%Paper: 
%From: "\"\"Harry N. Nelson\"\"" <hnn@lns598.lns.cornell.edu>
%Date: Fri, 18 Feb 94 23:43:55 -0500

% Instructions for stripping off figures:
%  1)Find text between lines filled with %-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%
%  2)copy that text to a file (perhaps call it marseille.tar.gz.uu)
%  3)uudecode it (for example, `uudecode marseille.tar.gz.uu')
%  4)gunzip the file produced, marseille.tar.gz (`gunzip marseille.tar.gz')
%  5)tar the file produced, marseille.tar (`tar -xvf marseille.tar')
%  6)you will then get the six .eps files to be pulled into the paper.
------------------------------------------------------------------------
\documentstyle[epsf]{article}
\catcode`\@=11
%  modified by Bob Taylor for University of Rochester 20-Mar-87:
%  \line macro in Cowan's code is disabled by LaTeX, so I've
%  changed all instances of \line in Cowan's code to the new
%  definition \tableline as defined right after this comment.
%
   \def\tableline{\hbox to \hsize}
%
% +--------------------------------------------------------------------+
% ]                                                                    ]
% ]                           TABLES.TEX                               ]
% ]                                                                    ]
% ]                     Ray F. Cowan  15-Feb-85                        ]
% ]                                                                    ]
% ]                       Princeton University                         ]
% ]                                                                    ]
% ]                     Last Revision: 21-Nov-85                       ]
% ]                                                                    ]
% ]   Macros I find handy for making tables.  See TABLEDOC TEX for     ]
% ]   a longer description.  The token-counting macros are straight    ]
% ]   from the TeXbook's "Dirty Tricks" appendix.                      ]
% ]                                                                    ]
% +--------------------------------------------------------------------+
%
\newbox\hdbox%
\newcount\hdrows%
\newcount\multispancount%
\newcount\ncase%
\newcount\ncols% This is the number of primary text columns in the table.
\newcount\nrows%
\newcount\nspan%
\newcount\ntemp%
\newdimen\hdsize%
\newdimen\newhdsize%
\newdimen\parasize%
\newdimen\spreadwidth%
\newdimen\thicksize%
\newdimen\thinsize%
\newdimen\tablewidth%
\newif\ifcentertables%
\newif\ifendsize%
\newif\iffirstrow%
\newif\iftableinfo%
\newtoks\dbt%
\newtoks\hdtks%
\newtoks\savetks%
\newtoks\tableLETtokens%
\newtoks\tabletokens%
\newtoks\widthspec%
%
%  Book-keeping stuff--see how often these macros are called.
%
%\immediate\write15{%
%CP SMSG GJMSINK TEXTABLE --> TABLE MACROS V. 851121 JOB = \jobname%
%}%
%
%  Turn on table diagnostics.
%
\tableinfotrue%
%\catcode`\@=11%  Allows use of "@" in macro names, like PLAIN.TEX does.
\def\out#1{\immediate\write16{#1}}%  Debugging aid.  Writes #1 on the
%                                    user's terminal and in the log file.
%
%  Define the \tstrut height, depth in terms of the x_height parameter.
%
\def\tstrut{\vrule height3.1ex depth1.2ex width0pt}%
\def\and{\char`\&}%  Allows us to get an `&' in the text.  This is the
%                    same as using the PLAIN TeX macro \&.
\def\tablerule{\noalign{\hrule height\thinsize depth0pt}}%
\thicksize=1.5pt%  Default thickness for fat rules.  The user should feel
%                  free to change this to his preference.
\thinsize=0.6pt%   Default thickness for thin rules.
\def\thickrule{\noalign{\hrule height\thicksize depth0pt}}%
\def\hrulefill{\leaders\hrule\hfill}%
\def\bigrulefill{\leaders\hrule height\thicksize depth0pt \hfill}%
\def\ctr#1{\hfil\ #1\hfil}%
\def\altctr#1{\hfil #1\hfil}%
\def\vctr#1{\hfil\vbox to0pt{\vss\hbox{#1}\vss}\hfil}%
%
%  Here are things for controlling the width of the finished table.
%
\tablewidth=-\maxdimen%
\spreadwidth=-\maxdimen%
\def\tabskipglue{0pt plus 1fil minus 1fil}%
%
%  Stuff for centering or not.
%
\centertablestrue%
\def\centeredtables{%
   \centertablestrue%
}%
\def\noncenteredtables{%
   \centertablesfalse%
}%
%
%  \vctr vertically centers its argument in the row.
%
\parasize=4in%
\long\def\para#1{%  Used to make little paragraphs out of one entry.
   {%
      \vtop{%
         \hsize=\parasize%
         \baselineskip14pt%
         \lineskip1pt%
         \lineskiplimit1pt%
         \noindent #1%
         \vrule width0pt depth6pt%
      }%
   }%
}%
%
\gdef\ARGS{########}%  Produces the correct number of #'s in the preamble
%                      by the time eveything is expanded and \halign sees
%                      it.
\gdef\headerARGS{####}%  Same as \ARGS, but used in \header macros.
\def\@mpersand{&}%  Allows us to get alignment tab characters later
%                   when we have made the character "&" an active macro.
{\catcode`\|=13%  Make |'s locally active.
\gdef\letbarzero{\let|0}%  Globally define a macro that allows us to
%                          keep active |'s from being expanded in edef's.
\gdef\letbartab{\def|{&&}}%
\gdef\letvbbar{\let\vb|}%
%  This \def will cause active |'s read by
%                            \ruledtable to be converted into double
%                            alignment tabs.
}%  End of locally active |'s.
%
{\catcode`\&=4%  Make these alignment tabs.
\def\ampskip{&\omit\hfil&}%  This local macro skips a vertical rule.
\catcode`\&=13%  Now make &'s into active macros.
\let&0%  This allows us to expand \ampskip in the next \xdef without
%        attempting to expand the & and getting an "undefined control
%        sequence" error.
\xdef\letampskip{\def&{\ampskip}}%
\gdef\letnovbamp{\let\novb&\let\tab&}
%  This will cause active &'s read by
%                                   \ruledtable to be converted into
%                                   double tabs and an \omit'ted \vrule.
}%  End of locally active &'s.
%
\def\begintable{%  Here we make |'s and &'s active characters so we can
%                  interpret them as macros.  Note that this action is
%                  true only until we encounter the matching \endgroup
%                  token later at the end of the \ruledtable macro.
   \begingroup%
   \catcode`\|=13\letbartab\letvbbar%
   \catcode`\&=13\letampskip\letnovbamp%
   \def\multispan##1{%  We must redefine \multispan to count the number
%                       of primary columns, not physical columns.
      \omit \mscount##1%
      \multiply\mscount\tw@\advance\mscount\m@ne%
      \loop\ifnum\mscount>\@ne \sp@n\repeat%
   }%  End of \multispan macro.
   \def\|{%
      &\omit\widevline&%
   }%
   \ruledtable%  Now we call \ruledtable to do the real work.
}%  End of \begintable macro.
%
\long\def\ruledtable#1\endtable{%
%
%  This macro reads in the user's data entries
%  and converts them into a ruled table.
%
%  Important note:  Many macros and parameters are re-defined here, and
%  these must be kept local to the table macros to avoid conflict with
%  their use outside of tables.  This is done by the \begingroup token
%  macro \begintable and the \endgroup token at the end of
%  this macro.
%
   \offinterlineskip%  Needed to make rules touch each other.
   \tabskip 0pt%  Needed for same reason as \offinterlineskip.
   \def\widevline{\vrule width\thicksize}%  Make outer \vrule's wider.
   \def\endrow{\@mpersand\omit\hfil\crnorm\@mpersand}%
   \def\crthick{\@mpersand\crnorm\thickrule\@mpersand}%
   \def\crnorule{\@mpersand\crnorm\@mpersand}%
   \let\nr=\crnorule%  A shorter abbreviation.
   \def\endtable{\@mpersand\crnorm\thickrule}%
%
   \let\crnorm=\cr%  Allows us to use \cr for our own purposes.
%
%  Cause user-typed \cr's to follow a row with a \tablerule.
%
   \edef\cr{\@mpersand\crnorm\tablerule\@mpersand}%
%
   \the\tableLETtokens%  Get the user's extra \let's, if any.
%
%  Put the data entries into a token register so we can scan through them
%  and see what the user is asking us to do.
%
   \tabletokens={&#1}%  We add an extra alignment tab to the beginning
%                       of the first row to allow for the first \vrule.
%
%  Now count how many rows are in the table and return the result in
%  count register \nrows; do the same for columns, and return that
%  in register \ncols.
%
   \countROWS\tabletokens\into\nrows%
   \countCOLS\tabletokens\into\ncols%
%
%  Now do a little arithmetic to convert the number of primary columns
%  into the number of physical columns that the alignment preamble must
%  prepare for;  similarly for rows.
%
   \advance\ncols by -1%
   \divide\ncols by 2%
   \advance\nrows by 1%
%
%  Tell the user how many rows and columns we found in his data, if he
%  wants to know.
%
   \iftableinfo %
      \immediate\write16{[Nrows=\the\nrows, Ncols=\the\ncols]}%
   \fi%
%
%  Now we actually go ahead and produce the table.
%
   \ifcentertables
      \ifhmode \par\fi%  Make sure we are in vertical mode.
      \tableline{%  The final table comes out as an \hbox of width the \hsize.
      \hss%  The final table will be centered left-to-right.
   \else %
      \hbox{%
   \fi
      \vbox{%
         \makePREAMBLE{\the\ncols}%  Generate the preamble.
         \edef\next{\preamble}%  This line and the next line force the
         \let\preamble=\next%    expansion of all \ARGS tokens into the
%                                appropriate number of #'s.
         \makeTABLE{\preamble}{\tabletokens}%  Go do the \halign here.
      }%  End of \vbox.
      \ifcentertables \hss}\else }\fi%  Finish the centering effect.
%                                       It is important that no spaces
%                                       follow the two `}' here.
%  }%  End of \tableline
   \endgroup%  Return all local macros and parameters to their outside
%              values.
   \tablewidth=-\maxdimen%  Reset \tablewidth to normal.
   \spreadwidth=-\maxdimen% Same for \spreadwidth.
}%  End of macro \ruledtable.
%
\def\makeTABLE#1#2{%  Does an \halign for the \ruledtable macro.
   {%  Start of local parameter values.
%
   \let\ifmath0%     These macros would cause trouble if they were to be
   \let\header0%     expanded in the following \xdef; we \let them be
   \let\multispan0%  equal to a digit, because digits can't be expanded.
%
%  Set up the width specification here.
%
   \ncase=0%
   \ifdim\tablewidth>-\maxdimen \ncase=1\fi%
   \ifdim\spreadwidth>-\maxdimen \ncase=2\fi%
   \relax%  This \relax is absolutely necessary, without it the following
%           \ifcase will always take \ncase=0.
%
   \ifcase\ncase %
      \widthspec={}%
   \or %
      \widthspec=\expandafter{\expandafter t\expandafter o%
                 \the\tablewidth}%
   \else %
      \widthspec=\expandafter{\expandafter s\expandafter p\expandafter r%
                 \expandafter e\expandafter a\expandafter d%
                 \the\spreadwidth}%
   \fi %
%\out{Widthspec=O\the\widthspecE}%
%\out{Preamble=O\preambleE}%
   \xdef\next{%  We must force the preamble to be expanded BEFORE the
      \halign\the\widthspec{%
%        \halign is done;  this \edef\next{...}\next construction
%                does the trick.
      #1%  This is the preamble text.
%
      \noalign{\hrule height\thicksize depth0pt}%  Makes the top \hrule.
%
      \the#2\endtable%  This is the main body.
%
%     \noalign{\hrule height0.7pt depth0pt}%  Makes the last \hrule.
      }%  End of \halign.
   }%  End of \next.
   }%  End of local values.
   \next%  This \next must be outside of the local values, because now
%          we want those troublesome macros in the \let's above to have
%          their normal actions.
}%  End of macro \makeTABLE.
%
\def\makePREAMBLE#1{%  This macro generates the necessary preamble for a
%                      ruled table with #1 primary columns.
%                      (Primary columns means the number of columns NOT
%                       counting those used for vertical rules.)
   \ncols=#1%  Get the number of columns desired.
   \begingroup%  Start local parameter definitions.
   \let\ARGS=0%  This is the key to the whole thing; it prevents \ARGS
%                from being expanded in the following \edef's.
   \edef\xtp{\widevline\ARGS\tabskip\tabskipglue%
   &\ctr{\ARGS}\tstrut}%  A 1-column preamble.  Gets the sizing right.
   \advance\ncols by -1%  One column has been generated; decrement the
%                         counter.
   \loop%  Append as many further columns as needed to the preamble.
      \ifnum\ncols>0 %
      \advance\ncols by -1%
      \edef\xtp{\xtp&\vrule width\thinsize\ARGS&\ctr{\ARGS}}%
   \repeat
   \xdef\preamble{\xtp&\widevline\ARGS\tabskip0pt%
   \crnorm}%  Adds the last \vrule.
   \endgroup%  End of local parameters.
}%  End of macro \makePREAMBLE.
%
\def\countROWS#1\into#2{%  This counts the number of rows in #1 by
%                          looking for control sequences that end a row,
%                          e.g., \cr, \crthick, etc., and puts the result
%                          into count register #2.
   \let\countREGISTER=#2%
   \countREGISTER=0%
%  \out{In countROWS:  tokens are O\the#1E}%
   \expandafter\ROWcount\the#1\endcount%
}%
%
\def\ROWcount{%
   \afterassignment\subROWcount\let\next= %
}%
\def\subROWcount{%
%  \out{In subROWcount:  next is O\meaning\nextE}%  Debugging aid.
   \ifx\next\endcount %
      \let\next=\relax%
   \else%
      \ncase=0%
      \ifx\next\cr %
         \global\advance\countREGISTER by 1%
         \ncase=0%
      \fi%
      \ifx\next\endrow %
         \global\advance\countREGISTER by 1%
         \ncase=0%
      \fi%
      \ifx\next\crthick %
         \global\advance\countREGISTER by 1%
         \ncase=0%
      \fi%
      \ifx\next\crnorule %
         \global\advance\countREGISTER by 1%
         \ncase=0%
      \fi%
      \ifx\next\header %
%     \out{In subROWcount:  next=header, ncase set=1}%
         \ncase=1%
      \fi%
%     \out{In subROWcount:  ncase is O\the\ncaseE}%
      \relax%
      \ifcase\ncase %
         \let\next\ROWcount%
%        \out{subROWcount---> ncase=\the\ncase}%
      \or %
         \let\next\argROWskip%
%        \out{subROWcount---> ncase=\the\ncase}%
      \else %
      \fi%
   \fi%
%  \out{subROWcount---> NEXT=\meaning\next}%
   \next%
}%  End of macro \subROWcount.
%
\def\counthdROWS#1\into#2{%
\dvr{10}%
   \let\countREGISTER=#2%
   \countREGISTER=0%
\dvr{11}%
%  \out{In counthdROWS:  tokens are O\the#1E}%
\dvr{13}%
   \expandafter\hdROWcount\the#1\endcount%
\dvr{12}%
}%
%
\def\hdROWcount{%
   \afterassignment\subhdROWcount\let\next= %
}%
\def\subhdROWcount{%
%\out{In subhdROWcount:  next is O\meaning\nextE}%
   \ifx\next\endcount %
      \let\next=\relax%
   \else%
      \ncase=0%
      \ifx\next\cr %
         \global\advance\countREGISTER by 1%
         \ncase=0%
      \fi%
      \ifx\next\endrow %
         \global\advance\countREGISTER by 1%
         \ncase=0%
      \fi%
      \ifx\next\crthick %
         \global\advance\countREGISTER by 1%
         \ncase=0%
      \fi%
      \ifx\next\crnorule %
         \global\advance\countREGISTER by 1%
         \ncase=0%
      \fi%
      \ifx\next\header %
%\out{In subhdROWcount:  next=header, ncase set=1}%
         \ncase=1%
      \fi%
%\out{In subhdROWcount:  ncase is O\the\ncaseE}%
\relax%
      \ifcase\ncase %
         \let\next\hdROWcount%
%\out{subhdROWcount---> ncase=\the\ncase}%
      \or%
         \let\next\arghdROWskip%
%\out{subhdROWcount---> ncase=\the\ncase}%
      \else %
      \fi%
   \fi%
%\out{subhdROWcount---> NEXT=\meaning\next}%
   \next%
}%
%
{\catcode`\|=13\letbartab
\gdef\countCOLS#1\into#2{%
%  \out{In countCOLS:  tokens are O\the#1E}
   \let\countREGISTER=#2%
   \global\countREGISTER=0%
   \global\multispancount=0%
   \global\firstrowtrue
   \expandafter\COLcount\the#1\endcount%
   \global\advance\countREGISTER by 3%
   \global\advance\countREGISTER by -\multispancount
%  \out{countCOLS-->O\the\countREGISTERE}
}%
%
\gdef\COLcount{%
   \afterassignment\subCOLcount\let\next= %
}%
{\catcode`\&=13%
\gdef\subCOLcount{%
%\out{In subCOLcount: next is O\meaning\nextE}
   \ifx\next\endcount %
      \let\next=\relax%
   \else%
      \ncase=0%
      \iffirstrow
         \ifx\next& %
            \global\advance\countREGISTER by 2%
            \ncase=0%
         \fi%
         \ifx\next\span %
            \global\advance\countREGISTER by 1%
            \ncase=0%
         \fi%
         \ifx\next| %
            \global\advance\countREGISTER by 2%
            \ncase=0%
         \fi
         \ifx\next\|
            \global\advance\countREGISTER by 2%
            \ncase=0%
         \fi
         \ifx\next\multispan
            \ncase=1%
            \global\advance\multispancount by 1%
         \fi
         \ifx\next\header
            \ncase=2%
         \fi
         \ifx\next\cr       \global\firstrowfalse \fi
         \ifx\next\endrow   \global\firstrowfalse \fi
         \ifx\next\crthick  \global\firstrowfalse \fi
         \ifx\next\crnorule \global\firstrowfalse \fi
      \fi%  End of \iffirstrow.
\relax%\out{subCOL-->  ncase=O\the\ncaseE}
% \out{subCOL-->  next=\meaning\next}
      \ifcase\ncase %
         \let\next\COLcount%
      \or %
         \let\next\spancount%
      \or %
         \let\next\argCOLskip%
      \else %
      \fi %
   \fi%
%  \out{subCOL-->  countREGISTER=O\the\countREGISTERE}
   \next%
}%
\gdef\argROWskip#1{%
%  Deletes the next balanced, undelimited argument from a
%                 token list.
% \out{---> Entering argROWskip <---}
% \out{In argROWskip:  deleted arg is O#1E}%
   \let\next\ROWcount \next%
}%  End of macro \argskip.
\gdef\arghdROWskip#1{%
%  Deletes the next balanced, undelimited argument from a
%                 token list.
% \out{---> Entering arghdROWskip <---}
% \out{In arghdROWskip:  deleted arg is O#1E}%
   \let\next\ROWcount \next%
}%  End of macro \arghdROWskip.
\gdef\argCOLskip#1{%
%  Deletes the next balanced, undelimited argument from a
%                 token list.
% \out{---> Entering argCOLskip <---}
% \out{In argCOLskip:  deleted arg is O#1E}%
   \let\next\COLcount \next%
}%  End of macro \argskip.
}%  End of active &'s.
}%  End of active |'s.
\def\spancount#1{%\out{spancount--->\meaning#1}
   \nspan=#1\multiply\nspan by 2\advance\nspan by -1%
   \global\advance \countREGISTER by \nspan
%  \out{number spancount--->\the\nspan; \the\countREGISTER}
   \let\next\COLcount \next}%
%
%\def\dvr#1{\vrule width 1.0pt depth 0pt height 12pt$_{#1}$}
\def\dvr#1{\relax}%
% \omit\hfil%
% \parindent=0pt\hsize=1.1in\valign{%
% \vfil#\vfil&\vfil#\vfil\cr\hfil\hbox{\ Added to\ }\hfil&%
% \hfil\hbox{\ empty events\ }\hfil\cr}\hfil%
\def\header#1{%
\dvr{1}{\let\cr=\@mpersand%
\hdtks={#1}%
%\out{In header:  hdtks=O\the\hdtksE}%
\counthdROWS\hdtks\into\hdrows%
\advance\hdrows by 1%
\ifnum\hdrows=0 \hdrows=1 \fi%
%\out{In header:  Nhdrows=O\the\hdrowsE}%
\dvr{5}\makehdPREAMBLE{\the\hdrows}%
%\out{In header:  headerpreamble=O\headerpreambleE}%
\dvr{6}\getHDdimen{#1}%
%\out{In header:  hdsize=O\the\hdsizeE}%
%\striplastCR{#1}%
{\parindent=0pt\hsize=\hdsize{\let\ifmath0%
\xdef\next{\valign{\headerpreamble #1\crnorm}}}\dvr{7}\next\dvr{8}%
}%
}\dvr{2}}%  End of macro \header.
%\def\striplastCR#1\cr{\xdef\headerbody{#1}}%
\def\makehdPREAMBLE#1{%This macro generates the necessary preamble for a
\dvr{3}%
%                      ruled table with \ncols primary columns.
%                      (Primary columns means the number of columns NOT
%                       counting those used for vertical rules.
\hdrows=#1%  Get the number of columns desired.
{%  Start local parameter definitions.
\let\headerARGS=0%
%  This is the key to the whole thing; it prevents \ARGS
\let\cr=\crnorm%
%                from being expanded in the followin \edef's.
\edef\xtp{\vfil\hfil\hbox{\headerARGS}\hfil\vfil}%
\advance\hdrows by -1%  One row has been generated; decrement the
%                         counter.
\loop%  Append as many further rows as needed to the preamble.
\ifnum\hdrows>0%
\advance\hdrows by -1%
\edef\xtp{\xtp&\vfil\hfil\hbox{\headerARGS}\hfil\vfil}%
\repeat%
\xdef\headerpreamble{\xtp\crcr}%
}%  End of local parameters.
\dvr{4}}%  End of \makehdPREAMBLE.
%
\def\getHDdimen#1{%
%\out{In getHDdimen:  Arg 1=O#1E}%
\hdsize=0pt%
\getsize#1\cr\end\cr%
}%  End of macro getHDdimen.
\def\getsize#1\cr{%
%\out{In getsize:  Arg 1=O#1E}%
%  Here we have to check arg#1 and see if the first token in #1 is an
%    \end; if so, we stop, else we check the width of arg#1.
%  We recall that each arg#1 will be terminated with a \cr token.
\endsizefalse\savetks={#1}%
%\out{In getsize:  the savetks = O\the\savetksE}%
\expandafter\lookend\the\savetks\cr%
%\out{In getsize:  ifendsize = O\meaning\ifendsizeE}%
\relax \ifendsize \let\next\relax \else%
\setbox\hdbox=\hbox{#1}\newhdsize=1.0\wd\hdbox%
\ifdim\newhdsize>\hdsize \hdsize=\newhdsize \fi%
%\out{In getsize:  hdsize=O\the\hdsizeE}%
%\out{In getsize:  newhdsize=O\the\newhdsizeE}%
\let\next\getsize \fi%
\next%
}%
\def\lookend{\afterassignment\sublookend\let\looknext= }%
\def\sublookend{\relax%
%\out{In sublookend:  looknext = O\looknextE}%
\ifx\looknext\cr %
%\out{In sublooknext:  looknext=cr}%
\let\looknext\relax \else %
%\out{In sublooknext:  looknext/=cr}%
   \relax
   \ifx\looknext\end \global\endsizetrue \fi%
   \let\looknext=\lookend%
    \fi \looknext%
}%
%
%  Allow the user to make his own names for crthick, etc.
%
\def\tablelet#1{%
   \tableLETtokens=\expandafter{\the\tableLETtokens #1}%
}%
%\catcode`\@=12%  Change @'s back to their normal category code.
%
\oddsidemargin -0.50in \evensidemargin -0.46in
\topmargin -1.8cm \headheight 15pt \headsep 45pt
\footheight 12pt \footskip 15pt
\textheight 9.4in \textwidth 7.5in
\parindent 1em \leftmargini 2em \leftmargin\leftmargini
\leftmarginv .5em \leftmarginvi .5em

\newdimen\Parindent\newdimen\Parskip
\columnsep0.47in \columnseprule0pt
\Parindent=\parindent\Parskip=\parskip%save old values
\parindent5mm\parskip3mm

%  Define page numbering style (used only for drafts)
\def\@oddhead{}\def\@evenhead{}
\def\ps@myheadings{\let\@mkboth\@gobbletwo
\def\@oddhead{\hbox{}\sl\rightmark}
\def\@oddfoot{\hfil}\def\@evenhead{\hfil\sl\leftmark\hbox
{}}\def\@evenfoot{\hfil}\def\sectionmark##1{}\def\subsectionmark##1{}}

\newdimen\Parindent\newdimen\Parskip
\newenvironment{Abstracts}%
{\Parindent=\parindent\Parskip=\parskip%save old values
\parindent0pt\parskip3mm\columnsep11mm}%set new values
{\parindent\Parindent\parskip\Parskip}%end{Abstracts}
\newenvironment{Questions}%
{\Parindent=\parindent\Parskip=\parskip%save old values
\parindent0pt\parskip3mm\columnsep11mm}%set new values
{\parindent\Parindent\parskip\Parskip}%end{Questions}

%  Define the Abstract
\gdef\abstract#1{\gdef\@abstract{#1}}

%  Define the Title style
\def\maketitle{\par
 \begingroup
 \def\thefootnote{\fnsymbol{footnote}}
 \def\@makefnmark{\hbox
 to 0pt{$^{\@thefnmark}$\hss}}
 \twocolumn[\@maketitle]
 \@thanks
 \endgroup
 \setcounter{footnote}{0}
 \let\maketitle\relax
 \let\@maketitle\relax
 \gdef\@thanks{}\gdef\@author{}\gdef\@title{}\let\thanks\relax}
%-------- change if box height too small -----------------
%\def\@maketitle{\vbox to 1in{\hsize\textwidth
\def\@maketitle{\vbox to 1in{\hsize\textwidth
 \linewidth\hsize \vfil \centering
 { \Large\bf \@title \par} \vskip 1.3em {\begin{tabular}[t]{c}\@author
\end{tabular}\par}
 \vfil}
\hsize\textwidth \linewidth\hsize
\begin{center} ABSTRACT \end{center} \par \small\rm \@abstract \vskip 2em }

\def\copyrightspace{\footnotetext[0]{\mbox{}\vrule height 97pt width 0pt}}

\def\section{\@startsection {section}{1}{\z@}{-3.5ex plus -1ex minus
 -.2ex}{2.3ex plus .2ex}{\normalsize\bf}}
\def\subsection{\@startsection{subsection}{2}{\z@}{-3.25ex plus -1ex minus
 -.2ex}{1.5ex plus .2ex}{\normalsize\bf}}
\def\subsubsection{\@startsection{subsubsection}{3}{\z@}{-3.25ex plus
-1ex minus -.2ex}{1.5ex plus .2ex}{\normalsize\bf}}
\def\paragraph{\@startsection
 {paragraph}{4}{\z@}{3.25ex plus 1ex minus .2ex}{-1em}{\normalsize\bf}}
\def\subparagraph{\@startsection
 {subparagraph}{4}{\parindent}{3.25ex plus 1ex minus
 .2ex}{-1em}{\normalsize\bf}}
\catcode`\@=12
\def\sto{\!\to\!}
\def\diha{$\Delta I\sheq 1/2$}
\def\sheq{\!=\!}
\def\particleone{\rm}
\def\particletwo{\sl}

\def\tiny{\vrule width 0pt}
\def\star{{\bf *}}
\def\conventionone{

 \def\PM{\relax\ifmmode{\pm}\else{$\pm$}\fi}

 \def\decays{\relax\ifmmode{\rightarrow}\else{$\rightarrow$}\fi\tiny}

 \def\EPEM{\relax\ifmmode{e^+e^-}\else{$e^+e^-$}\fi}
 \def\epem{\relax\ifmmode{e^+e^-}\else{$e^+e^-$}\fi}

 %Gamma

 \def\G{\relax\ifmmode{\gamma}\else{$\gamma$}\fi}

 %W

 \def\W{\relax\ifmmode{{\particleone W}}\else{{\particleone W}}\fi}
 \def\WP{\relax\ifmmode{{\particleone W}^+}\else{{\particleone W}$^+$}\fi}
 \def\WM{\relax\ifmmode{{\particleone W}^-}\else{{\particleone W}$^-$}\fi}
 \def\WPM{\relax\ifmmode{{\particleone W}^\pm}\else{{\particleone W}$^\pm$}\fi}
 \def\WMP{\relax\ifmmode{{\particleone W}^\mp}\else{{\particleone W}$^\mp$}\fi}

%Z

 \def\Z{\relax\ifmmode{{\particleone Z}}\else{{\particleone Z}}\fi}
 \def\ZZ{\relax\ifmmode{{\particleone Z}^0}\else{{\particleone Z}$^0$}\fi}

%Nu

 \def\NU{\relax\ifmmode{\nu}\else{$\nu$}\fi}
 \def\NUB{\relax\ifmmode{\overline{\nu}}
	\else{$\overline{\nu}$}\fi}
%Nu e

 \def\NE{\relax\ifmmode{\nu_e}\else{$\nu_e$}\fi}
 \def\NEB{\relax\ifmmode{\overline{\nu}\tiny_e}
	\else{$\overline{\nu}\tiny_e$}\fi}

%Electron

 \def\E{\relax\ifmmode{e}\else{$e$}\fi}
 \def\EP{\relax\ifmmode{e^+}\else{$e^+$}\fi}
 \def\EM{\relax\ifmmode{e^-}\else{$e^-$}\fi}
 \def\EPM{\relax\ifmmode{e^\pm}\else{$e^\pm$}\fi}
 \def\EMP{\relax\ifmmode{e^\mp}\else{$e^\mp$}\fi}

%Nu mu

 \def\NM{\relax\ifmmode{\nu_\mu}\else{$\nu_\mu$}\fi}
 \def\NMB{\relax\ifmmode{\overline{\nu}\tiny_\mu}
	\else{$\overline{\nu}\tiny_\mu$}\fi}

%MU

 \def\M{\relax\ifmmode{\mu}\else{$\mu$}\fi}
 \def\MP{\relax\ifmmode{\mu^+}\else{$\mu^+$}\fi}
 \def\MM{\relax\ifmmode{\mu^-}\else{$\mu^-$}\fi}
 \def\MPM{\relax\ifmmode{\mu^\pm}\else{$\mu^\pm$}\fi}
 \def\MMP{\relax\ifmmode{\mu^\mp}\else{$\mu^\mp$}\fi}

%Nu tau

 \def\NT{\relax\ifmmode{\nu_\tau}\else{$\nu_\tau$}\fi}
 \def\NTB{\relax\ifmmode{\overline{\nu}\tiny_\tau}
	\else{$\overline{\nu}\tiny_\tau$}\fi}

%Tau

 \def\T{\relax\ifmmode{\tau}\else{$\tau$}\fi}
 \def\TP{\relax\ifmmode{\tau^+}\else{$\tau^+$}\fi}
 \def\TM{\relax\ifmmode{\tau^-}\else{$\tau^-$}\fi}
 \def\TPM{\relax\ifmmode{\tau^\pm}\else{$\tau^\pm$}\fi}
 \def\TMP{\relax\ifmmode{\tau^\mp}\else{$\tau^\mp$}\fi}

%Nu lep

 \def\NL{\relax\ifmmode{\nu_\ell}\else{$\nu_\ell$}\fi}
 \def\NLB{\relax\ifmmode{\overline{\nu}\tiny_\ell}
	\else{$\overline{\nu}\tiny_\ell$}\fi}

%ell

 \def\L{\relax\ifmmode{\ell}\else{$\ell$}\fi}
 \def\LP{\relax\ifmmode{\ell^+}\else{$\ell^+$}\fi}
 \def\LM{\relax\ifmmode{\ell^-}\else{$\ell^-$}\fi}
 \def\LPM{\relax\ifmmode{\ell^\pm}\else{$\ell^\pm$}\fi}
 \def\LMP{\relax\ifmmode{\ell^\mp}\else{$\ell^\mp$}\fi}

%Pi

 \def\PI{\relax\ifmmode{\pi}\else{$\pi$}\fi}
 \def\PIP{\relax\ifmmode{\pi^+}\else{$\pi^+$}\fi}
 \def\PIZ{\relax\ifmmode{\pi^0}\else{$\pi^0$}\fi}
 \def\PIM{\relax\ifmmode{\pi^-}\else{$\pi^-$}\fi}
 \def\PIPM{\relax\ifmmode{\pi^\pm}\else{$\pi^\pm$}\fi}
 \def\PIMP{\relax\ifmmode{\pi^\mp}\else{$\pi^\mp$}\fi}
 \def\PIPMZ{\relax\ifmmode{\pi^{\pm,0}}\else{$\pi^{\pm,0}$}\fi}

%eta

 \def\ET{\relax\ifmmode{\eta}\else{$\eta$}\fi}
 \def\ETZ{\relax\ifmmode{\eta^0}\else{$\eta^0$}\fi}

%K

 \def\K{\relax\ifmmode{{\particleone K}}\else{{\particleone K}}\fi}
 \def\KB{\relax\ifmmode{\overline{{\particleone K}}}
	\else{$\overline{{\particleone K}}$}\fi}

 \def\KZ{\relax\ifmmode{{\particleone K}^0}\else{{\particleone K}$^0$}\fi}
 \def\KSH{\relax\ifmmode{{\particleone K}^0_S}\else{{\particleone K}$^0_S$}\fi}
 \def\KLO{\relax\ifmmode{{\particleone K}^0_L}\else{{\particleone K}$^0_L$}\fi}
 \def\KZB{\relax\ifmmode{\overline{{\particleone K}}\tiny^0}
	\else{$\overline{{\particleone K}}\tiny^0$}\fi}

 \def\KP{\relax\ifmmode{{\particleone K}^+}\else{{\particleone K}$^+$}\fi}
 \def\KM{\relax\ifmmode{{\particleone K}^-}\else{{\particleone K}$^-$}\fi}
 \def\KPM{\relax\ifmmode{{\particleone K}^\pm}\else{{\particleone K}$^\pm$}\fi}
 \def\KMP{\relax\ifmmode{{\particleone K}^\mp}\else{{\particleone K}$^\mp$}\fi}

%D

 \def\D{\relax\ifmmode{{\particleone D}}\else{{\particleone D}}\fi\tiny}
 \def\DB{\relax\ifmmode{\overline{{\particleone D}}}
	\else{$\overline{{\particleone D}}$}\fi}

 \def\DZ{\relax\ifmmode{{\particleone D}^0}\else{{\particleone D}$^0$}\fi}
 \def\DZB{\relax\ifmmode{\overline{{\particleone D}}\tiny^0}
	\else{$\overline{{\particleone D}}\tiny^0$}\fi}

 \def\DP{\relax\ifmmode{{\particleone D}^+}\else{{\particleone D}$^+$}\fi}
 \def\DM{\relax\ifmmode{{\particleone D}^-}\else{{\particleone D}$^-$}\fi}
 \def\DPM{\relax\ifmmode{{\particleone D}^\pm}\else{{\particleone D}$^\pm$}\fi}
 \def\DMP{\relax\ifmmode{{\particleone D}^\mp}\else{{\particleone D}$^\mp$}\fi}

%F

 \def\F{\relax\ifmmode{{\particleone F}}\else{{\particleone F}}\fi}
 \def\FP{\relax\ifmmode{{\particleone F}^+}\else{{\particleone F}$^+$}\fi}
 \def\FM{\relax\ifmmode{{\particleone F}^-}\else{{\particleone F}$^-$}\fi}
 \def\FPM{\relax\ifmmode{{\particleone F}^\pm}\else{{\particleone F}$^\pm$}\fi}
 \def\FMP{\relax\ifmmode{{\particleone F}^\mp}\else{{\particleone F}$^\mp$}\fi}

%D_S

 \def\DUS{\relax\ifmmode{{\particletwo D}_s}\else{{\particletwo D}$_s$}\fi}
 \def\DUSO{\relax\ifmmode{{\particletwo D}_{s1}}
      \else{{\particletwo D}$_{s1}$}\fi}
 \def\DUSP{\relax\ifmmode{{\particletwo D}_s^+}
      \else{{\particletwo D}$^+$}\fi}
 \def\DUSM{\relax\ifmmode{{\particletwo D}_s^-}
      \else{{\particletwo D}$^-$}\fi}
 \def\DUSPM{\relax\ifmmode{{\particletwo D}_s^\pm}
           \else{{\particletwo D}$_s^\pm$}\fi}
 \def\DUSMP{\relax\ifmmode{{\particletwo D}_s^\mp}
           \else{{\particletwo D}$_s^\mp$}\fi}

%B

 \def\B{\relax\ifmmode{{\particleone B}}\else{{\particleone B}}\fi\tiny}
 \def\BB{\relax\ifmmode{\overline{{\particleone B}}}
	\else{$\overline{{\particleone B}}$}\fi}

 \def\BZ{\relax\ifmmode{{\particleone B}^0}\else{{\particleone B}$^0$}\fi}
 \def\BZB{\relax\ifmmode{\overline{{\particleone B^0}}}
	\else{$\overline{{\particleone B}^0}$}\fi}

 \def\BP{\relax\ifmmode{{\particleone B}^+}\else{{\particleone B}$^+$}\fi}
 \def\BM{\relax\ifmmode{{\particleone B}^-}\else{{\particleone B}$^-$}\fi}
 \def\BPM{\relax\ifmmode{{\particleone B}^\pm}\else{{\particleone B}$^\pm$}\fi}
 \def\BMP{\relax\ifmmode{{\particleone B}^\mp}\else{{\particleone B}$^\mp$}\fi}

%M (Generic Meson)

 \def\eM{\relax\ifmmode{{\particleone M}}\else{{\particleone M}}\fi\tiny}
 \def\eMB{\relax\ifmmode{\overline{{\particleone M}}}
	\else{$\overline{{\particleone M}}$}\fi}

 \def\eMZ{\relax\ifmmode{{\particleone M}^0}\else{{\particleone M}$^0$}\fi}
 \def\eMZB{\relax\ifmmode{\overline{{\particleone M}}\tiny^0}
	\else{$\overline{{\particleone M}}\tiny^0$}\fi}

 \def\eMP{\relax\ifmmode{{\particleone M}^+}\else{{\particleone M}$^+$}\fi}
 \def\eMM{\relax\ifmmode{{\particleone M}^-}\else{{\particleone M}$^-$}\fi}
 \def\eMPM{\relax\ifmmode{{\particleone M}^\pm}
   \else{{\particleone M}$^\pm$}\fi}
 \def\eMMP{\relax\ifmmode{{\particleone M}^\mp}
   \else{{\particleone M}$^\mp$}\fi}


%proton

 \def\PR{\relax\ifmmode{{\particleone p}}\else{{\particleone p}}\fi}
 \def\PB{\relax\ifmmode{\overline{{\particleone p}}}
	\else{$\overline{{\particleone p}}$}\fi}

%neutron

 \def\NR{\relax\ifmmode{{\particleone n}}\else{{\particleone n}}\fi}
 \def\NB{\relax\ifmmode{\overline{{\particleone n}}}
	\else{$\overline{{\particleone n}}$}\fi}

%lambda

 \def\LA{\relax\ifmmode{\Lambda}\else{$\Lambda$}\fi}
 \def\LAB{\relax\ifmmode{\overline{\Lambda}}
	\else{$\overline{\Lambda}$}\fi}
 \def\LAZ{\relax\ifmmode{\Lambda^0}\else{$\Lambda^0$}\fi}
 \def\LAZB{\relax\ifmmode{\overline{\Lambda}\tiny^0}
	\else{$\overline{\Lambda}\tiny^0$}\fi}

%SIGMA

 \def\SI{\relax\ifmmode{\Sigma}\else{$\Sigma$}\fi}
 \def\SIB{\relax\ifmmode{\overline{\Sigma}}
	\else{$\overline{\Sigma}$}\fi}
 \def\SIZ{\relax\ifmmode{\Sigma^0}\else{$\Sigma^0$}\fi}
 \def\SIZB{\relax\ifmmode{\overline{\Sigma}\tiny^0}
	\else{$\overline{\Sigma}\tiny^0$}\fi}
 \def\SIP{\relax\ifmmode{\Sigma^+}\else{$\Sigma^+$}\fi}
 \def\SIM{\relax\ifmmode{\Sigma^-}\else{$\Sigma^-$}\fi}
 \def\SIPM{\relax\ifmmode{\Sigma^\pm}\else{$\Sigma^\pm$}\fi}
 \def\SIMP{\relax\ifmmode{\Sigma^\mp}\else{$\Sigma^\mp$}\fi}
 \def\SIPB{\relax\ifmmode{\overline{\Sigma}\tiny^+}
	\else{$\overline{\Sigma}\tiny^+$}\fi}
 \def\SIMB{\relax\ifmmode{\overline{\Sigma}\tiny^-}
	\else{$\overline{\Sigma}\tiny^-$}\fi}
 \def\SIPMB{\relax\ifmmode{\overline{\Sigma}\tiny^\pm}
	\else{$\overline{\Sigma}\tiny^\pm$}\fi}
 \def\SIMPB{\relax\ifmmode{\overline{\Sigma}\tiny^\mp}
	\else{$\overline{\Sigma}\tiny^\mp$}\fi}

%Xi

 \def\XI{\relax\ifmmode{\Xi}\else{$\Xi$}\fi}
 \def\XIB{\relax\ifmmode{\overline{\Xi}}
	\else{$\overline{\Xi}$}\fi}
 \def\XIZ{\relax\ifmmode{\Xi^0}\else{$\Xi^0$}\fi}
 \def\XIZB{\relax\ifmmode{\overline{\Xi}\tiny^0}
	\else{$\overline{\Xi}\tiny^0$}\fi}
 \def\XIM{\relax\ifmmode{\Xi^-}\else{$\Xi^-$}\fi}
 \def\XIPB{\relax\ifmmode{\overline{\Xi}\tiny^+}
	\else{$\overline{\Xi}\tiny^+$}\fi}

%Omega

 \def\OMM{\relax\ifmmode{\Omega^-}\else{$\Omega^-$}\fi}
 \def\OMPB{\relax\ifmmode{\overline{\Omega}\tiny^+}
	\else{$\overline{\Omega}\tiny^+$}\fi}

%lambda c

 \def\LC{\relax\ifmmode{\Lambda_c}\else{$\Lambda_c$}\fi}
 \def\LCB{\relax\ifmmode{\overline{\Lambda_c}}
	\else{$\overline{\Lambda}\tiny_c$}\fi}
 \def\LCP{\relax\ifmmode{\Lambda^+_c}\else{$\Lambda^+_c$}\fi}
 \def\LCMB{\relax\ifmmode{\overline{\Lambda}\tiny^-_c}
	\else{$\overline{\Lambda}\tiny^-_c$}\fi}

%RH

 \def\RH{\relax\ifmmode{\rho}\else{$\rho$}\fi}
 \def\RHP{\relax\ifmmode{\rho^+}\else{$\rho^+$}\fi}
 \def\RHZ{\relax\ifmmode{\rho^0}\else{$\rho^0$}\fi}
 \def\RHM{\relax\ifmmode{\rho^-}\else{$\rho^-$}\fi}
 \def\RHPM{\relax\ifmmode{\rho^\pm}\else{$\rho^\pm$}\fi}
 \def\RHMP{\relax\ifmmode{\rho^\mp}\else{$\rho^\mp$}\fi}
 \def\RHPMZ{\relax\ifmmode{\rho^{\pm,0}}\else{$\rho^{\pm,0}$}\fi}


%oM

 \def\oM{\relax\ifmmode{\omega}\else{$\omega$}\fi}
 \def\oMZ{\relax\ifmmode{\omega^0}\else{$\omega^0$}\fi}

%etap

 \def\ETP{\relax\ifmmode{\eta'}\else{$\eta'$}\fi}
 \def\ETPZ{\relax\ifmmode{\eta'\tiny^0}\else{$\eta'\tiny^0$}\fi}

%PH

 \def\PH{\relax\ifmmode{\phi}\else{$\phi$}\fi}

%psi

 \def\PS{\relax\ifmmode{J/\psi}\else{$J/\psi$}\fi}
 \def\PSP{\relax\ifmmode{\psi'}\else{$\psi'$}\fi}
 \def\PSPP{\relax\ifmmode{\psi''}\else{$\psi''$}\fi}
 \def\PSPPP{\relax\ifmmode{\psi'''}\else{$\psi'''$}\fi}
 \def\PSPPPP{\relax\ifmmode{\psi''''}\else{$\psi''''$}\fi}

%Upsilon

 \def\US{\relax\ifmmode{\Upsilon{\particleone (1S)}}
	\else{$\Upsilon{\particleone (1S)}$}\fi}
 \def\USS{\relax\ifmmode{\Upsilon{\particleone (2S)}}
	\else{$\Upsilon{\particleone (2S)}$}\fi}
 \def\USSS{\relax\ifmmode{\Upsilon{\particleone (3S)}}
	\else{$\Upsilon{\particleone (3S)}$}\fi}
 \def\USSSS{\relax\ifmmode{\Upsilon{\particleone (4S)}}
	\else{$\Upsilon{\particleone (4S)}$}\fi}
 \def\USSSSS{\relax\ifmmode{\Upsilon{\particleone (5S)}}
	\else{$\Upsilon{\particleone (5S)}$}\fi}
 \def\USSSSSS{\relax\ifmmode{\Upsilon{\particleone (6S)}}
	\else{$\Upsilon{\particleone (6S)}$}\fi}

%K star

 \def\KS{\relax\ifmmode{{\particleone K}^\star}
  \else{{\particleone K}$^\star$}\fi}
 \def\KSB{\relax\ifmmode{\overline{{\particleone K}}\tiny^\star}
	\else{$\overline{{\particleone K}}\tiny^\star$}\fi}

 \def\KSZ{\relax\ifmmode{{\particleone K}^{\star0}}
  \else{{\particleone K}$^{\star0}$}\fi}
 \def\KSZB{\relax\ifmmode{\overline{{\particleone K}}\tiny^{\star0}}
	\else{$\overline{{\particleone K}}\tiny^{\star0}$}\fi}

 \def\KSP{\relax\ifmmode{{\particleone K}^{\star+}}
  \else{{\particleone K}$^{\star+}$}\fi}
 \def\KSM{\relax\ifmmode{{\particleone K}^{\star-}}
  \else{{\particleone K}$^{\star-}$}\fi}
 \def\KSPM{\relax\ifmmode{{\particleone K}^{\star\pm}}
  \else{{\particleone K}$^{\star\pm}$}\fi}
 \def\KSMP{\relax\ifmmode{{\particleone K}^{\star\mp}}
\else{{\particleone K}$^{\star\mp}$}\fi}


%D star

 \def\DS{\relax\ifmmode{{\particleone D}^\star}
\else{{\particleone D}$^\star$}\fi}
 \def\DSB{\relax\ifmmode{\overline{{\particleone D}}\tiny^\star}
	\else{$\overline{{\particleone D}}\tiny^\star$}\fi}

 \def\DSZ{\relax\ifmmode{{\particleone D}^{\star0}}
\else{{\particleone D}$^{\star0}$}\fi}
 \def\DSZB{\relax\ifmmode{\overline{{\particleone D}}\tiny^{\star0}}
	\else{$\overline{{\particleone D}}\tiny^{\star0}$}\fi}

 \def\DSP{\relax\ifmmode{{\particleone D}^{\star+}}
\else{{\particleone D}$^{\star+}$}\fi}
 \def\DSM{\relax\ifmmode{{\particleone D}^{\star-}}
\else{{\particleone D}$^{\star-}$}\fi}
 \def\DSPM{\relax\ifmmode{{\particleone D}^{\star\pm}}
\else{{\particleone D}$^{\star\pm}$}\fi}
 \def\DSMP{\relax\ifmmode{{\particleone D}^{\star\mp}}
\else{{\particleone D}$^{\star\mp}$}\fi}

%D star

 \def\DDS{\relax\ifmmode{{\particleone D}^{\star\star}}
\else{{\particleone D}$^{\star\star}$}\fi}
 \def\DDSB{\relax\ifmmode{\overline{{\particleone D}}\tiny^{\star\star}}
	\else{$\overline{{\particleone D}}\tiny^{\star\star}$}\fi}

 \def\DDSZ{\relax\ifmmode{{\particleone D}^{\star\star0}}
\else{{\particleone D}$^{\star\star0}$}\fi}
 \def\DDSZB{\relax\ifmmode{\overline{{\particleone D}}\tiny^{\star\star0}}
	\else{$\overline{{\particleone D}}\tiny^{\star\star0}$}\fi}

 \def\DDSP{\relax\ifmmode{{\particleone D}^{\star\star+}}
\else{{\particleone D}$^{\star\star+}$}\fi}
 \def\DDSM{\relax\ifmmode{{\particleone D}^{\star\star-}}
\else{{\particleone D}$^{\star\star-}$}\fi}
 \def\DDSPM{\relax\ifmmode{{\particleone D}^{\star\star\pm}}
	\else{{\particleone D}$^{\star\star\pm}$}\fi}
 \def\DDSMP{\relax\ifmmode{{\particleone D}^{\star\star\mp}}
	\else{{\particleone D}$^{\star\star\mp}$}\fi}

}

\def\conventiontwo{

 \def\epem{\relax\ifmmode{e^+e^-}\else{$e^+e^-$}\fi}

 \def\decays{\relax\ifmmode{\rightarrow}\else{$\rightarrow$}\fi\tiny}

 %Gamma

\def\gamma{\relax\ifmmode{\mathchar"10D}\else{$\mathchar"10D$}\fi}

 %W

 \def\W{\relax\ifmmode{{\particletwo W}}\else{{\particletwo W}}\fi}
 \def\Wplus{\relax\ifmmode{{\particletwo W}^+}\else{{\particletwo W}$^+$}\fi}
 \def\Wminus{\relax\ifmmode{{\particletwo W}^-}\else{{\particletwo W}$^-$}\fi}
 \def\Wpm{\relax\ifmmode{{\particletwo W}^\pm}\else{{\particletwo W}$^\pm$}\fi}
 \def\Wmp{\relax\ifmmode{{\particletwo W}^\mp}\else{{\particletwo W}$^\mp$}\fi}

%Z

 \def\Z{\relax\ifmmode{{\particletwo Z}}\else{{\particletwo Z}}\fi}
 \def\Zzero{\relax\ifmmode{{\particletwo Z}^0}\else{{\particletwo Z}$^0$}\fi}

%Nu

 \def\nu{\relax\ifmmode{\mathchar"117}\else{$\mathchar"117$}\fi}
 \def\nubar{\relax\ifmmode{\overline{\nu}}
	\else{$\overline{\nu}$}\fi}

%Nu e

 \def\nue{\relax\ifmmode{\nu_e}\else{$\nu_e$}\fi}
 \def\nuebar{\relax\ifmmode{\overline{\nu}\tiny_e}
	\else{$\overline{\nu}\tiny_e$}\fi}

%Electron

 \def\e{\relax\ifmmode{e}\else{$e$}\fi}
 \def\eplus{\relax\ifmmode{e^+}\else{$e^+$}\fi}
 \def\eminus{\relax\ifmmode{e^-}\else{$e^-$}\fi}
 \def\epm{\relax\ifmmode{e^\pm}\else{$e^\pm$}\fi}
 \def\emp{\relax\ifmmode{e^\mp}\else{$e^\mp$}\fi}

%Nu mu

 \def\numu{\relax\ifmmode{\nu_\mu}\else{$\nu_\mu$}\fi}
 \def\numubar{\relax\ifmmode{\overline{\nu}\tiny_\mu}
	\else{$\overline{\nu}\tiny_\mu$}\fi}

%MU

 \def\mu{\relax\ifmmode{\mathchar"116}\else{$\mathchar"116$}\fi}
 \def\muplus{\relax\ifmmode{\mu^+}\else{$\mu^+$}\fi}
 \def\muminus{\relax\ifmmode{\mu^-}\else{$\mu^-$}\fi}
 \def\mupm{\relax\ifmmode{\mu^\pm}\else{$\mu^\pm$}\fi}
 \def\mump{\relax\ifmmode{\mu^\mp}\else{$\mu^\mp$}\fi}

%Nu tau

 \def\nutau{\relax\ifmmode{\nu_\tau}\else{$\nu_\tau$}\fi}
 \def\nutaubar{\relax\ifmmode{\overline{\nu}\tiny_\tau}
	\else{$\overline{\nu}\tiny_\tau$}\fi}

%Tau

 \def\tau{\relax\ifmmode{\mathchar"11C}\else{$\mathchar"11C$}\fi}
 \def\tauplus{\relax\ifmmode{\tau^+}\else{$\tau^+$}\fi}
 \def\tauminus{\relax\ifmmode{\tau^-}\else{$\tau^-$}\fi}
 \def\taupm{\relax\ifmmode{\tau^\pm}\else{$\tau^\pm$}\fi}
 \def\taump{\relax\ifmmode{\tau^\mp}\else{$\tau^\mp$}\fi}

%Nu lep

 \def\nulep{\relax\ifmmode{\nu_\ell}\else{$\nu_\ell$}\fi}
 \def\nulepbar{\relax\ifmmode{\overline{\nu}\tiny_\ell}
	\else{$\overline{\nu}\tiny_\ell$}\fi}

%ell

 \def\lep{\relax\ifmmode{\ell}\else{$\ell$}\fi}
 \def\lepplus{\relax\ifmmode{\ell^+}\else{$\ell^+$}\fi}
 \def\lepminus{\relax\ifmmode{\ell^-}\else{$\ell^-$}\fi}
 \def\leppm{\relax\ifmmode{\ell^\pm}\else{$\ell^\pm$}\fi}
 \def\lepmp{\relax\ifmmode{\ell^\mp}\else{$\ell^\mp$}\fi}

%Pi

 \def\pi{\relax\ifmmode{\mathchar"119}\else{$\mathchar"119$}\fi}
 \def\piplus{\relax\ifmmode{\pi^+}\else{$\pi^+$}\fi}
 \def\pizero{\relax\ifmmode{\pi^0}\else{$\pi^0$}\fi}
 \def\piminus{\relax\ifmmode{\pi^-}\else{$\pi^-$}\fi}
 \def\pipm{\relax\ifmmode{\pi^\pm}\else{$\pi^\pm$}\fi}
 \def\pimp{\relax\ifmmode{\pi^\mp}\else{$\pi^\mp$}\fi}
 \def\pipmz{\relax\ifmmode{\pi^{\pm,0}}\else{$\pi^{\pm,0}$}\fi}



%eta

 \def\eta{\relax\ifmmode{\mathchar"111}\else{$\mathchar"111$}\fi}
 \def\etazero{\relax\ifmmode{\eta^0}\else{$\eta^0$}\fi}

%K

 \def\K{\relax\ifmmode{{\particletwo K}}\else{{\particletwo K}}\fi}
 \def\Kbar{\relax\ifmmode{\overline{{\particletwo K}}}
	\else{$\overline{{\particletwo K}}$}\fi}

 \def\Kzero{\relax\ifmmode{{\particletwo K}^0}\else{{\particletwo K}$^0$}\fi}
 \def\Kshort{\relax\ifmmode{{\particletwo K}^0_{\rm S}}
            \else{{\particletwo K}$^0_{\rm S}$}\fi}
 \def\Klong{\relax\ifmmode{{\particletwo K}^0_{\rm L}}
            \else{{\particletwo K}$^0_{\rm L}$}\fi}
 \def\Kzerobar{\relax\ifmmode{\overline{{\particletwo K}}\tiny^0}
	\else{$\overline{{\particletwo K}}\tiny^0$}\fi}

 \def\Kplus{\relax\ifmmode{{\particletwo K}^+}\else{{\particletwo K}$^+$}\fi}
 \def\Kminus{\relax\ifmmode{{\particletwo K}^-}\else{{\particletwo K}$^-$}\fi}
 \def\Kpm{\relax\ifmmode{{\particletwo K}^\pm}\else{{\particletwo K}$^\pm$}\fi}
 \def\Kmp{\relax\ifmmode{{\particletwo K}^\mp}\else{{\particletwo K}$^\mp$}\fi}

%D

 \def\D{\relax\ifmmode{{\particletwo D}}\else{{\particletwo D}}\fi}
 \def\Dbar{\relax\ifmmode{\overline{{\particletwo D}}}
	\else{$\overline{{\particletwo D}}$}\fi}

 \def\Dzero{\relax\ifmmode{{\particletwo D}^0}\else{{\particletwo D}$^0$}\fi}
 \def\Dzerobar{\relax\ifmmode{\overline{{\particletwo D}}\tiny^0}
	\else{$\overline{{\particletwo D}}\tiny^0$}\fi}

 \def\Dplus{\relax\ifmmode{{\particletwo D}^+}\else{{\particletwo D}$^+$}\fi}
 \def\Dminus{\relax\ifmmode{{\particletwo D}^-}\else{{\particletwo D}$^-$}\fi}
 \def\Dpm{\relax\ifmmode{{\particletwo D}^\pm}\else{{\particletwo D}$^\pm$}\fi}
 \def\Dmp{\relax\ifmmode{{\particletwo D}^\mp}\else{{\particletwo D}$^\mp$}\fi}

%F

 \def\F{\relax\ifmmode{{\particletwo F}}\else{{\particletwo F}}\fi}
 \def\Fplus{\relax\ifmmode{{\particletwo F}^+}\else{{\particletwo F}$^+$}\fi}
 \def\Fminus{\relax\ifmmode{{\particletwo F}^-}\else{{\particletwo F}$^-$}\fi}
 \def\Fpm{\relax\ifmmode{{\particletwo F}^\pm}\else{{\particletwo F}$^\pm$}\fi}
 \def\Fmp{\relax\ifmmode{{\particletwo F}^\mp}\else{{\particletwo F}$^\mp$}\fi}

%D_S

 \def\DUS{\relax\ifmmode{{\particletwo D}_s}\else{{\particletwo D}$_s$}\fi}
 \def\DUSO{\relax\ifmmode{{\particletwo D}_{s1}}
      \else{{\particletwo D}$_{s1}$}\fi}
 \def\DUSP{\relax\ifmmode{{\particletwo D}_s^+}
      \else{{\particletwo D}$_s^+$}\fi}
 \def\DUSM{\relax\ifmmode{{\particletwo D}_s^-}
      \else{{\particletwo D}$_s^-$}\fi}
 \def\DUSPM{\relax\ifmmode{{\particletwo D}_s^\pm}
           \else{{\particletwo D}$_s^\pm$}\fi}
 \def\DUSMP{\relax\ifmmode{{\particletwo D}_s^\mp}
           \else{{\particletwo D}$_s^\mp$}\fi}

%B

 \def\B{\relax\ifmmode{{\particletwo B}}\else{{\particletwo B}}\fi}
 \def\Bbar{\relax\ifmmode{\overline{{\particletwo B}}}
	\else{$\overline{{\particletwo B}}$}\fi}

 \def\Bzero{\relax\ifmmode{{\particletwo B}^0}\else{{\particletwo B}$^0$}\fi}
 \def\Bzerobar{\relax\ifmmode{\overline{{\particletwo B}}\tiny^0}
	\else{$\overline{{\particletwo B}}\tiny^0$}\fi}

 \def\Bplus{\relax\ifmmode{{\particletwo B}^+}\else{{\particletwo B}$^+$}\fi}
 \def\Bminus{\relax\ifmmode{{\particletwo B}^-}\else{{\particletwo B}$^-$}\fi}
 \def\Bpm{\relax\ifmmode{{\particletwo B}^\pm}\else{{\particletwo B}$^\pm$}\fi}
 \def\Bmp{\relax\ifmmode{{\particletwo B}^\mp}\else{{\particletwo B}$^\mp$}\fi}

%proton

 \def\pro{\relax\ifmmode{{\particletwo p}}\else{{\particletwo p}}\fi}
 \def\probar{\relax\ifmmode{\overline{{\particletwo p}}}
	\else{$\overline{{\particletwo p}}$}\fi}


%neutron

 \def\neu{\relax\ifmmode{{\particletwo n}}\else{{\particletwo n}}\fi}
 \def\neubar{\relax\ifmmode{\overline{{\particletwo n}}}
	\else{$\overline{{\particletwo n}}$}\fi}

%lambda

 \def\Lambda{\relax\ifmmode{\mathchar"7003}\else{$\mathchar"7003$}\fi}
 \def\Lambdabar{\relax\ifmmode{\overline{\Lambda}}
	\else{$\overline{\Lambda}$}\fi}
 \def\Lambdazero{\relax\ifmmode{\Lambda^0}\else{$\Lambda^0$}\fi}
 \def\Lambdazerobar{\relax\ifmmode{\overline{\Lambda}\tiny^0}
	\else{$\overline{\Lambda}\tiny^0$}\fi}

%SIGMA

 \def\Sigma{\relax\ifmmode{\mathchar"7006}\else{$\mathchar"7006$}\fi}
 \def\Sigmabar{\relax\ifmmode{\overline{\Sigma}}
	\else{$\overline{\Sigma}$}\fi}
 \def\Sigmazero{\relax\ifmmode{\Sigma^0}\else{$\Sigma^0$}\fi}
 \def\Sigmazerobar{\relax\ifmmode{\overline{\Sigma}\tiny^0}
	\else{$\overline{\Sigma}\tiny^0$}\fi}
 \def\Sigmaplus{\relax\ifmmode{\Sigma^+}\else{$\Sigma^+$}\fi}
 \def\Sigmaminus{\relax\ifmmode{\Sigma^-}\else{$\Sigma^-$}\fi}
 \def\Sigmapm{\relax\ifmmode{\Sigma^\pm}\else{$\Sigma^\pm$}\fi}
 \def\Sigmamp{\relax\ifmmode{\Sigma^\mp}\else{$\Sigma^\mp$}\fi}
 \def\Sigmaplusbar{\relax\ifmmode{\overline{\Sigma}\tiny^+}
	\else{$\overline{\Sigma}\tiny^+$}\fi}
 \def\Sigmaminusbar{\relax\ifmmode{\overline{\Sigma}\tiny^-}
	\else{$\overline{\Sigma}\tiny^-$}\fi}
 \def\Sigmapmbar{\relax\ifmmode{\overline{\Sigma}\tiny^\pm}
	\else{$\overline{\Sigma}\tiny^\pm$}\fi}
 \def\Sigmampbar{\relax\ifmmode{\overline{\Sigma}\tiny^\mp}
	\else{$\overline{\Sigma}\tiny^\mp$}\fi}

%Xi

 \def\Xi{\relax\ifmmode{\mathchar"7004}\else{$\mathchar"7004$}\fi}
 \def\Xibar{\relax\ifmmode{\overline{\Xi}}
	\else{$\overline{\Xi}$}\fi}
 \def\Xizero{\relax\ifmmode{\Xi^0}\else{$\Xi^0$}\fi}
 \def\Xizerobar{\relax\ifmmode{\overline{\Xi}\tiny^0}
	\else{$\overline{\Xi}\tiny^0$}\fi}
 \def\Ximinus{\relax\ifmmode{\Xi^-}\else{$\Xi^-$}\fi}
 \def\Xiplusbar{\relax\ifmmode{\overline{\Xi}\tiny^+}
	\else{$\overline{\Xi}\tiny^+$}\fi}

%Omega

 \def\Omegaminus{\relax\ifmmode{\Omega^-}\else{$\Omega^-$}\fi}
 \def\Omegaplusbar{\relax\ifmmode{\overline{\Omega}\tiny^+}
	\else{$\overline{\Omega}\tiny^+$}\fi}

%lambda c

 \def\Lambdac{\relax\ifmmode{\Lambda_c}\else{$\Lambda_c$}\fi}
 \def\Lambdacbar{\relax\ifmmode{\overline{\Lambda_c}}
	\else{$\overline{\Lambda}\tiny_c$}\fi}
 \def\Lambdacplus{\relax\ifmmode{\Lambda^+_c}\else{$\Lambda^+_c$}\fi}
 \def\Lambdacminusbar{\relax\ifmmode{\overline{\Lambda}\tiny^-_c}
	\else{$\overline{\Lambda}\tiny^-_c$}\fi}

%RH

 \def\rho{\relax\ifmmode{\mathchar"11A}\else{$\mathchar"11A$}\fi}
 \def\rhoplus{\relax\ifmmode{\rho^+}\else{$\rho^+$}\fi}
 \def\rhozero{\relax\ifmmode{\rho^0}\else{$\rho^0$}\fi}
 \def\rhominus{\relax\ifmmode{\rho^-}\else{$\rho^-$}\fi}
 \def\rhopm{\relax\ifmmode{\rho^\pm}\else{$\rho^\pm$}\fi}
 \def\rhomp{\relax\ifmmode{\rho^\mp}\else{$\rho^\mp$}\fi}
 \def\rhopmz{\relax\ifmmode{\rho^{\pm,0}}\else{$\rho^{\pm,0}$}\fi}


%oM

 \def\omega{\relax\ifmmode{\mathchar"121}\else{$\mathchar"121$}\fi}
 \def\omegazero{\relax\ifmmode{\omega^0}\else{$\omega^0$}\fi}

%etap

 \def\etaprime{\relax\ifmmode{\eta'}\else{$\eta'$}\fi}
 \def\etaprimezero{\relax\ifmmode{\eta'\tiny^0}\else{$\eta'\tiny^0$}\fi}


%PH

 \def\phi{\relax\ifmmode{\mathchar"11E}\else{$\mathchar"11E$}\fi}

%psi

 \def\psi{\relax\ifmmode{\mathchar"120}\else{$\mathchar"120$}\fi}
 \def\psiprime{\relax\ifmmode{\psi'}\else{$\psi'$}\fi}
 \def\psidoubleprime{\relax\ifmmode{\psi''}\else{$\psi''$}\fi}
 \def\psitripleprime{\relax\ifmmode{\psi'''}\else{$\psi'''$}\fi}
 \def\psifourprime{\relax\ifmmode{\psi''''}\else{$\psi''''$}\fi}

%Upsilon

 \def\Uones{\relax\ifmmode{\Upsilon{\particletwo (1S)}}
	\else{$\Upsilon{\particletwo (1S)}$}\fi}
 \def\Utwos{\relax\ifmmode{\Upsilon{\particletwo (2S)}}
	\else{$\Upsilon{\particletwo (2S)}$}\fi}
 \def\Uthrees{\relax\ifmmode{\Upsilon{\particletwo (3S)}}
	\else{$\Upsilon{\particletwo (3S)}$}\fi}
 \def\Ufours{\relax\ifmmode{\Upsilon{\particletwo (4S)}}
	\else{$\Upsilon{\particletwo (4S)}$}\fi}
 \def\Ufives{\relax\ifmmode{\Upsilon{\particletwo (5S)}}
	\else{$\Upsilon{\particletwo (5S)}$}\fi}
 \def\Usixs{\relax\ifmmode{\Upsilon{\particletwo (6S)}}
	\else{$\Upsilon{\particletwo (6S)}$}\fi}

%K star

 \def\Kstar{\relax\ifmmode{{\particletwo K}^\star}
\else{{\particletwo K}$^\star$}\fi}
 \def\Kstarbar{\relax\ifmmode{\overline{{\particletwo K}}\tiny^\star}
	\else{$\overline{{\particletwo K}}\tiny^\star$}\fi}

 \def\Kstarzero{\relax\ifmmode{{\particletwo K}^{\star0}}
\else{{\particletwo K}$^{\star0}$}\fi}
 \def\Kstarzerobar{\relax\ifmmode{\overline{{\particletwo K}}\tiny^{\star0}}
	\else{$\overline{{\particletwo K}}\tiny^{\star0}$}\fi}

 \def\Kstarplus{\relax\ifmmode{{\particletwo K}^{\star+}}
\else{{\particletwo K}$^{\star+}$}\fi}
 \def\Kstarminus{\relax\ifmmode{{\particletwo K}^{\star-}}
\else{{\particletwo K}$^{\star-}$}\fi}
 \def\Kstarpm{\relax\ifmmode{{\particletwo K}^{\star\pm}}
\else{{\particletwo K}$^{\star\pm}$}\fi}
 \def\Kstarmp{\relax\ifmmode{{\particletwo K}^{\star\mp}}
\else{{\particletwo K}$^{\star\mp}$}\fi}


%D star

 \def\Dstar{\relax\ifmmode{{\particletwo D}^\star}
\else{{\particletwo D}$^\star$}\fi}
 \def\Dstarbar{\relax\ifmmode{\overline{{\particletwo D}}\tiny^\star}
	\else{$\overline{{\particletwo D}}\tiny^\star$}\fi}

 \def\Dstarzero{\relax\ifmmode{{\particletwo D}^{\star0}}
\else{{\particletwo D}$^{\star0}$}\fi}
 \def\Dstarzerobar{\relax\ifmmode{\overline{{\particletwo D}}\tiny^{\star0}}
	\else{$\overline{{\particletwo D}}\tiny^{\star0}$}\fi}

 \def\Dstarplus{\relax\ifmmode{{\particletwo D}^{\star+}}
\else{{\particletwo D}$^{\star+}$}\fi}
 \def\Dstarminus{\relax\ifmmode{{\particletwo D}^{\star-}}
\else{{\particletwo D}$^{\star-}$}\fi}
 \def\Dstarpm{\relax\ifmmode{{\particletwo D}^{\star\pm}}
\else{{\particletwo D}$^{\star\pm}$}\fi}
 \def\Dstarmp{\relax\ifmmode{{\particletwo D}^{\star\mp}}
\else{{\particletwo D}$^{\star\mp}$}\fi}

%D star

 \def\Ddoublestar{\relax\ifmmode{{\particletwo D}^{\star\star}}
\else{{\particletwo D}$^{\star\star}$}\fi}
 \def\Ddoublestarbar{\relax\ifmmode{\overline{{\particletwo D}}
\tiny^{\star\star}}
	\else{$\overline{{\particletwo D}}\tiny^{\star\star}$}\fi}

 \def\Ddoublestarzero{\relax\ifmmode{{\particletwo D}^{\star\star0}}
	\else{{\particletwo D}$^{\star\star0}$}\fi}
 \def\Ddoublestarzerobar{\relax\ifmmode
{\overline{{\particletwo D}}\tiny^{\star\star0}}
	\else{$\overline{{\particletwo D}}\tiny^{\star\star0}$}\fi}

 \def\Ddoublestarplus{\relax\ifmmode{{\particletwo D}^{\star\star+}}
	\else{{\particletwo D}$^{\star\star+}$}\fi}
 \def\Ddoublestarminus{\relax\ifmmode{{\particletwo D}^{\star\star-}}
	\else{{\particletwo D}$^{\star\star-}$}\fi}
 \def\Ddoublestarpm{\relax\ifmmode{{\particletwo D}^{\star\star\pm}}
	\else{{\particletwo D}$^{\star\star\pm}$}\fi}
 \def\Ddoublestarmp{\relax\ifmmode{{\particletwo D}^{\star\star\mp}}
	\else{{\particletwo D}$^{\star\star\mp}$}\fi}

%B star

 \def\Bstar{\relax\ifmmode{{\particletwo B}^\star}
\else{{\particletwo B}$^\star$}\fi}
 \def\Bstarbar{\relax\ifmmode{\overline{{\particletwo B}}\tiny^\star}
	\else{$\overline{{\particletwo B}}\tiny^\star$}\fi}

 \def\Bstarzero{\relax\ifmmode{{\particletwo B}^{\star0}}
\else{{\particletwo B}$^{\star0}$}\fi}
 \def\Bstarzerobar{\relax\ifmmode{\overline{{\particletwo B}}\tiny^{\star0}}
	\else{$\overline{{\particletwo B}}\tiny^{\star0}$}\fi}

 \def\Bstarplus{\relax\ifmmode{{\particletwo B}^{\star+}}
\else{{\particletwo B}$^{\star+}$}\fi}
 \def\Bstarminus{\relax\ifmmode{{\particletwo B}^{\star-}}
\else{{\particletwo B}$^{\star-}$}\fi}
 \def\Bstarpm{\relax\ifmmode{{\particletwo B}^{\star\pm}}
\else{{\particletwo B}$^{\star\pm}$}\fi}
 \def\Bstarmp{\relax\ifmmode{{\particletwo B}^{\star\mp}}
\else{{\particletwo B}$^{\star\mp}$}\fi}

 \def\Vud{\relax\ifmmode{{\rm V}_{ud}}\else{{\rm V}$_{ud}$}\fi}
 \def\Vcd{\relax\ifmmode{{\rm V}_{cd}}\else{{\rm V}$_{cd}$}\fi}
 \def\Vtd{\relax\ifmmode{{\rm V}_{td}}\else{{\rm V}$_{td}$}\fi}
 \def\Vus{\relax\ifmmode{{\rm V}_{us}}\else{{\rm V}$_{us}$}\fi}
 \def\Vcs{\relax\ifmmode{{\rm V}_{cs}}\else{{\rm V}$_{cs}$}\fi}
 \def\Vts{\relax\ifmmode{{\rm V}_{ts}}\else{{\rm V}$_{ts}$}\fi}
 \def\Vub{\relax\ifmmode{{\rm V}_{ub}}\else{{\rm V}$_{ub}$}\fi}
 \def\Vcb{\relax\ifmmode{{\rm V}_{cb}}\else{{\rm V}$_{cb}$}\fi}
 \def\Vtb{\relax\ifmmode{{\rm V}_{tb}}\else{{\rm V}$_{tb}$}\fi}
 \def\u{\relax\ifmmode{{\rm u}}\else{{\rm u}}\fi}

}
\conventionone
\pagestyle{plain}
\thispagestyle{myheadings}
\markboth{\hfil}{\kern2.1in\vbox{\hbox to 5in{\hfil\bf UCSB-94-01}
                 \vskip3pt plus 2pt minus 3pt
                 \hbox to 5in{\hfil January, 1994}
                 \vskip3pt plus 2pt minus 3pt
                 \hbox to 5in{\hfil 
                 \vskip3pt plus 2pt minus 3pt
  \hbox to 5in{\hfil\tt URL http://w4.lns.cornell.edu%
/public/TALK/1993/Index.html}}}
\begin{document}
\title{Heavy Quark Hadronic Weak Decays from CLEO-II}
\author{Harry N. Nelson\footnotemark[1]\ \\
       {\it Department of Physics} \\
       {\it University of California } \\
       {\it Santa Barbara, California 93106-9530, USA}}

\abstract{\rightskip=1.5pc
          \leftskip=1.5pc
We present preliminary results from the CLEO-II collaboration
on a variety of hadronic final states of mesons
containing heavy quarks.  In particular, the
pattern of 2-body \B\ decays is now decisively
different that that of \D\ and \K\ decays;
perhaps a consequence will be that
$\tau_{\BM}<\tau_{\BZB}$.
We have
observed `wrong-sign' $\DZ\sto\KP\PIM$ decays,
which are probably due to a doubly Cabibbo-suppressed
transition.}

\maketitle

\def\thefootnote{\fnsymbol{footnote}}
\footnotetext[1]{Invited Talk Presented
at the International Europhysics Conference on {\bf High Energy
Physics}, Marseille, July 22 - July 28, 1993; supported by the
U.S. Department of Energy Award No. DE--FG03--92--ER40618-L.}
\vspace{2.4mm}
{\bf \noindent \underline{Introduction}}
\vspace{0.9mm}
\par
\nobreak
We present preliminary results on the decays
of mesons containing $b$ and $c$ quarks to
a variety of hadronic final states.   The data
sample for these analyses is typically
$1-1.8{\rm fb}^{-1}$ accumulated by the CLEO-II
detector, 2/3 of which is on the \USSSS,
and 1/3 of which is in the continuum just below that
resonance.

 Of primary importance are the high statistics
measurements of the decays of \B-mesons to two
body final states.  The evidence is now 
that the description of decays to two body final states for
\D\ and \K\ mesons {\it does not pertain for\/} \B's.

 We present results on inclusive
measurements of \D\ and \PS\ mesons in \B\ decays.
Also, results on Cabibbo-suppressed decays of \D\ mesons,
the observation of the wrong-sign decay $\DZ\sto\KP\PIM$,
and precision measurement of absolute branching ratios for
the \DZ\ and \DP\ are presented.
 
\vspace{2.3mm}
{\bf \noindent \underline{\boldmath Two Body Decays of \B's}}
\vspace{0.9mm}
\par
\nobreak
Consider the generic Cabibbo-favored
decay of a flavored pseudoscalar
meson with one light quark,
\eM, to two pseudoscalars.
The neutral pseudoscalar, \eMZ, can
decay either to a charged final state $-+$
or a neutral final state $(00)$; the charged
pseudoscalar, \eMP, decays to a mixed charge
final state, $0+$; consider 
$\Gamma(\eMZ\sto-+)/\Gamma(\eMP\to0+)$.  In the
kaon system, due to the \diha\ rule:
\begin{equation}
\Gamma(\KZB\sto\PIP\PIM)/\Gamma(\KM\sto\PIM\PIZ)\approx225
\end{equation}
In the \D\ system, where the relative enhancement of the
amplitude that produces the smallest change in isospin
is not as prominent,
\begin{equation}
\Gamma(\DZ\sto\KM\PIP)/\Gamma(\DP\sto\KZB\PIP)\approx3.6
\end{equation}
However, the results we present here indicate, assuming
$\tau_{\BM}=\tau_{\BZB}$, and that the
\USSSS\ decays equally to \BP\BM\
and \BZ\BZB\ $(f_{+-}=f_{00})$,
\begin{equation}
\Gamma(\BZB\sto\DP\PIM)/\Gamma(\BM\sto\DZ\PIM)\approx0.6\pm0.1
\end{equation}
decisively {\it less\/} than unity.  Because the ratio
$\Gamma(-+)/\Gamma(0+)$ is near to unity,
the spectator quark 
processes shown in Fig.~\ref{fig:spectators}, rather
than processes with more complicated light quark
interactions in the final state,
presumably dominate the two-body
decay amplitudes for the \B\ system.  Because
$\Gamma(-+)/\Gamma(0+)<1$, the two
amplitudes for \BM\ decay that lead to identical
final states add {\it constructively}.

\epsfxsize=3.0in
\begin{figure}[ht]
\hbox{\hfill\hskip0.1in\epsffile{spectators.eps}\hfill} 
\caption{Spectator Diagrams for Two-Body \B\ Decay:
(a) External, which under the assumption of factorization
can be related to an exclusive semileptonic amplitude,
and (b) Internal, which can suffer color suppression.
For the \BM, the two amplitudes add {\it constructively},
according the results presented here.}
\label{fig:spectators}
\end{figure}
\vspace{2.3mm}

\begin{table}[ht]
\begintable
            Mode         | ${\cal B}$ Assumed     | Source \cr
$\DZ\sto\KM\PIP$         | $(3.91\pm0.10)\%$ | CLEO-II \nr
$\DZ\sto\KM\PIP\PIZ$      | $(12.1\pm1.1)\%$  | PDG    \nr
$\DZ\sto\KM\PIP\PIP\PIM$ | $(8.0\pm0.5)\%$   | PDG     \nr 
$\DP\sto\KM\PIP\PIP$     | $(10.0\pm1.4)\%$  | CLEO-II \cr
$\DSP\sto\DZ\PIP$        | $(67.9\pm2.3)\%$  | CLEO-II \nr
$\DSZ\sto\DZ\PIZ$        | $(62.5\pm4.2)\%$  | CLEO-II
\endtable
\caption{ Charm Decay Modes and Branching Ratios
used in the \B\ reconstructions.}
\label{tab:dmodes}
\end{table}
\vspace{2.3mm}

The reconstructed \D\ decay modes are shown in Table~\ref{tab:dmodes}.
Two variables, the beam constrained mass, 
$M^2_{\B}=E^2_{\rm beam}-(\sum_i\vec{p_i})^2$, and the
energy difference with the beam, $\Delta E =E_{\rm beam}-(\sum_i E_i)$
where the sums run over the particles assigned to the $\D(\overline{u}d)$
system, are important in the \B\ reconstruction.  Typically
$\sigma_{M_{\B}}\approx2.6\,{\rm MeV}$, and is insensitive to the
final state mode, while $\sigma_{\Delta E}\approx15-40\,{\rm MeV}$
and is sensitive to the final state mode. 

\epsfxsize=3.0in
\begin{figure}[ht]
\hbox{\hfill\hskip0.1in\epsffile{bexcl_dnorm.eps}\hfill} 
\caption{Beam constrained mass ($M_{\B}$) distributions for
(a) $\BM\sto\DZ\PIM$ decays; 
(b) $\BM\sto\DZ\RHM$ decays;
(c) $\BZB\sto\DP\PIM$ decays;
and (d) $\BZB\sto\DP\RHM$ decays.}
\label{fig:typsig}
\end{figure}
\vspace{2.3mm}

Typical signals in the $\B\sto\D(\PI{\rm or}\RH)$ modes are
shown in Fig.~\ref{fig:typsig}.  The background function
is determined in several ways, including studies of the
sidebands and Monte Carlo simulations: the background function
shape is linear far from the \B\ mass, and parabolic just
under the \B\ mass.
Branching ratio results for $+-$ and $0-$ modes are given
in Tables~\ref{tab:resone} and~\ref{tab:restwo}, in which
the assumption that the \USSSS\ decays equally to \BP\BM\
and \BZ\BZB\ $(f_{+-}=f_{00})$ is made.

\begin{table}[ht]
\begintable
 \BZB$\sto$ & \# & ${\cal B}(\%)$ \cr 
 \DP\PIM & 76\PM10 & $0.22^{\PM 0.03}_{\PM 0.02 \PM 0.03}$  \cr
\DSP\PIM & 73\PM10 & $0.27^{\PM 0.04}_{\PM 0.04 \PM 0.013}$ \cr
 \DP\RHM & 86\PM11 & $0.62^{\PM 0.08}_{\PM 0.08 \PM 0.09}$  \cr
\DSP\RHM & 52\PM8  & $0.74^{\PM 0.11}_{\PM 0.13 \PM 0.03}$
\endtable
\caption{Two body decay modes of the \BZB\@. The top error
is statistical, on the inner bottom is intrinsic systematic
error, and on the outer bottom is the extrinsic systematic
error from, for example, errors in \D\ branching ratios.}
\label{tab:resone}
\end{table}
\vspace{2.3mm}

\begin{table}[ht]
\begintable
 \BM$\sto$  & \# & ${\cal B}(\%)$ \cr     
\DZ\PIM  & 302\PM22 & $0.47^{\PM 0.03}_{\PM 0.05 \PM 0.02}$  \cr
\DSZ\PIM & 93\PM12  & $0.50^{\PM 0.06}_{\PM 0.07 \PM 0.04}$  \cr
\DZ\RHM  & 248\PM22 & $1.07^{\PM 0.10}_{\PM 0.16 \PM 0.04}$  \cr
\DSZ\RHM & 92\PM12  & $1.41^{\PM 0.19}_{\PM 0.13 \PM 0.11}$
\endtable
\caption{Two body decay modes of the \BM\@.  The error notation
is the same as the previous table.}
\label{tab:restwo}
\end{table}
\vspace{8mm}

One can see in all cases that ${\cal B}(\BM\sto0-)>{\cal B}(\BZB\sto+-)$.
One simple physical explanation is that the diagrams of Fig.~1(a) and
Fig.~1(b) add constructively for the \BM\@.

No evidence exists in our data sample for the mode $\BZB\sto00$.
The plots for $M_{\B}$ for the various modes are shown in
Fig.~\ref{fig:aytoo}.  Based upon the absence of signal in these
plots, one arrives at the limits in Table~\ref{tab:aytoo}.  Note
that the ratio $\Gamma(00)/\Gamma(+-)$ is at least less than
$1/4$ for the \BZB, in marked contrast to the situation for the
\DZ and the \KZB, where this ratio is typically $1/2$.

\epsfxsize=3.0in
\begin{figure}[ht]
\hbox{\hfill\hskip0.1in\epsffile{bexcl_fig28.eps}\hfill} 
\caption{Beam constrained mass ($M_{\B}$) distributions for
(a) $\BZB\sto\DZ\PIZ$ decays; 
(b) $\BZB\sto\DSZ\PIZ$ decays;
(c) $\BZB\sto\DZ\RHZ$ decays;
and (d) $\BZB\sto\DSZ\RHZ$ decays.  The solid curves show just the
background shape, the dotted curves the 90\% CL upper limit.}
\label{fig:aytoo}
\end{figure}
\vspace{2.3mm}

\begin{table}[ht]
\begintable
 \BZB$\rightarrow$ & ${\cal B}\%$ (90\% C.L.) & %
$\Gamma(00)\over{\Gamma(+-)}$ \% & BSW (\%) \cr
 \DZ\PIZ & $<0.03$ & $<14$ & $76\vert{a_2\over a_1}\vert^2$ \cr
 \DSZ\PIZ & $<0.06$ & $<22$ & 
 $84\vert{a_2\over a_1}\vert^2$ \cr
 \DZ\RHZ & $<0.08$ & $<13$ & 
 $22\vert{a_2\over a_1}\vert^2$ \cr
 \DSZ\RHZ & $<0.17$ & $<23$ & 
$32\vert{a_2\over a_1}\vert^2$ \endtable
\caption{Limits on decays of the type $\BZ\sto00$, which
can proceed via the internal spectator amplitude of Fig.~1(b).
In addition to $f_{+-}=f_{00}$, $\tau_{\BM}=\tau_{\BZB}$ is assumed for
all extractions of the BSW parameters $a_1$ and $a_2$.}
\label{tab:aytoo}
\end{table}
\vspace{2.3mm}

The two body decay data can be described by the phenomenology
of Bauer, Stech, and Wirbel (BSW)[1], where the external spectator in 
Fig.~\ref{fig:spectators}(a) is associated with the coefficient
$a_1$, and the internal spectator in Fig.~\ref{fig:spectators}(b)
is associated with the coefficient $a_2$.  From the decays
$\BZB\sto+-$, which are purely external spectator, one can
infer $|a_1|=0.98\pm0.03\pm0.04\pm0.09$, as detailed in
Table~\ref{tab:ayone}.  One can also test the correctness
of the association of $\BZB\sto+-$ with the external spectator
by relating its branching ratio to $\B\sto\D\ell\nu$, an
association known also as factorization.  The physical content
is simply the replacement of the hadronization of the 
$W^-\sto\overline{u}d\sto\pi^-$ with $W^-\sto\ell^-\overline{\nu}$.
Factorization predicts ${\cal B}(\BZB\sto\DSP\PIM)=
6\pi^2{c_1^2} f_{\pi}^2\vert V_{ud}\vert^2\!\times\! 
{{d {\cal B}}\over{dQ^2}}(B\!\to\!D^* \L~\nu)\vert_{Q^2=m_{\pi}^2} 
=(0.26\PM0.04\%)$, and ${\cal B}(\BZB\sto\DSP\RHM)=
6\pi^2{c_1^2} f_{\rho}^2\vert V_{ud}\vert^2\!\times\! 
{{d {\cal B}}\over{dQ^2}}(B\!\to D^*\!\L~\nu)\vert_{Q^2=m_{\rho}^2}$=
$(0.75\PM0.10\%)$, in good agreement with the measurements.

\begin{table}[ht]
\begintable
 \BZB$\to$ & ${\cal B}$(\%) & BSW \cr 
\DP\PIM  & 0.22\PM0.05  & 0.264$\vert a_1\vert^2$    \nr
\DSP\PIM & 0.27\PM0.05  & 0.254$\vert a_1\vert^2$    \nr
\DP\RHM  & 0.62\PM0.14  & 0.621$\vert a_1\vert^2$    \nr
\DSP\RHM & 0.74\PM0.17  & 0.702$\vert a_1\vert^2$
\endtable
\caption{Comparison of measured $\BZB\sto+-$ branching ratios
with the BSW parameterization}
\label{tab:ayone}
\end{table}

We see, from
Table~\ref{tab:aytoo}, that the absence of $\BZB\sto00$ modes
imply that $|a_2|<0.5$ or so.  There are two ways in which we
obtain increased sensitivity to $a_2$: first, for the \BM\ decays,
in the BSW phenomenology, the external and internal amplitudes
coherently interfere, so the rates for $\BM\sto0-$ are crudely
$\propto|a_1+a_2|^2$, yielding a linear sensitivity to $a_2$ in the
interference term; second, we can measure the modes produced
by the internal spectator diagram where the \W\ hadronizes as
a $\overline{c}s$ rather than $\overline{u}d$, such as
$\BZB\sto\PS\KSH$.  For the first method, define:
\begin{eqnarray}
R_1 & = {{\cal B}(\BZB\to\DP\PIM) \over {\cal B}(\BM\to\DZ\PIM)}
                & = {1\over{(1 + 1.23 a_2/a_1)^2}}    \\
R_2 & = {{\cal B}(\BZB\to\DSM\PIM) \over {\cal B}(\BM\to\DSZ\PIM)}
                & = {1\over{(1 + 1.292 a_2/a_1)^2}}   \\
R_3 & = {{\cal B}(\BZB\to\DP\RHM) \over {\cal B}(\BM\to \DZ\RHM) }
                & = {1\over{(1 + 0.662 a_2 /a_1)^2}}  \\
R_4 & = {{\cal B}(\BZB\to\DSM\RHM) \over {\cal B}(\BM\to\DSZ\RHM)}
                & \approx {1\over{(1 + 1.5 a_2/a_1)^2}}
\end{eqnarray}

With these definitions, we find the results given in 
Table~\ref{tab:aytwoint}, which indicate $a_2/a_1\approx0.24$.
Note the relative sign is {\it positive}, in contradiction to
the destructive interference obtained in the BSW analysis of the
analogous charm decays.

\begin{table}[ht]
\begintable
Ratio &${a_2\over a_1} =-0.24 $ & ${a_2\over a_1} =0.24 $ & {\bf CLEO-II} \cr
$R_1 $& 2.0  & 0.59 & $ 0.56 \pm 0.09 \pm 0.11$ \nr
$R_2 $& 2.1  & 0.58 & $ 0.64 \pm 0.06 \pm 0.05$ \nr
$R_3 $& 1.4  & 0.74 & $ 0.69 \pm 0.11 \pm 0.12$ \nr
$R_4 $& 1.3  & 0.54 & $ 0.63 \pm 0.07 \pm 0.05$ 
\endtable
\caption{Estimation of $a_2$ by interference in $\BM\sto0-$
decays.}
\label{tab:aytwoint}
\end{table}

When the \W\ hadronizes as $\overline{c}s$, the internal
spectator can produce the decays $\B\sto\PS\K$.  The decays
of the \BZB\ of this type produce CP eigenstates, and are
expected to be useful in the measurement of CP violation in
the $\BZ\!-\!\BZB$ system, in particular to extract $\sin{2\beta}$.
The CLEO-II signals in these modes, where the $\PS\sto\ell^+\ell^-$,
are shown in Fig.~\ref{fig:kjpsi}.  The numbers for extraction
of $a_2$ are shown in Table~\ref{tab:kjpsi}, and yield
$|a_2|=0.25\pm0.013\pm0.006\pm0.02$, in agreement with the
determination from interference.

\epsfxsize=3.0in
\begin{figure}[ht]
\hbox{\hfill\hskip0.1in\epsffile{bexcl_psi.eps}\hfill}
\caption{Beam constrained mass ($M_{\B}$) distributions for
(a) $\BM\sto\PS\KM$ decays; 
(b) $\BZB\sto\PS\KSH$ decays;
(c) $\BM\sto\PS\KSM$ decays;
and (d) $\BZB\sto\PS\KSZB$ decays.}
\label{fig:kjpsi}
\end{figure}
\vspace{2.3mm}

\begin{table}[ht]
\begintable
 \BZB$\to$ & ${\cal B}(\%)$ | BSW (\%) | ${\cal B}(\%)$  &
\BM$\rightarrow$ \cr      
 \PS\KSH & $0.08^{\PM0.03}_{\PM0.01}$ | $1.82\vert a_2\vert^2$ |
                 $0.11^{\PM0.02}_{\PM0.01}$ & \PS\KM \nr
 \PS\KSZB & $0.19^{\PM0.04}_{\PM0.02}$ | $2.93\vert a_2\vert^2$ |
                 $0.21^{\PM0.06}_{\PM0.03}$ &  \PS\KSM
\endtable
\caption{ Measurement of $|a_2|$ by rate of $\B\sto\PS\K$ decays.}
\label{tab:kjpsi}
\end{table}

To conclude this discussion of the two body decays of the \B:
given that a number of branching ratios for the \BM\ are greater
than those for the \BZB, one can wonder whether the
oft-quoted prediction that $\tau_{\BM}>\tau_{\BZB}$ really has a
solid foundation.  One can see that differences
between exclusive $\BM\sto0-$ and $\BZB\sto+-$ partial rates where the
\W\ hadronizes as $\overline{u}d$, will wash out in the inclusive
decay rate: partial widths when the \W\ hadronizes as $\overline{c}s$
or couples to leptons are surely the same between \BM\ and \BZB\@.
What is hard to see is how the remaining decay rates, predominantly
high multiplicity decays where the \W\ hadronizes $\overline{u}d$,
could push the inclusive \BZB\ decay rate higher than the \BM\@.

{\bf \noindent\
\underline{\boldmath Inclusive measurements of \D's and $J/\psi$'s}}
\vspace{0.9mm}
\par
\nobreak
We have recently made new measurements of the inclusive branching
ratios of \B\ mesons to various openly charmed and hidden charmed
mesons.  The statistics involved in these measurements is
much better than earlier results: for example, about 1500 events
are used to measure $\B\sto\PS X$.
These measurements are summarized in Table~\ref{tab:inclus}.
Whether the excess of \DSZ\ relative to \DSP\ is due to isospin
breaking in the decay sequence of excited \D's, $f_{+-}\neq f_{00}$,
or $\tau_{\BM}<\tau_{\BZB}$ remains to be seen.

\begin{table}[ht]
\begintable
  $\B\sto$           &  ${\cal B}$ (\%)             \cr
  $\DZ X$            & $59.1\pm 2.3\pm2.1\pm1.6$    \nr
   $\DP X$           & $20.2\pm1.3\pm0.9\pm2.8$     \nr
   $\DSZ X$          & $25.1\pm1.9\pm1.2\pm1.7$     \nr
   $\DSP X$          & $20.6\pm1.5\pm0.9\pm0.7$     \cr
$\DZ_{\rm direct} X$ & $19.9\pm3.1\pm1.0$           \nr
$\DP_{\rm direct} X$ & $14.3\pm1.6\pm2.3$           \cr
   $\PS X$           & $1.10\pm0.05\pm0.08$         \nr
   $\PSP X$          & $0.28\pm0.05\pm0.05$ 
\endtable
\caption{Results on inclusive branching ratios.  The
second systematic error, when given, reflects the extrinsic
systematic from propagation of errors on branching ratios
used in reconstruction.}
\label{tab:inclus}
\end{table}

\vspace{2.3mm}
{\bf\boldmath \noindent \underline{$D\PI\PI$}}
\vspace{0.9mm}
\par
\nobreak
The CsI calorimeter of CLEO-II has allowed the observation
of the decay modes $\DP\sto\PIP\PIZ$ and $\DZ\sto2\PIZ$.
The $\DP\sto\PIP\PIZ$ signal is shown in Fig.~\ref{fig:ppp}.
CLEO-II results on all three $\PI\PI$ decay modes are given
in Table~\ref{tab:ppp}. 

One can see from Table~\ref{tab:ppp} and the \D\ lifetimes
that $\Gamma(-+)/\Gamma(0+)=1.19\pm0.26$, which is rather
low for the \D\ system.  Before concluding that this
process is spectator driven, however, note
$\Gamma(00)/\Gamma(-+)=0.63\pm0.12$, which is similar
to the \K\ system, so an isospin analysis is appropriate.
The result of such an analysis is that the ratio of
$\Delta I=2$ to $\Delta I=0$ amplitudes, 
$|A_2/A_0|=0.72\pm0.13\pm0.11$, which is far greater
than the \K\ system, while 
$\delta_2-\delta_0=82^\circ\pm8^\circ\pm5^\circ$,
a large phase shift.

\epsfxsize=3.0in
\begin{figure}[ht]
\hbox{\hfill\hskip0.1in\epsffile{ppp0.eps}\hfill}
\caption{\PIZ\PIM mass; the peak at the \DP\ mass is
evident.  The background is from \K\RH\ and \KS\PI\@.
Data are the solid circles, the connected lines are Monte Carlo.}
\label{fig:ppp}
\end{figure}
\vspace{2.3mm}

\begin{table}[ht]
\begintable
  $\D\sto$           &  ${\cal B}$ (\%)             \cr
  $\PIM\PIP$         &  $0.136\pm0.012\pm0.012$     \nr
  $\PIZ\PIZ$         &  $0.086\pm0.016\pm0.015$     \nr
  $\PIZ\PIP$         &  $0.24\pm0.05\pm0.05$        \endtable
\caption{Results on $\D\sto2\PI$ branching ratios}
\label{tab:ppp}
\end{table}

\vspace{2.3mm}
{\bf \noindent\underline{\boldmath Wrong Sign Decays of the $D^0$}}
\vspace{0.9mm}
\par
\nobreak
We have observed a signal from tagged $\DZ$'s decaying
to $\KP\PIM$.  We tag the $\DZ$ with the charge of the
soft pion from $\DSP(\DSM)\sto\DZ\PIP(\DZB\PIM)$.  The
$\KP\PIM$ could either result from the doubly Cabibbo-suppressed
decay of the $\DZ$, or from $\DZ\sto\DZB$ mixing, followed
by Cabibbo-allowed decay of the $\DZB$.

The basic quantities of the analysis are the mass of the
putative $\KP\PIM$ system, $m_{\KP\PIM}$,
and the mass difference computed
by addition of the soft pion to this system, $\delta m$.
Backgrounds from $\K/\PI$ misidentification will tend
to peak in $\delta m$, but $m_{\KP\PIM}$ will not peak at $m_{\DZ}$; 
in fact, any $m_{\KP\PIM}$ that reconstructs near $m_{\DZ}$ under the
hypothesis that a misidentification occurred is cut.
Backgrounds from random slow pion tags
will tend not to peak in $\delta m$.

The distribution of $\delta m$ for $\DZ\sto\KP\PIM$ candidates is
shown in Fig.~\ref{fig:dcsd}(a).  For this figure, hard $\K/\PI$
separation cuts have been made.  A signal region is defined
in $\delta m$, and the projection of this signal region on the
$m_{\KP\PIM}$ axis is shown in Fig.~\ref{fig:dcsd}(c).  Sidebands
in $\delta m$ are projected onto the $m_{\KP\PIM}$ axis
and shown in Fig.~\ref{fig:dcsd}(d); little peaking is evident.
The difference between (c) and (d) is the signal, shown
if Fig.~\ref{fig:dcsd}(b), and is 14.9 events on an expected
background of 0.9, a rather significant result.

\epsfxsize=3.0in
\begin{figure}[ht]
\hbox{\hfill\hskip0.1in\epsffile{dcsd.eps}\hfill}
\caption{$\DZ\sto\KP\PIM$ candidates, (a) projected
on the $\delta m$ axis; (c) after a cut around the
expected $\delta m$, and projected on the $m_{\KP\PIM}$
axis, (d) taken from sidebands of $\delta m$ and projected
on the $m_{\KP\PIM}$ axis; and (b), the difference between
(c) and (d), showing the signal of 14.9 events.}
\label{fig:dcsd}
\end{figure}
\vspace{2.3mm}

Having established the signal, the particle ID cuts are relaxed
to get a measure of the branching ratio.  The result is:
\begin{eqnarray}
R\equiv&{\Gamma({\DZ\{\sto \DZB\}\sto\KP\PIM})\over\Gamma({\DZ\sto\KM\PIP})}
= & \!\!\!\!\!\!\![0.77\pm0.25\pm0.25]\%\\
=& &\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!(2.92\pm0.95\pm0.95)\tan^4{\theta_c}
\end{eqnarray}
where $\theta_c$ is the Cabibbo angle.

\vspace{2.3mm}
{\bf\boldmath\noindent\underline{Absolute 
$D^0$ and $D^+$ Branching Ratios}}
\vspace{0.9mm}

\nobreak
CLEO-II has also used the soft pions \DS\ decays to provide
the normalization in new, precise measurements of the
absolute branching ratios for $\DZ\sto\KM\PIP$ and
$\DP\sto\KM\PIP\PIP$.  The possibility of soft pion tags
from $\SIZB\sto\PIP\LCMB$ has been excluded in a Monte Carlo
independent way.  The result for the $\DZ$, where the
tags are only \PIP\ from the \DSP,
is:
\begin{equation}
{\cal B}(\DZ\sto\KM\PIP)=(3.912\pm0.082\pm0.17)\%
\end{equation}
The largest contribution to the systematic error results from
uncertainty in track reconstruction efficiency.

For the $\DP$ decay, the soft $\PIZ$ from the $\DSP$ must be
be used, which brings in background from $\DSZ\sto\DZ\PIZ$.
The analysis is specially designed to suppress systematic
uncertainty from the $\DS$ branching ratios.  The result is:
\begin{equation}
{\cal B}(\DP\sto\KM\PIP\PIP)=(10.0\pm0.5\pm0.7\pm1.4)\%
\end{equation}
The second systematic error results only from uncertainty
on the relative efficiency of soft $\PIZ$ to soft $\PIP$
reconstruction.

\vspace{2.3mm}
{\bf\noindent\underline{Conclusions}}
\vspace{0.9mm}
\par
\nobreak
CLEO-II's large data sample has been exploited to further
understanding of a number of hadronic weak decays of heavy
mesons.  There is clear evidence that a number of two
body branching ratios for the \BM\ are larger than the
analogous branching ratios for the \BZB\@.  It remains
to be seen whether $\tau_{\BM}<\tau_{\BZB}$.

\vspace{2.3mm}
{\bf \noindent\underline{Acknowledgements}}
\vspace{0.9mm}

\nobreak
Many thanks to John Carr for his tolerance and persistence.

\vspace{2.3mm}
{\bf \noindent\underline{References}}
\vspace{0.9mm}
\par
\def\PRref#1&#2&(#3)#4{\unskip\ #1~\bf#2\rm, (#3) #4}
\def\ZPC{\it Z. Phys. C}
\def\etal{{\it et al.}}
\noindent
[1] M. Bauer, B. Stech, and M. Wirbel, \PRref\ZPC&29&(1985)637; 
{\it ibid} {\bf 34}, (1987) 103; {\it ibid} {\bf 42}, (1989) 671.


\end{document}

