%Paper: 
%From: PALLANTE@roma2.infn.it
%Date: Thu, 4 Aug 1994 18:16:12 +0200 (WET-DST)

% begin of Latex file
%
\documentstyle[12pt]{article}

\renewcommand{\baselinestretch}{1.2}
\renewcommand{\topfraction}{1}
\renewcommand{\bottomfraction}{1}
\renewcommand{\textfraction}{0}
\def\thefootnote{\fnsymbol{footnote}}
\topmargin 2.5cm
\sloppy
\parindent 0.5cm
\textwidth 15.0cm
\textheight 21.5cm
\hoffset=-0.8cm
\voffset=-3cm
%
%\let\Huge=\large
%\let\huge=\large
%\let\Large=\normalsize
%\let\large=\normalsize
%************************
% \footline={\hfill}
% \headline={\hss\tenrm\folio\hss}
% \voffset=1\baselineskip
%***********************
%\newcommand{p1k2}{p_1\cdot k_2}
%\newcommand{p2k1}{p_2\cdot k_1}
%\newcommand{l12}{l_1^2}
%\newcommand{l22}{l_2^2}
%\newcommand{\q12}{q_1^2}
%\newcommand{\q22}{q_2^2}
%\newcommand{\q14}{q_1^4}
%\newcommand{\q24}{q_2^4}
%\newcommand{\l14}{l_1^4}
%\newcommand{\l24}{l_2^4}
\newcommand{\eps}{\epsilon}
\newcommand{\epsmnab}{\epsilon_{\mu\nu\alpha\beta}}
\newcommand{\Udag}{U^{\dagger}}
\newcommand{\udag}{u^{\dagger}}
\newcommand{\s}{\Sigma}
\newcommand{\fmunu}{f_{\mu\nu}}
\newcommand{\Lmunu}{L_{\mu\nu}}
\newcommand{\Rmunu}{R_{\mu\nu}}
\newcommand{\Lab}{L_{\alpha\beta}}
\newcommand{\Rab}{R_{\alpha\beta}}
\newcommand{\Rtab}{\tilde{R}_{\alpha\beta}}
\newcommand{\Rtmunu}{\tilde{R}_{\mu\nu}}
\newcommand{\lmu}{{\cal L}_{\mu}}
\newcommand{\lnu}{{\cal L}_{\nu}}
\newcommand{\lalfa}{{\cal L}_{\alpha}}
\newcommand{\lbeta}{{\cal L}_{\beta}}
\newcommand{\llambda}{{\cal L}_{\lambda}}
\newcommand{\DUdag}{DU^{\dagger}}
\newcommand{\Dslash}{\mbox{ $\not \!\! D$}}
\newcommand{\half}{\mbox{\small $\frac{1}{2}$}}
\newcommand{\quarter}{\mbox{\small $\frac{1}{4}$}}
\newcommand{\piT}{\tilde{\pi}}
\newcommand{\rhoT}{\tilde{\rho}}
\newcommand{\beq}{\begin{equation}}
\newcommand{\eeq}{\end{equation}}
\newcommand{\lab}{\protect\label}
\newcommand{\cutoff}{\Lambda_\chi}
\newcommand{\capt}{\protect\caption}
\begin{document}

\begin{titlepage}
\begin{flushright}
ROM2F/94/32\\
\end{flushright}
\vspace{0.5cm}
\begin{center}

{
%\Large
\bf
The S parameter in a technicolour model \\
with explicit chiral symmetry breaking}

\vspace*{1.0cm}

\vspace*{1.2cm}
         {\bf E. Pallante\footnotemark
      \footnotetext{ email: pallante@vaxtov.roma2.infn.it\\
      \hspace*{6.5mm}fax: ++39-6-9403-427}} \\
{\footnotesize{ I.N.F.N., Laboratori Nazionali di Frascati,
Via E. Fermi, 00144 Frascati ITALY}} \\
\end{center}

\vspace*{3.0cm}

\begin{abstract}

We derive the S parameter of the electroweak radiative corrections in a
scaled-QCD technicolour and using a Nambu-Jona Lasinio model for
hadronic low energy interactions.  In this framework deviations from low
energy QCD can be quantitatively deduced.  We induce explicit chiral
symmetry breaking in the NJL model through the current-quarks mass term.
It is shown that the prediction for the S parameter can be sensitively
reduced respect to the chiral prediction.

\end{abstract}
\vspace*{1.5cm}
\begin{flushleft}
ROM2F/94/32  \\

\end{flushleft}
\end{titlepage}
\newpage

The S parameter of the electroweak radiative corrections is defined in
terms of two of the gauge bosons vacuum polarization functions as
\cite{Peskin}

\beq
\alpha S \equiv 4e^2 [\Pi_{33}^\prime (0) - \Pi_{3Q}^\prime (0) ],
\lab{SDEF}
\eeq

where $\alpha$ is the electromagnetic fine structure constant, the index
3 refers to the isospin $SU(2)_L$ current, while the index Q refers to
the $U(1)_{em}$ current.  The primed functions arise from the expansion
in $q^2$ of the $\Pi$ functions defined as

\beq
i\int d^4x~ e^{-iqx}<J^\mu_X(x)J^\nu_Y(0)>\equiv -g^{\mu\nu}
\Pi_{XY}(q^2)+q^\mu q^\nu terms,
\lab{2PF}
\eeq

with XY = 33, 3Q. By neglecting terms of order higher than
 $q^2$ one has:

\begin{eqnarray}
\Pi_{33}(q^2)&\sim& \Pi_{33}(0)+q^2\Pi_{33}^\prime (0),\nonumber\\
\Pi_{3Q}(q^2)&\sim&q^2\Pi_{3Q}^\prime (0),
\end{eqnarray}

where $\Pi_{3Q}(0)=0$ because of the QED Ward identity.

In a technicolour model where isospin and parity are conserved the $S$
parameter can be reexpressed in terms of the isospin-vector and axial
vector two point Green's functions through the relations

\beq
\Pi_{33}={1\over 4}(\Pi_{VV}+\Pi_{AA}), ~~~~\Pi_{3Q}={1\over 2}
\Pi_{VV},
\lab{REL}
\eeq

where $\Pi_{VV}$ and $\Pi_{AA}$ are defined according to eq.
(\ref{2PF}) with XY = VV, AA.

{}From eq. (\ref{SDEF}) and relations (\ref{REL}) the S parameter can be
written in terms of the Vector and Axial two-point functions as:

\beq
S = - 4\pi ( \Pi^\prime_{VV}(0) - \Pi^\prime_{AA}(0) ),
\eeq

where $\Pi_{XY}^\prime (0) = d/dq^2 \Pi_{XY}(q^2)\vert_{q^2 =0}$.

The two-point vector and axial functions can be explicitely derived in
effective quark models {\em \`a la} Nambu-Jona Lasinio (for a review see
also \cite{NJL,MANYNJL}) formulated for hadronic low energy interactions
\cite{ENJL,2point,QR}.  They have been calculated in the ENJL model with
$n_f=2,3$ and in the chiral limit in \cite{2point}, while a calculation
in the non chiral limit with a different from the present approach can
be found in \cite{3point}.  They can be written in the usual VMD form
with scale dependent meson parameters and $Q^2=-q^2$:

\begin{eqnarray}
{1\over -Q^2}\Pi_{VV}(Q^2)&=&- {f_V^2(Q^2) M_V^2(Q^2)\over M_V^2(Q^2)
+Q^2 }
\nonumber\\
{1\over -Q^2}\Pi_{AA}(Q^2) &=&- {f_\pi^2(Q^2)\over Q^2} -
{f_A^2(Q^2) M_A^2(Q^2)\over M_A^2(Q^2) +Q^2 },
\end{eqnarray}

\noindent where in QCD $f_\pi=93.3$ MeV is the pion decay constant,
$f_V$ and $f_A$ are the couplings of the vector meson to the external
vector current and of the axial meson to the external axial current,
$M_V$ and $M_A$ are the masses of the vector and axial mesons.

By substituting $\Pi^\prime_{VV}(0)$ and $\Pi^\prime_{AA}(0)$ in the
definition of the S parameter we obtain:

\beq
S = 4\pi [f_V^2(0) - f_A^2(0)].
\eeq

Using the effective action approach the values at $Q^2=0$ of $f_V^2$
and $f_A^2$ in the chiral limit are \cite{ENJL}:

\begin{eqnarray}
f_V^2(0)&=& {N_c\over 16\pi^2} {2\over 3} \Gamma
\biggl ( 0,{M_Q^2\over \cutoff^2}\biggr )\nonumber\\
f_A^2(0)&=&{N_c\over 16\pi^2} {2\over 3} g_A^2(0)\biggl [
\Gamma \biggl ( 0,{M_Q^2\over \cutoff^2}\biggr ) -
\Gamma \biggl ( 1,{M_Q^2\over \cutoff^2}\biggr ) \biggr ] .
\end{eqnarray}

The expression for S results:

\beq
S = 4\pi \biggl [
{N_c\over 16\pi^2}{2\over 3}\Gamma \biggl ( 0,{M_Q^2\over
\cutoff^2}\biggr )
(1-g_A^2(0))+{N_c\over 16\pi^2} {2\over 3}g_A^2 \Gamma \biggl (
1,{M_Q^2\over \cutoff^2}\biggr )
\biggr ] .
\lab{schiral}
\eeq

The $g_A$ parameter is the mixing parameter between axial and
pseudoscalar mesons given by:

\beq
g_A(0) = {1\over 1+4G_V{M_Q^2\over \cutoff^2}
\Gamma \biggl ( 0,{M_Q^2\over \cutoff^2}\biggr )} ,
\eeq

with $G_V$ the four-quark vector coupling constant
and the $\Gamma$ functions are defined as

\beq
\Gamma (n-2,\epsilon ) = \int_\epsilon^\infty~ dz~ {1\over z}~
e^{-z}~z^{n-2}.
\eeq

The function $\Gamma (0,\epsilon ) = -\ln \epsilon - \gamma_E + {\cal
O}(\epsilon )$ corresponds to the divergent contribution in a
momentum-cutoff regularization scheme, while $\Gamma (1,\epsilon )$
gives the first finite contribution.

The S parameter is a function of the adimensional ratio
$M_Q^2/\cutoff^2$, where $M_Q$ is the infrared cutoff of the effective
techni-meson theory and $\cutoff$ is the ultraviolet cutoff of the
effective techni-meson theory.  By assuming a technicolour model which
is a scaled QCD model (i.e.  by assuming the same adimensional ratio
$M_Q^2/\cutoff^2$ for both QCD and technicolour theories) we will use
the numerical low energy QCD values for $M_Q$ and $\cutoff$ to get a
prediction for the S parameter.

By inserting the numerical values $\cutoff = 1.160$ GeV, $M_Q = 0.265$
GeV and $g_A(0) = 0.61$, with $G_V=1.263$,
 valid in the chiral limit \cite{ENJL} we obtain

\beq
S = N_c \cdot (0.1 + 0.02).
\lab{chiral}
\eeq

The first term, which is the logarithmically divergent term, gives the
bulk of the contribution, while a small correction comes from the second
term which is finite.  The value of eq. (\ref{chiral}) is in good
agreement with the estimation by Peskin and Takeuchi \cite{Peskin}
obtained from the experimental data by using low energy QCD dispersion
relations and rescaling to technicolour energies.

The present parametrization gives the possibility to study a strong
dynamics which is like the low energy QCD dynamics, but which can
include deviations in the mass spectrum.

In what follows we induce explicit chiral symmetry breaking (E$\chi$SB)
in the ENJL model with the addition of the current-quark mass term and
study its effect on the S parameter.

By assuming a technicolour spectrum with $N_d$ isodoublets of
technifermions $(\tilde{u}, \tilde{d})$ two different pictures can be
analysed:

I) $m_{\tilde{u}}=m_{\tilde{d}}\neq 0$, for each isodoublet; the mass
matrix is given by $N_d$ $(2\times 2)$ degenerate subblocks and isospin
is conserved.

II) $m_{\tilde{u}}\neq m_{\tilde{d}}$ in each isodoublet; the mass
matrix is non degenerate and isospin symmetry is broken.

We focus on item $I)$, while item $II)$ is under study.

\section{ S in the non chiral limit}

The NJL effective fermion Lagrangian is

\beq
{\cal{L}} = \bar{q}(\hat{D}-{\cal M})q +
{8\pi^2G_S\over N_c\cutoff^2}
(\bar{q}^aq^b)(\bar{q}^bq^a) -{8\pi^2G_V\over N_c\cutoff^2}
[(\bar{q}_L^a\gamma_\mu q_L^b)(\bar{q}_L^b\gamma_\mu q_L^a)
+L\to R],
\lab{LAGF}
\eeq

where we have introduced the explicit $\chi$SB current-quark mass term;
the non-renormalizable four-fermion scalar and vector interactions are
generated by the integration over the high frequency modes of quarks and
gluons.  $G_S(\cutoff )$ and $G_V(\cutoff )$ are non perturbative
coupling constants and $\cutoff$ is the ultraviolet cutoff of the
effective theory.  Bosonization of the Lagrangian (\ref{LAGF})
introduces scalar, pseudoscalar, vector and axial meson degrees of
freedom: the integration over quarks degrees of freedom gives rise to
the effective meson Lagrangian whose parameters are generated by one
quark-loop calculation.  To derive the S parameter in the presence of
E$\chi$SB mass term one has a priori to take into account two effects:
the solution $M_i$ of the mass-gap equation, which is the pole of the
constituent-quark propagator, becomes a function of the current-quark
mass $m_i$ where $i$ is the flavour index.  After the bosonization
corrections to the vector and axial meson parameters can be expressed in
terms of the masses $M_i$.

\subsection{The Mass-Gap equation}

The mass-gap equation given by the Lagrangian (\ref{LAGF}) defines the
dressed current-quark propagator as the sum of the bare current-quark
propagator with mass $m_i$ and the tadpole contribution generated by the
four-quark interaction with coupling $G_S$. The mass of the dressed
current-quark propagator is then

\beq
M_i = m_i-{1\over 2}\biggl ( {8\pi^2G_S\over N_c\cutoff^2}\biggr )
<\bar{q}_iq_i>
\eeq

where $<\bar{q}_iq_i>$ is given by

\begin{eqnarray}
<\bar{q}_iq_i> &=& -{i}N_c \int~{d^4p\over (2\pi )^4}
{M_i\over p^2-M_i^2}\nonumber\\
&=&-{N_c\over 16\pi^2}~4M_i^3~\Gamma(-1,{M_i^2\over \cutoff^2}).
\end{eqnarray}

The graph of figure 1 shows the solution $M_i(m_i)$ rescaled for
technicolour as a function of the coupling $G_S$ for different values of
the current-quark masses $m_i$, while the graph of figure 2 shows the
solution $M_i(m_i)$ for $G_S=1.216$ which is the value obtained from the
best fit of ref. \cite{ENJL} in the chiral limit. Assuming for the
techni-pion decay constant the value $f_\pi^T =250$ GeV \cite{Peskin},
in a QCD like effective technicolour theory we define the ultraviolet
cutoff $\Lambda_T\simeq 4\pi f_\pi^T\simeq 3$ TeV. The values of both
masses $M_i$ and $m_i$ in the graphs can be thought as QCD values
rescaled by the relation $M_T = M_{QCD}\cdot \Lambda_T/\cutoff$ with
$\cutoff = 1.160$ GeV.

$M_i$ is a sensitively increasing function of the current-quark mass
$m_i$. The perturbative expansion in powers of the current-quark masses
has a limited validity range.


\subsection{The calculation}

To calculate the non chiral corrections to the $f_V$ and $f_A$
parameters which enter $S$ we use the effective action approach, already
used in the chiral limit in ref. \cite{ENJL}.

The bosonization of the Lagrangian (\ref{LAGF}) and the transformation
from current-quarks to constituent-quarks

\beq
Q_L=\xi q_L~~~~~~~~~~~~~~~~~Q_R=\xi^\dagger q_R,
\eeq

with $\xi = \sqrt{U} = \exp (2i/f_\pi~\Phi )$ the square root of the
usual exponential representation of the pseudoscalar meson octet $\Phi$,
leads to the effective low energy action for physical mesons after the
integration over quarks and gluons degrees of freedom:

\beq
e^{i\Gamma_{eff}[H,W^\pm_\mu;v,a,s,p]} = \int {\cal D}G_\mu~
e^{i\int~d^4x~-
{1\over 4}G_{\mu\nu}^2} \int~{\cal D}\bar{Q}{\cal D}Q~
e^{-i\int~d^4x~\bar{Q}D_E Q}.
\lab{EFFAC}
\eeq

$H,W^\pm_\mu$ on the right-end side are the scalar, vector and
axial meson fields which are the {\em auxiliary} fields of the
 bosonized Lagrangian (\ref{LAGF}) and the effective action is
calculated in the presence of external sources $v,a,s,p$.

The fermionic euclidean operator in the constituent-quark base is:

\beq
D_E = \gamma_\mu \nabla_\mu -{1\over 2} (\Sigma -\gamma_5\Delta )
 -H(x).
\lab{OPER}
\eeq

The covariant derivative $\nabla_\mu$

\begin{eqnarray}
\nabla_\mu&=& \partial_\mu +iG_\mu
+\Gamma_\mu -{i\over 2}\gamma_5 (\xi_\mu - W_\mu^-)
-{i\over 2}W_\mu^+
\end{eqnarray}

contains the vector and axial meson fields $W_\mu^+$ and $W_\mu^-$ and
the vector and axial-vector currents

\begin{eqnarray}
\Gamma_\mu&=& {1\over 2}\{\xi^\dagger [\partial_\mu -i(v_\mu +
a_\mu )]
\xi + \xi [\partial_\mu -i(v_\mu - a_\mu )]\xi^\dagger )\}
\nonumber\\
\xi_\mu&=& i\{\xi^\dagger [\partial_\mu -i(v_\mu + a_\mu )]
\xi - \xi [\partial_\mu -i(v_\mu - a_\mu )]\xi^\dagger )\} .
\end{eqnarray}

The scalar fields $\Sigma$ and $\Delta$ are proportional to
the current quark mass matrix ${\cal M}$

\begin{eqnarray}
\Sigma&=&\xi^\dagger {\cal M}\xi^\dagger + \xi{\cal M}^\dagger\xi
\nonumber\\
\Delta&=&\xi^\dagger {\cal M}\xi^\dagger - \xi{\cal M}^\dagger\xi .
\end{eqnarray}



The scalar field $H(x)$ acquires a non-zero vacuum expectation value
(VEV) which is responsible of the spontaneous chiral symmetry breaking
in the chiral limit: $H(x) = <H>+\sigma (x)$
 where the fluctuation $\sigma (x)$ defines the true scalar meson
field. Its VEV is the solution of the equation

\beq
{N_c\cutoff^2\over 8\pi^2G_S}2<H>_i + <\bar{Q}_iQ_i> = 0,
\lab{VEVEQ}
\eeq

which arises from imposing the extremum condition of the effective
action (\ref{EFFAC}) in the absence of external sources and vector
fields, i.e. in the mean field approximation:

\beq
{\delta\Gamma_{eff}\over \delta H}\vert_{H=<H>,\xi=1,W_\mu^\pm =0,
s=p=v=a=0}=0.
\eeq

In the mean field approximation (which implies $\xi =1$) the VEV of the
scalar density of the constituent-quarks $<\bar{Q}_iQ_i>$ coincides with
$<\bar{q}_iq_i>$ of the current-quarks.  Then eq. (\ref{VEVEQ}) implies
that the VEV of the scalar field is related to the masses $M_i(m_i)$
solutions of the mass-gap equation through the scalar density
$<\bar{q}_iq_i>$.  In the presence of current-quark masses $m_i$ the
identity $M_i=m_i+<H>_i$ is implied for each flavour $i$.

The effective low energy action (i.e. for $Q^2<\Lambda_T^2$) for
techni-meson fields is given by the determinant of the fermionic
operator $D_E$.  Because we are interested in the real part of it we can
compute the determinant of the squared operator

\beq
\Gamma_{eff} = -{1\over 2}\ln det (D_E^\dagger D_E)_\epsilon
\eeq

regularized in some scheme. The squared operator $D_E^\dagger D_E$ is a
bosonic differential operator bounded below by the constituent quark
masses squared $\tilde{M}_i^2$:

\beq
D_E^\dagger D_E \equiv -\nabla_\mu\nabla_\mu +\tilde{M}_i^2+E,
\eeq

where, referring to eq. (\ref{OPER}), $\tilde{M}_i{\bf{1}} = 1/2 ~\Sigma
+<H> = {\cal {M}}+<H>$ with $\xi = 1$ in first approximation.  This
shows that the constituent-quark masses $\tilde{M}_i$ coincide with the
current-quark masses solution of the mass gap equation.  Form now on
$\tilde{M}_i\equiv M_i$.

In the loop-expansion approach the effective action is given by the
perturbative series around the free part of the operator $D_E^\dagger
D_E$: $D_E^\dagger D_E \equiv (D_E^\dagger D_E)_0 + \delta =
-\partial_\mu\partial^\mu + M_i^2 + \delta$. This defines the
constituent free quark propagator $-\partial_\mu\partial^\mu + M_i^2$
and the perturbation $\delta$.

In ref. \cite{ENJL} the fermionic determinant has been calculated in the
chiral limit using the heat-kernel expansion in the proper-time
regularization scheme (for details on this technique see \cite{Ball}).
This method has the advantage to preserve gauge covariance at each step
of the expansion.

Consistency with the loop-expansion approach requires that
the infrared cutoff of the heat-kernel expansion of the fermionc
squared operator is the constituent quark mass matrix $M_i{\bf{1}}$,
 both in the chiral and non chiral limit.  In the first case $M_i$
coincides with the VEV of the scalar field:
$M_i{\bf{1}}=<H>_i{\bf{1}}=M_Q{\bf{1}}$, where $M_Q$ appeared in the
calculation (\ref{schiral}) of the S parameter in the chiral limit.

In the non chiral limit a simple result follows: the low energy meson
parameters $f_V$ and $f_A$ are those calculated in the chiral limit with
the consitutent-quark mass $M_Q$ replaced by its non chiral value
$M_i=<H>_i(M_i)+m_i$, where $<H>$ is in turn a function of $M_i$,
solution of the mass-gap equation for each flavour $i$.  The S parameter
of eq. (\ref{schiral}) follows with the same substitution and its
numerical value corresponds to the contribution of one technicolour
isodoublet $(\tilde{u},\tilde{d})$ in the isospin limit.

Figure 3 shows the parameter $S/N_c$ as a function of the
constituent-quark mass $M_i$ in the case of one isodoublet
$(\tilde{u},\tilde{d})$ with degenerate masses.  It is noticeable that
the maximum value of S is for the ratio $M_i/\Lambda_T$, or equivalently
$M_i/\cutoff$, which approximately corresponds to the chiral limit in
low energy QCD, while its numerical value decreases rather sensitively
by increasing the current techni-quark masses.

Non-perturbative values of the current-techni-quark masses can push the
S parameter towards zero.

In the case that all masses of the isodoublets in the model are equal
the formula (\ref{schiral}) is easely generalized to $n_f$ flavours by
multiplying by $n_f/2=n_d$ with $n_d$ the number of isodoublets in the
model.  Although no extra-information is given on the techni-particles
spectrum the present parametrization reproduces in a clear form the
effect of explicitely chiral symmetry breaking.

$q\bar{q}$ states with current masses $m_i>\Lambda_T$ cannot be treated
in this framework.  Alternative Heavy-quark-effective-theory as an
expansion in inverse powers of the mass $m_i$ could be used.  Although,
from the present behaviour one can infer that the higher mass of the
state the lower is its contribution to the S parameter.

If E$\chi$SB terms are relevant, higher dimensional effective fermion
interactions, proportional to the current techni-quark masses and
suppressed by inverse powers of the ultraviolet cutoff, can modify the
leading behaviour of the NJL model. The relevance of higher dimensional
operators proportional to powers of momenta $Q^2$ has been studied in
\cite{QR}.  The presence of higher dimensional terms can extend the
range of validity of the perturbative expansion in powers of the
current-quark masses and further reduce the numerical value of the S
parameter.

\vspace{3.cm}
{\bf{Acknowledgements}}
\vspace{0.8cm}

\noindent I am grateful to Roberto Petronzio for having called my
attention to this problem and for many stimulating and useful
discussions.

\vfill\eject

\centerline {{\bf FIGURE CAPTIONS}}
\vskip2.truecm

\begin{description}

\item[1)] The solution of the mass-gap equation $M_i$ in TeV as a
function of the scalar coupling constant $G_S$ for given values of the
current techni-quark masses $m_i$=0, 0.3, 0.5, 0.8, 1.1 TeV. The values
of $M_i$ and $m_i$ can be thought as QCD values rescaled by the relation
$M_T = M_{QCD}\cdot \Lambda_T/\cutoff$. In particular tha values of the
techni-quark masses $m_i$ in figure correspond to QCD values $m_i$ = 0,
0.1, 0.2, 0.3, 0.4 GeV.

\item[2)] The solution of the mass-gap equation $M_i$ as a function of
the current-quark masses $m_i$ for a given value of $G_S=1.216$ given by
the fit of ref.  \cite{ENJL} in the chiral limit.

\item[3)] The parameter $S/N_c$ as a function of the solution of the
mass-gap equation $M_i$. The maximum is approximately at the value of
$M_i$ obtained in the chiral limit.

\end{description}
\vfill\eject


\begin{thebibliography}{99}

\bibitem {Peskin}
M.E. Peskin and T. Takeuchi, {\em Phys. Rev.} {\bf D46} (1992) 381.

\bibitem{NJL}
Y. Nambu and G. Jona-Lasinio, {\em Phys. Rev.} {\bf 122} (1961) 345;

Y. Nambu and G. Jona-Lasinio, {\em Phys. Rev.} {\bf 124} (1961) 246;

D. J. Gross and A. Neveu, {\em Phys. Rev.} {\bf D10} (1974) 3235.

\bibitem{MANYNJL}
T. Eguchi, {\em Phys. Rev.} {\bf D14} (1976) 2755;

D. Ebert and H. Reinhard, {\em Nucl. Phys.} {\bf B271} (1986) 188;

V. Bernard, R. L. Jaffe and U.-G. Meissner,
{\em Nucl. Phys.} {\bf B308} (1988) 753;

M. Schaden et al., {\em Nucl. Phys.} {\bf B339} (1990) 595;

M. Wakamatsu, {\em Annals of Phys.} {\bf 193} (1989) 287.

\bibitem{ENJL}
J. Bijnens, C. Bruno and E. de Rafael, {\em Nucl. Phys.}
{\bf B390} (1993) 501.

\bibitem{2point}
J. Bijnens, E. de Rafael and H. Zheng, Preprint CERN-TH 6924/93,
CTP-93/P2917, NORDITA-93/43 N,P;

\bibitem{QR}
E. Pallante and R. Petronzio, "Quark-Resonance model", preprint
ROM2F 93/37, submitted to Z. Ph. C.

\bibitem{3point}
J. Bijnens and J. Prades, preprint NORDITA - 94/11 N/P.

\bibitem{Ball}
R.D. Ball, {\em Phys. Rep.} {\bf 182} (1989) 1.

\end{thebibliography}

\end{document}
%
%   figure 1 - postscript file
%
 initgraphics
 0.072 0.072 scale  %units are mils
     0 rotate
   250  1500 translate
 /vsml /Helvetica findfont  97 scalefont def
 /smal /Helvetica findfont 139 scalefont def
 /larg /Helvetica findfont 194 scalefont def
 /vlrg /Helvetica findfont 250 scalefont def
1
 gsave
  4553  4307 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (mi = 0,0.3,0.5,0.8,1.1 TeV) show
 grestore
 gsave
  4215  2707 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (Gs) show
 grestore
 gsave
   554  4676 translate
   90. rotate
   -61   -61 moveto
  smal setfont
 (Mi (TeV)) show
 grestore
 gsave
  4061   615 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (Fig. 1) show
 grestore
     9 setlinewidth
  1600  7384 moveto
  1600  3077 lineto
  1600  3077 moveto
  7199  3077 lineto
  7199  3077 moveto
  7199  7384 lineto
  7199  7384 moveto
  1600  7384 lineto
  3466  3077 moveto
  3495  3225 lineto
  3525  3374 lineto
  3559  3521 lineto
  3600  3665 lineto
  3653  3806 lineto
  3686  3882 lineto
  3721  3956 lineto
  3758  4030 lineto
  3797  4102 lineto
  3840  4172 lineto
  3876  4230 lineto
  3912  4288 lineto
  3949  4345 lineto
  3987  4402 lineto
  4026  4458 lineto
  4062  4507 lineto
  4099  4555 lineto
  4136  4603 lineto
  4174  4651 lineto
  4213  4697 lineto
  4249  4740 lineto
  4286  4782 lineto
  4323  4823 lineto
  4361  4864 lineto
  4399  4905 lineto
  4436  4942 lineto
  4473  4980 lineto
  4510  5016 lineto
  4548  5053 lineto
  4586  5089 lineto
  4623  5122 lineto
  4660  5156 lineto
  4697  5189 lineto
  4735  5222 lineto
  4773  5254 lineto
  4810  5284 lineto
  4847  5315 lineto
  4884  5345 lineto
  4921  5375 lineto
  4959  5404 lineto
  4996  5432 lineto
  5033  5460 lineto
  5071  5487 lineto
  5108  5514 lineto
  5146  5541 lineto
  5183  5567 lineto
  5220  5593 lineto
  5257  5618 lineto
  5295  5643 lineto
  5333  5668 lineto
  5370  5692 lineto
  5407  5716 lineto
  5444  5740 lineto
  5482  5763 lineto
  5519  5786 lineto
  5556  5808 lineto
  5594  5831 lineto
  5631  5853 lineto
  5668  5874 lineto
  5706  5896 lineto
  5743  5917 lineto
  5780  5938 lineto
  5818  5958 lineto
  5855  5978 lineto
  5893  5999 lineto
  5930  6018 lineto
  5967  6038 lineto
  6004  6057 lineto
  6042  6076 lineto
  6079  6095 lineto
  6116  6114 lineto
  6154  6132 lineto
  6191  6151 lineto
  6228  6169 lineto
  6266  6187 lineto
  6303  6204 lineto
  6340  6222 lineto
  6378  6239 lineto
  6415  6256 lineto
  6453  6273 lineto
  6490  6290 lineto
  6527  6306 lineto
  6564  6323 lineto
  6602  6339 lineto
  6639  6355 lineto
  6676  6371 lineto
  6714  6387 lineto
  6751  6402 lineto
  6788  6418 lineto
  6826  6433 lineto
  6863  6448 lineto
  6900  6463 lineto
  6938  6478 lineto
  6975  6493 lineto
  7012  6507 lineto
  7050  6522 lineto
  7087  6536 lineto
  7124  6550 lineto
  7162  6564 lineto
  7199  6578 lineto
  1600  3077 moveto
  1600  3261 lineto
  1786  3077 moveto
  1786  3138 lineto
  1973  3077 moveto
  1973  3138 lineto
  2160  3077 moveto
  2160  3138 lineto
  2346  3077 moveto
  2346  3138 lineto
  2533  3077 moveto
  2533  3261 lineto
  2720  3077 moveto
  2720  3138 lineto
  2906  3077 moveto
  2906  3138 lineto
  3093  3077 moveto
  3093  3138 lineto
  3280  3077 moveto
  3280  3138 lineto
  3466  3077 moveto
  3466  3261 lineto
  3653  3077 moveto
  3653  3138 lineto
  3840  3077 moveto
  3840  3138 lineto
  4026  3077 moveto
  4026  3138 lineto
  4213  3077 moveto
  4213  3138 lineto
  4399  3077 moveto
  4399  3261 lineto
  4586  3077 moveto
  4586  3138 lineto
  4773  3077 moveto
  4773  3138 lineto
  4959  3077 moveto
  4959  3138 lineto
  5146  3077 moveto
  5146  3138 lineto
  5333  3077 moveto
 stroke
 gsave
  1600  2929 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (0) show
 grestore
 gsave
  2422  2929 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (0.5) show
 grestore
 gsave
  3466  2929 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (1) show
 grestore
 gsave
  4289  2929 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (1.5) show
 grestore
 gsave
  5333  2929 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (2) show
 grestore
 gsave
  6155  2929 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (2.5) show
 grestore
 gsave
  7199  2929 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (3) show
 grestore
 gsave
  1268  3077 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (0.0) show
 grestore
 gsave
  1268  3874 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (0.5) show
 grestore
 gsave
  1268  4672 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (1.0) show
 grestore
 gsave
  1268  5469 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (1.5) show
 grestore
 gsave
  1268  6267 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (2.0) show
 grestore
 gsave
  1268  7065 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (2.5) show
 grestore
     9 setlinewidth
  5333  3077 moveto
  5333  3261 lineto
  5519  3077 moveto
  5519  3138 lineto
  5706  3077 moveto
  5706  3138 lineto
  5893  3077 moveto
  5893  3138 lineto
  6079  3077 moveto
  6079  3138 lineto
  6266  3077 moveto
  6266  3261 lineto
  6453  3077 moveto
  6453  3138 lineto
  6639  3077 moveto
  6639  3138 lineto
  6826  3077 moveto
  6826  3138 lineto
  7012  3077 moveto
  7012  3138 lineto
  7199  3077 moveto
  7199  3261 lineto
  1600  7199 moveto
  1600  7384 lineto
  1786  7322 moveto
  1786  7384 lineto
  1973  7322 moveto
  1973  7384 lineto
  2160  7322 moveto
  2160  7384 lineto
  2346  7322 moveto
  2346  7384 lineto
  2533  7199 moveto
  2533  7384 lineto
  2720  7322 moveto
  2720  7384 lineto
  2906  7322 moveto
  2906  7384 lineto
  3093  7322 moveto
  3093  7384 lineto
  3280  7322 moveto
  3280  7384 lineto
  3466  7199 moveto
  3466  7384 lineto
  3653  7322 moveto
  3653  7384 lineto
  3840  7322 moveto
  3840  7384 lineto
  4026  7322 moveto
  4026  7384 lineto
  4213  7322 moveto
  4213  7384 lineto
  4399  7199 moveto
  4399  7384 lineto
  4586  7322 moveto
  4586  7384 lineto
  4773  7322 moveto
  4773  7384 lineto
  4959  7322 moveto
  4959  7384 lineto
  5146  7322 moveto
  5146  7384 lineto
  5333  7199 moveto
  5333  7384 lineto
  5519  7322 moveto
  5519  7384 lineto
  5706  7322 moveto
  5706  7384 lineto
  5893  7322 moveto
  5893  7384 lineto
  6079  7322 moveto
  6079  7384 lineto
  6266  7199 moveto
  6266  7384 lineto
  6453  7322 moveto
  6453  7384 lineto
  6639  7322 moveto
  6639  7384 lineto
  6826  7322 moveto
  6826  7384 lineto
  7012  7322 moveto
  7012  7384 lineto
  7199  7199 moveto
  7199  7384 lineto
  1600  3077 moveto
  1784  3077 lineto
  1600  3236 moveto
  1661  3236 lineto
  1600  3396 moveto
  1661  3396 lineto
  1600  3555 moveto
  1661  3555 lineto
  1600  3715 moveto
  1661  3715 lineto
  1600  3874 moveto
  1784  3874 lineto
  1600  4034 moveto
  1661  4034 lineto
  1600  4193 moveto
  1661  4193 lineto
  1600  4353 moveto
  1661  4353 lineto
  1600  4512 moveto
  1661  4512 lineto
  1600  4672 moveto
  1784  4672 lineto
  1600  4831 moveto
  1661  4831 lineto
  1600  4991 moveto
  1661  4991 lineto
  1600  5150 moveto
  1661  5150 lineto
  1600  5310 moveto
  1661  5310 lineto
  1600  5469 moveto
  1784  5469 lineto
  1600  5629 moveto
  1661  5629 lineto
  1600  5788 moveto
  1661  5788 lineto
  1600  5948 moveto
  1661  5948 lineto
  1600  6107 moveto
  1661  6107 lineto
  1600  6267 moveto
  1784  6267 lineto
  1600  6427 moveto
  1661  6427 lineto
  1600  6586 moveto
  1661  6586 lineto
  1600  6746 moveto
  1661  6746 lineto
  1600  6905 moveto
  1661  6905 lineto
  1600  7065 moveto
  1784  7065 lineto
  1600  7224 moveto
  1661  7224 lineto
  1600  7384 moveto
  1661  7384 lineto
  7015  3077 moveto
  7199  3077 lineto
  7138  3236 moveto
  7199  3236 lineto
  7138  3396 moveto
  7199  3396 lineto
  7138  3555 moveto
  7199  3555 lineto
  7138  3715 moveto
  7199  3715 lineto
 stroke
     9 setlinewidth
  7015  3874 moveto
  7199  3874 lineto
  7138  4034 moveto
  7199  4034 lineto
  7138  4193 moveto
  7199  4193 lineto
  7138  4353 moveto
  7199  4353 lineto
  7138  4512 moveto
  7199  4512 lineto
  7015  4672 moveto
  7199  4672 lineto
  7138  4831 moveto
  7199  4831 lineto
  7138  4991 moveto
  7199  4991 lineto
  7138  5150 moveto
  7199  5150 lineto
  7138  5310 moveto
  7199  5310 lineto
  7015  5469 moveto
  7199  5469 lineto
  7138  5629 moveto
  7199  5629 lineto
  7138  5788 moveto
  7199  5788 lineto
  7138  5948 moveto
  7199  5948 lineto
  7138  6107 moveto
  7199  6107 lineto
  7015  6267 moveto
  7199  6267 lineto
  7138  6427 moveto
  7199  6427 lineto
  7138  6586 moveto
  7199  6586 lineto
  7138  6746 moveto
  7199  6746 lineto
  7138  6905 moveto
  7199  6905 lineto
  7015  7065 moveto
  7199  7065 lineto
  7138  7224 moveto
  7199  7224 lineto
  7138  7384 moveto
  7199  7384 lineto
  1600  3509 moveto
  1637  3517 lineto
  1675  3526 lineto
  1712  3535 lineto
  1749  3544 lineto
  1786  3554 lineto
  1824  3564 lineto
  1861  3575 lineto
  1899  3586 lineto
  1936  3597 lineto
  1973  3609 lineto
  2011  3622 lineto
  2048  3635 lineto
  2086  3648 lineto
  2123  3662 lineto
  2160  3677 lineto
  2198  3692 lineto
  2235  3708 lineto
  2272  3724 lineto
  2310  3742 lineto
  2346  3759 lineto
  2384  3778 lineto
  2422  3798 lineto
  2459  3818 lineto
  2496  3839 lineto
  2533  3861 lineto
  2571  3884 lineto
  2609  3908 lineto
  2646  3933 lineto
  2683  3958 lineto
  2720  3984 lineto
  2758  4012 lineto
  2796  4041 lineto
  2833  4070 lineto
  2870  4100 lineto
  2906  4130 lineto
  2944  4162 lineto
  2982  4194 lineto
  3019  4227 lineto
  3056  4260 lineto
  3093  4294 lineto
  3130  4329 lineto
  3168  4364 lineto
  3205  4399 lineto
  3242  4434 lineto
  3280  4470 lineto
  3317  4506 lineto
  3354  4542 lineto
  3392  4578 lineto
  3429  4613 lineto
  3466  4649 lineto
  3503  4685 lineto
  3541  4720 lineto
  3578  4756 lineto
  3615  4791 lineto
  3653  4826 lineto
  3690  4861 lineto
  3727  4895 lineto
  3764  4929 lineto
  3802  4963 lineto
  3840  4997 lineto
  3876  5029 lineto
  3914  5062 lineto
  3951  5094 lineto
  3988  5126 lineto
  4026  5158 lineto
  4063  5188 lineto
  4100  5219 lineto
  4138  5249 lineto
  4175  5279 lineto
  4213  5309 lineto
  4250  5338 lineto
  4287  5367 lineto
  4324  5395 lineto
  4362  5423 lineto
  4399  5451 lineto
  4436  5478 lineto
  4474  5505 lineto
  4511  5532 lineto
  4548  5558 lineto
  4586  5584 lineto
  4623  5610 lineto
  4660  5635 lineto
  4698  5660 lineto
  4735  5684 lineto
  4773  5709 lineto
  4810  5733 lineto
  4847  5756 lineto
  4884  5780 lineto
  4922  5803 lineto
  4959  5826 lineto
  4996  5848 lineto
  5034  5870 lineto
  5071  5892 lineto
  5108  5914 lineto
  5146  5936 lineto
  5183  5957 lineto
  5220  5978 lineto
  5258  5999 lineto
  5295  6019 lineto
  5333  6039 lineto
  5370  6059 lineto
  5407  6079 lineto
  5444  6099 lineto
 stroke
     9 setlinewidth
  5444  6099 moveto
  5482  6118 lineto
  5519  6137 lineto
  5556  6156 lineto
  5594  6175 lineto
  5631  6193 lineto
  5668  6212 lineto
  5706  6230 lineto
  5743  6248 lineto
  5780  6265 lineto
  5818  6283 lineto
  5855  6300 lineto
  5893  6318 lineto
  5930  6335 lineto
  5967  6351 lineto
  6004  6368 lineto
  6042  6385 lineto
  6079  6401 lineto
  6116  6417 lineto
  6154  6433 lineto
  6191  6449 lineto
  6228  6465 lineto
  6266  6481 lineto
  6303  6496 lineto
  6340  6511 lineto
  6378  6526 lineto
  6415  6541 lineto
  6453  6556 lineto
  6490  6571 lineto
  6527  6586 lineto
  6564  6600 lineto
  6602  6614 lineto
  6639  6629 lineto
  6676  6643 lineto
  6714  6657 lineto
  6751  6671 lineto
  6788  6684 lineto
  6826  6698 lineto
  6863  6711 lineto
  6900  6725 lineto
  6938  6738 lineto
  6975  6751 lineto
  7012  6764 lineto
  7050  6777 lineto
  7087  6790 lineto
  7124  6803 lineto
  7162  6816 lineto
  7199  6828 lineto
  1600  3941 moveto
  1637  3956 lineto
  1675  3972 lineto
  1712  3989 lineto
  1749  4005 lineto
  1786  4023 lineto
  1824  4041 lineto
  1862  4059 lineto
  1899  4078 lineto
  1936  4097 lineto
  1973  4116 lineto
  2011  4137 lineto
  2048  4158 lineto
  2086  4179 lineto
  2123  4201 lineto
  2160  4223 lineto
  2198  4247 lineto
  2235  4270 lineto
  2272  4294 lineto
  2310  4319 lineto
  2346  4344 lineto
  2384  4370 lineto
  2422  4396 lineto
  2459  4422 lineto
  2496  4449 lineto
  2533  4476 lineto
  2571  4504 lineto
  2608  4532 lineto
  2646  4561 lineto
  2683  4589 lineto
  2720  4618 lineto
  2757  4648 lineto
  2795  4677 lineto
  2832  4707 lineto
  2869  4737 lineto
  2906  4767 lineto
  2944  4797 lineto
  2981  4827 lineto
  3018  4858 lineto
  3056  4888 lineto
  3093  4918 lineto
  3130  4949 lineto
  3168  4979 lineto
  3205  5009 lineto
  3242  5039 lineto
  3280  5069 lineto
  3317  5099 lineto
  3354  5129 lineto
  3391  5158 lineto
  3429  5188 lineto
  3466  5217 lineto
  3503  5246 lineto
  3541  5275 lineto
  3578  5303 lineto
  3615  5332 lineto
  3653  5360 lineto
  3690  5388 lineto
  3727  5415 lineto
  3764  5442 lineto
  3802  5469 lineto
  3840  5496 lineto
  3877  5523 lineto
  3914  5549 lineto
  3951  5575 lineto
  3989  5601 lineto
  4026  5626 lineto
  4063  5652 lineto
  4100  5676 lineto
  4138  5701 lineto
  4175  5726 lineto
  4213  5750 lineto
  4250  5774 lineto
  4287  5797 lineto
  4324  5821 lineto
  4362  5844 lineto
  4399  5867 lineto
  4437  5889 lineto
  4474  5912 lineto
  4511  5934 lineto
  4549  5956 lineto
  4586  5977 lineto
  4623  5999 lineto
  4660  6020 lineto
  4698  6041 lineto
  4735  6062 lineto
  4773  6082 lineto
  4810  6102 lineto
  4847  6122 lineto
  4884  6142 lineto
  4922  6162 lineto
  4959  6181 lineto
  4997  6201 lineto
  5034  6220 lineto
  5071  6238 lineto
  5109  6257 lineto
  5146  6276 lineto
  5183  6294 lineto
  5220  6312 lineto
  5258  6330 lineto
  5295  6348 lineto
  5333  6365 lineto
  5370  6382 lineto
 stroke
     9 setlinewidth
  5370  6382 moveto
  5407  6400 lineto
  5444  6417 lineto
  5482  6434 lineto
  5519  6450 lineto
  5557  6467 lineto
  5594  6483 lineto
  5631  6499 lineto
  5669  6516 lineto
  5706  6532 lineto
  5743  6547 lineto
  5780  6563 lineto
  5818  6578 lineto
  5855  6594 lineto
  5893  6609 lineto
  5930  6624 lineto
  5967  6639 lineto
  6004  6654 lineto
  6042  6668 lineto
  6079  6683 lineto
  6116  6697 lineto
  6154  6712 lineto
  6191  6726 lineto
  6228  6740 lineto
  6266  6754 lineto
  6303  6768 lineto
  6340  6781 lineto
  6378  6795 lineto
  6415  6808 lineto
  6453  6822 lineto
  6490  6835 lineto
  6527  6848 lineto
  6564  6861 lineto
  6602  6874 lineto
  6639  6887 lineto
  6676  6900 lineto
  6714  6912 lineto
  6751  6925 lineto
  6788  6937 lineto
  6826  6949 lineto
  6863  6962 lineto
  6900  6974 lineto
  6938  6986 lineto
  6975  6998 lineto
  7012  7010 lineto
  7050  7021 lineto
  7087  7033 lineto
  7124  7045 lineto
  7162  7056 lineto
  7199  7068 lineto
  1600  4373 moveto
  1637  4394 lineto
  1675  4415 lineto
  1712  4436 lineto
  1749  4458 lineto
  1786  4480 lineto
  1824  4503 lineto
  1862  4526 lineto
  1899  4549 lineto
  1936  4573 lineto
  1973  4597 lineto
  2011  4622 lineto
  2048  4646 lineto
  2086  4672 lineto
  2123  4697 lineto
  2160  4723 lineto
  2197  4749 lineto
  2235  4775 lineto
  2272  4802 lineto
  2309  4828 lineto
  2346  4855 lineto
  2384  4882 lineto
  2421  4910 lineto
  2459  4937 lineto
  2496  4965 lineto
  2533  4992 lineto
  2570  5020 lineto
  2608  5048 lineto
  2645  5076 lineto
  2682  5104 lineto
  2720  5131 lineto
  2757  5159 lineto
  2794  5187 lineto
  2832  5215 lineto
  2869  5243 lineto
  2906  5270 lineto
  2943  5298 lineto
  2981  5325 lineto
  3018  5353 lineto
  3056  5380 lineto
  3093  5407 lineto
  3130  5434 lineto
  3167  5461 lineto
  3205  5487 lineto
  3242  5514 lineto
  3280  5540 lineto
  3317  5566 lineto
  3354  5592 lineto
  3391  5618 lineto
  3429  5643 lineto
  3466  5668 lineto
  3503  5693 lineto
  3541  5718 lineto
  3578  5743 lineto
  3615  5767 lineto
  3653  5791 lineto
  3690  5815 lineto
  3727  5839 lineto
  3765  5862 lineto
  3802  5886 lineto
  3840  5909 lineto
  3877  5932 lineto
  3914  5954 lineto
  3951  5977 lineto
  3989  5999 lineto
  4026  6021 lineto
  4063  6042 lineto
  4101  6064 lineto
  4138  6085 lineto
  4175  6106 lineto
  4213  6127 lineto
  4250  6148 lineto
  4287  6168 lineto
  4325  6188 lineto
  4362  6209 lineto
  4399  6228 lineto
  4437  6248 lineto
  4474  6267 lineto
  4511  6287 lineto
  4549  6306 lineto
  4586  6325 lineto
  4623  6343 lineto
  4661  6362 lineto
  4698  6380 lineto
  4735  6398 lineto
  4773  6416 lineto
  4810  6434 lineto
  4847  6452 lineto
  4885  6469 lineto
  4922  6486 lineto
  4959  6504 lineto
  4997  6520 lineto
  5034  6537 lineto
  5071  6554 lineto
  5109  6570 lineto
  5146  6587 lineto
  5183  6603 lineto
  5221  6619 lineto
  5258  6635 lineto
  5295  6650 lineto
 stroke
     9 setlinewidth
  5295  6650 moveto
  5333  6666 lineto
  5370  6681 lineto
  5407  6697 lineto
  5445  6712 lineto
  5482  6727 lineto
  5519  6742 lineto
  5557  6757 lineto
  5594  6771 lineto
  5631  6786 lineto
  5669  6800 lineto
  5706  6815 lineto
  5743  6829 lineto
  5780  6843 lineto
  5818  6857 lineto
  5855  6870 lineto
  5893  6884 lineto
  5930  6898 lineto
  5967  6911 lineto
  6004  6924 lineto
  6042  6938 lineto
  6079  6951 lineto
  6117  6964 lineto
  6154  6977 lineto
  6191  6990 lineto
  6228  7002 lineto
  6266  7015 lineto
  6303  7027 lineto
  6340  7040 lineto
  6378  7052 lineto
  6415  7064 lineto
  6453  7076 lineto
  6490  7088 lineto
  6527  7100 lineto
  6564  7112 lineto
  6602  7124 lineto
  6639  7136 lineto
  6676  7147 lineto
  6714  7159 lineto
  6751  7170 lineto
  6788  7181 lineto
  6826  7193 lineto
  6863  7204 lineto
  6900  7215 lineto
  6938  7226 lineto
  6975  7237 lineto
  7012  7248 lineto
  7050  7259 lineto
  7087  7269 lineto
  7124  7280 lineto
  7162  7290 lineto
  7199  7301 lineto
  1600  4805 moveto
  1637  4829 lineto
  1675  4853 lineto
  1712  4878 lineto
  1749  4902 lineto
  1786  4927 lineto
  1824  4952 lineto
  1861  4978 lineto
  1899  5003 lineto
  1936  5029 lineto
  1973  5055 lineto
  2010  5081 lineto
  2048  5107 lineto
  2085  5134 lineto
  2123  5160 lineto
  2160  5186 lineto
  2197  5213 lineto
  2234  5240 lineto
  2272  5266 lineto
  2309  5293 lineto
  2346  5320 lineto
  2384  5346 lineto
  2421  5373 lineto
  2458  5399 lineto
  2496  5426 lineto
  2533  5452 lineto
  2570  5479 lineto
  2608  5505 lineto
  2645  5531 lineto
  2682  5557 lineto
  2720  5583 lineto
  2757  5609 lineto
  2794  5634 lineto
  2831  5660 lineto
  2869  5685 lineto
  2906  5711 lineto
  2943  5736 lineto
  2981  5760 lineto
  3018  5785 lineto
  3055  5810 lineto
  3093  5834 lineto
  3130  5858 lineto
  3167  5882 lineto
  3205  5906 lineto
  3242  5929 lineto
  3280  5953 lineto
  3317  5976 lineto
  3354  5999 lineto
  3391  6022 lineto
  3429  6044 lineto
  3466  6067 lineto
  3503  6089 lineto
  3541  6110 lineto
  3578  6132 lineto
  3615  6154 lineto
  3653  6175 lineto
  3690  6196 lineto
  3727  6217 lineto
  3765  6238 lineto
  3802  6258 lineto
  3840  6279 lineto
  3877  6299 lineto
  3914  6319 lineto
  3951  6338 lineto
  3989  6358 lineto
  4026  6378 lineto
  4063  6397 lineto
  4101  6416 lineto
  4138  6434 lineto
  4175  6453 lineto
  4213  6472 lineto
  4250  6490 lineto
  4287  6508 lineto
  4325  6526 lineto
  4362  6544 lineto
  4399  6561 lineto
  4437  6579 lineto
  4474  6596 lineto
  4511  6613 lineto
  4549  6630 lineto
  4586  6647 lineto
  4623  6663 lineto
  4661  6680 lineto
  4698  6696 lineto
  4735  6712 lineto
  4773  6728 lineto
  4810  6744 lineto
  4847  6760 lineto
  4885  6776 lineto
  4922  6791 lineto
  4959  6806 lineto
  4997  6822 lineto
  5034  6837 lineto
  5071  6851 lineto
  5109  6866 lineto
  5146  6881 lineto
  5183  6895 lineto
  5221  6910 lineto
 stroke
     9 setlinewidth
  5221  6910 moveto
  5258  6924 lineto
  5295  6938 lineto
  5333  6952 lineto
  5370  6966 lineto
  5407  6980 lineto
  5445  6994 lineto
  5482  7007 lineto
  5519  7021 lineto
  5557  7034 lineto
  5594  7047 lineto
  5631  7060 lineto
  5669  7073 lineto
  5706  7086 lineto
  5743  7099 lineto
  5781  7112 lineto
  5818  7124 lineto
  5855  7137 lineto
  5893  7149 lineto
  5930  7162 lineto
  5967  7174 lineto
  6005  7186 lineto
  6042  7198 lineto
  6079  7210 lineto
  6117  7222 lineto
  6154  7234 lineto
  6191  7245 lineto
  6229  7257 lineto
  6266  7268 lineto
  6303  7280 lineto
  6340  7291 lineto
  6378  7302 lineto
  6415  7313 lineto
  6453  7325 lineto
  6490  7336 lineto
  6527  7347 lineto
  6564  7358 lineto
  6602  7368 lineto
  6639  7379 lineto
  6662  7384 lineto
 stroke
 copypage
 erasepage
%
%   figure 2 - postscript file
%
 initgraphics
 0.072 0.072 scale  %units are mils
     0 rotate
   250  1500 translate
 /vsml /Helvetica findfont  97 scalefont def
 /smal /Helvetica findfont 139 scalefont def
 /larg /Helvetica findfont 194 scalefont def
 /vlrg /Helvetica findfont 250 scalefont def
1
 gsave
  3846  2707 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (mi (TeV)) show
 grestore
 gsave
   554  4676 translate
   90. rotate
   -61   -61 moveto
  smal setfont
 (Mi (TeV)) show
 grestore
 gsave
  5538  6768 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (Gs = 1.216) show
 grestore
 gsave
  4061   615 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (Fig. 2) show
 grestore
 gsave
  1600  2929 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (0) show
 grestore
 gsave
  2422  2929 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (0.5) show
 grestore
 gsave
  3466  2929 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (1) show
 grestore
 gsave
  4289  2929 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (1.5) show
 grestore
 gsave
  5333  2929 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (2) show
 grestore
 gsave
  6155  2929 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (2.5) show
 grestore
 gsave
  7199  2929 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (3) show
 grestore
     9 setlinewidth
  1600  7384 moveto
  1600  3077 lineto
  1600  3077 moveto
  7199  3077 lineto
  7199  3077 moveto
  7199  7384 lineto
  7199  7384 moveto
  1600  7384 lineto
  1600  4222 moveto
  1674  4362 lineto
  1750  4502 lineto
  1829  4639 lineto
  1913  4773 lineto
  2005  4901 lineto
  2105  5023 lineto
  2185  5110 lineto
  2266  5196 lineto
  2349  5280 lineto
  2434  5361 lineto
  2521  5441 lineto
  2611  5518 lineto
  2694  5587 lineto
  2777  5657 lineto
  2861  5726 lineto
  2945  5794 lineto
  3030  5861 lineto
  3116  5927 lineto
  3200  5989 lineto
  3283  6052 lineto
  3367  6113 lineto
  3452  6175 lineto
  3536  6235 lineto
  3622  6295 lineto
  3706  6353 lineto
  3789  6411 lineto
  3874  6468 lineto
  3958  6526 lineto
  4042  6583 lineto
  4127  6639 lineto
  4211  6694 lineto
  4295  6749 lineto
  4380  6804 lineto
  4464  6859 lineto
  4548  6914 lineto
  4633  6969 lineto
  4716  7023 lineto
  4800  7078 lineto
  4885  7131 lineto
  4969  7185 lineto
  5053  7238 lineto
  5138  7291 lineto
  5215  7331 lineto
  5296  7358 lineto
  5381  7375 lineto
  5467  7384 lineto
  5468  7384 lineto
  1600  3077 moveto
  1600  3261 lineto
  1786  3077 moveto
  1786  3138 lineto
  1973  3077 moveto
  1973  3138 lineto
  2160  3077 moveto
  2160  3138 lineto
  2346  3077 moveto
  2346  3138 lineto
  2533  3077 moveto
  2533  3261 lineto
  2720  3077 moveto
  2720  3138 lineto
  2906  3077 moveto
  2906  3138 lineto
  3093  3077 moveto
  3093  3138 lineto
  3280  3077 moveto
  3280  3138 lineto
  3466  3077 moveto
  3466  3261 lineto
  3653  3077 moveto
  3653  3138 lineto
  3840  3077 moveto
  3840  3138 lineto
  4026  3077 moveto
  4026  3138 lineto
  4213  3077 moveto
  4213  3138 lineto
  4399  3077 moveto
  4399  3261 lineto
  4586  3077 moveto
  4586  3138 lineto
  4773  3077 moveto
  4773  3138 lineto
  4959  3077 moveto
  4959  3138 lineto
  5146  3077 moveto
  5146  3138 lineto
  5333  3077 moveto
  5333  3261 lineto
  5519  3077 moveto
  5519  3138 lineto
  5706  3077 moveto
  5706  3138 lineto
  5893  3077 moveto
  5893  3138 lineto
  6079  3077 moveto
  6079  3138 lineto
  6266  3077 moveto
  6266  3261 lineto
  6453  3077 moveto
  6453  3138 lineto
  6639  3077 moveto
  6639  3138 lineto
  6826  3077 moveto
  6826  3138 lineto
  7012  3077 moveto
  7012  3138 lineto
  7199  3077 moveto
  7199  3261 lineto
  1600  7199 moveto
  1600  7384 lineto
  1786  7322 moveto
  1786  7384 lineto
  1973  7322 moveto
  1973  7384 lineto
  2160  7322 moveto
  2160  7384 lineto
  2346  7322 moveto
  2346  7384 lineto
  2533  7199 moveto
  2533  7384 lineto
  2720  7322 moveto
  2720  7384 lineto
  2906  7322 moveto
  2906  7384 lineto
  3093  7322 moveto
  3093  7384 lineto
  3280  7322 moveto
  3280  7384 lineto
  3466  7199 moveto
  3466  7384 lineto
  3653  7322 moveto
  3653  7384 lineto
  3840  7322 moveto
  3840  7384 lineto
  4026  7322 moveto
  4026  7384 lineto
  4213  7322 moveto
  4213  7384 lineto
  4399  7199 moveto
  4399  7384 lineto
 stroke
 gsave
  1268  3077 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (0.0) show
 grestore
 gsave
  1268  3874 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (0.5) show
 grestore
 gsave
  1268  4672 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (1.0) show
 grestore
 gsave
  1268  5469 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (1.5) show
 grestore
 gsave
  1268  6267 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (2.0) show
 grestore
 gsave
  1268  7065 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (2.5) show
 grestore
     9 setlinewidth
  4586  7322 moveto
  4586  7384 lineto
  4773  7322 moveto
  4773  7384 lineto
  4959  7322 moveto
  4959  7384 lineto
  5146  7322 moveto
  5146  7384 lineto
  5333  7199 moveto
  5333  7384 lineto
  5519  7322 moveto
  5519  7384 lineto
  5706  7322 moveto
  5706  7384 lineto
  5893  7322 moveto
  5893  7384 lineto
  6079  7322 moveto
  6079  7384 lineto
  6266  7199 moveto
  6266  7384 lineto
  6453  7322 moveto
  6453  7384 lineto
  6639  7322 moveto
  6639  7384 lineto
  6826  7322 moveto
  6826  7384 lineto
  7012  7322 moveto
  7012  7384 lineto
  7199  7199 moveto
  7199  7384 lineto
  1600  3077 moveto
  1784  3077 lineto
  1600  3236 moveto
  1661  3236 lineto
  1600  3396 moveto
  1661  3396 lineto
  1600  3555 moveto
  1661  3555 lineto
  1600  3715 moveto
  1661  3715 lineto
  1600  3874 moveto
  1784  3874 lineto
  1600  4034 moveto
  1661  4034 lineto
  1600  4193 moveto
  1661  4193 lineto
  1600  4353 moveto
  1661  4353 lineto
  1600  4512 moveto
  1661  4512 lineto
  1600  4672 moveto
  1784  4672 lineto
  1600  4831 moveto
  1661  4831 lineto
  1600  4991 moveto
  1661  4991 lineto
  1600  5150 moveto
  1661  5150 lineto
  1600  5310 moveto
  1661  5310 lineto
  1600  5469 moveto
  1784  5469 lineto
  1600  5629 moveto
  1661  5629 lineto
  1600  5788 moveto
  1661  5788 lineto
  1600  5948 moveto
  1661  5948 lineto
  1600  6107 moveto
  1661  6107 lineto
  1600  6267 moveto
  1784  6267 lineto
  1600  6427 moveto
  1661  6427 lineto
  1600  6586 moveto
  1661  6586 lineto
  1600  6746 moveto
  1661  6746 lineto
  1600  6905 moveto
  1661  6905 lineto
  1600  7065 moveto
  1784  7065 lineto
  1600  7224 moveto
  1661  7224 lineto
  1600  7384 moveto
  1661  7384 lineto
  7015  3077 moveto
  7199  3077 lineto
  7138  3236 moveto
  7199  3236 lineto
  7138  3396 moveto
  7199  3396 lineto
  7138  3555 moveto
  7199  3555 lineto
  7138  3715 moveto
  7199  3715 lineto
  7015  3874 moveto
  7199  3874 lineto
  7138  4034 moveto
  7199  4034 lineto
  7138  4193 moveto
  7199  4193 lineto
  7138  4353 moveto
  7199  4353 lineto
  7138  4512 moveto
  7199  4512 lineto
  7015  4672 moveto
  7199  4672 lineto
  7138  4831 moveto
  7199  4831 lineto
  7138  4991 moveto
  7199  4991 lineto
  7138  5150 moveto
  7199  5150 lineto
  7138  5310 moveto
  7199  5310 lineto
  7015  5469 moveto
  7199  5469 lineto
  7138  5629 moveto
  7199  5629 lineto
  7138  5788 moveto
  7199  5788 lineto
  7138  5948 moveto
  7199  5948 lineto
  7138  6107 moveto
  7199  6107 lineto
  7015  6267 moveto
  7199  6267 lineto
  7138  6427 moveto
  7199  6427 lineto
  7138  6586 moveto
  7199  6586 lineto
  7138  6746 moveto
  7199  6746 lineto
  7138  6905 moveto
  7199  6905 lineto
  7015  7065 moveto
  7199  7065 lineto
  7138  7224 moveto
  7199  7224 lineto
  7138  7384 moveto
  7199  7384 lineto
 stroke
 copypage
 erasepage
%
%   figure 3 - postscript file
%
 initgraphics
 0.072 0.072 scale  %units are mils
     0 rotate
   250  1500 translate
 /vsml /Helvetica findfont  97 scalefont def
 /smal /Helvetica findfont 139 scalefont def
 /larg /Helvetica findfont 194 scalefont def
 /vlrg /Helvetica findfont 250 scalefont def
1
 gsave
  3846  2707 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (Mi (TeV)) show
 grestore
 gsave
   554  4922 translate
   90. rotate
   -61   -61 moveto
  smal setfont
 (S/Nc) show
 grestore
 gsave
  4061   615 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (Fig. 3) show
 grestore
 gsave
  1600  2929 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (0) show
 grestore
 gsave
  2422  2929 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (0.5) show
 grestore
 gsave
  3466  2929 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (1) show
 grestore
 gsave
  4289  2929 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (1.5) show
 grestore
 gsave
  5333  2929 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (2) show
 grestore
 gsave
  6155  2929 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (2.5) show
 grestore
 gsave
  7199  2929 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (3) show
 grestore
     9 setlinewidth
  1600  7384 moveto
  1600  3077 lineto
  1600  3077 moveto
  7199  3077 lineto
  7199  3077 moveto
  7199  7384 lineto
  7199  7384 moveto
  1600  7384 lineto
  2105  5912 moveto
  2182  5990 lineto
  2263  6062 lineto
  2347  6121 lineto
  2433  6159 lineto
  2521  6169 lineto
  2611  6142 lineto
  2701  6092 lineto
  2789  6038 lineto
  2875  5980 lineto
  2958  5919 lineto
  3038  5854 lineto
  3116  5786 lineto
  3201  5708 lineto
  3284  5630 lineto
  3368  5552 lineto
  3452  5474 lineto
  3536  5397 lineto
  3622  5321 lineto
  3705  5248 lineto
  3788  5175 lineto
  3872  5102 lineto
  3957  5031 lineto
  4042  4960 lineto
  4127  4890 lineto
  4209  4825 lineto
  4291  4762 lineto
  4375  4701 lineto
  4460  4641 lineto
  4546  4582 lineto
  4633  4525 lineto
  4715  4472 lineto
  4798  4420 lineto
  4882  4369 lineto
  4967  4320 lineto
  5052  4272 lineto
  5138  4225 lineto
  5221  4182 lineto
  5304  4140 lineto
  5388  4099 lineto
  5473  4059 lineto
  5558  4021 lineto
  5644  3984 lineto
  5727  3950 lineto
  5811  3916 lineto
  5895  3883 lineto
  5979  3852 lineto
  6064  3821 lineto
  6149  3792 lineto
  6233  3764 lineto
  6316  3737 lineto
  6401  3711 lineto
  6485  3686 lineto
  6570  3662 lineto
  6655  3640 lineto
  1600  3077 moveto
  1600  3261 lineto
  1786  3077 moveto
  1786  3138 lineto
  1973  3077 moveto
  1973  3138 lineto
  2160  3077 moveto
  2160  3138 lineto
  2346  3077 moveto
  2346  3138 lineto
  2533  3077 moveto
  2533  3261 lineto
  2720  3077 moveto
  2720  3138 lineto
  2906  3077 moveto
  2906  3138 lineto
  3093  3077 moveto
  3093  3138 lineto
  3280  3077 moveto
  3280  3138 lineto
  3466  3077 moveto
  3466  3261 lineto
  3653  3077 moveto
  3653  3138 lineto
  3840  3077 moveto
  3840  3138 lineto
  4026  3077 moveto
  4026  3138 lineto
  4213  3077 moveto
  4213  3138 lineto
  4399  3077 moveto
  4399  3261 lineto
  4586  3077 moveto
  4586  3138 lineto
  4773  3077 moveto
  4773  3138 lineto
  4959  3077 moveto
  4959  3138 lineto
  5146  3077 moveto
  5146  3138 lineto
  5333  3077 moveto
  5333  3261 lineto
  5519  3077 moveto
  5519  3138 lineto
  5706  3077 moveto
  5706  3138 lineto
  5893  3077 moveto
  5893  3138 lineto
  6079  3077 moveto
  6079  3138 lineto
  6266  3077 moveto
  6266  3261 lineto
  6453  3077 moveto
  6453  3138 lineto
  6639  3077 moveto
  6639  3138 lineto
  6826  3077 moveto
  6826  3138 lineto
  7012  3077 moveto
  7012  3138 lineto
  7199  3077 moveto
  7199  3261 lineto
  1600  7199 moveto
  1600  7384 lineto
  1786  7322 moveto
  1786  7384 lineto
  1973  7322 moveto
  1973  7384 lineto
  2160  7322 moveto
  2160  7384 lineto
  2346  7322 moveto
  2346  7384 lineto
  2533  7199 moveto
  2533  7384 lineto
  2720  7322 moveto
  2720  7384 lineto
  2906  7322 moveto
  2906  7384 lineto
  3093  7322 moveto
  3093  7384 lineto
  3280  7322 moveto
  3280  7384 lineto
  3466  7199 moveto
  3466  7384 lineto
  3653  7322 moveto
  3653  7384 lineto
  3840  7322 moveto
 stroke
 gsave
  1046  3077 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (0.000) show
 grestore
 gsave
  1046  3794 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (0.025) show
 grestore
 gsave
  1046  4512 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (0.050) show
 grestore
 gsave
  1046  5230 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (0.075) show
 grestore
 gsave
  1046  5948 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (0.100) show
 grestore
 gsave
  1046  6666 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (0.125) show
 grestore
 gsave
  1046  7384 translate
    0. rotate
   -61   -61 moveto
  smal setfont
 (0.150) show
 grestore
     9 setlinewidth
  3840  7322 moveto
  3840  7384 lineto
  4026  7322 moveto
  4026  7384 lineto
  4213  7322 moveto
  4213  7384 lineto
  4399  7199 moveto
  4399  7384 lineto
  4586  7322 moveto
  4586  7384 lineto
  4773  7322 moveto
  4773  7384 lineto
  4959  7322 moveto
  4959  7384 lineto
  5146  7322 moveto
  5146  7384 lineto
  5333  7199 moveto
  5333  7384 lineto
  5519  7322 moveto
  5519  7384 lineto
  5706  7322 moveto
  5706  7384 lineto
  5893  7322 moveto
  5893  7384 lineto
  6079  7322 moveto
  6079  7384 lineto
  6266  7199 moveto
  6266  7384 lineto
  6453  7322 moveto
  6453  7384 lineto
  6639  7322 moveto
  6639  7384 lineto
  6826  7322 moveto
  6826  7384 lineto
  7012  7322 moveto
  7012  7384 lineto
  7199  7199 moveto
  7199  7384 lineto
  1600  3077 moveto
  1784  3077 lineto
  1600  3220 moveto
  1661  3220 lineto
  1600  3364 moveto
  1661  3364 lineto
  1600  3507 moveto
  1661  3507 lineto
  1600  3651 moveto
  1661  3651 lineto
  1600  3794 moveto
  1784  3794 lineto
  1600  3938 moveto
  1661  3938 lineto
  1600  4082 moveto
  1661  4082 lineto
  1600  4225 moveto
  1661  4225 lineto
  1600  4369 moveto
  1661  4369 lineto
  1600  4512 moveto
  1784  4512 lineto
  1600  4656 moveto
  1661  4656 lineto
  1600  4799 moveto
  1661  4799 lineto
  1600  4943 moveto
  1661  4943 lineto
  1600  5087 moveto
  1661  5087 lineto
  1600  5230 moveto
  1784  5230 lineto
  1600  5374 moveto
  1661  5374 lineto
  1600  5517 moveto
  1661  5517 lineto
  1600  5661 moveto
  1661  5661 lineto
  1600  5804 moveto
  1661  5804 lineto
  1600  5948 moveto
  1784  5948 lineto
  1600  6092 moveto
  1661  6092 lineto
  1600  6235 moveto
  1661  6235 lineto
  1600  6379 moveto
  1661  6379 lineto
  1600  6522 moveto
  1661  6522 lineto
  1600  6666 moveto
  1784  6666 lineto
  1600  6809 moveto
  1661  6809 lineto
  1600  6953 moveto
  1661  6953 lineto
  1600  7097 moveto
  1661  7097 lineto
  1600  7240 moveto
  1661  7240 lineto
  1600  7384 moveto
  1784  7384 lineto
  7015  3077 moveto
  7199  3077 lineto
  7138  3220 moveto
  7199  3220 lineto
  7138  3364 moveto
  7199  3364 lineto
  7138  3507 moveto
  7199  3507 lineto
  7138  3651 moveto
  7199  3651 lineto
  7015  3794 moveto
  7199  3794 lineto
  7138  3938 moveto
  7199  3938 lineto
  7138  4082 moveto
  7199  4082 lineto
  7138  4225 moveto
  7199  4225 lineto
  7138  4369 moveto
  7199  4369 lineto
  7015  4512 moveto
  7199  4512 lineto
  7138  4656 moveto
  7199  4656 lineto
  7138  4799 moveto
  7199  4799 lineto
  7138  4943 moveto
  7199  4943 lineto
  7138  5087 moveto
  7199  5087 lineto
  7015  5230 moveto
  7199  5230 lineto
  7138  5374 moveto
  7199  5374 lineto
  7138  5517 moveto
  7199  5517 lineto
  7138  5661 moveto
  7199  5661 lineto
  7138  5804 moveto
  7199  5804 lineto
  7015  5948 moveto
  7199  5948 lineto
  7138  6092 moveto
  7199  6092 lineto
  7138  6235 moveto
  7199  6235 lineto
  7138  6379 moveto
  7199  6379 lineto
  7138  6522 moveto
  7199  6522 lineto
 stroke
     9 setlinewidth
  7015  6666 moveto
  7199  6666 lineto
  7138  6809 moveto
  7199  6809 lineto
  7138  6953 moveto
  7199  6953 lineto
  7138  7097 moveto
  7199  7097 lineto
  7138  7240 moveto
  7199  7240 lineto
  7015  7384 moveto
  7199  7384 lineto
 stroke
 copypage
 erasepage

