1361 M
62 0 V
-62 197 R
62 0 V
634 1104 M
0 414 V
603 1104 M
62 0 V
-62 414 R
62 0 V
644 1169 M
0 517 V
613 1169 M
62 0 V
-62 517 R
62 0 V
654 1139 M
0 150 V
623 1139 M
62 0 V
-62 150 R
62 0 V
656 710 M
0 723 V
625 710 M
62 0 V
-62 723 R
62 0 V
-6 -410 R
0 148 V
650 1023 M
62 0 V
-62 148 R
62 0 V
707 901 M
0 148 V
676 901 M
62 0 V
-62 148 R
62 0 V
718 932 M
0 131 V
687 932 M
62 0 V
-62 131 R
62 0 V
734 949 M
0 42 V
703 949 M
62 0 V
-62 42 R
62 0 V
760 843 M
0 158 V
729 843 M
62 0 V
-62 158 R
62 0 V
787 766 M
0 198 V
756 766 M
62 0 V
756 964 M
62 0 V
813 806 M
0 47 V
782 806 M
62 0 V
-62 47 R
62 0 V
919 727 M
0 33 V
888 727 M
62 0 V
-62 33 R
62 0 V
1078 612 M
0 34 V
-31 -34 R
62 0 V
-62 34 R
62 0 V
74 -95 R
0 44 V
-31 -44 R
62 0 V
-62 44 R
62 0 V
128 -47 R
0 46 V
-31 -46 R
62 0 V
-62 46 R
62 0 V
75 -69 R
0 43 V
-31 -43 R
62 0 V
-62 43 R
62 0 V
128 -87 R
0 27 V
-31 -27 R
62 0 V
-62 27 R
62 0 V
180 -3 R
0 42 V
-31 -42 R
62 0 V
-62 42 R
62 0 V
181 -60 R
0 44 V
-31 -44 R
62 0 V
-62 44 R
62 0 V
stroke
grestore
end
}
\put(2154,1946){\makebox(0,0)[r]{64.65s$^{-0.5397}=5\Delta_{\pi^-p}$}}
\put(1700,-50){\makebox(0,0){s \small{(GeV$^2$)}}}
\put(350,1180){%
\special{ps: gsave currentpoint currentpoint translate
270 rotate neg exch neg exch translate}%
\makebox(0,0)[b]{\shortstack{$\Delta_{\bar{p}p}$ \small{(mb)}}}%
\special{ps: currentpoint grestore moveto}%
}
\put(2517,151){\makebox(0,0){700}}
\put(2235,151){\makebox(0,0){600}}
\put(1953,151){\makebox(0,0){500}}
\put(1671,151){\makebox(0,0){400}}
\put(1389,151){\makebox(0,0){300}}
\put(1107,151){\makebox(0,0){200}}
\put(826,151){\makebox(0,0){100}}
\put(540,2109){\makebox(0,0)[r]{18}}
\put(540,1903){\makebox(0,0)[r]{16}}
\put(540,1696){\makebox(0,0)[r]{14}}
\put(540,1490){\makebox(0,0)[r]{12}}
\put(540,1283){\makebox(0,0)[r]{10}}
\put(540,1077){\makebox(0,0)[r]{8}}
\put(540,870){\makebox(0,0)[r]{6}}
\put(540,664){\makebox(0,0)[r]{4}}
\put(540,457){\makebox(0,0)[r]{2}}
\put(540,251){\makebox(0,0)[r]{0}}
\end{picture}}
\hspace{-1cm}\subfigure[]{\special{!
%!PS-Adobe-2.0
%%Creator: gnuplot
%%DocumentFonts: Helvetica
%%BoundingBox: 50 50 590 554
%%Pages: (atend)
%%EndComments
/gnudict 40 dict def
gnudict begin
/Color false def
/Solid false def
/gnulinewidth 5.000 def
/vshift -33 def
/dl {10 mul} def
/hpt 31.5 def
/vpt 31.5 def
/M {moveto} bind def
/L {lineto} bind def
/R {rmoveto} bind def
/V {rlineto} bind def
/vpt2 vpt 2 mul def
/hpt2 hpt 2 mul def
/Lshow { currentpoint stroke M
  0 vshift R show } def
/Rshow { currentpoint stroke M
  dup stringwidth pop neg vshift R show } def
/Cshow { currentpoint stroke M
  dup stringwidth pop -2 div vshift R show } def
/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
 {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
/BL { stroke gnulinewidth 2 mul setlinewidth } def
/AL { stroke gnulinewidth 2 div setlinewidth } def
/PL { stroke gnulinewidth setlinewidth } def
/LTb { BL [] 0 0 0 DL } def
/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def
/LT0 { PL [] 0 1 0 DL } def
/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def
/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def
/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
/P { stroke [] 0 setdash
  currentlinewidth 2 div sub M
  0 currentlinewidth V stroke } def
/D { stroke [] 0 setdash 2 copy vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath stroke
  P } def
/A { stroke [] 0 setdash vpt sub M 0 vpt2 V
  currentpoint stroke M
  hpt neg vpt neg R hpt2 0 V stroke
  } def
/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V closepath stroke
  P } def
/C { stroke [] 0 setdash exch hpt sub exch vpt add M
  hpt2 vpt2 neg V currentpoint stroke M
  hpt2 neg 0 R hpt2 vpt2 V stroke } def
/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath stroke
  P  } def
/S { 2 copy A C} def
end
%%EndProlog
}
\begin{picture}(2700,2160)(0,0)
\special{"
%%Page: 1 1
gnudict begin
gsave
50 50 translate
0.100 0.100 scale
0 setgray
/Helvetica findfont 100 scalefont setfont
newpath
-500.000000 -500.000000 translate
LTa
LTb
600 251 M
63 0 V
1854 0 R
-63 0 V
600 623 M
63 0 V
1854 0 R
-63 0 V
600 994 M
63 0 V
1854 0 R
-63 0 V
600 1366 M
63 0 V
1854 0 R
-63 0 V
600 1737 M
63 0 V
1854 0 R
-63 0 V
600 2109 M
63 0 V
1854 0 R
-63 0 V
826 251 M
0 63 V
0 1795 R
0 -63 V
1107 251 M
0 63 V
0 1795 R
0 -63 V
1389 251 M
0 63 V
0 1795 R
0 -63 V
1671 251 M
0 63 V
0 1795 R
0 -63 V
1953 251 M
0 63 V
0 1795 R
0 -63 V
2235 251 M
0 63 V
0 1795 R
0 -63 V
2517 251 M
0 63 V
0 1795 R
0 -63 V
600 251 M
1917 0 V
0 1858 V
-1917 0 V
600 251 L
LT0
2214 1946 M
180 0 V
600 1386 M
19 -113 V
20 -75 V
19 -55 V
19 -42 V
20 -33 V
19 -28 V
20 -23 V
19 -20 V
19 -18 V
20 -15 V
19 -13 V
19 -12 V
20 -11 V
19 -10 V
19 -9 V
20 -8 V
19 -8 V
20 -7 V
19 -7 V
19 -6 V
20 -5 V
19 -6 V
19 -5 V
20 -5 V
19 -4 V
19 -4 V
20 -4 V
19 -4 V
20 -4 V
19 -3 V
19 -4 V
20 -3 V
19 -3 V
19 -3 V
20 -2 V
19 -3 V
19 -3 V
20 -2 V
19 -2 V
20 -3 V
19 -2 V
19 -2 V
20 -2 V
19 -2 V
19 -2 V
20 -2 V
19 -2 V
19 -1 V
20 -2 V
19 -2 V
20 -1 V
19 -2 V
19 -2 V
20 -1 V
19 -1 V
19 -2 V
20 -1 V
19 -2 V
19 -1 V
20 -1 V
19 -1 V
20 -2 V
19 -1 V
19 -1 V
20 -1 V
19 -1 V
19 -1 V
20 -1 V
19 -1 V
19 -1 V
20 -1 V
19 -1 V
20 -1 V
19 -1 V
19 -1 V
20 -1 V
19 -1 V
19 -1 V
20 0 V
19 -1 V
19 -1 V
20 -1 V
19 -1 V
20 0 V
19 -1 V
19 -1 V
20 -1 V
19 0 V
19 -1 V
20 -1 V
19 0 V
19 -1 V
20 -1 V
19 0 V
20 -1 V
19 -1 V
19 0 V
20 -1 V
19 0 V
LT1
602 1388 D
612 1618 D
623 1604 D
628 1159 D
633 1552 D
644 1009 D
654 1180 D
655 1152 D
681 1118 D
708 1079 D
734 1088 D
761 909 D
787 1044 D
814 977 D
919 937 D
1078 868 D
1184 884 D
1343 799 D
1449 809 D
1608 793 D
1820 763 D
2032 754 D
602 1166 M
0 444 V
571 1166 M
62 0 V
-62 444 R
62 0 V
612 1316 M
0 605 V
581 1316 M
62 0 V
-62 605 R
62 0 V
623 1301 M
0 605 V
592 1301 M
62 0 V
-62 605 R
62 0 V
628 998 M
0 323 V
597 998 M
62 0 V
-62 323 R
62 0 V
-26 -72 R
0 605 V
602 1249 M
62 0 V
-62 605 R
62 0 V
644 328 M
0 1362 V
613 328 M
62 0 V
613 1690 M
62 0 V
654 1104 M
0 152 V
623 1104 M
62 0 V
-62 152 R
62 0 V
655 880 M
0 544 V
624 880 M
62 0 V
-62 544 R
62 0 V
681 963 M
0 310 V
650 963 M
62 0 V
-62 310 R
62 0 V
708 924 M
0 309 V
677 924 M
62 0 V
-62 309 R
62 0 V
-5 -172 R
0 53 V
-31 -53 R
62 0 V
-62 53 R
62 0 V
761 755 M
0 309 V
730 755 M
62 0 V
-62 309 R
62 0 V
787 881 M
0 325 V
756 881 M
62 0 V
-62 325 R
62 0 V
814 949 M
0 55 V
783 949 M
62 0 V
-62 55 R
62 0 V
74 -83 R
0 32 V
888 921 M
62 0 V
-62 32 R
62 0 V
1078 851 M
0 34 V
-31 -34 R
62 0 V
-62 34 R
62 0 V
75 -24 R
0 46 V
-31 -46 R
62 0 V
-62 46 R
62 0 V
1343 772 M
0 54 V
-31 -54 R
62 0 V
-62 54 R
62 0 V
75 -43 R
0 52 V
-31 -52 R
62 0 V
-62 52 R
62 0 V
128 -57 R
0 30 V
-31 -30 R
62 0 V
-62 30 R
62 0 V
181 -74 R
0 58 V
-31 -58 R
62 0 V
-62 58 R
62 0 V
181 -66 R
0 57 V
-31 -57 R
62 0 V
-62 57 R
62 0 V
stroke
grestore
end
showpage
}
\put(2154,1946){\makebox(0,0)[r]{51.72s$^{-0.5397}=4\Delta{\pi^-p}$}}
\put(1700,-50){\makebox(0,0){s \small{(GeV$^2$)}}}
\put(350,1180){%
\special{ps: gsave currentpoint currentpoint translate
270 rotate neg exch neg exch translate}%
\makebox(0,0)[b]{\shortstack{$\Delta_{\bar{p}^-n}$ \small{(mb)}}}%
\special{ps: currentpoint grestore moveto}%
}
\put(2517,151){\makebox(0,0){700}}
\put(2235,151){\makebox(0,0){600}}
\put(1953,151){\makebox(0,0){500}}
\put(1671,151){\makebox(0,0){400}}
\put(1389,151){\makebox(0,0){300}}
\put(1107,151){\makebox(0,0){200}}
\put(826,151){\makebox(0,0){100}}
\put(540,2109){\makebox(0,0)[r]{20}}
\put(540,1737){\makebox(0,0)[r]{15}}
\put(540,1366){\makebox(0,0)[r]{10}}
\put(540,994){\makebox(0,0)[r]{5}}
\put(540,623){\makebox(0,0)[r]{0}}
\put(540,251){\makebox(0,0)[r]{-5}}
\end{picture}}}}
\put(0,300){\mbox{\hspace*{-0.5cm}
\subfigure[]{
\special{!
%!PS-Adobe-2.0
%%Creator: gnuplot
%%DocumentFonts: Helvetica
%%BoundingBox: 50 50 590 554
%%Pages: (atend)
%%EndComments
/gnudict 40 dict def
gnudict begin
/Color false def
/Solid false def
/gnulinewidth 5.000 def
/vshift -33 def
/dl {10 mul} def
/hpt 31.5 def
/vpt 31.5 def
/M {moveto} bind def
/L {lineto} bind def
/R {rmoveto} bind def
/V {rlineto} bind def
/vpt2 vpt 2 mul def
/hpt2 hpt 2 mul def
/Lshow { currentpoint stroke M
  0 vshift R show } def
/Rshow { currentpoint stroke M
  dup stringwidth pop neg vshift R show } def
/Cshow { currentpoint stroke M
  dup stringwidth pop -2 div vshift R show } def
/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
 {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
/BL { stroke gnulinewidth 2 mul setlinewidth } def
/AL { stroke gnulinewidth 2 div setlinewidth } def
/PL { stroke gnulinewidth setlinewidth } def
/LTb { BL [] 0 0 0 DL } def
/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def
/LT0 { PL [] 0 1 0 DL } def
/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def
/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def
/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
/P { stroke [] 0 setdash
  currentlinewidth 2 div sub M
  0 currentlinewidth V stroke } def
/D { stroke [] 0 setdash 2 copy vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath stroke
  P } def
/A { stroke [] 0 setdash vpt sub M 0 vpt2 V
  currentpoint stroke M
  hpt neg vpt neg R hpt2 0 V stroke
  } def
/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V closepath stroke
  P } def
/C { stroke [] 0 setdash exch hpt sub exch vpt add M
  hpt2 vpt2 neg V currentpoint stroke M
  hpt2 neg 0 R hpt2 vpt2 V stroke } def
/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath stroke
  P  } def
/S { 2 copy A C} def
end
%%EndProlog
}
\begin{picture}(2700,2160)(0,0)
\special{"
%%Page: 1 1
gnudict begin
gsave
50 50 translate
0.100 0.100 scale
0 setgray
/Helvetica findfont 100 scalefont setfont
newpath
-500.000000 -500.000000 translate
LTa
LTb
600 251 M
63 0 V
1854 0 R
-63 0 V
600 516 M
63 0 V
1854 0 R
-63 0 V
600 782 M
63 0 V
1854 0 R
-63 0 V
600 1047 M
63 0 V
1854 0 R
-63 0 V
600 1313 M
63 0 V
1854 0 R
-63 0 V
600 1578 M
63 0 V
1854 0 R
-63 0 V
600 1844 M
63 0 V
1854 0 R
-63 0 V
600 2109 M
63 0 V
1854 0 R
-63 0 V
864 251 M
0 63 V
0 1795 R
0 -63 V
1195 251 M
0 63 V
0 1795 R
0 -63 V
1525 251 M
0 63 V
0 1795 R
0 -63 V
1856 251 M
0 63 V
0 1795 R
0 -63 V
2186 251 M
0 63 V
0 1795 R
0 -63 V
2517 251 M
0 63 V
0 1795 R
0 -63 V
600 251 M
1917 0 V
0 1858 V
-1917 0 V
600 251 L
LT0
2214 1946 M
180 0 V
600 1614 M
19 -177 V
20 -124 V
19 -92 V
19 -73 V
20 -60 V
19 -49 V
20 -42 V
19 -36 V
19 -31 V
20 -28 V
19 -25 V
19 -22 V
20 -20 V
19 -18 V
19 -17 V
20 -16 V
19 -14 V
20 -13 V
19 -12 V
19 -12 V
20 -11 V
19 -10 V
19 -9 V
20 -9 V
19 -9 V
19 -8 V
20 -7 V
19 -8 V
20 -7 V
19 -6 V
19 -6 V
20 -6 V
19 -6 V
19 -6 V
20 -5 V
19 -5 V
19 -5 V
20 -5 V
19 -4 V
20 -5 V
19 -4 V
19 -4 V
20 -4 V
19 -4 V
19 -3 V
20 -4 V
19 -3 V
19 -4 V
20 -3 V
19 -3 V
20 -3 V
19 -3 V
19 -3 V
20 -3 V
19 -3 V
19 -2 V
20 -3 V
19 -3 V
19 -2 V
20 -2 V
19 -3 V
20 -2 V
19 -2 V
19 -3 V
20 -2 V
19 -2 V
19 -2 V
20 -2 V
19 -2 V
19 -2 V
20 -2 V
19 -2 V
20 -1 V
19 -2 V
19 -2 V
20 -2 V
19 -1 V
19 -2 V
20 -2 V
19 -1 V
19 -2 V
20 -1 V
19 -2 V
20 -1 V
19 -2 V
19 -1 V
20 -2 V
19 -1 V
19 -1 V
20 -2 V
19 -1 V
19 -1 V
20 -1 V
19 -2 V
20 -1 V
19 -1 V
19 -1 V
20 -1 V
19 -2 V
LT1
609 1392 D
612 1737 D
616 1127 D
621 1313 D
631 1271 D
636 1543 D
656 1392 D
662 1189 D
693 1058 D
724 1079 D
736 649 D
755 975 D
786 925 D
817 965 D
848 831 D
879 867 D
972 745 D
1158 675 D
1282 636 D
1449 777 D
1468 580 D
1592 519 D
1778 484 D
2026 522 D
2274 476 D
2460 458 D
609 1127 M
0 531 V
578 1127 M
62 0 V
-62 531 R
62 0 V
612 1550 M
0 375 V
581 1550 M
62 0 V
-62 375 R
62 0 V
616 908 M
0 438 V
585 908 M
62 0 V
-62 438 R
62 0 V
621 1068 M
0 489 V
590 1068 M
62 0 V
-62 489 R
62 0 V
631 1117 M
0 308 V
600 1117 M
62 0 V
-62 308 R
62 0 V
-26 -96 R
0 428 V
605 1329 M
62 0 V
-62 428 R
62 0 V
656 882 M
0 1021 V
625 882 M
62 0 V
625 1903 M
62 0 V
662 1072 M
0 235 V
631 1072 M
62 0 V
-62 235 R
62 0 V
0 -405 R
0 312 V
662 902 M
62 0 V
-62 312 R
62 0 V
0 -291 R
0 312 V
693 923 M
62 0 V
-62 312 R
62 0 V
736 499 M
0 300 V
705 499 M
62 0 V
705 799 M
62 0 V
-12 68 R
0 217 V
724 867 M
62 0 V
-62 217 R
62 0 V
0 -316 R
0 315 V
755 768 M
62 0 V
-62 315 R
62 0 V
0 -275 R
0 314 V
786 808 M
62 0 V
-62 314 R
62 0 V
0 -386 R
0 190 V
817 736 M
62 0 V
817 926 M
62 0 V
0 -220 R
0 322 V
848 706 M
62 0 V
-62 322 R
62 0 V
972 629 M
0 231 V
941 629 M
62 0 V
941 860 M
62 0 V
1158 547 M
0 256 V
1127 547 M
62 0 V
-62 256 R
62 0 V
93 -282 R
0 230 V
1251 521 M
62 0 V
-62 230 R
62 0 V
1449 477 M
0 599 V
1418 477 M
62 0 V
-62 599 R
62 0 V
1468 464 M
0 232 V
1437 464 M
62 0 V
-62 232 R
62 0 V
93 -292 R
0 230 V
1561 404 M
62 0 V
-62 230 R
62 0 V
1778 449 M
0 70 V
-31 -70 R
62 0 V
-62 70 R
62 0 V
217 -26 R
0 57 V
-31 -57 R
62 0 V
-62 57 R
62 0 V
2274 444 M
0 63 V
-31 -63 R
62 0 V
-62 63 R
62 0 V
2460 407 M
0 102 V
2429 407 M
62 0 V
-62 102 R
62 0 V
stroke
grestore
end
}
\put(2154,1946){\makebox(0,0)[r]{25.86s$^{-0.5397}=2\Delta_{\pi^-p}$}}
\put(1700,-50){\makebox(0,0){s \small{(GeV$^2$)}}}
\put(350,1180){%
\special{ps: gsave currentpoint currentpoint translate
270 rotate neg exch neg exch translate}%
\makebox(0,0)[b]{\shortstack{$\Delta_{K^-p}$ \small{(mb)}}}%
\special{ps: currentpoint grestore moveto}%
}
\put(2517,151){\makebox(0,0){600}}
\put(2186,151){\makebox(0,0){500}}
\put(1856,151){\makebox(0,0){400}}
\put(1525,151){\makebox(0,0){300}}
\put(1195,151){\makebox(0,0){200}}
\put(864,151){\makebox(0,0){100}}
\put(540,2109){\makebox(0,0)[r]{7}}
\put(540,1844){\makebox(0,0)[r]{6}}
\put(540,1578){\makebox(0,0)[r]{5}}
\put(540,1313){\makebox(0,0)[r]{4}}
\put(540,1047){\makebox(0,0)[r]{3}}
\put(540,782){\makebox(0,0)[r]{2}}
\put(540,516){\makebox(0,0)[r]{1}}
\put(540,251){\makebox(0,0)[r]{0}}
\end{picture}
}\hspace{-1cm}\subfigure[]{
\special{!
%!PS-Adobe-2.0
%%Creator: gnuplot
%%DocumentFonts: Helvetica
%%BoundingBox: 50 50 590 554
%%Pages: (atend)
%%EndComments
/gnudict 40 dict def
gnudict begin
/Color false def
/Solid false def
/gnulinewidth 5.000 def
/vshift -33 def
/dl {10 mul} def
/hpt 31.5 def
/vpt 31.5 def
/M {moveto} bind def
/L {lineto} bind def
/R {rmoveto} bind def
/V {rlineto} bind def
/vpt2 vpt 2 mul def
/hpt2 hpt 2 mul def
/Lshow { currentpoint stroke M
  0 vshift R show } def
/Rshow { currentpoint stroke M
  dup stringwidth pop neg vshift R show } def
/Cshow { currentpoint stroke M
  dup stringwidth pop -2 div vshift R show } def
/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
 {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
/BL { stroke gnulinewidth 2 mul setlinewidth } def
/AL { stroke gnulinewidth 2 div setlinewidth } def
/PL { stroke gnulinewidth setlinewidth } def
/LTb { BL [] 0 0 0 DL } def
/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def
/LT0 { PL [] 0 1 0 DL } def
/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def
/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def
/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
/P { stroke [] 0 setdash
  currentlinewidth 2 div sub M
  0 currentlinewidth V stroke } def
/D { stroke [] 0 setdash 2 copy vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath stroke
  P } def
/A { stroke [] 0 setdash vpt sub M 0 vpt2 V
  currentpoint stroke M
  hpt neg vpt neg R hpt2 0 V stroke
  } def
/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V closepath stroke
  P } def
/C { stroke [] 0 setdash exch hpt sub exch vpt add M
  hpt2 vpt2 neg V currentpoint stroke M
  hpt2 neg 0 R hpt2 vpt2 V stroke } def
/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath stroke
  P  } def
/S { 2 copy A C} def
end
%%EndProlog
}
\begin{picture}(2700,2160)(0,0)
\special{"
%%Page: 1 1
gnudict begin
gsave
50 50 translate
0.100 0.100 scale
0 setgray
/Helvetica findfont 100 scalefont setfont
newpath
-500.000000 -500.000000 translate
LTa
LTb
600 251 M
63 0 V
1854 0 R
-63 0 V
600 516 M
63 0 V
1854 0 R
-63 0 V
600 782 M
63 0 V
1854 0 R
-63 0 V
600 1047 M
63 0 V
1854 0 R
-63 0 V
600 1313 M
63 0 V
1854 0 R
-63 0 V
600 1578 M
63 0 V
1854 0 R
-63 0 V
600 1844 M
63 0 V
1854 0 R
-63 0 V
600 2109 M
63 0 V
1854 0 R
-63 0 V
864 251 M
0 63 V
0 1795 R
0 -63 V
1195 251 M
0 63 V
0 1795 R
0 -63 V
1525 251 M
0 63 V
0 1795 R
0 -63 V
1856 251 M
0 63 V
0 1795 R
0 -63 V
2186 251 M
0 63 V
0 1795 R
0 -63 V
2517 251 M
0 63 V
0 1795 R
0 -63 V
600 251 M
1917 0 V
0 1858 V
-1917 0 V
600 251 L
LT0
2214 1946 M
180 0 V
600 1729 M
19 -89 V
20 -61 V
19 -47 V
19 -36 V
20 -30 V
19 -25 V
20 -20 V
19 -19 V
19 -15 V
20 -14 V
19 -13 V
19 -11 V
20 -10 V
19 -9 V
19 -8 V
20 -8 V
19 -7 V
20 -7 V
19 -6 V
19 -6 V
20 -5 V
19 -5 V
19 -5 V
20 -4 V
19 -5 V
19 -4 V
20 -3 V
19 -4 V
20 -3 V
19 -4 V
19 -3 V
20 -3 V
19 -3 V
19 -3 V
20 -2 V
19 -3 V
19 -2 V
20 -3 V
19 -2 V
20 -2 V
19 -2 V
19 -2 V
20 -2 V
19 -2 V
19 -2 V
20 -2 V
19 -1 V
19 -2 V
20 -2 V
19 -1 V
20 -2 V
19 -1 V
19 -2 V
20 -1 V
19 -2 V
19 -1 V
20 -1 V
19 -1 V
19 -2 V
20 -1 V
19 -1 V
20 -1 V
19 -1 V
19 -2 V
20 -1 V
19 -1 V
19 -1 V
20 -1 V
19 -1 V
19 -1 V
20 -1 V
19 -1 V
20 0 V
19 -1 V
19 -1 V
20 -1 V
19 -1 V
19 -1 V
20 -1 V
19 0 V
19 -1 V
20 -1 V
19 -1 V
20 0 V
19 -1 V
19 -1 V
20 0 V
19 -1 V
19 -1 V
20 0 V
19 -1 V
19 -1 V
20 0 V
19 -1 V
20 -1 V
19 0 V
19 -1 V
20 0 V
19 -1 V
LT1
612 1153 D
625 1153 D
631 1398 D
637 1153 D
649 1153 D
662 1163 D
693 1394 D
724 1396 D
755 1148 D
786 1397 D
817 1398 D
848 1147 D
879 1398 D
972 1135 D
1159 1132 D
1283 1134 D
1469 1133 D
1593 1131 D
1780 1079 D
2028 1074 D
2277 1074 D
2463 1116 D
612 463 M
0 1381 V
581 463 M
62 0 V
581 1844 M
62 0 V
625 463 M
0 1381 V
594 463 M
62 0 V
594 1844 M
62 0 V
631 856 M
0 1083 V
600 856 M
62 0 V
600 1939 M
62 0 V
637 384 M
0 1539 V
606 384 M
62 0 V
606 1923 M
62 0 V
649 437 M
0 1433 V
618 437 M
62 0 V
618 1870 M
62 0 V
662 658 M
0 1009 V
631 658 M
62 0 V
631 1667 M
62 0 V
0 -734 R
0 921 V
662 933 M
62 0 V
-62 921 R
62 0 V
0 -967 R
0 1017 V
693 887 M
62 0 V
693 1904 M
62 0 V
755 751 M
0 793 V
724 751 M
62 0 V
-62 793 R
62 0 V
0 -471 R
0 648 V
755 1073 M
62 0 V
-62 648 R
62 0 V
0 -682 R
0 719 V
786 1039 M
62 0 V
-62 719 R
62 0 V
0 -935 R
0 648 V
817 823 M
62 0 V
-62 648 R
62 0 V
0 -424 R
0 702 V
848 1047 M
62 0 V
-62 702 R
62 0 V
972 809 M
0 653 V
941 809 M
62 0 V
-62 653 R
62 0 V
1159 888 M
0 488 V
1128 888 M
62 0 V
-62 488 R
62 0 V
93 -489 R
0 494 V
1252 887 M
62 0 V
-62 494 R
62 0 V
155 -378 R
0 260 V
-31 -260 R
62 0 V
-62 260 R
62 0 V
93 -267 R
0 271 V
1562 996 M
62 0 V
-62 271 R
62 0 V
1780 862 M
0 433 V
1749 862 M
62 0 V
-62 433 R
62 0 V
217 -280 R
0 118 V
-31 -118 R
62 0 V
-62 118 R
62 0 V
2277 997 M
0 154 V
2246 997 M
62 0 V
-62 154 R
62 0 V
155 -106 R
0 143 V
-31 -143 R
62 0 V
-62 143 R
62 0 V
stroke
grestore
end
}
\put(2154,1946){\makebox(0,0)[r]{12.93s$^{-0.5397}=\Delta_{\pi^-p}$}}
\put(1700,-50){\makebox(0,0){s \small{(GeV$^2$)}}}
\put(350,1180){%
\special{ps: gsave currentpoint currentpoint translate
270 rotate neg exch neg exch translate}%
\makebox(0,0)[b]{\shortstack{$\Delta_{K^-n}$ \small{(mb)}}}%
\special{ps: currentpoint grestore moveto}%
}
\put(2517,151){\makebox(0,0){600}}
\put(2186,151){\makebox(0,0){500}}
\put(1856,151){\makebox(0,0){400}}
\put(1525,151){\makebox(0,0){300}}
\put(1195,151){\makebox(0,0){200}}
\put(864,151){\makebox(0,0){100}}
\put(540,2109){\makebox(0,0)[r]{4}}
\put(540,1844){\makebox(0,0)[r]{3}}
\put(540,1578){\makebox(0,0)[r]{2}}
\put(540,1313){\makebox(0,0)[r]{1}}
\put(540,1047){\makebox(0,0)[r]{0}}
\put(540,782){\makebox(0,0)[r]{-1}}
\put(540,516){\makebox(0,0)[r]{-2}}
\put(540,251){\makebox(0,0)[r]{-3}}
\end{picture}
}}}
\end{picture}
\begin{figure}[h]
\setlength{\unitlength}{0.1bp}
{\mbox{\hspace*{-3cm} \subfigure[]{
\special{!
%!PS-Adobe-2.0
%%Creator: gnuplot
%%DocumentFonts: Helvetica
%%BoundingBox: 50 50 590 554
%%Pages: (atend)
%%EndComments
/gnudict 40 dict def
gnudict begin
/Color false def
/Solid false def
/gnulinewidth 5.000 def
/vshift -33 def
/dl {10 mul} def
/hpt 31.5 def
/vpt 31.5 def
/M {moveto} bind def
/L {lineto} bind def
/R {rmoveto} bind def
/V {rlineto} bind def
/vpt2 vpt 2 mul def
/hpt2 hpt 2 mul def
/Lshow { currentpoint stroke M
  0 vshift R show } def
/Rshow { currentpoint stroke M
  dup stringwidth pop neg vshift R show } def
/Cshow { currentpoint stroke M
  dup stringwidth pop -2 div vshift R show } def
/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
 {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
/BL { stroke gnulinewidth 2 mul setlinewidth } def
/AL { stroke gnulinewidth 2 div setlinewidth } def
/PL { stroke gnulinewidth setlinewidth } def
/LTb { BL [] 0 0 0 DL } def
/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def
/LT0 { PL [] 0 1 0 DL } def
/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def
/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def
/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
/P { stroke [] 0 setdash
  currentlinewidth 2 div sub M
  0 currentlinewidth V stroke } def
/D { stroke [] 0 setdash 2 copy vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath stroke
  P } def
/A { stroke [] 0 setdash vpt sub M 0 vpt2 V
  currentpoint stroke M
  hpt neg vpt neg R hpt2 0 V stroke
  } def
/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V closepath stroke
  P } def
/C { stroke [] 0 setdash exch hpt sub exch vpt add M
  hpt2 vpt2 neg V currentpoint stroke M
  hpt2 neg 0 R hpt2 vpt2 V stroke } def
/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath stroke
  P  } def
/S { 2 copy A C} def
end
%%EndProlog
}
\begin{picture}(2700,2160)(0,0)
\special{"
%%Page: 1 1
gnudict begin
gsave
50 50 translate
0.100 0.100 scale
0 setgray
/Helvetica findfont 100 scalefont setfont
newpath
-500.000000 -500.000000 translate
LTa
600 1047 M
1917 0 V
LTb
600 251 M
63 0 V
1854 0 R
-63 0 V
600 516 M
63 0 V
1854 0 R
-63 0 V
600 782 M
63 0 V
1854 0 R
-63 0 V
600 1047 M
63 0 V
1854 0 R
-63 0 V
600 1313 M
63 0 V
1854 0 R
-63 0 V
600 1578 M
63 0 V
1854 0 R
-63 0 V
600 1844 M
63 0 V
1854 0 R
-63 0 V
600 2109 M
63 0 V
1854 0 R
-63 0 V
826 251 M
0 63 V
0 1795 R
0 -63 V
1107 251 M
0 63 V
0 1795 R
0 -63 V
1389 251 M
0 63 V
0 1795 R
0 -63 V
1671 251 M
0 63 V
0 1795 R
0 -63 V
1953 251 M
0 63 V
0 1795 R
0 -63 V
2235 251 M
0 63 V
0 1795 R
0 -63 V
2517 251 M
0 63 V
0 1795 R
0 -63 V
600 251 M
1917 0 V
0 1858 V
-1917 0 V
600 251 L
LT0
600 1931 M
19 -236 V
20 -133 V
19 -85 V
19 -60 V
20 -45 V
19 -34 V
20 -27 V
19 -22 V
19 -19 V
20 -15 V
19 -14 V
19 -11 V
20 -11 V
19 -8 V
19 -8 V
20 -8 V
19 -6 V
20 -6 V
19 -5 V
19 -5 V
20 -5 V
19 -4 V
19 -4 V
20 -3 V
19 -4 V
19 -3 V
20 -3 V
19 -2 V
20 -3 V
19 -2 V
19 -3 V
20 -2 V
19 -2 V
19 -2 V
20 -2 V
19 -1 V
19 -2 V
20 -2 V
19 -1 V
20 -2 V
19 -1 V
19 -1 V
20 -2 V
19 -1 V
19 -1 V
20 -1 V
19 -1 V
19 -1 V
20 -1 V
19 -1 V
20 -1 V
19 -1 V
19 -1 V
20 -1 V
19 -1 V
19 0 V
20 -1 V
19 -1 V
19 -1 V
20 0 V
19 -1 V
20 -1 V
19 0 V
19 -1 V
20 -1 V
19 0 V
19 -1 V
20 0 V
19 -1 V
19 0 V
20 -1 V
19 0 V
20 -1 V
19 0 V
19 -1 V
20 0 V
19 -1 V
19 0 V
20 -1 V
19 0 V
19 -1 V
20 0 V
19 0 V
20 -1 V
19 0 V
19 0 V
20 -1 V
19 0 V
19 -1 V
20 0 V
19 0 V
19 -1 V
20 0 V
19 0 V
20 0 V
19 -1 V
19 0 V
20 0 V
19 -1 V
LT1
602 1425 D
612 1262 D
623 1268 D
628 1151 D
634 1347 D
644 1100 D
654 1074 D
654 998 D
665 892 D
670 816 D
681 1045 D
707 1114 D
734 1218 D
760 1087 D
787 1002 D
813 1236 D
840 1026 D
866 1065 D
919 1225 D
1078 1180 D
1184 1164 D
1343 1148 D
1449 1140 D
1607 1092 D
1819 1118 D
2031 1079 D
2190 1090 D
2348 1055 D
2507 1111 D
602 968 M
0 914 V
571 968 M
62 0 V
-62 914 R
62 0 V
612 810 M
0 904 V
581 810 M
62 0 V
-62 904 R
62 0 V
623 816 M
0 905 V
592 816 M
62 0 V
-62 905 R
62 0 V
628 658 M
0 985 V
597 658 M
62 0 V
-62 985 R
62 0 V
634 894 M
0 906 V
603 894 M
62 0 V
-62 906 R
62 0 V
644 647 M
0 907 V
613 647 M
62 0 V
-62 907 R
62 0 V
654 882 M
0 383 V
623 882 M
62 0 V
-62 383 R
62 0 V
654 651 M
0 694 V
623 651 M
62 0 V
-62 694 R
62 0 V
665 440 M
0 905 V
634 440 M
62 0 V
-62 905 R
62 0 V
670 555 M
0 523 V
639 555 M
62 0 V
-62 523 R
62 0 V
681 551 M
0 987 V
650 551 M
62 0 V
-62 987 R
62 0 V
707 622 M
0 984 V
676 622 M
62 0 V
-62 984 R
62 0 V
-4 -448 R
0 119 V
703 1158 M
62 0 V
-62 119 R
62 0 V
760 595 M
0 984 V
729 595 M
62 0 V
-62 984 R
62 0 V
787 510 M
0 984 V
756 510 M
62 0 V
-62 984 R
62 0 V
-5 -319 R
0 121 V
782 1175 M
62 0 V
-62 121 R
62 0 V
840 532 M
0 988 V
809 532 M
62 0 V
-62 988 R
62 0 V
866 572 M
0 986 V
835 572 M
62 0 V
-62 986 R
62 0 V
22 -376 R
0 86 V
-31 -86 R
62 0 V
-62 86 R
62 0 V
128 -131 R
0 86 V
-31 -86 R
62 0 V
-62 86 R
62 0 V
75 -102 R
0 86 V
-31 -86 R
62 0 V
-62 86 R
62 0 V
128 -102 R
0 86 V
-31 -86 R
62 0 V
-62 86 R
62 0 V
75 -93 R
0 84 V
-31 -84 R
62 0 V
-62 84 R
62 0 V
127 -108 R
0 35 V
-31 -35 R
62 0 V
-62 35 R
62 0 V
181 -9 R
0 37 V
-31 -37 R
62 0 V
-62 37 R
62 0 V
181 -76 R
0 35 V
-31 -35 R
62 0 V
-62 35 R
62 0 V
128 -31 R
0 49 V
-31 -49 R
62 0 V
-62 49 R
62 0 V
127 -91 R
0 65 V
-31 -65 R
62 0 V
-62 65 R
62 0 V
128 -4 R
0 54 V
-31 -54 R
62 0 V
-62 54 R
62 0 V
stroke
grestore
end
showpage
}
\put(1558,-50){\makebox(0,0){s \small{(GeV$^2$)}}}
\put(350,1180){%
\special{ps: gsave currentpoint currentpoint translate
270 rotate neg exch neg exch translate}%
\makebox(0,0)[b]{\shortstack{$\sigma_{pn}-\sigma_{pp}$ (mb)}}%
\special{ps: currentpoint grestore moveto}%
}
\put(2517,151){\makebox(0,0){700}}
\put(2235,151){\makebox(0,0){600}}
\put(1953,151){\makebox(0,0){500}}
\put(1671,151){\makebox(0,0){400}}
\put(1389,151){\makebox(0,0){300}}
\put(1107,151){\makebox(0,0){200}}
\put(826,151){\makebox(0,0){100}}
\put(540,2109){\makebox(0,0)[r]{4}}
\put(540,1844){\makebox(0,0)[r]{3}}
\put(540,1578){\makebox(0,0)[r]{2}}
\put(540,1313){\makebox(0,0)[r]{1}}
\put(540,1047){\makebox(0,0)[r]{0}}
\put(540,782){\makebox(0,0)[r]{-1}}
\put(540,516){\makebox(0,0)[r]{-2}}
\put(540,251){\makebox(0,0)[r]{-3}}
\end{picture}
}\hspace{-1cm}
\subfigure[]{
\special{!
%!PS-Adobe-2.0
%%Creator: gnuplot
%%DocumentFonts: Helvetica
%%BoundingBox: 50 50 590 554
%%Pages: (atend)
%%EndComments
/gnudict 40 dict def
gnudict begin
/Color false def
/Solid false def
/gnulinewidth 5.000 def
/vshift -33 def
/dl {10 mul} def
/hpt 31.5 def
/vpt 31.5 def
/M {moveto} bind def
/L {lineto} bind def
/R {rmoveto} bind def
/V {rlineto} bind def
/vpt2 vpt 2 mul def
/hpt2 hpt 2 mul def
/Lshow { currentpoint stroke M
  0 vshift R show } def
/Rshow { currentpoint stroke M
  dup stringwidth pop neg vshift R show } def
/Cshow { currentpoint stroke M
  dup stringwidth pop -2 div vshift R show } def
/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
 {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
/BL { stroke gnulinewidth 2 mul setlinewidth } def
/AL { stroke gnulinewidth 2 div setlinewidth } def
/PL { stroke gnulinewidth setlinewidth } def
/LTb { BL [] 0 0 0 DL } def
/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def
/LT0 { PL [] 0 1 0 DL } def
/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def
/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def
/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
/P { stroke [] 0 setdash
  currentlinewidth 2 div sub M
  0 currentlinewidth V stroke } def
/D { stroke [] 0 setdash 2 copy vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath stroke
  P } def
/A { stroke [] 0 setdash vpt sub M 0 vpt2 V
  currentpoint stroke M
  hpt neg vpt neg R hpt2 0 V stroke
  } def
/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V closepath stroke
  P } def
/C { stroke [] 0 setdash exch hpt sub exch vpt add M
  hpt2 vpt2 neg V currentpoint stroke M
  hpt2 neg 0 R hpt2 vpt2 V stroke } def
/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath stroke
  P  } def
/S { 2 copy A C} def
end
%%EndProlog
}
\begin{picture}(2700,2160)(0,0)
\special{"
%%Page: 1 1
gnudict begin
gsave
50 50 translate
0.100 0.100 scale
0 setgray
/Helvetica findfont 100 scalefont setfont
newpath
-500.000000 -500.000000 translate
LTa
600 1047 M
1917 0 V
LTb
600 251 M
63 0 V
1854 0 R
-63 0 V
600 516 M
63 0 V
1854 0 R
-63 0 V
600 782 M
63 0 V
1854 0 R
-63 0 V
600 1047 M
63 0 V
1854 0 R
-63 0 V
600 1313 M
63 0 V
1854 0 R
-63 0 V
600 1578 M
63 0 V
1854 0 R
-63 0 V
600 1844 M
63 0 V
1854 0 R
-63 0 V
600 2109 M
63 0 V
1854 0 R
-63 0 V
864 251 M
0 63 V
0 1795 R
0 -63 V
1195 251 M
0 63 V
0 1795 R
0 -63 V
1525 251 M
0 63 V
0 1795 R
0 -63 V
1856 251 M
0 63 V
0 1795 R
0 -63 V
2186 251 M
0 63 V
0 1795 R
0 -63 V
2517 251 M
0 63 V
0 1795 R
0 -63 V
600 251 M
1917 0 V
0 1858 V
-1917 0 V
600 251 L
LT0
612 1207 D
624 1100 D
631 1107 D
637 1242 D
649 1313 D
662 1191 D
693 1100 D
724 1031 D
755 1283 D
786 1100 D
817 1270 D
848 1227 D
879 1185 D
972 1090 D
1158 1146 D
1282 1095 D
1469 1191 D
1593 1100 D
1779 939 D
2027 1115 D
2275 1120 D
2461 1116 D
612 988 M
0 437 V
581 988 M
62 0 V
-62 437 R
62 0 V
624 881 M
0 438 V
593 881 M
62 0 V
-62 438 R
62 0 V
631 353 M
0 1509 V
600 353 M
62 0 V
600 1862 M
62 0 V
637 1018 M
0 448 V
606 1018 M
62 0 V
-62 448 R
62 0 V
649 1094 M
0 438 V
618 1094 M
62 0 V
-62 438 R
62 0 V
662 853 M
0 676 V
631 853 M
62 0 V
-62 676 R
62 0 V
693 374 M
0 1453 V
662 374 M
62 0 V
662 1827 M
62 0 V
724 301 M
0 1461 V
693 301 M
62 0 V
693 1762 M
62 0 V
0 -820 R
0 682 V
724 942 M
62 0 V
-62 682 R
62 0 V
786 366 M
0 1469 V
755 366 M
62 0 V
755 1835 M
62 0 V
817 534 M
0 1472 V
786 534 M
62 0 V
786 2006 M
62 0 V
848 889 M
0 676 V
817 889 M
62 0 V
-62 676 R
62 0 V
879 448 M
0 1474 V
848 448 M
62 0 V
848 1922 M
62 0 V
972 849 M
0 482 V
941 849 M
62 0 V
-62 482 R
62 0 V
1158 819 M
0 654 V
1127 819 M
62 0 V
-62 654 R
62 0 V
93 -616 R
0 477 V
1251 857 M
62 0 V
-62 477 R
62 0 V
1469 954 M
0 474 V
1438 954 M
62 0 V
-62 474 R
62 0 V
93 -561 R
0 467 V
1562 867 M
62 0 V
-62 467 R
62 0 V
1779 815 M
0 248 V
1748 815 M
62 0 V
-62 248 R
62 0 V
217 -40 R
0 184 V
-31 -184 R
62 0 V
-62 184 R
62 0 V
217 -171 R
0 168 V
-31 -168 R
62 0 V
-62 168 R
62 0 V
2461 957 M
0 319 V
2430 957 M
62 0 V
-62 319 R
62 0 V
stroke
grestore
end
showpage
}
\put(1558,-50){\makebox(0,0){s \small{(GeV$^2$)}}}
\put(300,1180){%
\special{ps: gsave currentpoint currentpoint translate
270 rotate neg exch neg exch translate}%
\makebox(0,0)[b]{\shortstack{$\sigma_{K^+p}-\sigma_{K^+n}$ \small{(mb)}}}%
\special{ps: currentpoint grestore moveto}%
}
\put(2517,151){\makebox(0,0){600}}
\put(2186,151){\makebox(0,0){500}}
\put(1856,151){\makebox(0,0){400}}
\put(1525,151){\makebox(0,0){300}}
\put(1195,151){\makebox(0,0){200}}
\put(864,151){\makebox(0,0){100}}
\put(540,2109){\makebox(0,0)[r]{2}}
%\put(540,1844){\makebox(0,0)[r]{1.5}}
\put(540,1578){\makebox(0,0)[r]{1}}
%\put(540,1313){\makebox(0,0)[r]{0.5}}
\put(540,1047){\makebox(0,0)[r]{0}}
%\put(540,782){\makebox(0,0)[r]{-0.5}}
\put(540,516){\makebox(0,0)[r]{-1}}
%put(540,251){\makebox(0,0)[r]{-1.5}}
\end{picture}}}}
\caption{Test of the I=1 exchange degeneracy relations (4).\
The solid curve in (a) represents a pure Pomeron-Regge cut fit.}
\end{figure}
\begin{figure}[p]
\setlength{\unitlength}{0.1bp}
\begin{picture}(4000,5000)(1000,0)
\put(0,3100){\mbox{\hspace*{-0.5cm}
\subfigure[]{
\special{!
%!PS-Adobe-2.0
%%Creator: gnuplot
%%DocumentFonts: Helvetica
%%BoundingBox: 50 50 1130 554
%%Pages: (atend)
%%EndComments
/gnudict 40 dict def
gnudict begin
/Color false def
/Solid false def
/gnulinewidth 5.000 def
/vshift -33 def
/dl {10 mul} def
/hpt 31.5 def
/vpt 31.5 def
/M {moveto} bind def
/L {lineto} bind def
/R {rmoveto} bind def
/V {rlineto} bind def
/vpt2 vpt 2 mul def
/hpt2 hpt 2 mul def
/Lshow { currentpoint stroke M
  0 vshift R show } def
/Rshow { currentpoint stroke M
  dup stringwidth pop neg vshift R show } def
/Cshow { currentpoint stroke M
  dup stringwidth pop -2 div vshift R show } def
/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
 {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
/BL { stroke gnulinewidth 2 mul setlinewidth } def
/AL { stroke gnulinewidth 2 div setlinewidth } def
/PL { stroke gnulinewidth setlinewidth } def
/LTb { BL [] 0 0 0 DL } def
/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def
/LT0 { PL [] 0 1 0 DL } def
/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def
/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def
/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
/P { stroke [] 0 setdash
  currentlinewidth 2 div sub M
  0 currentlinewidth V stroke } def
/D { stroke [] 0 setdash 2 copy vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath stroke
  P } def
/A { stroke [] 0 setdash vpt sub M 0 vpt2 V
  currentpoint stroke M
  hpt neg vpt neg R hpt2 0 V stroke
  } def
/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V closepath stroke
  P } def
/C { stroke [] 0 setdash exch hpt sub exch vpt add M
  hpt2 vpt2 neg V currentpoint stroke M
  hpt2 neg 0 R hpt2 vpt2 V stroke } def
/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath stroke
  P  } def
/S { 2 copy A C} def
end
%%EndProlog
}
\begin{picture}(5400,2160)(0,0)
\special{"
%%Page: 1 1
gnudict begin
gsave
50 50 translate
0.100 0.100 scale
0 setgray
/Helvetica findfont 100 scalefont setfont
newpath
-500.000000 -500.000000 translate
LTa
LTb
600 251 M
63 0 V
4554 0 R
-63 0 V
600 420 M
63 0 V
4554 0 R
-63 0 V
600 589 M
63 0 V
4554 0 R
-63 0 V
600 758 M
63 0 V
4554 0 R
-63 0 V
600 927 M
63 0 V
4554 0 R
-63 0 V
600 1096 M
63 0 V
4554 0 R
-63 0 V
600 1264 M
63 0 V
4554 0 R
-63 0 V
600 1433 M
63 0 V
4554 0 R
-63 0 V
600 1602 M
63 0 V
4554 0 R
-63 0 V
600 1771 M
63 0 V
4554 0 R
-63 0 V
600 1940 M
63 0 V
4554 0 R
-63 0 V
600 2109 M
63 0 V
4554 0 R
-63 0 V
736 251 M
0 31 V
0 1827 R
0 -31 V
861 251 M
0 31 V
0 1827 R
0 -31 V
921 251 M
0 63 V
0 1795 R
0 -63 V
1106 251 M
0 31 V
0 1827 R
0 -31 V
1350 251 M
0 31 V
0 1827 R
0 -31 V
1475 251 M
0 31 V
0 1827 R
0 -31 V
1535 251 M
0 63 V
0 1795 R
0 -63 V
1719 251 M
0 31 V
0 1827 R
0 -31 V
1964 251 M
0 31 V
0 1827 R
0 -31 V
2089 251 M
0 31 V
0 1827 R
0 -31 V
2148 251 M
0 63 V
0 1795 R
0 -63 V
2333 251 M
0 31 V
0 1827 R
0 -31 V
2577 251 M
0 31 V
0 1827 R
0 -31 V
2703 251 M
0 31 V
0 1827 R
0 -31 V
2762 251 M
0 63 V
0 1795 R
0 -63 V
2947 251 M
0 31 V
0 1827 R
0 -31 V
3191 251 M
0 31 V
0 1827 R
0 -31 V
3316 251 M
0 31 V
0 1827 R
0 -31 V
3376 251 M
0 63 V
0 1795 R
0 -63 V
3561 251 M
0 31 V
0 1827 R
0 -31 V
3805 251 M
0 31 V
0 1827 R
0 -31 V
3930 251 M
0 31 V
0 1827 R
0 -31 V
3990 251 M
0 63 V
0 1795 R
0 -63 V
4174 251 M
0 31 V
0 1827 R
0 -31 V
4419 251 M
0 31 V
0 1827 R
0 -31 V
4544 251 M
0 31 V
0 1827 R
0 -31 V
4603 251 M
0 63 V
0 1795 R
0 -63 V
4788 251 M
0 31 V
0 1827 R
0 -31 V
5032 251 M
0 31 V
0 1827 R
0 -31 V
5158 251 M
0 31 V
0 1827 R
0 -31 V
5217 251 M
0 63 V
0 1795 R
0 -63 V
600 251 M
4617 0 V
0 1858 V
-4617 0 V
600 251 L
LT0
600 433 M
47 -13 V
46 -11 V
47 -8 V
47 -6 V
46 -4 V
47 -3 V
46 -1 V
47 -1 V
47 1 V
46 1 V
47 2 V
47 3 V
46 3 V
47 4 V
47 4 V
46 4 V
47 5 V
46 5 V
47 5 V
47 6 V
46 6 V
47 6 V
47 6 V
46 7 V
47 7 V
47 7 V
46 7 V
47 7 V
46 8 V
47 8 V
47 8 V
46 8 V
47 8 V
47 9 V
46 9 V
47 9 V
47 9 V
46 10 V
47 10 V
46 10 V
47 10 V
47 11 V
46 10 V
47 11 V
47 12 V
46 11 V
47 12 V
47 12 V
46 13 V
47 12 V
46 13 V
47 14 V
47 13 V
46 14 V
47 15 V
47 14 V
46 15 V
47 16 V
47 15 V
46 17 V
47 16 V
46 17 V
47 17 V
47 18 V
46 18 V
47 19 V
47 19 V
46 19 V
47 20 V
47 21 V
46 20 V
47 22 V
46 22 V
47 22 V
47 23 V
46 24 V
47 24 V
47 24 V
46 26 V
47 26 V
47 26 V
46 27 V
47 28 V
46 28 V
47 29 V
47 30 V
46 31 V
47 31 V
47 32 V
46 33 V
47 33 V
47 34 V
46 36 V
47 36 V
46 36 V
47 38 V
47 39 V
46 39 V
47 41 V
LT1
613 398 D
616 398 D
616 386 D
616 407 D
628 403 D
640 420 D
641 415 D
644 406 D
646 398 D
654 386 D
659 393 D
664 401 D
664 415 D
667 403 D
670 396 D
672 404 D
675 404 D
678 405 D
689 410 D
696 391 D
696 401 D
708 410 D
713 415 D
719 401 D
721 398 D
724 408 D
729 400 D
739 401 D
743 400 D
762 418 D
776 396 D
794 393 D
816 394 D
816 394 D
851 395 D
866 393 D
881 394 D
898 395 D
909 390 D
909 394 D
909 382 D
920 384 D
934 393 D
957 394 D
993 364 D
997 391 D
1008 379 D
1086 379 D
1091 394 D
1096 401 D
1139 396 D
1144 369 D
1193 394 D
1198 398 D
1232 400 D
1235 376 D
1269 395 D
1275 427 D
1275 403 D
1275 403 D
1281 403 D
1323 407 D
1323 407 D
1364 410 D
1364 409 D
1376 414 D
1376 401 D
1376 410 D
1376 400 D
1376 407 D
1379 398 D
1382 427 D
1382 407 D
1382 431 D
1385 403 D
1391 413 D
1416 415 D
1438 416 D
1462 430 D
1517 422 D
1517 423 D
1517 421 D
1517 423 D
1517 422 D
1518 424 D
1519 422 D
1521 420 D
1719 449 D
1719 452 D
1722 454 D
1725 462 D
1808 460 D
1808 455 D
1808 466 D
1808 466 D
1808 471 D
1809 460 D
1812 469 D
1896 480 D
1897 472 D
1898 480 D
1900 470 D
1900 484 D
1900 489 D
1902 457 D
3047 873 D
3047 859 D
3048 808 D
3053 779 D
3053 790 D
3320 847 D
3689 1096 D
3689 974 D
5189 1771 D
613 373 M
0 50 V
582 373 M
62 0 V
-62 50 R
62 0 V
616 388 M
0 20 V
585 388 M
62 0 V
-62 20 R
62 0 V
616 361 M
0 50 V
585 361 M
62 0 V
-62 50 R
62 0 V
-31 -6 R
0 4 V
-31 -4 R
62 0 V
-62 4 R
62 0 V
628 378 M
0 50 V
597 378 M
62 0 V
-62 50 R
62 0 V
640 395 M
0 50 V
609 395 M
62 0 V
-62 50 R
62 0 V
641 390 M
0 50 V
610 390 M
62 0 V
-62 50 R
62 0 V
644 404 M
0 4 V
-31 -4 R
62 0 V
-62 4 R
62 0 V
646 388 M
0 20 V
615 388 M
62 0 V
-62 20 R
62 0 V
654 369 M
0 34 V
623 369 M
62 0 V
-62 34 R
62 0 V
659 383 M
0 20 V
628 383 M
62 0 V
-62 20 R
62 0 V
-26 -7 R
0 10 V
633 396 M
62 0 V
-62 10 R
62 0 V
664 390 M
0 50 V
633 390 M
62 0 V
-62 50 R
62 0 V
667 386 M
0 34 V
636 386 M
62 0 V
-62 34 R
62 0 V
670 386 M
0 20 V
639 386 M
62 0 V
-62 20 R
62 0 V
-29 -9 R
0 14 V
641 397 M
62 0 V
-62 14 R
62 0 V
-28 -9 R
0 4 V
-31 -4 R
62 0 V
-62 4 R
62 0 V
-28 -3 R
0 4 V
-31 -4 R
62 0 V
-62 4 R
62 0 V
689 384 M
0 51 V
658 384 M
62 0 V
-62 51 R
62 0 V
696 381 M
0 20 V
665 381 M
62 0 V
-62 20 R
62 0 V
-31 -2 R
0 4 V
-31 -4 R
62 0 V
-62 4 R
62 0 V
-19 -1 R
0 15 V
677 402 M
62 0 V
-62 15 R
62 0 V
713 390 M
0 50 V
682 390 M
62 0 V
-62 50 R
62 0 V
719 400 M
0 3 V
-31 -3 R
62 0 V
-62 3 R
62 0 V
721 373 M
0 50 V
690 373 M
62 0 V
-62 50 R
62 0 V
724 395 M
0 27 V
693 395 M
62 0 V
-62 27 R
62 0 V
729 393 M
0 14 V
698 393 M
62 0 V
-62 14 R
62 0 V
-21 -8 R
0 4 V
-31 -4 R
62 0 V
-62 4 R
62 0 V
-27 -8 R
0 10 V
712 395 M
62 0 V
-62 10 R
62 0 V
762 393 M
0 51 V
731 393 M
62 0 V
-62 51 R
62 0 V
776 389 M
0 14 V
745 389 M
62 0 V
-62 14 R
62 0 V
794 383 M
0 20 V
763 383 M
62 0 V
-62 20 R
62 0 V
-9 -11 R
0 4 V
-31 -4 R
62 0 V
-62 4 R
62 0 V
-31 -9 R
0 14 V
785 387 M
62 0 V
-62 14 R
62 0 V
4 -13 R
0 14 V
820 388 M
62 0 V
-62 14 R
62 0 V
866 392 M
0 3 V
-31 -3 R
62 0 V
-62 3 R
62 0 V
-16 -8 R
0 14 V
850 387 M
62 0 V
-62 14 R
62 0 V
-14 -8 R
0 3 V
-31 -3 R
62 0 V
-62 3 R
62 0 V
-20 -8 R
0 3 V
-31 -3 R
62 0 V
-62 3 R
62 0 V
-31 -4 R
0 14 V
878 387 M
62 0 V
-62 14 R
62 0 V
909 362 M
0 40 V
878 362 M
62 0 V
-62 40 R
62 0 V
920 382 M
0 4 V
-31 -4 R
62 0 V
-62 4 R
62 0 V
-17 0 R
0 14 V
903 386 M
62 0 V
-62 14 R
62 0 V
-8 -13 R
0 14 V
926 387 M
62 0 V
-62 14 R
62 0 V
5 -46 R
0 18 V
962 355 M
62 0 V
-62 18 R
62 0 V
-27 16 R
0 4 V
-31 -4 R
62 0 V
-62 4 R
62 0 V
-20 -32 R
0 37 V
977 361 M
62 0 V
-62 37 R
62 0 V
47 -37 R
0 37 V
-31 -37 R
62 0 V
-62 37 R
62 0 V
-26 -6 R
0 4 V
-31 -4 R
62 0 V
-62 4 R
62 0 V
-26 -8 R
0 27 V
-31 -27 R
62 0 V
-62 27 R
62 0 V
12 -21 R
0 4 V
-31 -4 R
62 0 V
-62 4 R
62 0 V
-26 -47 R
0 37 V
-31 -37 R
62 0 V
-62 37 R
62 0 V
18 -4 R
0 20 V
-31 -20 R
62 0 V
-62 20 R
62 0 V
-26 -8 R
0 4 V
-31 -4 R
62 0 V
-62 4 R
62 0 V
3 -2 R
0 4 V
-31 -4 R
62 0 V
-62 4 R
62 0 V
-28 -45 R
0 38 V
-31 -38 R
62 0 V
-62 38 R
62 0 V
3 -21 R
0 41 V
-31 -41 R
62 0 V
-62 41 R
62 0 V
-25 7 R
0 10 V
-31 -10 R
62 0 V
-62 10 R
62 0 V
-31 -30 R
0 1 V
-31 -1 R
62 0 V
-62 1 R
62 0 V
-31 -2 R
0 3 V
-31 -3 R
62 0 V
-62 3 R
62 0 V
-25 -18 R
0 34 V
-31 -34 R
62 0 V
-62 34 R
62 0 V
11 -14 R
0 2 V
-31 -2 R
62 0 V
-62 2 R
62 0 V
-31 -3 R
0 3 V
-31 -3 R
62 0 V
-62 3 R
62 0 V
10 1 R
0 2 V
-31 -2 R
62 0 V
-62 2 R
62 0 V
-31 -3 R
0 3 V
-31 -3 R
62 0 V
-62 3 R
62 0 V
-19 -2 R
0 10 V
-31 -10 R
62 0 V
-62 10 R
62 0 V
-31 -29 R
0 23 V
-31 -23 R
62 0 V
currentpoint stroke M
-62 23 R
62 0 V
-31 -8 R
0 10 V
-31 -10 R
62 0 V
-62 10 R
62 0 V
-31 -20 R
0 9 V
-31 -9 R
62 0 V
-62 9 R
62 0 V
-31 1 R
0 4 V
-31 -4 R
62 0 V
-62 4 R
62 0 V
-28 -23 R
0 24 V
-31 -24 R
62 0 V
-62 24 R
62 0 V
-28 12 R
0 9 V
-31 -9 R
62 0 V
-62 9 R
62 0 V
-31 -40 R
0 31 V
-31 -31 R
62 0 V
-62 31 R
62 0 V
-31 0 R
0 19 V
-31 -19 R
62 0 V
-62 19 R
62 0 V
-28 -55 R
0 34 V
-31 -34 R
62 0 V
-62 34 R
62 0 V
-25 -8 R
0 2 V
-31 -2 R
62 0 V
-62 2 R
62 0 V
-6 -1 R
0 3 V
-31 -3 R
62 0 V
-62 3 R
62 0 V
-9 -1 R
0 2 V
-31 -2 R
62 0 V
-62 2 R
62 0 V
-7 -7 R
0 40 V
-31 -40 R
62 0 V
-62 40 R
62 0 V
24 -33 R
0 9 V
-31 -9 R
62 0 V
-62 9 R
62 0 V
-31 -16 R
0 27 V
-31 -27 R
62 0 V
-62 27 R
62 0 V
-31 -20 R
0 8 V
-31 -8 R
62 0 V
-62 8 R
62 0 V
-31 -5 R
0 6 V
-31 -6 R
62 0 V
-62 6 R
62 0 V
-31 -11 R
0 13 V
-31 -13 R
62 0 V
-62 13 R
62 0 V
-30 -8 R
0 7 V
-31 -7 R
62 0 V
-62 7 R
62 0 V
-30 -9 R
0 7 V
-31 -7 R
62 0 V
-62 7 R
62 0 V
-29 -15 R
0 20 V
-31 -20 R
62 0 V
-62 20 R
62 0 V
167 12 R
0 13 V
-31 -13 R
62 0 V
-62 13 R
62 0 V
-31 -7 R
0 8 V
-31 -8 R
62 0 V
-62 8 R
62 0 V
-28 -6 R
0 7 V
-31 -7 R
62 0 V
-62 7 R
62 0 V
-28 -8 R
0 27 V
-31 -27 R
62 0 V
-62 27 R
62 0 V
52 -20 R
0 8 V
-31 -8 R
62 0 V
-62 8 R
62 0 V
-31 -12 R
0 7 V
-31 -7 R
62 0 V
-62 7 R
62 0 V
-31 1 R
0 12 V
-31 -12 R
62 0 V
-62 12 R
62 0 V
-31 -9 R
0 6 V
-31 -6 R
62 0 V
-62 6 R
62 0 V
-31 -3 R
0 9 V
-31 -9 R
62 0 V
-62 9 R
62 0 V
-30 -21 R
0 13 V
-31 -13 R
62 0 V
-62 13 R
62 0 V
-28 -10 R
0 24 V
-31 -24 R
62 0 V
-62 24 R
62 0 V
53 -7 R
0 12 V
-31 -12 R
62 0 V
-62 12 R
62 0 V
-30 -20 R
0 13 V
-31 -13 R
62 0 V
-62 13 R
62 0 V
-30 -3 R
0 8 V
-31 -8 R
62 0 V
-62 8 R
62 0 V
-29 -21 R
0 13 V
-31 -13 R
62 0 V
-62 13 R
62 0 V
-31 3 R
0 10 V
-31 -10 R
62 0 V
-62 10 R
62 0 V
-31 -15 R
0 30 V
-31 -30 R
62 0 V
-62 30 R
62 0 V
1902 398 M
0 118 V
1871 398 M
62 0 V
-62 118 R
62 0 V
3047 752 M
0 241 V
3016 752 M
62 0 V
-62 241 R
62 0 V
3047 714 M
0 290 V
3016 714 M
62 0 V
-62 290 R
62 0 V
3048 773 M
0 71 V
-31 -71 R
62 0 V
-62 71 R
62 0 V
-26 -81 R
0 32 V
-31 -32 R
62 0 V
-62 32 R
62 0 V
-31 -31 R
0 51 V
-31 -51 R
62 0 V
-62 51 R
62 0 V
236 -8 R
0 81 V
-31 -81 R
62 0 V
-62 81 R
62 0 V
338 170 R
0 76 V
-31 -76 R
62 0 V
-62 76 R
62 0 V
3689 922 M
0 104 V
3658 922 M
62 0 V
-62 104 R
62 0 V
1469 492 R
0 507 V
-31 -507 R
62 0 V
-62 507 R
62 0 V
stroke
grestore
end
showpage
}
\put(2908,-50){\makebox(0,0){$\log_{10}$~s \small{(GeV$^2$)}}}
\put(350,1180){%
\special{ps: gsave currentpoint currentpoint translate
270 rotate neg exch neg exch translate}%
\makebox(0,0)[b]{\shortstack{$\sigma_{pp}$ \small{(mb)}}}%
\special{ps: currentpoint grestore moveto}%
}
\put(5217,151){\makebox(0,0){9}}
\put(4603,151){\makebox(0,0){8}}
\put(3990,151){\makebox(0,0){7}}
\put(3376,151){\makebox(0,0){6}}
\put(2762,151){\makebox(0,0){5}}
\put(2148,151){\makebox(0,0){4}}
\put(1535,151){\makebox(0,0){3}}
\put(921,151){\makebox(0,0){2}}
\put(540,2109){\makebox(0,0)[r]{140}}
\put(540,1940){\makebox(0,0)[r]{130}}
\put(540,1771){\makebox(0,0)[r]{120}}
\put(540,1602){\makebox(0,0)[r]{110}}
\put(540,1433){\makebox(0,0)[r]{100}}
\put(540,1264){\makebox(0,0)[r]{90}}
\put(540,1096){\makebox(0,0)[r]{80}}
\put(540,927){\makebox(0,0)[r]{70}}
\put(540,758){\makebox(0,0)[r]{60}}
\put(540,589){\makebox(0,0)[r]{50}}
\put(540,420){\makebox(0,0)[r]{40}}
\put(540,251){\makebox(0,0)[r]{30}}
\end{picture}
}}}
\put(0,300){\mbox{\hspace*{-0.2cm}
\subfigure[]{
\special{!
%!PS-Adobe-2.0
%%Creator: gnuplot
%%DocumentFonts: Helvetica
%%BoundingBox: 50 50 590 554
%%Pages: (atend)
%%EndComments
/gnudict 40 dict def
gnudict begin
/Color false def
/Solid false def
/gnulinewidth 5.000 def
/vshift -33 def
/dl {10 mul} def
/hpt 31.5 def
/vpt 31.5 def
/M {moveto} bind def
/L {lineto} bind def
/R {rmoveto} bind def
/V {rlineto} bind def
/vpt2 vpt 2 mul def
/hpt2 hpt 2 mul def
/Lshow { currentpoint stroke M
  0 vshift R show } def
/Rshow { currentpoint stroke M
  dup stringwidth pop neg vshift R show } def
/Cshow { currentpoint stroke M
  dup stringwidth pop -2 div vshift R show } def
/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
 {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
/BL { stroke gnulinewidth 2 mul setlinewidth } def
/AL { stroke gnulinewidth 2 div setlinewidth } def
/PL { stroke gnulinewidth setlinewidth } def
/LTb { BL [] 0 0 0 DL } def
/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def
/LT0 { PL [] 0 1 0 DL } def
/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def
/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def
/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
/P { stroke [] 0 setdash
  currentlinewidth 2 div sub M
  0 currentlinewidth V stroke } def
/D { stroke [] 0 setdash 2 copy vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath stroke
  P } def
/A { stroke [] 0 setdash vpt sub M 0 vpt2 V
  currentpoint stroke M
  hpt neg vpt neg R hpt2 0 V stroke
  } def
/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V closepath stroke
  P } def
/C { stroke [] 0 setdash exch hpt sub exch vpt add M
  hpt2 vpt2 neg V currentpoint stroke M
  hpt2 neg 0 R hpt2 vpt2 V stroke } def
/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath stroke
  P  } def
/S { 2 copy A C} def
end
%%EndProlog
}
\begin{picture}(2700,2160)(0,0)
\special{"
%%Page: 1 1
gnudict begin
gsave
50 50 translate
0.100 0.100 scale
0 setgray
/Helvetica findfont 100 scalefont setfont
newpath
-500.000000 -500.000000 translate
LTa
LTb
600 251 M
63 0 V
1854 0 R
-63 0 V
600 420 M
63 0 V
1854 0 R
-63 0 V
600 589 M
63 0 V
1854 0 R
-63 0 V
600 758 M
63 0 V
1854 0 R
-63 0 V
600 927 M
63 0 V
1854 0 R
-63 0 V
600 1096 M
63 0 V
1854 0 R
-63 0 V
600 1264 M
63 0 V
1854 0 R
-63 0 V
600 1433 M
63 0 V
1854 0 R
-63 0 V
600 1602 M
63 0 V
1854 0 R
-63 0 V
600 1771 M
63 0 V
1854 0 R
-63 0 V
600 1940 M
63 0 V
1854 0 R
-63 0 V
600 2109 M
63 0 V
1854 0 R
-63 0 V
826 251 M
0 63 V
0 1795 R
0 -63 V
1107 251 M
0 63 V
0 1795 R
0 -63 V
1389 251 M
0 63 V
0 1795 R
0 -63 V
1671 251 M
0 63 V
0 1795 R
0 -63 V
1953 251 M
0 63 V
0 1795 R
0 -63 V
2235 251 M
0 63 V
0 1795 R
0 -63 V
2517 251 M
0 63 V
0 1795 R
0 -63 V
600 251 M
1917 0 V
0 1858 V
-1917 0 V
600 251 L
LT0
600 1396 M
19 -236 V
20 -129 V
19 -78 V
19 -49 V
20 -32 V
19 -21 V
20 -13 V
19 -8 V
19 -4 V
20 -2 V
19 1 V
19 2 V
20 3 V
19 4 V
19 5 V
20 5 V
19 6 V
20 6 V
19 7 V
19 6 V
20 7 V
19 7 V
19 7 V
20 7 V
19 7 V
19 7 V
20 7 V
19 7 V
20 7 V
19 7 V
19 7 V
20 7 V
19 7 V
19 6 V
20 7 V
19 7 V
19 6 V
20 7 V
19 7 V
20 6 V
19 6 V
19 7 V
20 6 V
19 6 V
19 6 V
20 6 V
19 6 V
19 6 V
20 6 V
19 6 V
20 6 V
19 6 V
19 5 V
20 6 V
19 6 V
19 5 V
20 6 V
19 5 V
19 5 V
20 6 V
19 5 V
20 5 V
19 5 V
19 5 V
20 5 V
19 6 V
19 5 V
20 4 V
19 5 V
19 5 V
20 5 V
19 5 V
20 5 V
19 4 V
19 5 V
20 5 V
19 4 V
19 5 V
20 4 V
19 5 V
19 4 V
20 5 V
19 4 V
20 4 V
19 5 V
19 4 V
20 4 V
19 4 V
19 4 V
20 5 V
19 4 V
19 4 V
20 4 V
19 4 V
20 4 V
19 4 V
19 4 V
20 4 V
19 4 V
LT1
609 1270 D
610 1366 D
610 1163 D
620 1332 D
620 1062 D
626 1123 D
626 1112 D
631 1082 D
636 1298 D
641 927 D
644 792 D
644 798 D
652 933 D
652 1129 D
652 893 D
654 1005 D
663 900 D
668 998 D
678 903 D
705 866 D
731 778 D
731 829 D
758 785 D
771 792 D
784 805 D
811 623 D
811 795 D
811 795 D
822 792 D
837 805 D
864 869 D
916 832 D
1075 869 D
1181 900 D
1324 1008 D
1340 927 D
1445 987 D
1604 1021 D
1604 1041 D
1816 1129 D
1816 1136 D
2027 1241 D
2345 1305 D
609 1244 M
0 53 V
-31 -53 R
62 0 V
-62 53 R
62 0 V
610 683 M
0 1366 V
579 683 M
62 0 V
579 2049 M
62 0 V
610 1096 M
0 135 V
579 1096 M
62 0 V
-62 135 R
62 0 V
620 649 M
0 1366 V
589 649 M
62 0 V
589 2015 M
62 0 V
620 994 M
0 135 V
589 994 M
62 0 V
-62 135 R
62 0 V
626 949 M
0 347 V
595 949 M
62 0 V
-62 347 R
62 0 V
626 1018 M
0 189 V
595 1018 M
62 0 V
-62 189 R
62 0 V
631 1048 M
0 68 V
-31 -68 R
62 0 V
-62 68 R
62 0 V
636 619 M
0 1358 V
605 619 M
62 0 V
605 1977 M
62 0 V
641 859 M
0 135 V
610 859 M
62 0 V
610 994 M
62 0 V
644 555 M
0 473 V
613 555 M
62 0 V
-62 473 R
62 0 V
644 572 M
0 453 V
613 572 M
62 0 V
-62 453 R
62 0 V
652 760 M
0 346 V
621 760 M
62 0 V
-62 346 R
62 0 V
652 400 M
0 1459 V
621 400 M
62 0 V
621 1859 M
62 0 V
652 825 M
0 135 V
621 825 M
62 0 V
621 960 M
62 0 V
-29 18 R
0 53 V
623 978 M
62 0 V
-62 53 R
62 0 V
663 867 M
0 66 V
632 867 M
62 0 V
-62 66 R
62 0 V
-26 -6 R
0 141 V
637 927 M
62 0 V
-62 141 R
62 0 V
678 730 M
0 346 V
647 730 M
62 0 V
-62 346 R
62 0 V
705 693 M
0 346 V
674 693 M
62 0 V
-62 346 R
62 0 V
731 605 M
0 346 V
700 605 M
62 0 V
700 951 M
62 0 V
731 760 M
0 138 V
700 760 M
62 0 V
700 898 M
62 0 V
758 612 M
0 346 V
727 612 M
62 0 V
727 958 M
62 0 V
771 748 M
0 87 V
740 748 M
62 0 V
-62 87 R
62 0 V
784 631 M
0 348 V
753 631 M
62 0 V
753 979 M
62 0 V
811 454 M
0 338 V
780 454 M
62 0 V
780 792 M
62 0 V
811 724 M
0 141 V
780 724 M
62 0 V
780 865 M
62 0 V
811 621 M
0 348 V
780 621 M
62 0 V
780 969 M
62 0 V
822 734 M
0 115 V
791 734 M
62 0 V
791 849 M
62 0 V
837 631 M
0 348 V
806 631 M
62 0 V
806 979 M
62 0 V
864 687 M
0 364 V
833 687 M
62 0 V
-62 364 R
62 0 V
916 762 M
0 141 V
885 762 M
62 0 V
885 903 M
62 0 V
1075 799 M
0 141 V
1044 799 M
62 0 V
-62 141 R
62 0 V
75 -109 R
0 138 V
1150 831 M
62 0 V
-62 138 R
62 0 V
1324 852 M
0 311 V
1293 852 M
62 0 V
-62 311 R
62 0 V
1340 858 M
0 138 V
1309 858 M
62 0 V
-62 138 R
62 0 V
74 -78 R
0 139 V
1414 918 M
62 0 V
-62 139 R
62 0 V
128 -49 R
0 27 V
-31 -27 R
62 0 V
-62 27 R
62 0 V
-31 -64 R
0 141 V
1573 971 M
62 0 V
-62 141 R
62 0 V
181 -6 R
0 47 V
-31 -47 R
62 0 V
-62 47 R
62 0 V
-31 -88 R
0 143 V
-31 -143 R
62 0 V
-62 143 R
62 0 V
180 -1 R
0 68 V
-31 -68 R
62 0 V
-62 68 R
62 0 V
287 -17 R
0 94 V
-31 -94 R
62 0 V
-62 94 R
62 0 V
stroke
grestore
end
showpage
}
\put(1558,-50){\makebox(0,0){s \small{(GeV$^2$)}}}
\put(300,1180){%
\special{ps: gsave currentpoint currentpoint translate
270 rotate neg exch neg exch translate}%
\makebox(0,0)[b]{\shortstack{$\sigma_{\pi^+p}$ \small{(mb)}}}%
\special{ps: currentpoint grestore moveto}%
}
\put(2517,151){\makebox(0,0){700}}
\put(2235,151){\makebox(0,0){600}}
\put(1953,151){\makebox(0,0){500}}
\put(1671,151){\makebox(0,0){400}}
\put(1389,151){\makebox(0,0){300}}
\put(1107,151){\makebox(0,0){200}}
\put(826,151){\makebox(0,0){100}}
\put(540,2109){\makebox(0,0)[r]{27}}
%\put(540,1940){\makebox(0,0)[r]{26.5}}
\put(540,1771){\makebox(0,0)[r]{26}}
%\put(540,1602){\makebox(0,0)[r]{25.5}}
\put(540,1433){\makebox(0,0)[r]{25}}
%\put(540,1264){\makebox(0,0)[r]{24.5}}
\put(540,1096){\makebox(0,0)[r]{24}}
%\put(540,927){\makebox(0,0)[r]{23.5}}
\put(540,758){\makebox(0,0)[r]{23}}
%\put(540,589){\makebox(0,0)[r]{22.5}}
\put(540,420){\makebox(0,0)[r]{22}}
%\put(540,251){\makebox(0,0)[r]{21.5}}
\end{picture}
}\hspace{-1cm}
\subfigure[]{
\special{!
%!PS-Adobe-2.0
%%Creator: gnuplot
%%DocumentFonts: Helvetica
%%BoundingBox: 50 50 590 554
%%Pages: (atend)
%%EndComments
/gnudict 40 dict def
gnudict begin
/Color false def
/Solid false def
/gnulinewidth 5.000 def
/vshift -33 def
/dl {10 mul} def
/hpt 31.5 def
/vpt 31.5 def
/M {moveto} bind def
/L {lineto} bind def
/R {rmoveto} bind def
/V {rlineto} bind def
/vpt2 vpt 2 mul def
/hpt2 hpt 2 mul def
/Lshow { currentpoint stroke M
  0 vshift R show } def
/Rshow { currentpoint stroke M
  dup stringwidth pop neg vshift R show } def
/Cshow { currentpoint stroke M
  dup stringwidth pop -2 div vshift R show } def
/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
 {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
/BL { stroke gnulinewidth 2 mul setlinewidth } def
/AL { stroke gnulinewidth 2 div setlinewidth } def
/PL { stroke gnulinewidth setlinewidth } def
/LTb { BL [] 0 0 0 DL } def
/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def
/LT0 { PL [] 0 1 0 DL } def
/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def
/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def
/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
/P { stroke [] 0 setdash
  currentlinewidth 2 div sub M
  0 currentlinewidth V stroke } def
/D { stroke [] 0 setdash 2 copy vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath stroke
  P } def
/A { stroke [] 0 setdash vpt sub M 0 vpt2 V
  currentpoint stroke M
  hpt neg vpt neg R hpt2 0 V stroke
  } def
/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V closepath stroke
  P } def
/C { stroke [] 0 setdash exch hpt sub exch vpt add M
  hpt2 vpt2 neg V currentpoint stroke M
  hpt2 neg 0 R hpt2 vpt2 V stroke } def
/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath stroke
  P  } def
/S { 2 copy A C} def
end
%%EndProlog
}
\begin{picture}(2700,2160)(0,0)
\special{"
%%Page: 1 1
gnudict begin
gsave
50 50 translate
0.100 0.100 scale
0 setgray
/Helvetica findfont 100 scalefont setfont
newpath
-500.000000 -500.000000 translate
LTa
LTb
600 251 M
63 0 V
1854 0 R
-63 0 V
600 437 M
63 0 V
1854 0 R
-63 0 V
600 623 M
63 0 V
1854 0 R
-63 0 V
600 808 M
63 0 V
1854 0 R
-63 0 V
600 994 M
63 0 V
1854 0 R
-63 0 V
600 1180 M
63 0 V
1854 0 R
-63 0 V
600 1366 M
63 0 V
1854 0 R
-63 0 V
600 1552 M
63 0 V
1854 0 R
-63 0 V
600 1737 M
63 0 V
1854 0 R
-63 0 V
600 1923 M
63 0 V
1854 0 R
-63 0 V
600 2109 M
63 0 V
1854 0 R
-63 0 V
864 251 M
0 63 V
0 1795 R
0 -63 V
1195 251 M
0 63 V
0 1795 R
0 -63 V
1525 251 M
0 63 V
0 1795 R
0 -63 V
1856 251 M
0 63 V
0 1795 R
0 -63 V
2186 251 M
0 63 V
0 1795 R
0 -63 V
2517 251 M
0 63 V
0 1795 R
0 -63 V
600 251 M
1917 0 V
0 1858 V
-1917 0 V
600 251 L
LT0
600 463 M
19 84 V
20 68 V
19 58 V
19 50 V
20 44 V
19 40 V
20 36 V
19 33 V
19 30 V
20 29 V
19 26 V
19 25 V
20 24 V
19 22 V
19 21 V
20 20 V
19 20 V
20 18 V
19 18 V
19 17 V
20 16 V
19 16 V
19 15 V
20 15 V
19 15 V
19 13 V
20 14 V
19 13 V
20 13 V
19 12 V
19 12 V
20 12 V
19 11 V
19 11 V
20 11 V
19 11 V
19 10 V
20 11 V
19 10 V
20 9 V
19 10 V
19 9 V
20 10 V
19 9 V
19 9 V
20 8 V
19 9 V
19 8 V
20 9 V
19 8 V
20 8 V
19 8 V
19 8 V
20 7 V
19 8 V
19 7 V
20 7 V
19 8 V
19 7 V
20 7 V
19 7 V
20 6 V
19 7 V
19 7 V
20 6 V
19 7 V
19 6 V
20 6 V
19 7 V
19 6 V
20 6 V
19 6 V
20 6 V
19 6 V
19 6 V
20 5 V
19 6 V
19 6 V
20 5 V
19 6 V
19 5 V
20 6 V
19 5 V
20 5 V
19 5 V
19 6 V
20 5 V
19 5 V
19 5 V
20 5 V
19 5 V
19 5 V
20 4 V
19 5 V
20 5 V
19 5 V
19 4 V
20 5 V
19 5 V
LT1
605 846 D
612 548 D
621 623 D
631 552 D
631 994 D
637 437 D
649 474 D
662 593 D
662 623 D
693 689 D
724 704 D
736 957 D
755 734 D
755 742 D
786 827 D
801 775 D
817 764 D
848 831 D
848 946 D
861 912 D
879 872 D
972 1002 D
1158 1069 D
1158 1135 D
1282 1232 D
1449 1373 D
1468 1314 D
1592 1418 D
1778 1518 D
1778 1514 D
2026 1633 D
2026 1656 D
2274 1719 D
2274 1789 D
605 585 M
0 521 V
574 585 M
62 0 V
-62 521 R
62 0 V
612 511 M
0 74 V
581 511 M
62 0 V
-62 74 R
62 0 V
621 400 M
0 446 V
590 400 M
62 0 V
590 846 M
62 0 V
631 396 M
0 312 V
600 396 M
62 0 V
600 708 M
62 0 V
-31 26 R
0 520 V
600 734 M
62 0 V
-62 520 R
62 0 V
637 400 M
0 74 V
606 400 M
62 0 V
-62 74 R
62 0 V
649 437 M
0 74 V
618 437 M
62 0 V
-62 74 R
62 0 V
662 433 M
0 320 V
631 433 M
62 0 V
631 753 M
62 0 V
662 585 M
0 75 V
631 585 M
62 0 V
-62 75 R
62 0 V
0 -124 R
0 307 V
662 536 M
62 0 V
662 843 M
62 0 V
0 -292 R
0 307 V
693 551 M
62 0 V
693 858 M
62 0 V
736 808 M
0 298 V
705 808 M
62 0 V
-62 298 R
62 0 V
755 581 M
0 306 V
724 581 M
62 0 V
724 887 M
62 0 V
755 625 M
0 233 V
724 625 M
62 0 V
724 858 M
62 0 V
0 -187 R
0 312 V
755 671 M
62 0 V
755 983 M
62 0 V
801 704 M
0 142 V
770 704 M
62 0 V
770 846 M
62 0 V
817 609 M
0 310 V
786 609 M
62 0 V
786 919 M
62 0 V
0 -204 R
0 231 V
817 715 M
62 0 V
817 946 M
62 0 V
848 792 M
0 308 V
817 792 M
62 0 V
-62 308 R
62 0 V
861 823 M
0 179 V
830 823 M
62 0 V
-62 179 R
62 0 V
879 714 M
0 315 V
848 714 M
62 0 V
-62 315 R
62 0 V
972 886 M
0 231 V
941 886 M
62 0 V
-62 231 R
62 0 V
1158 400 M
0 1337 V
1127 400 M
62 0 V
-62 1337 R
62 0 V
-31 -716 R
0 229 V
-31 -229 R
62 0 V
-62 229 R
62 0 V
93 -132 R
0 228 V
-31 -228 R
62 0 V
-62 228 R
62 0 V
136 -166 R
0 386 V
-31 -386 R
62 0 V
-62 386 R
62 0 V
-12 -367 R
0 229 V
-31 -229 R
62 0 V
-62 229 R
62 0 V
93 -124 R
0 228 V
-31 -228 R
62 0 V
-62 228 R
62 0 V
155 -55 R
0 82 V
-31 -82 R
62 0 V
-62 82 R
62 0 V
-31 -163 R
0 237 V
-31 -237 R
62 0 V
-62 237 R
62 0 V
217 -22 R
0 45 V
-31 -45 R
62 0 V
-62 45 R
62 0 V
-31 -115 R
0 229 V
-31 -229 R
62 0 V
-62 229 R
62 0 V
217 -77 R
0 52 V
-31 -52 R
62 0 V
-62 52 R
62 0 V
-31 -141 R
0 371 V
-31 -371 R
62 0 V
-62 371 R
62 0 V
stroke
grestore
end
showpage
}
\put(1558,-50){\makebox(0,0){s \small{(GeV$^2$)}}}
\put(300,1180){%
\special{ps: gsave currentpoint currentpoint translate
270 rotate neg exch neg exch translate}%
\makebox(0,0)[b]{\shortstack{$\sigma_{K^+p}$ \small{(mb)}}}%
\special{ps: currentpoint grestore moveto}%
}
\put(2517,151){\makebox(0,0){600}}
\put(2186,151){\makebox(0,0){500}}
\put(1856,151){\makebox(0,0){400}}
\put(1525,151){\makebox(0,0){300}}
\put(1195,151){\makebox(0,0){200}}
\put(864,151){\makebox(0,0){100}}
%\put(540,2109){\makebox(0,0)[r]{21.5}}
\put(540,1923){\makebox(0,0)[r]{21}}
%\put(540,1737){\makebox(0,0)[r]{20.5}}
\put(540,1552){\makebox(0,0)[r]{20}}
%\put(540,1366){\makebox(0,0)[r]{19.5}}
\put(540,1180){\makebox(0,0)[r]{19}}
%\put(540,994){\makebox(0,0)[r]{18.5}}
\put(540,808){\makebox(0,0)[r]{18}}
%\put(540,623){\makebox(0,0)[r]{17.5}}
\put(540,437){\makebox(0,0)[r]{17}}
%\put(540,251){\makebox(0,0)[r]{16.5}}
\end{picture}
}}}
\end{picture}
\caption{Fit of the form Eqs. (7), (8) to the three 
independent cross sections\ $\sigma_{pp},~\sigma_{\pi^+p},
~\sigma_{K^+p}$. The parameters of this fit are given in Eq. (9).}
\end{figure}
\setlength{\unitlength}{0.1bp}
\subfigure{
\special{!
%!PS-Adobe-2.0
%%Creator: gnuplot
%%DocumentFonts: Helvetica
%%BoundingBox: 50 50 590 554
%%Pages: (atend)
%%EndComments
/gnudict 40 dict def
gnudict begin
/Color false def
/Solid false def
/gnulinewidth 5.000 def
/vshift -33 def
/dl {10 mul} def
/hpt 31.5 def
/vpt 31.5 def
/M {moveto} bind def
/L {lineto} bind def
/R {rmoveto} bind def
/V {rlineto} bind def
/vpt2 vpt 2 mul def
/hpt2 hpt 2 mul def
/Lshow { currentpoint stroke M
  0 vshift R show } def
/Rshow { currentpoint stroke M
  dup stringwidth pop neg vshift R show } def
/Cshow { currentpoint stroke M
  dup stringwidth pop -2 div vshift R show } def
/DL { Color {setrgbcolor Solid {pop []} if 0 setdash }
 {pop pop pop Solid {pop []} if 0 setdash} ifelse } def
/BL { stroke gnulinewidth 2 mul setlinewidth } def
/AL { stroke gnulinewidth 2 div setlinewidth } def
/PL { stroke gnulinewidth setlinewidth } def
/LTb { BL [] 0 0 0 DL } def
/LTa { AL [1 dl 2 dl] 0 setdash 0 0 0 setrgbcolor } def
/LT0 { PL [] 0 1 0 DL } def
/LT1 { PL [4 dl 2 dl] 0 0 1 DL } def
/LT2 { PL [2 dl 3 dl] 1 0 0 DL } def
/LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def
/LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def
/LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def
/LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def
/LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def
/LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def
/P { stroke [] 0 setdash
  currentlinewidth 2 div sub M
  0 currentlinewidth V stroke } def
/D { stroke [] 0 setdash 2 copy vpt add M
  hpt neg vpt neg V hpt vpt neg V
  hpt vpt V hpt neg vpt V closepath stroke
  P } def
/A { stroke [] 0 setdash vpt sub M 0 vpt2 V
  currentpoint stroke M
  hpt neg vpt neg R hpt2 0 V stroke
  } def
/B { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M
  0 vpt2 neg V hpt2 0 V 0 vpt2 V
  hpt2 neg 0 V closepath stroke
  P } def
/C { stroke [] 0 setdash exch hpt sub exch vpt add M
  hpt2 vpt2 neg V currentpoint stroke M
  hpt2 neg 0 R hpt2 vpt2 V stroke } def
/T { stroke [] 0 setdash 2 copy vpt 1.12 mul add M
  hpt neg vpt -1.62 mul V
  hpt 2 mul 0 V
  hpt neg vpt 1.62 mul V closepath stroke
  P  } def
/S { 2 copy A C} def
end
%%EndProlog
}
\begin{picture}(2700,2160)(0,300)
\special{"
%%Page: 1 1
gnudict begin
gsave
50 50 translate
0.100 0.100 scale
0 setgray
/Helvetica findfont 100 scalefont setfont
newpath
-500.000000 -500.000000 translate
LTa
LTb
600 251 M
63 0 V
1854 0 R
-63 0 V
600 561 M
63 0 V
1854 0 R
-63 0 V
600 870 M
63 0 V
1854 0 R
-63 0 V
600 1180 M
63 0 V
1854 0 R
-63 0 V
600 1490 M
63 0 V
1854 0 R
-63 0 V
600 1799 M
63 0 V
1854 0 R
-63 0 V
600 2109 M
63 0 V
1854 0 R
-63 0 V
826 251 M
0 63 V
0 1795 R
0 -63 V
1107 251 M
0 63 V
0 1795 R
0 -63 V
1389 251 M
0 63 V
0 1795 R
0 -63 V
1671 251 M
0 63 V
0 1795 R
0 -63 V
1953 251 M
0 63 V
0 1795 R
0 -63 V
2235 251 M
0 63 V
0 1795 R
0 -63 V
2517 251 M
0 63 V
0 1795 R
0 -63 V
600 251 M
1917 0 V
0 1858 V
-1917 0 V
600 251 L
LT0
2214 1946 M
180 0 V
600 1665 M
19 -117 V
20 -78 V
19 -57 V
19 -44 V
20 -35 V
19 -29 V
20 -24 V
19 -21 V
19 -18 V
20 -16 V
19 -14 V
19 -12 V
20 -12 V
19 -10 V
19 -9 V
20 -9 V
19 -8 V
20 -7 V
19 -7 V
19 -7 V
20 -5 V
19 -6 V
19 -5 V
20 -5 V
19 -5 V
19 -4 V
20 -5 V
19 -4 V
20 -3 V
19 -4 V
19 -3 V
20 -4 V
19 -3 V
19 -3 V
20 -3 V
19 -2 V
19 -3 V
20 -3 V
19 -2 V
20 -3 V
19 -2 V
19 -2 V
20 -2 V
19 -2 V
19 -2 V
20 -2 V
19 -2 V
19 -2 V
20 -2 V
19 -1 V
20 -2 V
19 -2 V
19 -1 V
20 -2 V
19 -1 V
19 -2 V
20 -1 V
19 -2 V
19 -1 V
20 -1 V
19 -2 V
20 -1 V
19 -1 V
19 -1 V
20 -1 V
19 -2 V
19 -1 V
20 -1 V
19 -1 V
19 -1 V
20 -1 V
19 -1 V
20 -1 V
19 -1 V
19 -1 V
20 -1 V
19 -1 V
19 -1 V
20 0 V
19 -1 V
19 -1 V
20 -1 V
19 -1 V
20 -1 V
19 0 V
19 -1 V
20 -1 V
19 -1 V
19 0 V
20 -1 V
19 -1 V
19 0 V
20 -1 V
19 -1 V
20 0 V
19 -1 V
19 -1 V
20 0 V
19 -1 V
LT1
610 1492 D
620 1498 D
621 1405 D
626 1421 D
630 1730 D
631 1584 D
636 1211 D
644 1356 D
652 1408 D
653 1310 D
663 1379 D
668 1273 D
678 1291 D
705 1304 D
731 1245 D
758 1296 D
784 1220 D
811 1247 D
837 1285 D
864 1188 D
916 1112 D
1075 1078 D
1181 1069 D
1324 1025 D
1340 1059 D
1445 1034 D
1604 1040 D
1816 1025 D
2027 966 D
2186 994 D
2345 1013 D
610 1405 M
0 174 V
579 1405 M
62 0 V
-62 174 R
62 0 V
620 901 M
0 1194 V
589 901 M
62 0 V
589 2095 M
62 0 V
621 1370 M
0 71 V
-31 -71 R
62 0 V
-62 71 R
62 0 V
626 1272 M
0 299 V
595 1272 M
62 0 V
-62 299 R
62 0 V
630 1388 M
0 683 V
599 1388 M
62 0 V
-62 683 R
62 0 V
631 1222 M
0 724 V
600 1222 M
62 0 V
-62 724 R
62 0 V
636 352 M
0 1718 V
605 352 M
62 0 V
605 2070 M
62 0 V
644 1151 M
0 410 V
613 1151 M
62 0 V
-62 410 R
62 0 V
652 1274 M
0 269 V
621 1274 M
62 0 V
-62 269 R
62 0 V
653 1274 M
0 71 V
-31 -71 R
62 0 V
-62 71 R
62 0 V
-21 -5 R
0 78 V
-31 -78 R
62 0 V
-62 78 R
62 0 V
668 1181 M
0 183 V
637 1181 M
62 0 V
-62 183 R
62 0 V
678 1089 M
0 405 V
647 1089 M
62 0 V
-62 405 R
62 0 V
-4 -359 R
0 338 V
674 1135 M
62 0 V
-62 338 R
62 0 V
-5 -315 R
0 174 V
700 1158 M
62 0 V
-62 174 R
62 0 V
-4 -202 R
0 331 V
727 1130 M
62 0 V
-62 331 R
62 0 V
-5 -444 R
0 406 V
753 1017 M
62 0 V
-62 406 R
62 0 V
-4 -248 R
0 144 V
780 1175 M
62 0 V
-62 144 R
62 0 V
-5 -237 R
0 406 V
806 1082 M
62 0 V
-62 406 R
62 0 V
-4 -474 R
0 347 V
833 1014 M
62 0 V
-62 347 R
62 0 V
21 -341 R
0 183 V
885 1020 M
62 0 V
-62 183 R
62 0 V
1075 986 M
0 183 V
1044 986 M
62 0 V
-62 183 R
62 0 V
75 -190 R
0 179 V
1150 979 M
62 0 V
-62 179 R
62 0 V
1324 857 M
0 337 V
1293 857 M
62 0 V
-62 337 R
62 0 V
1340 970 M
0 179 V
1309 970 M
62 0 V
-62 179 R
62 0 V
74 -204 R
0 179 V
1414 945 M
62 0 V
-62 179 R
62 0 V
128 -104 R
0 41 V
-31 -41 R
62 0 V
-62 41 R
62 0 V
181 -63 R
0 55 V
-31 -55 R
62 0 V
-62 55 R
62 0 V
2027 930 M
0 72 V
-31 -72 R
62 0 V
-62 72 R
62 0 V
128 -47 R
0 79 V
-31 -79 R
62 0 V
-62 79 R
62 0 V
128 -71 R
0 100 V
2314 963 M
62 0 V
-62 100 R
62 0 V
stroke
grestore
end
}
\put(2154,1946){\makebox(0,0)[r]{12.93s$^{-0.5397}$}}
\put(1558,-50){\makebox(0,0){s \small{(GeV$^2$)}}}
\put(1548,-220){\makebox(0,0){\footnotesize (a)}}
\put(350,1180){%
\special{ps: gsave currentpoint currentpoint translate
270 rotate neg exch neg exch translate}%
\makebox(0,0)[b]{\shortstack{$\Delta_{\pi^-p}$ \small{(mb)}}}%
\special{ps: currentpoint grestore moveto}%
}
\put(2517,151){\makebox(0,0){700}}
\put(2235,151){\makebox(0,0){600}}
\put(1953,151){\makebox(0,0){500}}
\put(1671,151){\makebox(0,0){400}}
\put(1389,151){\makebox(0,0){300}}
\put(1107,151){\makebox(0,0){200}}
\put(826,151){\makebox(0,0){100}}
\put(540,2109){\makebox(0,0)[r]{4}}
\put(540,1799){\makebox(0,0)[r]{3}}
\put(540,1490){\makebox(0,0)[r]{2}}
\put(540,1180){\makebox(0,0)[r]{1}}
\put(540,870){\makebox(0,0)[r]{0}}
\put(540,561){\makebox(0,0)[r]{-1}}
\put(540,251){\makebox(0,0)[r]{-2}}
\end{picture}
}
\documentclass[12pt]{article}
\usepackage{subfigure}
\usepackage{epsfig} 
\begin{document}
\thispagestyle{empty}
\rightline{EFI 97-13}



\begin{center} \large {\bf High Energy Hadronic Total Cross-Sections}



\medskip\normalsize 
James A. Feigenbaum, Peter G.O. Freund and Mircea Pigli\\

             {\em Enrico Fermi Institute and Department of Physics\\
             The University of Chicago, Chicago, IL 60637, USA}

 \end{center}
 \bigskip
 \bigskip
\bigskip \bigskip \bigskip

\noindent{\bf Abstract}: High energy hadronic total cross-section data 
are found to agree with the predictions of a QCD-string picture.
\setcounter{page}{0}

\newpage

\bigskip

{\bf 1. Introduction}
\bigskip

High energy hadron-hadron scattering amplitudes at fixed momentum transfer
have two components: a diffractive component (Pomeron exchange) and a mesonic 
Regge exchange component. Since the latter decreases with energy, Froissart's
unitarity bound becomes a constraint on the diffractive 
component:
at high energies hadronic total cross-sections cannot exceed 
$\frac{\pi}{m_{\pi}^2} \ln^{2}s$. Although fits to total cross-section data
incorporating $\ln s$ and $\ln^2 s$ terms 
have been made, it has been noted 
that the unitarity bound does not rule out a term of the form 
$X (\frac{s}{m^2})^\epsilon$
with small but positive $\epsilon$. Indeed, for say $\epsilon = 0.08,~
m\approx 1$ GeV and 
$X \leq 25$ mb, the unitarity bound violation would not set in \cite{PDB} until energies 
of $10^{24}$ GeV are reached. At such super-Planckian energies the theoretical 
underpinnings of QCD become meaningless and experiments become impossible.
With this in mind, Donnachie and Landshoff \cite{DL} have  successfully fit
high energy hadronic total cross-sections to expressions of the type
$$
\sigma_{ AB}= X_{AB} s^{\epsilon} + Y_{AB} s^{-\eta}~~~~~~~~~~~~~~~~~~~\\
\epsilon=0.08, ~~~~\eta=0.45.
\eqno(1)
$$

For the 10 measured total cross-sections ($pp,~ \bar{p}p,~ pn,~
\bar{p}n, ~ \pi^{\pm} p, 
 ~ K^{\pm} p, ~ K^{\pm} n$) 15 (or 17) parameters (depending on whether
one requires $X_{np}=X_{pp}$ and $X_{K^+p}=X_{K^+n}$ or not)
are needed: five (or seven) 
$X$'s and ten $Y$'s. Taken at face value, these fits and 
subsequent refinements thereof \cite{DG} 
are at odds with a number of ideas grounded
in the quark model and a QCD-string approach to hadron scattering; we have
in mind ideas like
two-component duality, exchange degeneracy, Chan-Paton rules, 
flavor $U(3)$ symmetry, 
universality of vector-meson couplings.
We wish to show that one can 
successfully implement these ideas as constraints from the beginning 
and obtain fits different from, but 
of comparable quality to those of 
refs. \cite{DL, DG}.

\bigskip

{\bf 2. Some Theoretical Ideas on High Energy Hadron Scattering}

\bigskip

We start by explaining how each of the just mentioned ideas constrain
high energy hadronic total cross-sections.

{\em A) Universal and flavor U(3) symmetric vector meson coupling pattern}.

Although in QCD the nine light vector mesons appear as $q\bar{q}$
bound states whose coupling pattern is to be dynamically calculated,
it has been known for a long time that the observed 
pattern closely follows the pattern which
would be expected if these mesons were flavor gauge bosons.
Specifically this means that (suppressing Lorentz and Dirac indices) 
in the familiar $3\times 3$ matrix representation, the
coupling of these vector mesons $V$ to baryons $B$ is of the form
Tr$(\bar{B}[V,B]) +$Tr$(\bar{B} B)$Tr$V$ (here the ratio of the two terms' 
coefficients is determined by requiring the decoupling of the $\phi$ from the 
proton). Moreover 
$g_{\rho^{0} \bar{p} p}= \frac{1}{2} g_{\rho^{0} \pi^{-} \pi^{+}}$, since 
the third component of the proton's isospin is half that of the positive 
pion's. Strictly speaking, only at $t= m_{\rho}^2 \approx m_{\omega}^2$
does this coupling pattern 
determine 
the residue pattern of the 
odd-signature Regge poles on whose trajectory the vector mesons lie.
We will assume that the same pattern
is valid also at $t=0$. All this then yields four linear relations 
between the five odd-charge-conjugation total cross-section combinations.
With the notation $\Delta_{AB}=\sigma_{AB} - \sigma_{\bar{A} B}$,
where $\sigma_{AB}$ denotes the $AB$ total cross-section,
these four relations take the familiar form \cite{JT}, \cite{F}
$$
\Delta_{\bar{p} p}=5 \Delta_{\pi^{-} p} ~~~~~~~~
\Delta_{\bar{p} n}=4 \Delta_{\pi^{-} p}~~~~~~~~
\Delta_{K^{-} p}=2 \Delta_{\pi^{-} p}~~~~~~~
\Delta_{K^{-} n}=\Delta_{\pi^{-} p}.
\eqno(2)
$$
Of these five differences, $\Delta_{\pi^{-} p}$ involves only $\rho$ exchange,
whereas the remaining four involve both $\rho$ and $\omega$ exchange, 
predominantly the latter. The derivation of the relations (2) assumes the 
$\rho$ and $\omega$ trajectories' intercepts to be equal:
$\alpha_{\rho}(0)=\alpha_{\omega}(0)=1-\eta$. We first fit, in fig. 1a,
$\Delta_{\pi^{-} p}$ to an 
\vspace{-1cm}
\begin{figure}[h]
\begin{center}
\input{pipdif.tex}
\end{center}
\end{figure}
\begin{figure}[p,b,t]
\input{inc.tex}
\caption{Single Regge pole fits constrained by Eqs. (2) \ to the odd signature cross section differences.}
\end{figure}

\clearpage
\noindent expression of the form
$$
\Delta_{\pi^{-} p}=\delta_{\pi p} s^{-\eta}
\eqno(3a)
$$
and obtain
$$
\eta=0.54 ~~~~~~~~~ \delta_{\pi p} =12.93
\eqno(3b)
$$

Excellent fits to the remaining four cross-section differences are then 
obtained by multiplying the function (3) by the integers given in Eqs. (2).
We have checked that, not surprisingly, the parameters obtained in the 
fits of Refs. \cite{DL}, \cite{DG} also obey the constraints imposed
upon them by Eqs. (2).

We should point out that 
here and throughout 
this paper we normalize coefficients so that $s$ is measured in GeV$^2$ and 
we use the data of ref. \cite{DG}.

{\em B) Exchange Degeneracy/ Chan-Paton Rules.}

In the limit of large number of colors, QCD reduces to a string theory in 
which mesons are open strings with a quark at one end and an antiquark
at the other (fig. 2a). The strings themselves are tubes of color-electric 
flux.
Baryons are also viewed as systems of three strings with a quark at each
of the three open ends, the three other ends meeting at a node (fig. 2b).
\begin{figure}[b,t]
\input{strings.tex}
\caption{Mesonic and baryonic strings (\mbox{$\times=\bar{q}, \circ=q$})}
\end{figure}
When this string picture applies, hopefully for 3 colors already, then 
hadronic amplitudes obey duality (we use this word in the sense that the
sum of the resonance contributions in the $s$-channel gives 
rise to the imaginary part of the Regge contribution in the crossed
$t$-channel). This, in turn, requires the degeneracy of the odd and even
$t$-channel mesonic
Regge pole trajectories and the equality of their residues, for otherwise
the amplitude for say $pp$ scattering would have a Regge pole 
contribution with nonvanishing imaginary part even though there are no
$pp$ resonances. The near degeneracy of the 
observed $\omega$ and $\rho$ meson masses on the one hand and of 
the $f$ and $a2$ meson masses on the other is as required by exchange
degeneracy. The equality of the isospin $I=1$ 
residues yields further constraints, to wit
$$
\sigma_{pn} -\sigma_{pp} = 0 ~~~~~~~~~~~~~~~~~~~~
\sigma_{K^{+} n} -\sigma_{K^{+} p} = 0
\eqno(4)
$$
As can be seen from fig. 3, the kaon difference is compatible with zero, 
but the $pn-pp$ difference, though very small, appears not to strictly vanish.
It can be fit to a combination of a Pomeron-Regge cut and of a small
Regge pole term, though the individual contribution of these terms is
hard to determine from the data. Even a pure cut gives a good fit.
We can therefore safely assume that at string tree level both equations (4) are
obeyed.
By combining 
with the just discussed $I=1$ exchange degeneracy relations
their isospin $I=0$ counterparts,
one imposes the full Chan-Paton rules and this then requires the absence 
of a mesonic Regge exchange contribution in $pp, pn, K^{+}p$ and $K^{+} n$
total cross-sections. This requirement is strongly violated in the fits
of references \cite{DL, DG}. The reason for this is simple to understand.
Before its ultimate rise at very high energies,\input{inc2.tex} 
any of these cross-sections, $\sigma_{pp}$ in 
particular, decreases with energy. In a fit of type (1) this is only 
possible if a Regge term is present and the particular Regge term needed
to fit the decrease in the low energy $\sigma_{pp}$ turns out to be very large:
$\approx 7\Delta_{\pi^{-} p}$. The fits of type (1) make two simplifying,
but otherwise arbitrary
assumptions, one concerning the nature of the Pomeron 
as a unique ``effective" Regge pole, and the other
concerning the absence of Regge-Regge cuts.
We shall see below that by relaxing these assumptions, 
fits of comparable quality
which do not violate this $I=0$ exchange degeneracy requirement are readily 
obtained. 

\bigskip
{\bf 3. Experimental Test of Principles A) and B)}
\bigskip


Before we get to these new fits, we must first analyse in some detail the full 
implications of the assumptions A) and B) above. There are 10 
measured total cross-sections and Eqs. (2) and (4) provide 6 linear relations 
among them, thus leaving 4 independent combinations, which we choose as
$\Delta_{\pi^{-} p}$, $\sigma_{pp}$, $\sigma_{\pi^{+} p}$ and 
$\sigma_{ K^{+} p}$. Of these, the odd charge-conjugation combination
$\Delta_{\pi^{-} p}$ is dominated, 
as was already mentioned, by the exchange of the $\rho$ Regge pole
and this is well borne out by the data, as was known for decades. So we
really have to fit only the remaining three cross-sections. To do so, let us
consider each of them separately. Let us start with 
$\sigma_{pp}$. We write for it the generic formula
$$
 \sigma_{pp}= P_p(s) + Y_p s^{-\eta} +Z_p s^{-\lambda},
\eqno(5)
$$
where $P_p(s)$ is the Pomeron contribution, $Y_p s^{-\eta}$ is the 
$f$-$\omega$-$a2$-$\rho$ Regge
contribution and $Z_p s^{-\lambda}$ is a contribution due to Regge-Regge
cuts and to the $f'$ Regge pole. Now let us consider each of these terms.
First of all, the Regge contribution $Y_p s^{-\eta}$ would be absent at
the string tree level.
At this level the other two terms would be absent as well. Indeed in
a string approach, the Pomeron is ``$f$-dominated" \cite{CGZ, CF} 
at both ends. In other words,
one of the protons emits an open $f$-string, which closes up into a Pomeron
and then reopens into another $f$-string which gets 
absorbed by the other proton (see fig. 4).
This process gets iterated and at the next and later 
steps involves the $f'$ as well, as shown in fig. 4. The consecutive steps 
are suppressed by OZI rule breaking so that the ensuing breaking of
exchange degeneracy is small. There is strong evidence in favor of this 
``$f$-dominated" Pomeron in the photoproduction of the $\rho, \omega,
\phi, J/\psi$ vector mesons \cite{CF}. For us
the important point is that {\em exchange 
degeneracy is exact  only at the string tree level}. 
Its small breaking is caused 
primarily by 
Pomeron-$f$-$f'$ mixing. As such, the first two terms in 
Eq. (5) are expected to be there, 
with the understanding 
\newpage
\begin{figure}[hp]
\vspace*{-1cm}
\input{versf.tex}
\caption{The $f$-dominated Pomeron}
\end{figure}
\noindent that the coefficient of the Regge term is small when compared to 
that in the fit to $\Delta_{\pi^- p}$. The last term in Eq. (5) represents 
the contribution of Regge-Regge cuts and of the $f'$ Regge pole term induced 
by the string loop effect of  Pomeron-$f$-$f'$ mixing (see fig.4). 
Both the Regge-Regge cuts and the $f'$ pole have an intercept $\sim 0$,
so  $\lambda\approx 1$ in Eq. (5).

We now turn to the Pomeron term $P_p(s)$. This term is a stand-in for the 
Pomeron Regge pole and for the multi-Pomeron cuts, as was already
pointed out in ref. \cite{DL}. There all this complexity was lumped
into a unique power law $s^\epsilon$, for reasons of simplicity,
rather than on the basis of any theoretical considerations. 
Here we will relax this ``simplicity" constraint and set

$$
P_p(s) = X_p s^\epsilon + C_p s^\mu  ~~~~~~~~~~~~ 0\leq \mu<\epsilon
\eqno(6)
$$
The best fits we obtain for $\mu=0$, so that the last term in Eq. (6)
will be a constant.

We will thus simultaneously fit $\sigma_{pp}$, $\sigma_{\pi^+p}$ and 
$\sigma_{K^+p}$ to the forms:
\setcounter{equation}{6}
\begin{eqnarray}
\sigma_{pp}    & = & X_p s^\epsilon + C_p  + Y_p s^{-\eta} +Z_p s^{-\lambda}
\nonumber\\
\sigma_{\pi^+p} & = &X_{\pi} s^\epsilon + C_{\pi}+ (Y_{\pi}+\delta_{\pi p}) s^{-\eta} +Z_{\pi} s^{-\lambda}\\
\sigma_{K^+p}   & = & X_K s^\epsilon + C_K 
 + Y_K s^{-\eta} +Z_K s^{-\lambda} \nonumber
\end{eqnarray}


The two old parameters $\eta$ and $\delta_{\pi p}$,
which appear here, have been
determined above from fitting the odd charge conjugation combinations of
total cross-sections: $\eta=0.54$, $\delta_{\pi p}=12.93$. That it is
precisely $\delta_{\pi p}$ which appears in Eq. (7) is a straightforward 
consequence of assumptions A) and B) above.
The 14 new parameters which appear in Eq. (7) are fortunately 
not all independent or unconstrained.
First, all the $Y$'s originate in exchange degeneracy
breaking and must therefore be small compared to $\delta_{\pi p}$. The value 
of $\lambda$ must, as we saw, be near $1$. The quark model determines
the ratios
$$
\frac{3X_{\pi}}{2X_p} \approx \frac{3C_{\pi}}{2C_p} \approx 1
\eqno(8a)
$$
and the ``$f$-dominated Pomeron" requires 
$$
\frac{X_K}{X_{\pi}} \approx \frac{C_K}{C_{\pi}} \approx 
\frac{1}{2}\Bigl(1+\frac{m_{\rho}^2}{m_{\phi}^2} \Bigr)=0.886.
\eqno(8b)
$$
Eq. (7) then really introduces only 7 parameters and the small departures
from unity of the other just mentioned combinations of parameters. 
With all this in mind we now present our fits of type Eq. (7) in fig. 5.
The corresponding values of the parameters are
\setcounter{equation}{8}
\begin{eqnarray}
\epsilon=0.135 ~~~~~ \eta&=&0.54 ~~~~~ \lambda=1.01\nonumber \\
X_{p}=6.26 ~~~~~C_{p}=24.4 ~~&~&~~Y_p=0.88 ~~~~ Z_p=196 \nonumber \\
 \frac{3X_{\pi}}{2X_p} = 1.04 ~~~~ \frac{3C_{\pi}}{2C_p}=0.84 ~~&~&~~ Y_{\pi}=-1.9~~~~~ Z_{\pi}=51 \\
\frac{X_K}{X_{\pi}} = 0.9 ~~~~ \frac{C_K}{C_{\pi}} = 0.83 ~~&~&~~ Y_K=-0.88~~~~ Z_K=0.12.\nonumber
\end{eqnarray}
\begin{figure}[p]
\vspace*{-1cm}
\subfigure{\begin{picture}(450,500)(50,50)
\put(0,0){
\epsfig{file=pp2.eps, width = 8in, height=6in, angle=90}
}
\put(200,15){\makebox(0,0){$\sigma_{pp}$ \small{(mb)}}}
\put(460,300){%
\special{ps: gsave currentpoint currentpoint translate
270 rotate neg exch neg exch translate}%
\makebox(0,0)[b]{\shortstack{s \small{(GeV$^2$)}}}%
\special{ps: currentpoint grestore moveto}%
}
\put(475,300){%
\special{ps: gsave currentpoint currentpoint translate
270 rotate neg exch neg exch translate}%
\makebox(0,0)[b]{\shortstack{\footnotesize (a)}}%
\special{ps: currentpoint grestore moveto}%
}
\end{picture}}

\end{figure}
\input{inc3.tex}
This fit is of comparable quality to the fits of refs. \cite{DL}, \cite{DG}.
It has the following characteristic features: 

--- The exchange degeneracy breaking parameters $Y_p$, $Y_{\pi}$ and 
$Y_K$ are indeed very small as compared to $\Delta_{\pi p}$.

---The Pomeron exponent $\epsilon$ is larger than in most previous fits,
but such a larger value was already contemplated in ref. \cite{A} in the 
context of very high energies. In any case, even with this larger exponent 
the Froissart bound is comfortably obeyed even beyond the Planck energy.

--- The constraints (8) are well obeyed by the leading Pomeron terms ($X$
coefficients) and obeyed at the 15\% level for the subdominant terms 
($C$ coefficients).

--- At first sight the $f'$-Regge-Regge-cut parameter $Z_p$ appears 
large. $Z_p$ plays for our fit a role similar to that of the large exchange
degeneracy breaking $Y_p$ parameter in refs. \cite{DL}, \cite{DG}. This 
$f'$-Regge-Regge-cut term falls much faster with energy than an 
ordinary Regge term, so it makes sense to compare its low energy contribution
in the $pp$ amplitude, ${\cal CUT} \sim 196s^{-\lambda+1}\approx 196$,
to the {\em nonvanishing real part} of the $pp$ Regge term which is 
Re$(R) \sim 5\Delta_{\pi p} s^{-\eta+ 1} \approx 65 s^{0.46}$. Even at the low
value $s=40$ GeV$^2$, we find ${\cal CUT} /$Re$(R) \approx 0.55$ 
and this ratio 
decreases as $s^{-0.46}$. The Regge cut and $f'$ contributions
are thus consistently smaller than the Regge pole contributions.
Similar arguments can be made for the $\pi p$ and $Kp$ amplitudes as well.
The important new feature here is that this $f'$-Regge-Regge-cut term 
represents a theoretically expected exchange degeneracy and duality violation.

\bigskip
{\bf 4. Conclusions}
\bigskip

 From all this we conclude that all hadronic total cross-section data are 
compatible with the stringy principles A) and B) above. 
The reason for the apparent discrepancy between the fits of references
\cite{DL, DG} and these principles is that for simplicity,
they i) ignored Regge-Regge cuts and 
ii) fit the Pomeron to a single power law.
The remarkable power of the principles A) and B) is that, even after
abandoning these simplifications, the necessary number of parameters 
did not increase. Actually, after all constraints were met, 
we found this number to have {\em decreased}.

In a forthcoming paper we shall further explore these principles in the light
of recent developments in open string theory. 

\newpage
{\bf Acknowledgment}
\bigskip

This paper was supported in part by NSF grant -A3.





\newpage
\begin{thebibliography}{99}

\bibitem{PDB} P.D.B. Collins and F.D. Gault, Phys. Lett. {\bf B73}, 330 (1978).

\bibitem{DL} A. Donnachie and P.V. Landshoff, Phys. Lett. {\bf B296}, 227 (1992). 

\bibitem{DG} Particle Data Group, Phys Rev. {\bf D54}, 1 (1996); 
http://pdg.lbl.gov/.

\bibitem{JT} K. Johnson and S.B. Treiman, Phys. Rev. Lett. {\bf 14}, 189 (1965).

\bibitem{F} P.G.O. Freund, Phys. Rev. Lett. {\bf 15}, 929 (1965).

\bibitem{CGZ} R. Carlitz, M.B. Green and A. Zee, Phys. Rev. Lett. {\bf 26}, 1515 (1971).

\bibitem{CF} C.E. Carlson and P.G.O. Freund, Phys. Rev. {\bf D11}, 2453 (1975).

\bibitem{A} F. Abe et al., Phys. Rev. {\bf D50}, 5550 (1994).

\end{thebibliography}








\end{document}








\setlength{\unitlength}{0.012500in}%
%
\begingroup\makeatletter
% extract first six characters in \fmtname
\def\x#1#2#3#4#5#6#7\relax{\def\x{#1#2#3#4#5#6}}%
\expandafter\x\fmtname xxxxxx\relax \def\y{splain}%
\ifx\x\y   % LaTeX or SliTeX?
\gdef\SetFigFont#1#2#3{%
  \ifnum #1<17\tiny\else \ifnum #1<20\small\else
  \ifnum #1<24\normalsize\else \ifnum #1<29\large\else
  \ifnum #1<34\Large\else \ifnum #1<41\LARGE\else
     \huge\fi\fi\fi\fi\fi\fi
  \csname #3\endcsname}%
\else
\gdef\SetFigFont#1#2#3{\begingroup
  \count@#1\relax \ifnum 25<\count@\count@25\fi
  \def\x{\endgroup\@setsize\SetFigFont{#2pt}}%
  \expandafter\x
    \csname \romannumeral\the\count@ pt\expandafter\endcsname
    \csname @\romannumeral\the\count@ pt\endcsname
  \csname #3\endcsname}%
\fi
\endgroup
\begin{picture}(348,109)(150,685)
\thicklines
\put(499,789){\circle{10}}
\put(499,784){\line( 0,-1){ 43}}
\put(455,716){\circle{10}}
\put(460,719){\line( 5, 3){ 38.382}}
\put(543,716){\circle{10}}
\put(539,719){\line(-5, 3){ 39.118}}
\put(273,742){\circle{14}}
\put(212,748){\line(-1,-1){ 12}}
\put(200,748){\line( 1,-1){ 12}}
\put(206,742){\line( 1, 0){ 60}}
\put(235,685){\makebox(0,0)[lb]{\smash{\SetFigFont{12}{14.4}{rm}(a)}}}
\put(495,685){\makebox(0,0)[lb]{\smash{\SetFigFont{12}{14.4}{rm}(b)}}}
\end{picture}
\setlength{\unitlength}{0.012500in}%
\begingroup\makeatletter
% extract first six characters in \fmtname
\def\x#1#2#3#4#5#6#7\relax{\def\x{#1#2#3#4#5#6}}%
\expandafter\x\fmtname xxxxxx\relax \def\y{splain}%
\ifx\x\y   % LaTeX or SliTeX?
\gdef\SetFigFont#1#2#3{%
  \ifnum #1<17\tiny\else \ifnum #1<20\small\else
  \ifnum #1<24\normalsize\else \ifnum #1<29\large\else
  \ifnum #1<34\Large\else \ifnum #1<41\LARGE\else
     \huge\fi\fi\fi\fi\fi\fi
  \csname #3\endcsname}%
\else
\gdef\SetFigFont#1#2#3{\begingroup
  \count@#1\relax \ifnum 25<\count@\count@25\fi
  \def\x{\endgroup\@setsize\SetFigFont{#2pt}}%
  \expandafter\x
    \csname \romannumeral\the\count@ pt\expandafter\endcsname
    \csname @\romannumeral\the\count@ pt\endcsname
  \csname #3\endcsname}%
\fi
\endgroup
\begin{picture}(384,460)(80,340)
\thicklines
\put(185,658){\line( 0,-1){ 76}}
\put(185,620){\line( 1, 0){ 34}}
\put(354,658){\line( 0,-1){ 76}}
\put(219,620){\linethickness{9pt}\line( 1, 0){ 34}}
\put(287,620){\linethickness{9pt}\line( 1, 0){ 34}}
\put(359,578){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}p}}}
\put(177,578){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}p}}}
\put(202,603){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}f}}}
\put(236,603){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}P}}}
\put(304,603){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}P}}}
\put(261,603){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}f,f$'$}}}
\put(337,603){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}f}}}
\put(371,616){\makebox(0,0)[lb]{\smash{\SetFigFont{14}{16.8}{rm}+}}}
\put(388,620){\makebox(0,0)[lb]{\smash{\SetFigFont{14}{16.8}{rm}.  .  .  .}}}
\put(177,658){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}p}}}
\put(359,658){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}p}}}
\put(253,620){\line( 1, 0){ 34}}
\put(321,620){\makebox(0.4444,0.6667){\SetFigFont{10}{12}{rm}.}}
\put(321,620){\line( 1, 0){ 33}}
\put(354,620){\line( 0, 1){  0}}
\put(354,620){\line( 0, 1){  0}}
\put(329,754){\linethickness{9pt}\line( 1, 0){ 59}}
\put(278,792){\line( 0,-1){ 76}}
\put(278,716){\line( 0, 1){  5}}
\put(278,754){\line( 1, 0){ 64}}
\put(434,792){\line( 0,-1){ 76}}
\put(439,792){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}p}}}
\put(299,738){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}f}}}
\put(354,738){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}P}}}
\put(413,738){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}f}}}
\put(270,712){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}p}}}
\put(456,750){\makebox(0,0)[lb]{\smash{\SetFigFont{14}{16.8}{rm}+}}}
\put(270,792){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}p}}}
\put(321,754){\line( 1, 0){113}}
\put(439,712){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}p}}}
\put( 88,792){\line( 0, 1){  0}}
\put( 88,792){\line( 0,-1){ 76}}
\put(190,792){\line( 0,-1){ 76}}
\put( 88,754){\line( 1, 0){102}}
\put( 80,792){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}p}}}
\put(194,792){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}p}}}
\put( 80,712){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}p}}}
\put(194,712){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}p}}}
\put(232,750){\makebox(0,0)[lb]{\smash{\SetFigFont{14}{16.8}{rm}+}}}
\put(139,616){\makebox(0,0)[lb]{\smash{\SetFigFont{14}{16.8}{rm}+}}}
\put(139,738){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}f}}}
\put(180,448){\line( 0, 1){  0}}
\multiput(180,448)(0.36364,0.45455){12}{\makebox(0.4444,0.6667){\SetFigFont{7}{8.4}{rm}.}}
\multiput(180,453)(0.36364,-0.45455){12}{\makebox(0.4444,0.6667){\SetFigFont{7}{8.4}{rm}.}}
\put(182,416){\circle{6}}
\put(182,451){\line( 0,-1){ 32}}
\put(148,373){\circle{6}}
\put(122,396){\line( 1, 0){  6}}
\put(126,398){\line( 0,-1){  6}}
\put(126,396){\line( 1,-1){ 21}}
\put(157,381){\circle{6}}
\put(131,404){\line( 1, 0){  6}}
\put(134,407){\line( 0,-1){  6}}
\put(134,404){\line( 1,-1){ 20.500}}
\put(165,389){\circle{6}}
\put(139,413){\line( 1, 0){  6}}
\put(142,415){\line( 0,-1){  6}}
\put(142,413){\line( 1,-1){ 22}}
\put(140,364){\circle{6}}
\put(114,387){\line( 1, 0){  6}}
\put(117,390){\line( 0,-1){  5}}
\put(117,387){\line( 1,-1){ 20.500}}
\put(164,474){\circle{6}}
\put(139,451){\line( 1, 0){  6}}
\put(142,455){\line( 0,-1){  6}}
\put(142,451){\line( 1, 1){ 20.500}}
\put(156,482){\circle{6}}
\put(131,460){\line( 1, 0){  6}}
\put(133,463){\line( 0,-1){  6}}
\put(133,460){\line( 1, 1){ 19.500}}
\put(148,490){\circle{6}}
\put(122,468){\line( 1, 0){  6}}
\put(125,472){\line( 0,-1){  6}}
\put(125,468){\line( 1, 1){ 20}}
\put(139,499){\circle{6}}
\put(114,477){\line( 1, 0){  6}}
\put(116,479){\line( 0,-1){  5}}
\put(116,477){\line( 6, 5){ 21.738}}
\put(413,386){\circle{6}}
\put(388,364){\line( 1, 0){  6}}
\put(391,367){\line( 0,-1){  6}}
\put(391,364){\line( 1, 1){ 20}}
\put(405,394){\circle{6}}
\put(380,372){\line( 1, 0){  6}}
\put(382,375){\line( 0,-1){  5}}
\put(382,372){\line( 1, 1){ 19.500}}
\put(396,402){\circle{6}}
\put(371,381){\line( 1, 0){  6}}
\put(374,384){\line( 0,-1){  6}}
\put(374,381){\line( 1, 1){ 19.500}}
\put(388,411){\circle{6}}
\put(363,388){\line( 1, 0){  6}}
\put(365,391){\line( 0,-1){  5}}
\put(365,388){\line( 1, 1){ 20.500}}
\put(397,461){\circle{6}}
\put(371,483){\line( 1, 0){  6}}
\put(375,486){\line( 0,-1){  6}}
\put(375,483){\line( 1,-1){ 20.500}}
\put(406,469){\circle{6}}
\put(380,492){\line( 1, 0){  6}}
\put(383,494){\line( 0,-1){  5}}
\put(383,492){\line( 1,-1){ 20.500}}
\put(414,478){\circle{6}}
\put(388,500){\line( 1, 0){  6}}
\put(391,503){\line( 0,-1){  6}}
\put(391,500){\line( 1,-1){ 21.500}}
\put(389,452){\circle{6}}
\put(363,476){\line( 1, 0){  6}}
\put(366,478){\line( 0,-1){  5}}
\put(366,476){\line( 1,-1){ 21}}
\put(349,448){\line( 0, 1){  0}}
\multiput(349,448)(0.36364,0.45455){12}{\makebox(0.4444,0.6667){\SetFigFont{7}{8.4}{rm}.}}
\multiput(349,453)(0.36364,-0.45455){12}{\makebox(0.4444,0.6667){\SetFigFont{7}{8.4}{rm}.}}
\put(351,416){\circle{6}}
\put(351,451){\line( 0,-1){ 32}}
\multiput(198,449)(0.40000,0.40000){11}{\makebox(0.4444,0.6667){\SetFigFont{7}{8.4}{rm}.}}
\multiput(198,453)(0.40000,-0.40000){11}{\makebox(0.4444,0.6667){\SetFigFont{7}{8.4}{rm}.}}
\put(200,435){\oval(  8, 32)[tl]}
\put(200,435){\oval(  8, 34)[bl]}
\put(200,415){\circle{6}}
\multiput(334,449)(-0.40000,0.40000){11}{\makebox(0.4444,0.6667){\SetFigFont{7}{8.4}{rm}.}}
\multiput(334,453)(-0.40000,-0.40000){11}{\makebox(0.4444,0.6667){\SetFigFont{7}{8.4}{rm}.}}
\put(332,435){\oval(  8, 34)[br]}
\put(332,435){\oval(  8, 32)[tr]}
\put(332,415){\circle{6}}
\put(228,433){\oval( 36, 36)[tl]}
\put(228,433){\oval( 36, 38)[bl]}
\multiput(225,448)(0.42857,0.35714){15}{\makebox(0.4444,0.6667){\SetFigFont{7}{8.4}{rm}.}}
\multiput(225,453)(0.42857,-0.35714){15}{\makebox(0.4444,0.6667){\SetFigFont{7}{8.4}{rm}.}}
\put(232,414){\circle{6}}
\put(303,433){\oval( 34, 36)[br]}
\put(303,433){\oval( 34, 36)[tr]}
\multiput(305,448)(-0.42857,0.35714){15}{\makebox(0.4444,0.6667){\SetFigFont{7}{8.4}{rm}.}}
\multiput(305,453)(-0.42857,-0.35714){15}{\makebox(0.4444,0.6667){\SetFigFont{7}{8.4}{rm}.}}
\put(299,415){\circle{6}}
\put(266,432){\circle{42}}
\put(198,386){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}f}}}
\put(333,386){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}f}}}
\put(266,386){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}P}}}
\put(114,486){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}$\pi^+$}}}
\put(114,365){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}$\pi^+$}}}
\put(418,486){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}$\pi^+$}}}
\put(418,365){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}$\pi^+$}}}
\put(257,558){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}(a)}}}
\put(257,340){\makebox(0,0)[lb]{\smash{\SetFigFont{10}{12.0}{rm}(b)}}}
\end{picture}

