%Paper: 
%From: leike@znsun1.ifh.de (Leike)
%Date: Thu, 26 Aug 93 22:56:00 MET

%  Ralf B\"onisch, Arnd Leike

%  EXPERIMENTAL CONSTRAINTS ON THE SCALE OF NEW PHYSICS
%  IN TOP CONDENSATE MODELS

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\begin{titlepage}
\begin{flushleft}
{\bf DESY 93-111 \\ LMU-04/93} \\ {\em August 1993}
\end{flushleft}
\vspace{1.5cm}
\begin{center}
{\bf EXPERIMENTAL CONSTRAINTS ON THE SCALE OF NEW PHYSICS
\\ IN TOP CONDENSATE MODELS}
\end{center}
\vspace{1cm}
\begin{center}{\bf Ralf B\"{O}NISCH$^1$
 and Arnd LEIKE$^2$}

\vspace{1cm}
$^{1}$Ludwig-Maximilians-Universit\"{a}t M\"{u}nchen, Sektion Physik  \\
80333 M\"{u}nchen, Germany \\
\vspace{0.2cm}
$^{2}$DESY - Institut f\"ur Hochenergiephysik, \\
Platanenallee 6, 15735 Zeuthen, Germany
\end{center}
\vspace{1cm}
\begin{abstract}
We obtain mass limits on the extra neutral gauge boson which is predicted in a
model with hidden gauge symmetry and
dynamical breaking of the electroweak symmetry by a top quark condensate.
For typical model assumptions, present LEP data exclude masses below 3\,TeV.
With LEP200 or an electron-positron collider of a c.m. energy
of 500 GeV masses below 15\,TeV or 50\,TeV could be excluded, respectively.
Such high mass limits allow the calculation of the observables used in the
analysis in the context of the Nambu-Jona-Lasinio model.
\end{abstract}
\vspace{2cm}
\end{titlepage}
\renewcommand{\thefootnote}{\fnsymbol{footnote}}
% ===============================================================
%
\section{Introduction}
%
It is well known that precision experiments at $e^+e^-$ colliders
can give indirect limits on masses of extra neutral gauge bosons.
However, the best mass limits on weakly coupled gauge bosons are usually
set by direct production at hadron colliders.
In this letter, we consider a model which contains an extra, strongly coupled
neutral gauge boson originating in top condensate models. We derive
mass limits from present and future $e^+e^-$ colliders
and find that here they
are superior in comparison with hadron colliders.

The large mass of the top quark motivates a specific dynamical
breakdown of the electroweak symmetry by the formation of a top
quark condensate \cite{claro}.
The Top Mode Standard Model (TMSM) possesses
scalar four fermion interactions of Nambu-Jona-Lasinio type instead of
elementary scalar Higgs-fields, \cite{nambu} - \cite{bhl}.
In its minimal form \cite{bhl} it hardly matches the experimentally
allowed top mass window \cite{rho}.
Moreover, the TMSM has been found unsatisfactory for theoretical reasons
concerning predictability beyond the Standard Model (SM) \cite{critics,boe}.
The naturalness requirement demands the scale of next physics beyond the
SM to be in the TeV range.
Here, far below a GUT scale,
one does not expect to already leave the framework of quantum
gauge field theories and the TMSM has never been meant to solve the fundamental
mass problem.
The simple possibility to assume a well-defined gauge theory as the origin
of the NJL-type model \cite{boe} attempts to find the structure beyond the SM
in using the fact of the large top mass.
A variety of gauge extensions to $SU(2)_L \times U(1)_Y \times G$
was proposed on these grounds \cite{boe2,models,boekneur}.
The breaking of non-standard symmetries is thereby
often described by scalar fields and this
does not disturb the concept of looking for structures at the TeV scale.
 The value of the new scale, related to the mass of new bosons,
is essential for theoretical predictions of the models.

In this letter, we derive lower bounds for the mass of
non-standard gauge bosons within the Hidden Symmetry Model \cite{boekneur}
from $e^+e^-$ data.

In section 2 we briefly introduce the features of the Hidden Symmetry Model
needed for the analysis of experimental data. In section 3 we
describe the analysis and discuss the results. We conclude in section 4.
% ===============================================================
%
\section{The Hidden Symmetry Model}
%
The extension to the hidden gauge group $SU(2)_V$
has been discussed in
\cite{bmw} and recently in  \cite{ks}.
It was applied to the top condensate mechanism in
\cite{boe,boekneur}.

Starting point is the symmetry $SU(2)_L \times U(1)_{Y^\pr} \times
SU(2)_V$. [As none of the features of the model, which make
it special for top quark condensation, depends on the dimension
of the hidden group, it could as well be any hidden $SU(N)$ including $U(1)$.]
$U(1)_{Y^\pr}$ differs from the standard $U(1)_Y$ only by the definition
of the gauge coupling constant.
$SU(2)_V$ is a hidden symmetry, i.e.
fermions are standard: they do not possess new degrees of freedom and
transform as singlets.
These local symmetries are broken down to electromagnetism in two steps:
\be  \begin{array} {lcr}
SU(2)_L \times U(1)_{Y^\pr}  \times SU(2)_V
& \stackrel{spontaneously\hspace{.1cm} by\hspace{.1cm} scalars}
{\longrightarrow}& \\
SU(2)_L \times U(1)_{Y}
&\stackrel{dynamically\hspace{.1cm} by\hspace{.1cm} \langle \bar{t}t \rangle}
{\longrightarrow} &
U(1)_{em}
\lb{breakpattern}\end{array}
\ee
The first step looks very much like the spontaneous symmetry breaking
in the SM, but
here SU(2)$_V \times $ U(1)$_{Y^\pr}$ is broken down to U(1)$_Y$.
Diagonalization causes a mixing of primordial U(1)$_Y^\pr$
and SU(2)$_V$ fields
$\bar{B}$ and $\bar{V}$ to a massless $B$ and a massive $v^0$ in the neutral
sector. The mixing angle $\xi$ is given by
\be \sin \xi = \frac{g^\pr}
{\sqrt{ g^{\pr \pr 2} + g^{\pr 2} }}.  \ee
Between the new scale and the Fermi scale, i.e. in the
$SU(2)_L \times U(1)_{Y} $ symmetric phase,
the interaction of neutral gauge bosons with fermions
is given as \cite{boekneur}
% ------------------------
\begin{eqnarray}
{\cal L}_{0} = g J_i^\mu W_{\mu i} + g'\cos\xi J_Y^\mu B_\mu
- g'\sin\xi J_Y^\mu v^0_\mu .
\lb{ww}
\end{eqnarray}
% ------------------------
$J_i^\mu$ and  $J_Y^\mu$ are exactly the SM-isospin and hypercharge currents.
\ \ $g'\cos\xi$\ \ is restricted to have the value of the standard hypercharge
gauge coupling constant. Charged heavy bosons $v^\pm$ do not couple to standard
fermions.

A strong coupling
% ------------------------
\begin{equation}
(g'\sin\xi )^2\frac{2}{18} > \frac{8\pi ^2}{N} = G_c
\lb{gc}\end{equation}
causes the condensation of $\bar{t}t$. Down type quarks do not form
condensates because of a repulsive interaction by means of the hypercharge
quantum numbers. In flavor space, the mass matrix has rank one, so that
finally only the top achieves a mass as wanted \cite{boe2}.
The present model is special in not assuming a heavy top quark.
Instead, the only source of explicit $SU(2)_R$ violation in the SM,
the hypercharge, is used to produce a heavy top and a light bottom quark.

The strongly interacting new sector, eq. (\ref{gc}),
cannot be treated with perturbation theory.
It is handled by ladder
approximation and an expansion in $p^2/M^2_v$,
where $M_v$ is the mass of the new neutral gauge boson and
$p$ is the typical energy scale, i.e. $p^2=M_Z^2$ for LEP I.
Both expansions must be
motivated. The ladder diagrams are dominant in summing over an appropriate
large number $N$ of fermionic degrees of freedom. There is a very close
connection of the large $N$ expansion to the resulting mass matrix \cite{diss}.
In the Hidden Symmetry Model, $N$ is hidden and understood to carry information
of the inner structure of fermions. (It is not related to the size of the
hidden gauge group.) The restriction to first order in $p^2/M^2_v$ allows
the analytical calculation of bound states, because ladder diagrams sum as
geometric series in this limit. This approximation can always be used
as will be shown by experimental limits on $M_v$.
Deviations from these approximations would modify the relation of $\mt$ to the
$\rho$-parameter, as discussed in the minimal TMSM \cite{bhl,paschos}.
Other sources of deviations from those predictions are vector resonances, which
should additionally appear in the gauge models.

A typical model assumption is $N=3$. The corresponding critical coupling is
% ------------------------
\begin{equation}
g'\sin\xi > \nu 2 \pi \sqrt{6}  = 2 \pi \sqrt{6},\ \ \ \nu=\sqrt{3/N}.
\end{equation}
% ------------------------
% ===============================================================
%
\section{Analysis of $e^+e^-$ Data}
%
We now search for mass limits to the extra neutral gauge boson $V$ from
present and future electron-positron colliders.
The remarkable agreement of present experiments with the SM fix its
parameters with high precision and leads
to definite predictions at higher energies.
A direct production of extra neutral gauge bosons in $e^+e^-$ collisions is
very unlikely because of present mass limits from hadron colliders.
Although, it can be observed indirectly, if
one observable deviates from the SM prediction more than
the expected experimental uncertainty.

In our analysis, we take into account statistical and systematic errors as
well as radiative corrections.
We assume an integrated luminosity of
$L_{int}=20 fb^{-1}$ at $\sqrt{s} = 500GeV$ for a linear electron positron
collider (Linac) and $L_{int}=0.5 fb^{-1}$ at $\sqrt{s} = 190GeV$ for LEP200,
which corresponds roughly to one year of running time.
Dominant systematic errors at the Linac (LEP200) are due to luminosity
uncertainty and the errors of lepton and hadron energy measurements of
1\% (0.5\%), 0.5\% (0.5\%) and 1\% (1\%), respectively \cite{EE500}.

The necessary QED corrections are taken into account including a cut
$\Delta$ on the photon energy $E_\gamma /E_{beam} < \Delta = 0.7$. $\Delta$
is needed to remove the radiative tail and to
suppress the background \cite{EE500}.

We use an extended version of the program {\tt ZCAMEL} \cite{EE500} for the
calculation of observables (cross sections and asymmetries). It includes the
full $O(\alpha)$ QED corrections in theories with extra neutral gauge bosons
and soft photon exponentiation \cite{zecorr}.
We include the following observables in our analysis
% ------------------------
\begin{eqnarray}
\label{genobs}
\sigma_t(\bar{l}l),\ A_{FB}(\bar{l}l),
\ R=\sigma_t(\bar{l}l)/\sigma_t(\bar{q}q),\
A_{LR}(\bar{l}l),\\ \nonumber
\ A_{LR}(\bar{q}q),\
 \sigma_t(\bar{b}b),\ A_{FB}(\bar{b}b),
\ A_{LR}(\bar{b}b),\ P_\tau,\ P_\tau^{FB},
\end{eqnarray}
% ------------------------
where $\bar{l}l$ ($\bar{q}q$) refer to the production of leptons (5 quarks),
respectively, and $P_\tau$ and $P_\tau^{FB}$ are $\tau$ polarization
asymmetries.

We found that for LEP200 and for the Linac the total cross section of lepton
production gives the best mass limits to the $V$-boson mass.
For the special case $N=3$, we obtain
% ------------------------
\begin{eqnarray}
\label{lep2}
M_V & > & 15\, TeV, \mbox{\ \ 95\% c.l.\ \ for LEP200},\\ \nonumber
M_V & > & 50\, TeV, \mbox{\ \ 95\% c.l.\ \ for the Linac.}
\end{eqnarray}
% ------------------------
Beam polarization can improve these bounds due to
the left-right asymmetry of hadron production $A_{LR}(\bar{q}q)$.
For $N\ne 3$, the limits are shown in Fig.~1 and Fig.~2.

The mass limits from LEP~I data are different. In a full analysis one has to
constrain the Standard Model parameters, the mass of the extra neutral gauge
boson and its mixing with the $Z$-boson simultaneously \cite{zefitsr}.
LEP data constrain mainly the mixing.
In the Hidden Symmetry Model there is no mixing between
the $Z$ and $V$ by definition because they are mass eigenstates.

A full analysis of LEP data
in the Hidden Symmetry Model has not yet been done.
However, we observed that the leptonic forward-backward asymmetry at the
$Z$-peak $A_{FB}(\bar{l}l)$ is much more sensitive to $M_V$ than the other
observables at LEP.  We obtained an approximate mass limit to the $V$ by
the following procedure: We took the observables
% ------------------------
\begin{equation}
P_\tau,\ P_\tau^{FB},\ A_{FB}(\bar{b}b),\ A_{FB}(\bar{c}c),\ A_{FB}(\bar{q}q),
\end{equation}
% ------------------------
measured at the $Z$-peak \cite{moriond} and their errors and calculated a
prediction for $A_{FB}(\bar{l}l)$. It is, of course, consistent with
the measured value of $A_{FB}(\bar{l}l)$. Demanding that an additional neutral
gauge boson $V$ should not spoil
this consistency leads to the mass limits shown in Fig.~2. For $N=3$, we get
% ------------------------
\begin{equation}
\label{lep1}
M_V > 3\, TeV, \mbox{\ \ 95\% c.l.\ \ for LEP~I}.
\end{equation}
% ------------------------
%
% ----------Fig.1,2-----------------
\ \vspace{1cm}\\
\begin{minipage}[t]{7.8cm}{
%----- Fig. 1 ---
\begin{center}
%-------------------
\hspace{-1.7cm}
\mbox{
\epsfysize=7.0cm
\epsffile[0 0 500 500]{zp3lep12.ps}
}
%----------------
\end{center}
\noindent
{\small\bf Fig.~1: }{\small\it
The LEP mass limits for the additional neutral $V$-boson as function of the
coupling strength.
}
}\end{minipage}
\hspace{0.5cm}
%----------------------------------------
% Fig. 2
\begin{minipage}[t]{7.8cm} {
%----- Fig. 2 ---
\begin{center}
%----------------
\hspace{-1.7cm}
\mbox{
\epsfysize=7.0cm
\epsffile[0 0 500 500]{zp3nlc.ps}
}
%----------------
\end{center}
\noindent
{\small\bf Fig.~2: }{\small\it
The 500 GeV collider mass limits for the additional neutral $V$-boson as
function of the coupling strength.
}
}\end{minipage}
\vspace*{0.5cm}
%------------------------------------------------------------
%

The mass limits (\ref{lep2}), (\ref{lep1}) have a linear dependence on the
coupling constant $g'\sin\xi$, see Fig.~1, Fig.~2.
This is due to the large $V-$fermion coupling enabling us to be sensitive to
$V$-bosons, which are much heavier than the c.m. energy.
Thus, a deviation of any observable from the
SM prediction depends only on the ratio $g'\sin\xi / M_{V}$ and not on
$g'\sin\xi$ and $M_{V}$ separately:
% ------------------------
\begin{equation}
\mbox{SM  } - \mbox{  Hidd. Symm.}
= -\mbox{const.} \frac{(g'\sin\xi)^2}{s-M_{V}^2+i\Gamma_{V} M_{V}}
\approx \mbox{const.}\left(\frac{g'\sin\xi}{M_{V}}\right)^2.
\end{equation}
% ------------------------

The obtained limits on the $V$-mass constrain the mass scale of the hidden
symmetry breaking to be much larger than the mass scale of the electroweak
symmetry breaking, i.e. for all considered electron-positron colliders
$s/M_V^2 \ll 1$.
Hence, higher orders of the
parameter $s/M_V^2$ can be neglected and observables can be calculated
in the Hidden Symmetry Model.
Here we obtain consistency with our preliminary assumption
needed for the experimental analysis.
The case of a light $V$-boson can be also excluded because it would have
shown up in hadron colliders
or by an inconsistency of the observables at LEP with the SM due to its
large couplings to all fermions.

Finally, we mention that
we assumed the absence of unknown non-decoupling resonance effects
of the hidden strong interaction in the observables (\ref{genobs}).
% ===============================================================
\section{Conclusion}
%
Compared to hadron colliders, electron-positron colliders are superior in
setting mass limits to strongly coupled extra neutral gauge
bosons $V$. For the Hidden Symmetry Model considered
here, these bosons must be heavier than 3\,TeV to be consistent with present
LEP data. LEP200 or an $e^+e^-$
collider with a c.m. energy of 500\,GeV would improve these limits to 15\,TeV
or 50\,TeV.

As a consequence, higher orders in $p^2/M_V^2$ can be neglected, so that
ladder diagrams can be summed as usually done in the NJL model and
reliable predictions can be derived.
%
\vspace{1cm}\\ {\Large\bf Acknowledgement\hfill}\vspace{0.5cm}\\
We would like to thank T. Riemann for a careful reading of
the manuscript. \vspace{1cm}\\
%
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\end{document}
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710 D 6926 710 D S 7055 860 M 6984 860 D 6976 796 D 6984 803 D 7005 810 D
7026 810 D 7048 803 D 7062 789 D 7069 767 D 7069 753 D 7062 731 D 7048 717 D
7026 710 D 7005 710 D 6984 717 D 6976 724 D 6969 739 D S 7091 1000 M 7091
1075 D S 7227 1000 M 7227 1075 D S 7364 1000 M 7364 1075 D S 7500 1000 M 7500
1075 D S 1500 1000 M 1500 7000 D S 1500 1000 M 1612 1000 D S 1374 1075 M 1353
1068 D 1339 1046 D 1331 1011 D 1331 989 D 1339 954 D 1353 932 D 1374 925 D
1389 925 D 1410 932 D 1424 954 D 1431 989 D 1431 1011 D 1424 1046 D 1410 1068
D 1389 1075 D 1374 1075 D S 1500 1109 M 1575 1109 D S 1500 1218 M 1575 1218 D
S 1500 1327 M 1575 1327 D S 1500 1436 M 1575 1436 D S 1500 1545 M 1575 1545 D
S 1500 1655 M 1575 1655 D S 1500 1764 M 1575 1764 D S 1500 1873 M 1575 1873 D
S 1500 1982 M 1575 1982 D S 1500 2091 M 1612 2091 D S 1189 2130 M 1189 2137 D
1196 2152 D 1203 2159 D 1217 2166 D 1246 2166 D 1260 2159 D 1267 2152 D 1274
2137 D 1274 2123 D 1267 2109 D 1253 2087 D 1181 2016 D 1281 2016 D S 1367
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1500 2636 M 1575 2636 D S 1500 2745 M 1575 2745 D S 1500 2855 M 1575 2855 D S
1500 2964 M 1575 2964 D S 1500 3073 M 1575 3073 D S 1500 3182 M 1612 3182 D S
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1267 5389 D 1274 5403 D 1274 5418 D 1267 5432 D 1246 5439 D 1217 5439 D S
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1500 6236 M 1575 6236 D S 1500 6345 M 1575 6345 D S 1500 6455 M 1612 6455 D S
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D S 1500 6891 M 1575 6891 D S 1500 7000 M 1575 7000 D S 1500 7000 M 7500 7000
D S 1500 7000 M 1500 6925 D S 1636 7000 M 1636 6925 D S 1773 7000 M 1773 6925
D S 1909 7000 M 1909 6925 D S 2045 7000 M 2045 6925 D S 2182 7000 M 2182 6925
D S 2318 7000 M 2318 6925 D S 2455 7000 M 2455 6925 D S 2591 7000 M 2591 6925
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D S 3136 7000 M 3136 6925 D S 3273 7000 M 3273 6925 D S 3409 7000 M 3409 6925
D S 3545 7000 M 3545 6925 D S 3682 7000 M 3682 6925 D S 3818 7000 M 3818 6925
D S 3955 7000 M 3955 6925 D S 4091 7000 M 4091 6925 D S 4227 7000 M 4227 6925
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D S 6000 7000 M 6000 6925 D S 6136 7000 M 6136 6925 D S 6273 7000 M 6273 6925
D S 6409 7000 M 6409 6925 D S 6545 7000 M 6545 6925 D S 6682 7000 M 6682 6925
D S 6818 7000 M 6818 6925 D S 6955 7000 M 6955 6925 D S 7091 7000 M 7091 6925
D S 7227 7000 M 7227 6925 D S 7364 7000 M 7364 6925 D S 7500 7000 M 7500 6925
D S 7500 7000 M 7500 1000 D S 7500 7000 M 7425 7000 D S 7500 6891 M 7425 6891
D S 7500 6782 M 7425 6782 D S 7500 6673 M 7425 6673 D S 7500 6564 M 7425 6564
D S 7500 6455 M 7425 6455 D S 7500 6345 M 7425 6345 D S 7500 6236 M 7425 6236
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D S 7500 5473 M 7425 5473 D S 7500 5364 M 7425 5364 D S 7500 5255 M 7425 5255
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D S 7500 4818 M 7425 4818 D S 7500 4709 M 7425 4709 D S 7500 4600 M 7425 4600
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480 D 6197 468 D 6185 444 D 6149 432 D 6114 432 D 6078 444 D 6066 468 D S
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D 4192 1433 D 4228 1421 D 4251 1397 D 4263 1350 D 4263 1290 D 4251 1231 D
4228 1195 D 4192 1183 D 4168 1183 D 4132 1195 D 4120 1219 D S 4489 1433 M
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5287 1207 M 5275 1195 D 5287 1183 D 5299 1195 D 5287 1207 D S 2894 1558 M
2752 1558 D 2752 1808 D S 2927 1648 M 2935 1641 D 2942 1648 D 2935 1655 D
2927 1648 D S 2935 1598 M 2935 1498 D S 2992 1598 M 2992 1498 D S 2992 1569 M
3013 1591 D 3027 1598 D 3049 1598 D 3063 1591 D 3070 1569 D 3070 1498 D S
3135 1648 M 3135 1527 D 3142 1505 D 3156 1498 D 3170 1498 D S 3113 1598 M
3163 1598 D S 3233 1701 M 3447 1701 D S 3233 1629 M 3447 1629 D S 3542 1748 M
3542 1760 D 3554 1784 D 3566 1796 D 3590 1808 D 3637 1808 D 3661 1796 D 3673
1784 D 3685 1760 D 3685 1737 D 3673 1713 D 3649 1677 D 3530 1558 D 3697 1558
D S 3840 1808 M 3804 1796 D 3780 1760 D 3768 1701 D 3768 1665 D 3780 1606 D
3804 1570 D 3840 1558 D 3864 1558 D 3899 1570 D 3923 1606 D 3935 1665 D 3935
1701 D 3923 1760 D 3899 1796 D 3864 1808 D 3840 1808 D S 4018 1725 M 4018
1475 D S 4018 1689 M 4042 1713 D 4066 1725 D 4102 1725 D 4125 1713 D 4149
1689 D 4161 1653 D 4161 1629 D 4149 1594 D 4125 1570 D 4102 1558 D 4066 1558
D 4042 1570 D 4018 1594 D S 4245 1808 M 4245 1558 D S 4245 1689 M 4268 1713 D
4292 1725 D 4328 1725 D 4352 1713 D 4375 1689 D 4387 1653 D 4387 1629 D 4375
1594 D 4352 1570 D 4328 1558 D 4292 1558 D 4268 1570 D 4245 1594 D S 4495
1570 M 4483 1558 D 4471 1570 D 4483 1582 D 4495 1570 D 4495 1546 D 4483 1522
D 4471 1510 D S 4959 1689 M 4947 1713 D 4911 1725 D 4875 1725 D 4840 1713 D
4828 1689 D 4840 1665 D 4864 1653 D 4923 1641 D 4947 1629 D 4959 1606 D 4959
1594 D 4947 1570 D 4911 1558 D 4875 1558 D 4840 1570 D 4828 1594 D S 5037
1881 M 5051 1889 D 5073 1910 D 5073 1760 D S 5280 1939 M 5151 1710 D S 5323
1874 M 5323 1881 D 5330 1896 D 5337 1903 D 5351 1910 D 5380 1910 D 5394 1903
D 5401 1896 D 5408 1881 D 5408 1867 D 5401 1853 D 5387 1831 D 5315 1760 D
5415 1760 D S 5485 1701 M 5699 1701 D S 5485 1629 M 5699 1629 D S 5925 1808 M
5806 1808 D 5794 1701 D 5806 1713 D 5842 1725 D 5877 1725 D 5913 1713 D 5937
1689 D 5949 1653 D 5949 1629 D 5937 1594 D 5913 1570 D 5877 1558 D 5842 1558
D 5806 1570 D 5794 1582 D 5782 1606 D S 6092 1808 M 6056 1796 D 6032 1760 D
6020 1701 D 6020 1665 D 6032 1606 D 6056 1570 D 6092 1558 D 6116 1558 D 6151
1570 D 6175 1606 D 6187 1665 D 6187 1701 D 6175 1760 D 6151 1796 D 6116 1808
D 6092 1808 D S 6330 1808 M 6294 1796 D 6270 1760 D 6258 1701 D 6258 1665 D
6270 1606 D 6294 1570 D 6330 1558 D 6354 1558 D 6389 1570 D 6413 1606 D 6425
1665 D 6425 1701 D 6413 1760 D 6389 1796 D 6354 1808 D 6330 1808 D S 6616
1653 M 6675 1653 D 6675 1618 D 6663 1594 D 6639 1570 D 6616 1558 D 6568 1558
D 6544 1570 D 6520 1594 D 6508 1618 D 6497 1653 D 6497 1713 D 6508 1748 D
6520 1772 D 6544 1796 D 6568 1808 D 6616 1808 D 6639 1796 D 6663 1772 D 6675
1748 D S 6747 1653 M 6889 1653 D 6889 1677 D 6877 1701 D 6866 1713 D 6842
1725 D 6806 1725 D 6782 1713 D 6758 1689 D 6747 1653 D 6747 1629 D 6758 1594
D 6782 1570 D 6806 1558 D 6842 1558 D 6866 1570 D 6889 1594 D S 7127 1808 M
7032 1558 D 6937 1808 D S 10 W S 1954 2181 M 1981 2198 D 2008 2216 D 2036
2234 D 2063 2251 D 2090 2269 D 2118 2287 D 2145 2304 D 2172 2322 D 2199 2340
D 2227 2357 D 2254 2375 D 2281 2393 D 2290 2398 D S 2625 2616 M 2636 2623 D
2663 2640 D 2690 2658 D 2717 2676 D 2745 2693 D 2772 2711 D 2799 2729 D 2826
2746 D 2854 2764 D 2881 2782 D 2908 2799 D 2936 2817 D 2961 2834 D S 3296
3051 M 3317 3065 D 3344 3082 D 3372 3100 D 3399 3118 D 3426 3136 D 3454 3153
D 3481 3171 D 3508 3189 D 3535 3206 D 3563 3224 D 3590 3242 D 3617 3259 D
3632 3269 D S 3967 3487 M 3972 3489 D 3999 3507 D 4026 3525 D 4053 3542 D
4081 3560 D 4108 3578 D 4135 3595 D 4162 3613 D 4190 3631 D 4217 3648 D 4244
3666 D 4271 3684 D 4299 3702 D 4303 3704 D S 4639 3922 M 4653 3932 D 4680
3949 D 4708 3967 D 4735 3985 D 4762 4002 D 4789 4020 D 4817 4038 D 4844 4055
D 4871 4073 D 4898 4091 D 4926 4108 D 4953 4126 D 4974 4140 D S 5310 4358 M
5335 4374 D 5362 4391 D 5389 4409 D 5416 4427 D 5444 4445 D 5471 4462 D 5498
4480 D 5525 4498 D 5553 4515 D 5580 4533 D 5607 4551 D 5635 4568 D 5645 4575
D S 5981 4793 M 5989 4798 D 6016 4816 D 6043 4834 D 6071 4851 D 6098 4869 D
6125 4887 D 6153 4904 D 6180 4922 D 6207 4940 D 6234 4958 D 6262 4975 D 6289
4993 D 6316 5011 D 6316 5011 D S 6652 5228 M 6670 5241 D 6698 5258 D 6725
5276 D 6752 5294 D 6780 5311 D 6807 5329 D 6834 5347 D 6861 5364 D 6889 5382
D 6916 5400 D 6943 5418 D 6970 5435 D 6987 5446 D S 7323 5664 M 7325 5665 D
7352 5683 D 7379 5701 D 7407 5718 D S 1954 1749 M 1981 1760 D 2008 1771 D
2036 1783 D 2063 1794 D 2090 1805 D 2117 1817 D 2139 1825 D S 2323 1902 M
2335 1907 D 2363 1918 D 2390 1930 D 2417 1941 D 2444 1952 D 2472 1963 D 2499
1975 D 2508 1979 D S 2693 2055 M 2717 2065 D 2744 2076 D 2772 2088 D 2799
2099 D 2826 2110 D 2853 2122 D 2878 2132 D S 3062 2208 M 3071 2212 D 3099
2223 D 3126 2235 D 3153 2246 D 3180 2257 D 3208 2268 D 3235 2280 D 3247 2285
D S 3432 2361 M 3453 2370 D 3480 2381 D 3508 2393 D 3535 2404 D 3562 2415 D
3589 2426 D 3617 2438 D 3617 2438 D S 3802 2514 M 3807 2517 D 3835 2528 D
3862 2539 D 3889 2551 D 3916 2562 D 3944 2573 D 3971 2584 D 3986 2591 D S
4171 2667 M 4189 2675 D 4216 2686 D 4244 2697 D 4271 2708 D 4298 2720 D 4325
2731 D 4353 2742 D 4356 2744 D S 4541 2820 M 4544 2821 D 4571 2833 D 4598
2844 D 4625 2855 D 4653 2866 D 4680 2878 D 4707 2889 D 4726 2897 D S 4910
2973 M 4925 2979 D 4953 2990 D 4980 3002 D 5007 3013 D 5034 3024 D 5062 3035
D 5089 3047 D 5095 3049 D S 5280 3126 M 5307 3137 D 5334 3148 D 5362 3159 D
5389 3171 D 5416 3182 D 5443 3193 D 5465 3202 D S 5650 3279 M 5661 3283 D
5689 3295 D 5716 3306 D 5743 3317 D 5771 3329 D 5798 3340 D 5825 3351 D 5835
3355 D S 6019 3431 M 6043 3441 D 6070 3453 D 6098 3464 D 6125 3475 D 6152
3486 D 6180 3498 D 6204 3508 D S 6389 3584 M 6398 3588 D 6425 3599 D 6452
3610 D 6479 3622 D 6507 3633 D 6534 3644 D 6561 3655 D 6574 3661 D S 6759
3737 M 6779 3746 D 6807 3757 D 6834 3768 D 6861 3779 D 6888 3791 D 6916 3802
D 6943 3813 D 6944 3813 D S 7128 3890 M 7134 3892 D 7161 3903 D 7188 3915 D
7216 3926 D 7243 3937 D 7270 3948 D 7297 3960 D 7313 3966 D S 1954 1847 M
1981 1859 D 1999 1868 D S 2045 1889 M 2063 1897 D 2090 1910 D S 2135 1931 M
2145 1935 D 2172 1948 D 2181 1952 D S 2226 1973 M 2227 1973 D 2254 1986 D
2271 1994 D S 2317 2015 M 2336 2024 D 2362 2036 D S 2407 2057 M 2417 2062 D
2445 2074 D 2453 2078 D S 2498 2099 M 2499 2100 D 2527 2112 D 2544 2120 D S
2589 2141 M 2608 2150 D 2634 2162 D S 2680 2183 M 2690 2188 D 2717 2201 D
2725 2204 D S 2770 2225 M 2772 2226 D 2799 2239 D 2816 2246 D S 2861 2267 M
2881 2277 D 2906 2288 D S 2952 2310 M 2963 2315 D 2990 2327 D 2997 2331 D S
3042 2352 M 3045 2353 D 3072 2365 D 3088 2373 D S 3133 2394 M 3154 2403 D
3178 2415 D S 3224 2436 M 3235 2441 D 3263 2454 D 3269 2457 D S 3315 2478 M
3317 2479 D 3345 2492 D 3360 2499 D S 3405 2520 M 3426 2530 D 3451 2541 D S
3496 2562 M 3508 2568 D 3535 2581 D 3541 2583 D S 3587 2604 M 3590 2606 D
3617 2619 D 3632 2625 D S 3677 2646 M 3699 2657 D 3723 2668 D S 3768 2689 M
3781 2695 D 3808 2707 D 3813 2710 D S 3859 2731 M 3863 2733 D 3890 2745 D
3904 2752 D S 3949 2773 M 3972 2783 D 3995 2794 D S 4040 2815 M 4053 2821 D
4081 2834 D 4085 2836 D S 4131 2857 M 4135 2859 D 4162 2872 D 4176 2878 D S
4221 2899 M 4244 2910 D 4267 2920 D S 4312 2941 M 4326 2948 D 4353 2960 D
4358 2962 D S 4403 2984 M 4408 2986 D 4435 2998 D 4448 3005 D S 4494 3026 M
4517 3036 D 4539 3047 D S 4584 3068 M 4599 3074 D 4626 3087 D 4630 3089 D S
4675 3110 M 4680 3112 D 4708 3125 D 4720 3131 D S 4766 3152 M 4789 3163 D
4811 3173 D S 4856 3194 M 4871 3201 D 4899 3214 D 4902 3215 D S 4947 3236 M
4953 3239 D 4980 3252 D 4992 3257 D S 5038 3278 M 5062 3290 D 5083 3300 D S
5128 3321 M 5144 3328 D 5171 3341 D 5174 3342 D S 5219 3363 M 5226 3366 D
5253 3379 D 5264 3384 D S 5310 3405 M 5335 3417 D 5355 3426 D S 5400 3447 M
5417 3455 D 5444 3467 D 5446 3468 D S 5491 3489 M 5498 3493 D 5526 3505 D
5536 3510 D S 5582 3531 M 5607 3543 D 5627 3552 D S 5672 3573 M 5689 3581 D
5716 3594 D 5718 3595 D S 5763 3616 M 5771 3619 D 5798 3632 D 5808 3637 D S
5854 3658 M 5880 3670 D 5899 3679 D S 5945 3700 M 5962 3708 D 5989 3721 D
5990 3721 D S 6035 3742 M 6044 3746 D 6071 3759 D 6081 3763 D S 6126 3784 M
6153 3797 D 6171 3805 D S 6217 3826 M 6234 3835 D 6262 3847 D 6262 3847 D S
6307 3869 M 6316 3873 D 6343 3885 D 6353 3890 D S 6398 3911 M 6425 3923 D
6443 3932 D S 6489 3953 M 6507 3961 D 6534 3974 D S 6579 3995 M 6589 3999 D
6616 4012 D 6625 4016 D S 6670 4037 M 6671 4037 D 6698 4050 D 6715 4058 D S
6761 4079 M 6780 4088 D 6806 4100 D S 6851 4121 M 6861 4126 D 6889 4139 D
6897 4142 D S 6942 4164 M 6943 4164 D 6970 4177 D 6987 4185 D S 7033 4206 M
7052 4215 D 7078 4227 D S 7123 4248 M 7134 4253 D 7161 4265 D 7169 4269 D S
7214 4290 M 7216 4291 D 7243 4303 D 7259 4311 D S 7305 4332 M 7325 4341 D
7350 4353 D S 7395 4374 M 7407 4379 D S 3130 5389 M 3080 5389 D S 3030 5389 M
2980 5389 D S 2930 5389 M 2880 5389 D S 2830 5389 M 2780 5389 D S 2730 5389 M
2680 5389 D S 2630 5389 M 2580 5389 D S 2530 5389 M 2480 5389 D S 2430 5389 M
2380 5389 D S 2330 5389 M 2280 5389 D S 2230 5389 M 2180 5389 D S 3130 6139 M
2930 6139 D S 2730 6139 M 2530 6139 D S 2330 6139 M 2130 6139 D S 3130 6514 M
2730 6514 D S 2330 6514 M 2130 6514 D S showpage end grestore


