%From: "Elizabeth H. Simmons" <simmons@smyrd.bu.edu>
%Date: Tue, 26 Sep 95 09:58:54 -0400
%Date (revised): Tue, 26 Sep 95 10:28:14 -0400


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%   template.tex for PTPTeX.sty <ver.0.1>  %%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentstyle[seceq,wrapfig,epsf]{ptptex}
%\documentstyle[seceq,preprint,wrapfig,epsf]{ptptex}

%%%%% Personal Macros %%%%%%%%%%%%%%%%%%%

\newcommand\beq{\begin{equation}}
\newcommand\eeq{\end{equation}}
\newcommand\st{\sin\theta}
\newcommand\ct{\cos\theta}
\newcommand\esc{{e \over{\st \ct}}}
\newcommand\half{{1\over{2}}}
\newcommand{\NPB}[1]{{\it Nucl. Phys.}\ {\bf B{#1}}}
\newcommand{\PLB}[1]{{\it Phys. Lett.}\ {\bf B{#1}}}
\newcommand{\PRD}[1]{{\it Phys. Rev.}\ {\bf D{#1}}}
\newcommand{\PRL}[1]{{\it Phys. Rev. Lett.}\ {\bf #1}}
\newcommand{\NCA}[1]{{\it Nuovo Cim.}\ {\bf {#1}A}}
\newcommand{\hc}{ {\rm h.c.} }
\newcommand{\ME}{ M_{ETC} }
\newcommand{\gE}{ g_{ETC} }
\newcommand{\TC}{technicolor}
\newcommand{\ETC}{extended technicolor}
\newcommand{\lae}{$\stackrel{<}{\sim}$}
\newcommand{\gae}{$\stackrel{>}{\sim}$}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\notypesetlogo  %comment in if to eliminate PTPTeX logo

%\preprintnumber{BU-HEP-95-27\\hep-ph/9509392}

\markboth{%      %header of odd-page
E.H.~Simmons, R.S.~Chivukula, and J.~Terning
}{%              %header of even-page
Testing Extended Technicolor with $R_b$}

\title{%
Testing Extended Technicolor with $R_b$ \footnote{Talk given by
E.H.S. at the Yukawa International Seminar `95, Kyoto, August 21-15, 1995
and at the International Symposium on Heavy Flavor and Electroweak
Theory, Beijing, August 17-19, 1995. BU-HEP-95-27. hep-ph/9509392.} }

\author{%
Elizabeth H. {\sc Simmons}, {\sc R.S. Chivukula}, and J. {\sc
Terning}\footnote{E-mail: simmons@bu.edu, sekhar@bu.edu,
terning@calvin.bu.edu}
}

\inst{%
Physics Department, Boston University, 590 Commonwealth Ave., Boston
MA  02215
}

\recdate{%
\today
}

\abst{%
We review the connection between $m_t$ and
the $Zb\bar b$ vertex in ETC models and demonstrate the power of the
resulting experimental constraint on models with weak-singlet ETC bosons.
Some efforts to bring ETC models into agreement with experimental
data on the $Zb\bar b$ vertex are mentioned, and the most promising
one (non-commuting ETC) is discussed in detail.
}

\begin{document}

\maketitle

\section{Introduction}

Two outstanding questions in particle theory are the cause of
electroweak symmetry breaking and the origin of the masses and mixings
of the fermions.  Because theories that use light, weakly-coupled
scalar bosons to answer these questions suffer from the hierarchy and
triviality problems, it is interesting to consider the possibility that
electroweak symmetry breaking arises from strong dynamics at scales of
order 1 TeV.  This talk focuses on extended\cite{ETC}
technicolor\cite{tc} (ETC) models,
in which both the masses of the weak gauge bosons and those of the
fermions arise from gauge dynamics.

In extended technicolor models, the large mass of the top quark
generally arises from ETC dynamics at relatively
low energy scales.  Since the magnitude of the
Cabibbo-Kobayashi-Maskawa matrix element $\vert V_{tb}\vert$ is nearly
unity, $SU(2)_W$ gauge invariance insures that ETC bosons coupling to
the left-handed top quark couple with equal strength to the
left-handed bottom quark.   In particular, the
ETC dynamics
which generate the top quark's mass also couple to the left-handed
bottom quark thereby affecting the $Zb\bar b$ vertex.  This has been
shown\cite{zbbone} to provide
a powerful experimental constraint on extended technicolor models --
particularly on those models in which the ETC gauge group commutes
with $SU(2)_W$.

This talk begins by reviewing the connection between the top quark
mass and the $Zb\bar b$ vertex in ETC models.  Next, the power of the
resulting experimental constraint on ETC models with weak-singlet ETC
bosons is demonstrated.  Several recent attempts
\cite{walkrb,strongETC,comp,evans,yoshi,NCETC,NCETCtwo}
to bring ETC
models into agreement with experimental data on the $Zb\bar b$ vertex
are mentioned, and the most promising one (non-commuting ETC) is
discussed.

\section{From $m_t$ To A Signal of ETC Dynamics}

 Consider a model in which $m_t$
is generated by the exchange of  a
weak-singlet ETC gauge boson of mass $M_{ETC}$ coupling  with
strength $\gE$ to the current
\begin{equation}
{\xi} {\bar\psi^i}_L \gamma^\mu T_L^{ik}
+ {1\over\xi} {\bar t_R} \gamma^\mu U_R^k\ ,\ \ \ \ \ \ {\rm where}\ \
\psi_L\ \equiv\ \pmatrix{t \cr b \cr}_L\ \
T_L\ \equiv\ \pmatrix{U \cr D \cr}_L
\label{tmasscur}
\end{equation}
where $U$ and $D$ are technifermions, $i$ and $k$ are weak and technicolor
indices, and $\xi$ is an ETC Clebsch expected
to be of order one.  At energies below $\ME$, ETC  gauge boson exchange
may be approximated by local four-fermion operators.   For example, $m_t$
arises from an operator coupling the  left- and right-handed currents
in Eq. (\ref{tmasscur})
%
\beq
   - {\gE^2 \over  \ME^2}  \left({\bar\psi}_L^i \gamma^\mu
T_L^{iw}\right) \left( {\bar U^w}_R \gamma_\mu t_R \right) + \hc\ .
\label{topff}
\eeq
%
When this is Fierzed into a product of technicolor-singlet densities, it
generates a mass for the top quark when the technifermions' chiral
symmetries break. We can use the rules of naive  dimensional analysis
\cite{dimanal} to estimate the size of $m_t$ generated by
Eq. (\ref{topff}). Assuming, for simplicity, that there is only a
doublet of technifermions and that technicolor respects an
 $SU(2)_L \times SU(2)_R$ chiral symmetry (so that the technipion
decay constant, $F$, is $v= 246$ GeV) we have
%
\beq
   m_t\ = {\gE^2 \over \ME^2}
   \langle{\bar U}U\rangle\ \approx\ {\gE^2 \over \ME^2} (4\pi v^3)\ .
\label{topmass}
\eeq

The ETC boson responsible for
producing $m_t$ also affects the $Zb\bar b$ vertex\cite{zbbone}.
Consider the four-fermion
operator arising from the left-handed current in Eq.(\ref{tmasscur})
-- the part containing $b$ quarks.
\beq
  -\xi^2 {\gE^2\over\ME^2} \left({\bar \psi^i}_L \gamma^\mu
  T^{iw}_L \right) \left({\bar T^{jw}}_L \gamma_\mu \psi^j_L \right)\ .
\label{unfierz}
\eeq
When Fierzed into a product of technicolor singlet currents, this
includes
\beq
  -{\xi^2\over 2} {\gE^2\over
  \ME^2}\left({\bar\psi}_L\gamma^\mu\tau^a\psi_L \right) \left({\bar T}_L
  \gamma_\mu \tau^a T_L \right)\ ,
\label{fourferm}
\eeq
where the $\tau^a$ are weak isospin Pauli matrices.

Adopting an effective chiral Lagrangian description appropriate below
the technicolor chiral symmetry breaking scale, we may replace the
technifermion current by a sigma-model current \cite{howardbook}:
\beq
 \left({\bar T}_L \gamma_\mu \tau^a T_L \right) =
	{v^2 \over 2}Tr\left(\Sigma^\dagger\tau^a iD_\mu\Sigma\right)\
,
\eeq
where $\Sigma = \exp{(2i{\tilde\pi}/v)}$ transforms as
$\Sigma \rightarrow L\Sigma R^\dagger$ under $SU(2)_L \times SU(2)_R$,
and
\beq
D_\mu \Sigma = \partial_\mu\Sigma
\ +\ i\esc Z_\mu\left({\tau_3\over 2}\Sigma -
\st^2[Q,\Sigma]\right)\ +\ ...
\eeq
In unitary gauge $\Sigma=1$ this is seen to alter the $Z$-boson's
tree-level coupling
to left-handed bottom quarks $g_L = \esc(-\half + {1\over 3}\st^2)$ by
%
\begin{eqnarray}
\delta g_L^{ETC} &=& -{\xi^2 \over 2} {\gE^2 v^2\over\ME^2} \esc(I_3)
\label{ta}\\
	&=& {1\over 4} {\xi^2} {m_t\over{4\pi v}}
\cdot \esc \label{tb}
\end{eqnarray}
Here eq. (\ref{tb}) follows from applying eq. (\ref{topmass}) to eq.
(\ref{ta}).


\section{Comparison with the Standard Model and LEP data}

To show that $\delta g_L$ provides a test of ETC dynamics, we must
relate it to a shift in the value of an experimental observable, and
compare that shift both to radiative corrections in the
standard model and to the available experimental precision.

Because ETC gives a direct correction to the $Zb\bar b$ vertex, we
need an observable that is particularly sensitive to direct, rather
than oblique\cite{ST}, effects.  A natural choice is the ratio of $Z$
decay widths
\beq
R_b \equiv {\Gamma(Z\to b\bar b) \over {\Gamma(Z \to {\rm hadrons})}}
\eeq
because both the oblique and QCD corrections largely cancel in this ratio.
As
\beq
{\delta \Gamma_b \over {\Gamma_b}} = 2 { g_L \delta g_L \over {g_L^2 +
g_R^2}} \approx  -6.5\%\ \xi^2\ \left({m_t\over {175 {\rm GeV}}}\right)
\eeq
we find
\beq
{\delta R_b \over R_b} \approx -5.1\% \xi^2 \left({m_t
\over 175{\rm GeV}} \right).
\label{rbb}
\eeq
The one-loop $Zb\bar b$ vertex correction in the standard model, which
is largely due to exchange of longitudinal $W$ bosons, lies in the
range $[-0.5\% ... -2.0\%]$\cite{tcalc} for 100 GeV $\geq m_t \geq$
200 GeV.  The ETC-induced correction (\ref{rbb}) is larger and in the
same direction.  Furthermore, because ETC models include longitudinal
$W$ bosons, the full shift in $R_b$ in an ETC model is the sum of the
$W$-exchange and ETC contributions.

The LEP experiments now have sufficient precision to detect such large
shifts in $R_b$.  The experimental value of $R_b = 0.2202\pm 0.0020$
actually lies {\it above} the 1-loop standard model value of
$R_b = 0.2155$ \cite{langacker,blondel}. This implies that any
contribution from non-standard physics is positive: $\left[\delta R_b/
R_b\right]_{new} \approx + 2.2\%$, thereby excluding ETC models in
which the ETC and weak gauge groups commute.


\section{Interlude}

Having demonstrated that measurements of $R_b$ can exclude a
significant class of simple ETC models, we should check how
more realistic models fare.   Accordingly, we briefly review the
impact of certain features of recent ETC models on the value of
 $R_b$.

A slowly-running (`walking') technicolor beta-function is often
included in ETC models in order to provide the light fermions with
realistically large masses, while avoiding excessive flavor-changing
neutral currents\cite{walktc}.  Because a walking beta function
enhances the size
of the technifermion condensate $\langle \bar T T \rangle$, it leads
to larger fermion masses for a given ETC scale, $M_{ETC}$.  Enhancing
 $m_t$ relative to $M_{ETC}$ reduces the size of $\delta g_L$.
However, it is has been shown \cite{walkrb} that the shift in $R_b$
generally remains large enough to be visible at LEP.

It is possible to build ETC models in which the ETC coupling itself
becomes strong before the scale $M_{ETC}$ and plays a significant role
in electroweak symmetry breaking \cite{strongETC}.  The spectrum of
strongly-coupled ETC models include light composite scalars with
Yukawa couplings to ordinary fermions and technifermions \cite{comp} .
Exchange of the composite scalars produces corrections to $R_b$ that
are small enough to leave $R_b$ in agreement with experiment
\cite{evans}.  The disadvantage of this approach is the need to
fine-tune the ETC coupling close to the critical value.

ETC models also generally include `diagonal' techni-neutral ETC
bosons.  The effect of these gauge bosons on $R_b$ is discussed at
length in Ref. \citen{yoshi}.  Suffice it to say that while exchange of
the diagonal ETC bosons does tend to raise $R_b$, this effect is
significant only when the model includes large isospin violation --
leading to conflict with the measured value of the oblique parameter
$T$.

Finally, we should recall that our analysis explicitly assumed that
the weak and ETC gauge groups commute.  More recent work
\cite{NCETC,NCETCtwo} indicates that relaxing that assumption can
lead to models with experimentally acceptable values of $R_b$.
The remainder of this talk will therefore focus on `non-commuting'
extended technicolor models.

\section{Non-commuting ETC Models}

We begin by describing the symmetry-breaking pattern that enables
non-commuting ETC models to include both a heavy top quark and
approximate Cabibbo universality \cite{NCETC}.  A heavy top quark must
receive its
mass from ETC dynamics at low energy scales; if the ETC bosons
responsible for $m_t$ are weak-charged, the weak group $SU(2)_{heavy}$
under which $(t,b)_L$ is a doublet must be embedded in the low-scale
ETC group.  Conversely, the light quarks and leptons cannot be charged
under the low-scale ETC group lest they also receive large
contributions to their masses; hence the weak $SU(2)_{light}$ group
for the light quarks and leptons must be distinct from
$SU(2)_{heavy}$.  To approximately preserve low-energy Cabibbo
universality the two weak $SU(2)$'s must break to their diagonal
subgroup before technicolor dynamically breaks the remaining
electroweak symmetry.  The resulting
symmetry-breaking pattern is
%\footnote{The hypercharge group, $U(1)_Y$,
%is embedded partly in the ETC group, so that $U(1)' \neq U(1)_Y$.}
:
\begin{eqnarray}
ETC & \times& SU(2)_{light} \times U(1)' \nonumber\\
&\downarrow&\ \ \ \ \ f \nonumber \\
TC \times SU(2)_{heavy} & \times& SU(2)_{light} \times U(1)_Y  \nonumber\\
&\downarrow&\ \ \ \ \ u \\
TC & \times& SU(2)_W \times U(1)_Y \nonumber \\
&\downarrow&\ \ \ \ \ v \nonumber \\
TC & \times& U(1)_{EM}, \nonumber
\end{eqnarray}
\noindent{where $ETC$ and $TC$ stand, respectively, for the extended
technicolor and technicolor gauge groups, while $f$, $u$, and
$v = 246$ GeV are the expectation values of the order parameters for the
three different symmetry breakings ({\it i.e.} the analogs of $F_\pi$
for chiral symmetry breaking in QCD).  Note that, since we are
interested in the physics associated with top-quark mass generation,
only $t_L$, $b_L$ and $t_R$ need transform non-trivially under $ETC$.
But to ensure anomaly cancelation, it is more economical to assume
that the entire third generation has the same non-commuting ETC
interactions.  Thus we take $(t,b)_L$ and $(\nu_\tau,\tau)$ to be
doublets under $SU(2)_{heavy}$ but singlets under $SU(2)_{light}$,
while all other left-handed ordinary fermions have the opposite
$SU(2)$ assignment.}

Once again, the dynamics responsible for generating the top quark's
mass contributes to $R_b$.  This time the ETC gauge boson involved
transforms as a weak doublet coupling to
\beq
\xi\bar\psi_L \gamma^\mu U_L +
{1\over \xi}\bar t_R \gamma^\mu T_R
\eeq
where $\psi_L \equiv (t,b)_L$ and $T_R \equiv (U,D)_R$, are doublets
under $SU(2)_{heavy}$ while $U_L$ is an $SU(2)_{heavy}$ singlet.
Therefore, the four-fermion operator affecting the $Zb\bar b$ operator
is (after Fierzing)
\beq
- {2\xi^2\over f^2} \left( \bar\psi_L \gamma^\mu \psi_L
\right) \left( \bar U_L \gamma_\mu U_L \right) .
\label{a:2}
\eeq

Note that, since $\bar\psi_L \gamma^\mu
U_L$ and $\bar t_R \gamma^\mu T_R$ must transform in the same way, if
 $\psi_L$ is a 2 of $SU(2)_{heavy}$ then $T_R$ is a 2* instead.
Then in the effective chiral Lagrangian description, we find
%\beq
%D_\mu T_R = \partial_\mu T_R + i \esc Z_\mu ({1 \over
%2}(-\tau_3^*) -s^2 Q) T_R + . . .
%\eeq
%so that
\beq
D_\mu \Sigma = \partial_\mu \Sigma - {{i e}\over{\st \ct}} Z_\mu
\left({1\over 2} \Sigma \tau_3^*  + \sin^2\theta[\Sigma,Q]\right) + ...
\eeq
and in unitary gauge ($\Sigma = 1$) we have
\beq
\bar U_L \gamma_\mu U_L = - \esc {v^2 \over
4} Z_\mu.
\eeq
The effect of operator (\ref{a:2}) on the coupling of $b_L$ to the $Z$
is therefore
\beq
\delta g_L = -\esc {\xi^2 v^2 \over { 2 f^2}} \approx -
{\xi^2 \over 4} \esc {m_t \over {4 \pi v}} .
\label{a:1}
\eeq
 Since the tree-level $Z b_L
\bar b_L$ coupling is also negative, the ETC-induced change tends to
{\bf increase} the coupling -- and thereby increase $R_b$.  We find
that Eq. (\ref{a:1}) results in a change to $R_b$ of\cite{NCETCtwo}
\beq
{\delta R_b \over R_b} \approx +5.1\% \xi^2 \left({m_t
\over 175{\rm GeV}} \right).
\eeq
The change is similar in size to what was obtained in the
commuting ETC models, but is opposite in sign.

But that is not the full story of $R_b$ in non-commuting ETC.  Recall
that there are two sets of weak gauge bosons which mix at the scale
$u$.  Of the resulting mass eigenstates, one set is heavy and couples
mainly to the third-generation fermions while the other set is {\it
nearly} identical to the $W$ and $Z$ of the standard model.  That
`nearly' is important: it leads to a shift in the light $Z$'s coupling
to the $b$ of order\cite{NCETCtwo}
\beq
\delta g_L = {e \over{2 \st \ct}} {g_{ETC}^2 v^2\over u^2} \sin^2\alpha
\eeq
where $\tan\alpha = g_{light}/g_{heavy}$ is the ratio of the $SU(2)$
gauge couplings.  The couplings of the light $Z$ to other fermions are
similarly affected.  When this is included, mixing alters
$R_b$ by
\beq
{\delta R_b \over R_b} \approx -5.1\%
\sin^2\alpha {f^2\over u^2} \left({m_t
 \over 175{\rm GeV}} \right).
\eeq
The two effects on $R_b$ in non-commuting ETC models
are of similar size and opposite sign, and their precise values are
model-dependent.  Thus, non-commuting ETC theories can
yield values of $R_b$ that are consistent with experiment\cite{NCETCtwo}.

Since $R_b$ alone cannot confirm or exclude non-commuting ETC, we
should apply a broader set of precision electroweak tests.  Before
doing this, we must describe the $SU(2)\times SU(2)$ symmetry breaking
sector in more detail.  The two simplest possibilities for the
$SU(2)_{heavy} \times SU(2)_{light}$ transformation properties of the
order parameters that produce the correct combination of mixing and
breaking of these gauge groups are:
\begin{eqnarray}
&\langle \varphi \rangle& \sim (2,1)_{1/2},\ \ \ \ \langle
\sigma\rangle \sim (2,2)_0 ~,\ \ \ \ \ \ \ ``{\rm heavy\ case}"\\
&\langle \varphi \rangle& \sim (1,2)_{1/2},\ \ \ \ \langle
\sigma\rangle \sim (2,2)_0 ~,\ \ \ \ \ \ \ ``{\rm light\ case}"~.
\end{eqnarray}
Here the order parameter $\langle\varphi\rangle$ is responsible for
breaking $SU(2)_L$ while $\langle\sigma\rangle$ mixes
$SU(2)_{heavy}$ with $SU(2)_{light}$.  We refer to these two
possibilities as ``heavy'' and ``light'' according to whether
$\langle\varphi\rangle$
transforms non-trivially under $SU(2)_{heavy}$ or $SU(2)_{light}$.

The heavy case, in which $\langle\varphi\rangle$ couples to the heavy
group, is the choice made in \cite{NCETC}, and corresponds to the case
in which the technifermion condensation responsible for providing mass
for the third generation of quarks and leptons is also responsible for
the bulk of electroweak symmetry breaking.  The light case, in which
$\langle\varphi\rangle$ couples to the light group, corresponds to the
opposite scenario in which different physics provides mass to the
third generation fermions and the weak gauge bosons.  While this light
case is counter-intuitive (after
all, the third generation is the heaviest!), it may provide a
resolution to the issue of how large isospin breaking can exist in the
fermion (and technifermion) mass spectrum without leaking into the $W$
and $Z$ masses.

We have performed a global fit for the parameters of the non-commuting
ETC model ($s^2$, $1/x \equiv v^2/u^2$, and the $\delta g$'s) to all
precision electroweak data: the $Z$ line shape, forward backward
asymmetries, $\tau$ polarization, and left-right asymmetry measured at
LEP and SLC; the $W$ mass measured at FNAL and UA2; the electron and
neutrino neutral current couplings determined by deep-inelastic
scattering; the degree of atomic parity violation measured in Cesium;
and the ratio of the decay widths of $\tau \to \mu \nu \bar\nu$ and
$\mu\to e \nu \bar
\nu$.  Details of the calculation are reported in \cite{NCETCtwo}.

Table \ref{Pred} compares the predictions of the standard model
and the non-commuting ETC model (for particular values of $1/x$ and
$s^2$) with the experimental values.  For $s^2$, we have chosen a
value of 0.97, at which the ETC gauge coupling is strong yet does not
break the technifermion chiral symmetries by itself\cite{NCETCtwo}.
For $1/x$, in the heavy case we show the best fit
value of $1/x =0.0027$ or equivalently $M_W^H= 9$ TeV.  The best fit
for $1/x$ in the light case lies in the unphysical region of negative
 $x$ but has large uncertainty:  $1/x = -0.17 \pm 0.75$.  For
illustration, we choose a value of $1/x$ from the large range of
values that give a good fit to the data; our choice, $1/x = 0.055$,
corresponds to $M_W^H = 2$ TeV.  We use\cite{alphasmall,langacker}
$\alpha_s(M_Z) = 0.115$ in these fits.

\begin{table}[htbp]
\begin{center}
\begin{tabular}{|c|l|l|l|l|}\hline\hline
Quantity & Experiment & SM & ${\rm ETC}_{\rm heavy}$ &
${\rm ETC}_{\rm light}$ \\\hline \hline
$\Gamma_Z$ & 2.4976 $\pm$ 0.0038 & 2.4923 & 2.4991 & 2.5006 \\
$R_e$ & 20.86 $\pm$ 0.07 & 20.73 & 20.84 & 20.82 \\
$R_\mu$ & 20.82 $\pm$ 0.06 & 20.73 & 20.84 & 20.82 \\
$R_\tau$ & 20.75 $\pm$ 0.07 & 20.73 & 20.74 & 20.73 \\
$\sigma_h$ & 41.49 $\pm$ 0.11 & 41.50 & 41.48 & 41.40 \\
$R_b$ & 0.2202 $\pm$ 0.0020 & 0.2155 & 0.2194 & 0.2188 \\
$A_{FB}^e$ & 0.0156 $\pm$ 0.0034 & 0.0160 & 0.0159 & 0.0160 \\
$A_{FB}^\mu$ & 0.0143 $\pm$ 0.0021 & 0.0160 & 0.0159 & 0.0160 \\
$A_{FB}^\tau$ & 0.0230 $\pm$ 0.0026 & 0.0160 & 0.0164 & 0.0164 \\
$A_{\tau}(P_\tau)$ & 0.143 $\pm$ 0.010 & 0.146 & 0.150 & 0.150 \\
$A_{e}(P_\tau)$ & 0.135 $\pm$ 0.011 & 0.146 & 0.146 & 0.146 \\
$A_{FB}^b$ & 0.0967 $\pm$ 0.0038 & 0.1026 & 0.1026 & 0.1030 \\
$A_{FB}^c$ & 0.0760 $\pm$ 0.0091 & 0.0730 & 0.0728 & 0.0730 \\
$A_{LR}$ & 0.1637 $\pm$ 0.0075 & 0.1460 & 0.1457 & 0.1460 \\
$M_W$ & 80.17 $\pm$ 0.18 & 80.34 & 80.34 & 80.34 \\
$M_W/M_Z$ & 0.8813 $\pm$ 0.0041 & 0.8810 & 0.8810 & 0.8810 \\
$g_L^2(\nu N \rightarrow \nu X)$ & 0.3003 $\pm$ 0.0039 & 0.3030 & 0.3026 &
0.3030  \\
$g_R^2(\nu N \rightarrow \nu X)$ & 0.0323 $\pm$ 0.0033 & 0.0300 & 0.0301 &
0.0300  \\
$g_{eA}(\nu e \rightarrow \nu e)$ & -0.503 $\pm$ 0.018 & -0.506 & -0.506 &
-0.506 \\
$g_{eV}(\nu e \rightarrow \nu e)$ & -0.025 $\pm$ 0.019 & -0.039 & -0.038 &
-0.039 \\
$Q_W(Cs)$ & -71.04 $\pm$ 1.81 & -72.78 &  -72.78 & -72.78 \\
$R_{\mu \tau}$ & 0.9970 $\pm$ 0.0073 & 1.0 & 0.9946 & 1.0  \\
\hline\hline
\end{tabular}
\end{center}
\vskip 0.1in
\caption{Experimental \protect\cite{langacker,blondel,taudec} and
predicted values of
electroweak observables for the standard model and non-commuting ETC
model (heavy and light cases) for $\alpha_s(M_Z)=0.115$, and $s^2=0.97$.
For the heavy case $1/x$ is allowed to assume the best-fit value of
0.0027; for the light case, $1/x$ is set to  $0.055$. The standard
model values
correspond to the best-fit values (with $m_t=173$ GeV, $m_{\rm Higgs}
= 300$ GeV) in \protect\cite{langacker}, corrected for the change in
$\alpha_s(M_Z)$, and the revised extraction \protect\cite{swartz} of
$\alpha_{em}(M_Z)$.}
\label{Pred}
\end{table}

Table \ref{lightFit115} illustrates how well non-commuting ETC models
fit the precision data. This table shows the fit to the standard
model for comparison; as a further benchmark we have included a fit to
purely oblique corrections (the $S$ and $T$ parameters) \cite{ST}.
The percentage quoted in the Table is the probability of obtaining a
 $\chi^2$ as large or larger than that obtained in the fit, for the
given number of degrees of freedom (df), assuming that the model is
correct.  Thus a small probability corresponds to a poor fit.  The
$SM+S,T$ fit demonstrates that merely having more parameters does not
ensure a better fit.

\begin{table}[htbp]
\begin{center}
\begin{tabular}{|l||c||c||c||c|}\hline\hline
Model &  $\chi^2$&df&$\chi^2/{\rm df}$  & probability \\ \hline\hline
SM & $33.8$ & $22$& $1.53$ & $5\%$ \\ \hline
SM+$S$,$T$  &$32.8$ & $20$ & $1.64$ & $4\%$ \\ \hline
${\rm ETC}_{\rm light}$  &$22.6$ & $20$ & $1.13$ & $31\%$ \\ \hline
${\rm ETC}_{\rm heavy}$  &$20.7$ & $19$ & $1.09$ & $36\%$ \\ \hline
\hline
\end{tabular}
\end{center}
\vskip 0.1in
\caption{The best fits for the standard model, beyond the standard model
allowing $S$  and $T$
to vary, and the non-commuting ETC model (heavy and light cases).  The
inputs are: $\alpha_s(M_Z)=0.115$, $s^2=0.97$ (for both ETC models), and
 $1/x=0.055$ (light case ETC). $\chi^2$ is the sum
of the squares of the difference between prediction and experiment,
divided by the error.}
\label{lightFit115}
\end{table}


{}From Tables \ref{Pred} and \ref{lightFit115}
we see that because non-commuting ETC models accommodate
changes in the $Z$ partial widths, they give a
significantly better fit to the experimental data than the standard
model does, even after taking into account that in the fitting
procedure the non-commuting ETC models have two extra parameters.
In particular non-commuting ETC predicts values for
$\Gamma_Z$, $R_e$, $R_\mu$, $R_\tau$,  and $R_b$ that are closer to
experiment than those predicted by the standard model.

For comparison we also performed the fits using\cite{langacker}
$\alpha_s(M_Z)=0.124$;
the quality of the fit is summarized in Table \ref{lightFit124}.
While the standard model fit improves for a
larger value of $\alpha_s(M_Z)$, the light case of the non-commuting
ETC model remains a better fit.

\begin{table}
\begin{center}
\begin{tabular}{|l||c||c||c||c|}\hline\hline
Model &  $\chi^2$&df&$\chi^2/{\rm df}$  & probability \\ \hline\hline
SM & $27.8$ & $21$& $1.33$ & $15\%$ \\ \hline
SM+$S$,$T$  &$27.7$ & $20$ & $1.38$ & $12\%$ \\ \hline
 ${\rm ETC}_{\rm light}$  &$25.0$ & $20$ & $1.25$ & $20\%$ \\ \hline
 ${\rm ETC}_{\rm heavy}$  &$22.3$ & $19$ & $1.17$ & $27\%$ \\ \hline
\hline
\end{tabular}
\end{center}
\vskip 0.1in
\caption{The best fits for the standard model, beyond the standard model
allowing $S$ and $T$
to vary, and the non-commuting ETC model.  The inputs are:
 $\alpha_s(M_Z)=0.124$, $s^2 = 0.97$, and for the light case $1/x=0.055$.}
\label{lightFit124}
\end{table}

%
%%%
%%%FIG-1 GOES HERE
%%%
\begin{figure}
\epsfxsize=4.5truein
\centerline{\epsffile{fig1j.ps}}
\vskip -3in
\caption{Figure 1. Lower bound on $M_W^H$ at 95\% c.l. (solid
line) and 68\% c.l. (dotted line) as a function
of $s^2$ for the light case (using $\alpha_s(M_Z) = 0.115$)}
\label{fig:1}
\end{figure}

\vskip -.2cm
As a bonus, the extra $W$ and $Z$ bosons can be
relatively light.  Figure 1 displays the 95\% and 68\% confidence
level lower bounds
(solid and dotted lines) on the heavy $W$ mass ($M^H_{W}$) for different
values of $s^2$ (with $\alpha_s(M_Z)=0.115$).  The plot was
created as follows: for each value of $s^2$ we fit to the three
independent parameters ($\delta g_L^b$, $\delta g_L^\tau = \delta
g_L^{\nu_\tau}$, and $1/x$); we then found the lower bound on $x$ and
translated it into a lower bound on the heavy $W$ mass.
Note that for $s^2 > 0.85$, the heavy $W$ gauge boson can be as light
as $400$ GeV. In the heavy case, similar work shows that the lowest
possible heavy $W$ mass at the 95\% confidence level  is $\approx 1.6$
TeV, for $0.7< s^2 <0.8$.


\section{Conclusions}

The $Z b\bar b$ vertex is sensitive to the dynamics that generates the
top quark mass.  As such, it provides an excellent test of extended
technicolor models. Measurements of $R_b$ at LEP have already excluded
ETC models in which the ETC and weak gauge groups commute.  Models in
which ETC gauge bosons carry weak charge can give experimentally
allowed values of $R_b$ because contributions to the $Zb\bar b$ vertex
from $Z Z'$ mixing are similar in magnitude and opposite in sign to
those from exchange of the ETC boson that generates the top quark's
mass.  These non-commuting ETC models can actually fit the full set of
precision electroweak data better than the standard model.

\medskip
This work was supported in part by NSF grants PHY-9057173 and
PHY-9501249, and by DOE grant
DE-FG02-91ER40676.

\begin{thebibliography}{99}
\frenchspacing

\bibitem{ETC} S. Dimopoulos and L. Susskind, \NPB{155}
(1979) 237; E. Eichten and K. Lane, \PLB{90} (1980) 125.

\bibitem{tc} S. Weinberg, {\it Phys. Rev.} {\bf D13} (1976) 974 and
{\bf D19} (1979) 1277; L. Susskind, {\it Phys. Rev.} {\bf D20}
(1979) 2619.

\bibitem{zbbone} R.S. Chivukula, S.B. Selipsky, and E.H. Simmons,
{\it Phys. Rev. Lett.} {\bf 69} (1992) 575.

\bibitem{walkrb} R.S. Chivukula, E. Gates, E.H. Simmons, and
J. Terning, {\it Phys. Lett.} {\bf B311} (1993) 383. hep-ph/9305232.

\bibitem{strongETC} T. Appelquist, M. Einhorn, T. Takeuchi, and
L.C.R. Wijewardhana, {\it Phys. Lett.} {\bf 220B}, 223 (1989);
V.A. Miransky and K. Yamawaki, {\it Mod. Phys. Lett.} {\bf A4} (1989)
129; K. Matumoto {\it Prog. Theor. Phys. Lett.} {\bf 81} (1989) 277.

\bibitem{comp} R.~S.~Chivukula, K.~Lane, and A.~G.~Cohen, {\it
Nucl. Phys.} {\bf B 343} (1990) 554; T. Appelquist, J. Terning, and
L. Wijewardhana,  {\it Phys. Rev} {\bf 44} (1991) 871. E.H. Simmons,
{\it Nucl. Phys.} {\bf B312} (1989) 253.

\bibitem{evans} N. Evans, {\it Phys. Lett.} {\bf 331} (1994)
378, hep-ph/9403318; C.D. Carone, E.H. Simmons, and Y. Su.
{\it Phys. Lett.} {\bf B344} 287 (1995), hep-ph/9410242.

\bibitem{yoshi} T. Yoshikawa, {\it Mod. Phys. Lett} {\bf A10} (1995)
1601, hep-ph/9411280; G.-H. Wu, {\it Phys. Rev. Lett.} {\bf 74} (1995)
4137, hep-ph/9412206; K. Hagiwara and N. Kitazawa, hep-ph/9504332;
C.-X. Yue, Y.P. Kuang, G.-R. Lu, L.-D. Wan, hep-ph/9506480.

\bibitem{NCETC}
R.S. Chivukula, E.H. Simmons, and J. Terning, hep-ph/9404209,
{\em Phys. Lett.} {\bf B331} (1994) 383.

\bibitem{NCETCtwo} R.S. Chivukula, E.H. Simmons, and J. Terning,
hep-ph/9506427.

\bibitem{dimanal}A. Manohar and H. Georgi, \NPB{234} (1984) 189.

\bibitem{howardbook} H. Georgi, {\it Weak
Interactions and Modern Particle Theory}, (Benjamin-Cummings, Menlo
Park, 1984), p.77.

\bibitem{ST}B. Lynn, M. Peskin, and R. Stuart, in {\em Physics
at LEP}, J. Ellis and R. Peccei eds. CERN preprint {\bf 86-02} (1986).
M. Golden and L. Randall, {\em Nucl. Phys.} {\bf B361}, 3 (1991);
B. Holdom and J. Terning, {\em Phys. Lett} {\bf B247}, 88 (1990);
M. Peskin and T. Takeuchi, {\em Phys. Rev. Lett.} {\bf 65}, 964 (1990);
A. Dobado, D. Espriu, and M. Herrero, {\em Phys. Lett.} {\bf B253},
161 (1991);
M. Peskin and T. Takeuchi {\em Phys. Rev.} {\bf D46}
381 (1992).

\bibitem{tcalc}
 A.A. Akhundov, D.Yu. Bardin and T. Riemann, \NPB276 (1986) 1 ;
 W. Beenakker and W. Hollik, Z. Phys. C40 (1988) 141;
 J. Bernabeu, A. Pich and A. Santamaria, \PLB200 (1988) 569 ;
 B.W. Lynn and R.G. Stuart, \PLB252 (1990) 676.

\bibitem{walktc}B. Holdom, \PLB{105} (1985) 301;   K.
Yamawaki, M. Bando and K. Matumoto, \PRL{56} (1986)
1335;   V.A. Miransky, \NCA{90} (1985); T. Appelquist, D. Karabali,
and L.C.R. Wijewardhana, \PRD{35}(1987) 389; 149; T. Appelquist
and L.C.R Wijewardhana, \PRD{35} (1987) 774; \PRD{36} (1987) 568.

\bibitem{langacker}P. Langacker, hep-ph/9408310; see also
P. Langacker and J. Erler,
http://www-pdg.lbl.gov/rpp/book/page1304.html,
{\it Phys. Rev.} {\bf D50} (1994) 1304.

\bibitem{blondel}A.Blondel,
http://alephwww.cern.ch/ALEPHGENERAL/reports/reports.html,
CERN PPE/94-133.

\bibitem{taudec}Particle Data Group, {\it Phys. Rev.} {\bf D 50}
(1994); See also A. Pich and J.P. Silva hep-ph/95-5327, FTUV/95-21,
IFIC/95-21.

\bibitem{alphasmall} C.T.H. Davies et. al., hep-ph/9408328,
OHSTPY-HEP-T-94-013, FSU-SCRI-94-79; I. Hinchliffe,
http://www-pdg.lbl.gov/rpp/book/page1297.html,
{\it Phys. Rev.} {\bf D50} (1994) 1297;
M. Virchaux, Saclay preprint, DAPHNIA/SPP 92-30, presented
at the ``QCD 20 years later" workshop,  Aachen Germany, (1992);
R. Voss, in {\it Proceedings of the 1993 International Symposium on
Lepton and Photon Interactions at High Energies}, Ithaca NY (1993).

\bibitem{swartz}M. Swartz,  hep-ph/9411353, SLAC-PUB-6710; see also
A.D. Martin and D. Zeppenfeld, hep-ph/9411377, MADPH-94-855;
S. Eidelman and F. Jegerlehner, hep-ph/9502298, PSI-PR-95-1.


\end{thebibliography}


\end{document}








(1994) 1297;
M. Virchaux, Saclay preprint, DAPHNIA/SPP 92-30, presented
at the ``QCD 20 years later" workshop,  Aachen Germany, (1992);
R. Voss, in {\it Proceedings of the 1993 International Symposium on
Lepton and Photon Interactions at High Energies}, Ithaca NY (1993).

\bibitem{swartz}M. Swartz,  hep-ph/9411353, SLAC-PUB-fig1j.ps000064400000440000044000000534430611714634600140150ustar00e-printse-prints00000000000000%!PS-Adobe-2.0 
%%Title: ncl.SP  -  /Users/terning/LEP
%%Creator: SciPlot
%%CreationDate: Thu Jun 15 16:18:45 1995
%%For: terning
%%DocumentFonts: (atend)
%%Pages: 0 0
%%BoundingBox: 0 0 612 792
%%NXNextStepVersion: 3.0
%%EndComments

%%BeginProcSet: /usr/lib/NextStep/printPackage.ps 3.0
%!
% NeXT Printing Package
% Version: 3.0
% Copyright: 1988, NeXT, Inc.

/__NXdef{1 index where{pop pop pop}{def}ifelse}bind def
/__NXbdef{1 index where{pop pop pop}{bind def}ifelse}bind def
/UserObjects 10 array __NXdef
/defineuserobject{
	exch dup 1 add dup UserObjects length gt{
		array dup 0 UserObjects putinterval
		/UserObjects exch def
	}{pop}ifelse UserObjects exch 3 -1 roll put
}__NXbdef
/undefineuserobject{UserObjects exch null put}__NXbdef
/execuserobject{UserObjects exch get exec}__NXbdef
/__NXRectPath{4 2 roll moveto 1 index 0 rlineto
0 exch rlineto neg 0 rlineto closepath}__NXbdef
/__NXProcessRectArgs{
	1 index type /arraytype eq{
		exch 0 4 2 index length 1 sub{
			dup 3 add 1 exch{1 index exch get exch}for
			5 1 roll 5 index exec
		}for pop pop
	}{exec}ifelse
}__NXbdef
/rectfill{gsave newpath {__NXRectPath fill} __NXProcessRectArgs grestore}__NXbdef
/rectclip{newpath {__NXRectPath} __NXProcessRectArgs clip newpath}__NXbdef
/rectstroke{
	gsave newpath dup type /arraytype eq{dup length 6 eq}{false}ifelse{
		{gsave __NXRectPath null concat stroke grestore}
		dup length array cvx copy dup 2 4 -1 roll put __NXProcessRectArgs
	}{{__NXRectPath stroke} __NXProcessRectArgs}ifelse grestore
}__NXbdef
/_NXLevel2 systemdict /languagelevel known {languagelevel 2 ge}{false}ifelse __NXdef
/xyshow{
	0 1 3 index length 1 sub{
		currentpoint 4 index 3 index 1 getinterval show
		3 index 3 index 2 mul 1 add get add exch
		3 index	3 index 2 mul get add exch moveto pop
	}for pop pop
}__NXbdef
/xshow{
	0 1 3 index length 1 sub{
		currentpoint 4 index 3 index 1 getinterval show
		exch 3 index 3 index get add exch moveto pop
	}for pop pop
}__NXbdef
/yshow{
	0 1 3 index length 1 sub{
		currentpoint 4 index 3 index 1 getinterval show
		3 index 3 index get add moveto pop
	}for pop pop
}__NXbdef
/arct{arcto pop pop pop pop}__NXbdef
/setbbox{pop pop pop pop}__NXbdef
/ucache{}__NXbdef
/ucachestatus{mark 0 0 0 0 0}__NXbdef
/setucacheparams{cleartomark}__NXbdef
/uappend{systemdict begin cvx exec end}__NXbdef
/ueofill{gsave newpath uappend eofill grestore}__NXbdef
/ufill{gsave newpath uappend fill grestore}__NXbdef
/ustroke{
	gsave newpath dup length 6 eq
	{exch uappend concat}{uappend}ifelse
	stroke grestore
}__NXbdef
/__NXustrokepathMatrix dup where {pop pop}{matrix def}ifelse
/ustrokepath{
	newpath dup length 6 eq{
		exch uappend __NXustrokepathMatrix currentmatrix exch concat
		strokepath setmatrix
	}{uappend strokepath}ifelse
} __NXbdef
/upath{
	[exch {/ucache cvx}if pathbbox /setbbox cvx
	 {/moveto cvx}{/lineto cvx}{/curveto cvx}{/closepath cvx}pathforall]cvx
} __NXbdef
/setstrokeadjust{pop}__NXbdef
/currentstrokeadjust{false}__NXbdef
/selectfont{exch findfont exch
dup type /arraytype eq {makefont}{scalefont}ifelse setfont}__NXbdef
/_NXCombineArrays{
	counttomark dup 2 add index dup length 3 -1 roll {
		2 index length sub dup 4 1 roll 1 index exch 4 -1 roll putinterval exch
	}repeat pop pop pop
}__NXbdef
/flushgraphics{}def
/setwindowtype{pop pop}def
/currentwindowtype{pop 0}def
/setalpha{pop}def
/currentalpha{1.0}def
/hidecursor{}def
/obscurecursor{}def
/revealcursor{}def
/setcursor{4 {pop}repeat}bind def
/showcursor{}def
/NextStepEncoding where not{
/NextStepEncoding StandardEncoding 256 array copy def
0 [129/Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/Ccedilla/Egrave
/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex/Idieresis
/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis/Ugrave/Uacute
/Ucircumflex/Udieresis/Yacute/Thorn/mu/multiply/divide/copyright
176/registered 181/brokenbar 190/logicalnot 192/onesuperior 201/twosuperior
204/threesuperior 209/plusminus/onequarter/onehalf/threequarters/agrave
/aacute/acircumflex/atilde/adieresis/aring/ccedilla/egrave/eacute
/ecircumflex/edieresis/igrave 226/iacute 228/icircumflex/idieresis/eth
/ntilde 236/ograve/oacute/ocircumflex/otilde/odieresis 242/ugrave/uacute
/ucircumflex 246/udieresis/yacute 252/thorn/ydieresis]
{dup type /nametype eq
 {NextStepEncoding 2 index 2 index put pop 1 add}{exch pop}ifelse
}forall pop
/NextStepEncoding NextStepEncoding readonly def
/_NXfstr 128 string dup 0 (_NX) putinterval def
/_NXfindfont /findfont load def
/findfont{
 % Because we can never let NextStepEncoding get into
 % SharedFontDirectory, we cannot reencode a font to NextStepEncoding
 % if we are in shared mode.  So if currentshared is true,
 % we call the normal findfont and return that
 /currentshared where {pop currentshared} {false} ifelse
 {_NXfindfont}
 {dup _NXfstr 3 125 getinterval cvs length 3 add _NXfstr 0 3 -1 roll
  getinterval cvn exch FontDirectory 2 index known 
  {pop FontDirectory exch get}
  {_NXfindfont dup /Encoding get StandardEncoding eq
   {	dup length dict exch
	{1 index /FID ne {2 index 3 1 roll put}{pop pop}ifelse}forall
	 dup /Encoding NextStepEncoding put definefont
	}{exch pop} ifelse
   }ifelse
 }ifelse
}bind def
}{pop}ifelse
/_NXImageString {/__NXImageString where{pop}{/__NXImageString 4000 string __NXdef}ifelse __NXImageString}__NXbdef
/_NXDoImageOp{
	3 dict begin /parr 5 array def 1 index{dup}{1}ifelse /chans exch def
	chans 2 add 2 roll parr 0 chans getinterval astore pop
	5 index 4 index mul 2 index{1 sub 8 idiv 1 add mul}{mul 1 sub 8 idiv 1 add}ifelse
	4 index mul /totbytes exch def pop exch pop
	gsave matrix invertmatrix concat 0.5 setgray 0 0 4 2 roll rectfill grestore
	{0 1 chans 1 sub{parr exch get exec length totbytes exch sub /totbytes exch def}for totbytes 0 le{exit}if}loop end
}__NXbdef
/alphaimage{1 add _NXDoImageOp}def
_NXLevel2{ 
	/NXCalibratedRGBColorSpace where{pop}{
		/NXCalibratedRGBColorSpace
		{mark /NXCalibratedRGB /ColorSpace findresource exch pop}stopped
		{cleartomark /NXCalibratedRGB[/CIEBasedABC 2 dict dup begin 
		/MatrixLMN[.4124 .2126 .0193 .3576 .7152 .1192 .1805 .0722 .9505]def
		/WhitePoint[.9505 1 1.089] def end] /ColorSpace defineresource}if def}ifelse
	/nxsetrgbcolor{NXCalibratedRGBColorSpace setcolorspace setcolor}__NXbdef
	/nxsetgray{dup dup nxsetrgbcolor}__NXbdef
	/_NXCalibratedImage{exch{array astore dup length true}{false}ifelse
		8 -1 roll{NXCalibratedRGBColorSpace setcolorspace}if
		8 dict dup 9 1 roll begin /ImageType 1 def /MultipleDataSources exch def
		currentcolorspace 0 get /Indexed eq{pop /Decode[0 2 6 index exp 1 sub]def}
		{2 mul dup array /Decode exch def 1 sub 0 1 3 -1 roll{Decode exch dup 2 mod put}for}ifelse
		/DataSource exch def /ImageMatrix exch def 
		/BitsPerComponent exch def /Height exch def /Width exch def end image}__NXbdef
} {
	/setcmykcolor{
		1.0 exch sub dup dup 6 -1 roll sub dup 0 lt{pop 0}if 5 1 roll
		4 -1 roll sub dup 0 lt{pop 0}if 3 1 roll exch sub dup 0 lt{pop 0}if setrgbcolor}__NXbdef
	/currentcmykcolor{currentrgbcolor 3{1.0 exch sub 3 1 roll}repeat 0}__NXbdef
	/colorimage{_NXDoImageOp}__NXbdef
	/nxsetrgbcolor{setrgbcolor}__NXbdef /nxsetgray{setgray}__NXbdef
	/setpattern{pop .5 setgray}__NXbdef
	/_NXCalibratedImage{dup 1 eq {pop pop image}{colorimage}ifelse pop}__NXbdef
} ifelse
/_NXSetCMYKOrRGB where{pop}{
	mark{systemdict /currentwindow get exec}stopped
	{{pop pop pop setcmykcolor}}{{nxsetrgbcolor pop pop pop pop}}ifelse /_NXSetCMYKOrRGB exch def cleartomark
}ifelse
%%EndProcSet

gsave
-1 -9 translate
 /__NXbasematrix matrix currentmatrix def
grestore
%%EndProlog
%%BeginSetup
%%EndSetup
%%90 rotate
0 390 translate
gsave
0 setgray
2 setlinecap
0 nxsetgray
/Helvetica findfont
16 scalefont setfont
0 nxsetgray
100 60 moveto
0.5 setlinewidth
0 setlinecap
0 8 rlineto
100 367 moveto
0 -8 rlineto
stroke
0 nxsetgray
/Helvetica findfont
16 scalefont setfont
100 50 moveto
-4.448 0 rmoveto
0 -12.48 rmoveto
(0) show
stroke
0 nxsetgray
206 60 moveto
0.5 setlinewidth
0 setlinecap
0 8 rlineto
206 367 moveto
0 -8 rlineto
stroke
0 nxsetgray
/Helvetica findfont
16 scalefont setfont
206 50 moveto
-11.12 0 rmoveto
0 -12.48 rmoveto
(0.2) show
stroke
0 nxsetgray
312 60 moveto
0.5 setlinewidth
0 setlinecap
0 8 rlineto
312 367 moveto
0 -8 rlineto
stroke
0 nxsetgray
/Helvetica findfont
16 scalefont setfont
312 50 moveto
-11.12 0 rmoveto
0 -12.48 rmoveto
(0.4) show
stroke
0 nxsetgray
418 60 moveto
0.5 setlinewidth
0 setlinecap
0 8 rlineto
418 367 moveto
0 -8 rlineto
stroke
0 nxsetgray
/Helvetica findfont
16 scalefont setfont
418 50 moveto
-11.12 0 rmoveto
0 -12.48 rmoveto
(0.6) show
stroke
0 nxsetgray
524 60 moveto
0.5 setlinewidth
0 setlinecap
0 8 rlineto
524 367 moveto
0 -8 rlineto
stroke
0 nxsetgray
/Helvetica findfont
16 scalefont setfont
524 50 moveto
-11.12 0 rmoveto
0 -12.48 rmoveto
(0.8) show
stroke
0 nxsetgray
630 60 moveto
0.5 setlinewidth
0 setlinecap
0 8 rlineto
630 367 moveto
0 -8 rlineto
stroke
0 nxsetgray
/Helvetica findfont
16 scalefont setfont
630 50 moveto
-4.448 0 rmoveto
0 -12.48 rmoveto
(1) show
stroke
0 nxsetgray
/Helvetica findfont
18 scalefont setfont
/Helvetica findfont
18 scalefont setfont
/Helvetica findfont
14.4 scalefont setfont
365 27.52 moveto
-8.503201 0 rmoveto
0 -14.04 rmoveto
/Helvetica findfont
18 scalefont setfont
(s) show
0 7.3008 rmoveto
/Helvetica findfont
14.4 scalefont setfont
(2) show
0 -7.3008 rmoveto
0 setgray
0 nxsetgray
/Helvetica findfont
16 scalefont setfont
0 nxsetgray
100 60 moveto
0.5 setlinewidth
0 setlinecap
8 0 rlineto
630 60 moveto
-8 0 rlineto
stroke
0 nxsetgray
/Helvetica findfont
16 scalefont setfont
90 60 moveto
-8.896 0 rmoveto
0 -6.24 rmoveto
(0) show
stroke
0 nxsetgray
100 162.333328 moveto
0.5 setlinewidth
0 setlinecap
8 0 rlineto
630 162.333328 moveto
-8 0 rlineto
stroke
0 nxsetgray
/Helvetica findfont
16 scalefont setfont
90 162.333328 moveto
-8.896 0 rmoveto
0 -6.24 rmoveto
(1) show
stroke
0 nxsetgray
100 264.666656 moveto
0.5 setlinewidth
0 setlinecap
8 0 rlineto
630 264.666656 moveto
-8 0 rlineto
stroke
0 nxsetgray
/Helvetica findfont
16 scalefont setfont
90 264.666656 moveto
-8.896 0 rmoveto
0 -6.24 rmoveto
(2) show
stroke
0 nxsetgray
100 367 moveto
0.5 setlinewidth
0 setlinecap
8 0 rlineto
630 367 moveto
-8 0 rlineto
stroke
0 nxsetgray
/Helvetica findfont
16 scalefont setfont
90 367 moveto
-8.896 0 rmoveto
0 -6.24 rmoveto
(3) show
stroke
0 nxsetgray
/Helvetica findfont
18 scalefont setfont
/Helvetica findfont
18 scalefont setfont
/Helvetica findfont
14.4 scalefont setfont
/Helvetica findfont
18 scalefont setfont
/Helvetica findfont
14.4 scalefont setfont
/Helvetica findfont
18 scalefont setfont
66.104004 213.5 moveto
0 -39.295799 rmoveto
90 rotate
/Helvetica findfont
18 scalefont setfont
(M) show
0 -3.9312 rmoveto
/Helvetica findfont
14.4 scalefont setfont
(W) show
0 3.9312 rmoveto
0 7.3008 rmoveto
-13.593599 0 rmoveto
/Helvetica findfont
14.4 scalefont setfont
(H) show
0 -7.3008 rmoveto
3.196799 0 rmoveto
/Helvetica findfont
18 scalefont setfont
( \(TeV\)) show
270 rotate
0 setgray
0 nxsetgray
0 nxsetgray
/Helvetica findfont
18 scalefont setfont
365 387 moveto
-33.012001 0 rmoveto
(Figure 1) show
stroke
0 setgray
0 nxsetgray
0 setgray
0 setgray
[] 0 setdash
1.8 setlinewidth
2 setlinecap
0 nxsetgray
100 60 moveto
100 367 lineto
stroke
100 60 moveto
630 60 lineto
stroke
630 60 moveto
630 367 lineto
stroke
100 367 moveto
630 367 lineto
stroke
0 setgray
0 nxsetgray
1 setlinewidth
0 setlinecap
[] 0 setdash
1 setlinejoin
gsave
newpath
systemdict
begin
151.421661 101.790886 624.170532 352.116333 setbbox
151.421661 352.116333 moveto
157.186996 334.385742 lineto
162.952332 319.015991 lineto
168.717682 305.505127 lineto
174.482483 293.490082 lineto
180.247833 282.699951 lineto
186.013168 272.92865 lineto
191.778519 264.015717 lineto
197.54332 255.834488 lineto
203.308655 248.283203 lineto
209.074005 241.278992 lineto
214.83934 234.753922 lineto
220.604675 228.651367 lineto
226.369492 222.924088 lineto
232.134827 217.531631 lineto
237.900162 212.439926 lineto
243.665512 207.61972 lineto
249.430328 203.045731 lineto
255.195663 198.695953 lineto
260.960999 194.550934 lineto
266.726349 190.594223 lineto
272.491669 186.810852 lineto
278.2565 183.187836 lineto
284.02182 179.713409 lineto
289.78717 176.377457 lineto
295.552521 173.170532 lineto
301.317841 170.084473 lineto
307.082672 167.112091 lineto
312.847992 164.246353 lineto
318.613342 161.481506 lineto
324.378693 158.812256 lineto
330.143494 156.233353 lineto
335.908844 153.740707 lineto
341.674164 151.330246 lineto
347.439514 148.998276 lineto
353.204834 146.741623 lineto
358.969666 144.557205 lineto
364.735016 142.442291 lineto
370.500336 140.394699 lineto
376.265686 138.412003 lineto
382.031006 136.492218 lineto
387.795837 134.633743 lineto
393.561157 132.834824 lineto
399.326508 131.093933 lineto
405.091858 129.409836 lineto
410.856659 127.781509 lineto
416.622009 126.207825 lineto
422.387329 124.687767 lineto
428.152679 123.220718 lineto
433.91803 121.805855 lineto
439.682831 120.442673 lineto
445.448181 119.130554 lineto
451.213501 117.869095 lineto
456.978851 116.657867 lineto
462.744202 115.49649 lineto
468.509003 114.38485 lineto
474.274353 113.322418 lineto
480.039673 112.309219 lineto
485.805023 111.344933 lineto
491.569824 110.429459 lineto
497.335175 109.562386 lineto
503.100525 108.74382 lineto
508.865845 107.973358 lineto
514.631165 107.250679 lineto
520.395996 106.57579 lineto
526.161316 105.948074 lineto
531.926697 105.367332 lineto
537.692017 104.833054 lineto
543.457336 104.344719 lineto
549.222168 103.901817 lineto
554.987488 103.503738 lineto
560.752869 103.149666 lineto
566.518188 102.838882 lineto
572.283508 102.570465 lineto
578.04834 102.34359 lineto
583.81366 102.157036 lineto
589.579041 102.00988 lineto
595.34436 101.900894 lineto
601.109192 101.828957 lineto
606.874512 101.792732 lineto
612.639832 101.790886 lineto
618.405212 101.822205 lineto
624.170532 101.885139 lineto
end
stroke
grestore
stroke
[] 0 setdash
0 setlinejoin
0 setgray
[] 0 setdash
2 setlinecap
0 nxsetgray
1 setlinewidth
0 setlinecap
2 setlinejoin
0 setlinecap
1 setlinewidth
179.747833 358.972565 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
185.513168 346.200012 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
191.278519 334.555817 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
197.04332 323.872742 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
202.808655 314.016296 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
208.574005 304.877716 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
214.33934 296.367371 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
220.104675 288.410339 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
225.869492 280.944305 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
231.634827 273.916382 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
237.400162 267.281281 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
243.165512 261.00058 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
248.930328 255.040985 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
254.695663 249.373352 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
260.460999 243.972412 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
266.226349 238.816254 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
271.991669 233.885208 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
277.7565 229.162109 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
283.52182 224.631622 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
289.28717 220.280304 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
295.052521 216.095886 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
300.817841 212.067749 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
306.582672 208.186035 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
312.347992 204.441956 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
318.113342 200.827866 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
323.878693 197.336655 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
329.643494 193.961807 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
335.408844 190.697678 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
341.174164 187.539154 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
346.939514 184.481445 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
352.704834 181.520416 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
358.469666 178.652115 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
364.235016 175.873154 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
370.000336 173.180557 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
375.765686 170.571472 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
381.531006 168.043335 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
387.295837 165.594086 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
393.061157 163.221695 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
398.826508 160.92421 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
404.591858 158.700287 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
410.356659 156.548645 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
416.122009 154.468094 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
421.887329 152.457443 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
427.652679 150.51619 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
433.41803 148.643173 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
439.182831 146.83812 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
444.948181 145.100708 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
450.713501 143.430328 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
456.478851 141.826859 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
462.244202 140.290009 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
468.009003 138.819901 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
473.774353 137.416199 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
479.539673 136.078995 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
485.305023 134.808426 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
491.069824 133.604584 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
496.835175 132.467255 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
502.600525 131.396744 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
508.365845 130.392853 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
514.131165 129.45578 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
519.895996 128.585342 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
525.661316 127.781303 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
531.426697 127.043579 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
537.192017 126.371864 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
542.957336 125.765747 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
548.722168 125.224602 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
554.487488 124.748039 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
560.252869 124.33522 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
566.018188 123.985146 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
571.783508 123.696976 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
577.54834 123.469696 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
583.31366 123.301971 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
589.079041 123.192368 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
594.84436 123.139664 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
600.609192 123.14212 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
606.374512 123.198303 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
612.139832 123.306366 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
617.905212 123.464882 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
623.670532 123.671288 moveto
1 0 rlineto
stroke
1 setlinewidth
stroke
0 setgray
[] 0 setdash
2 setlinecap
0 setgray
2 setlinecap
1.8 setlinewidth
stroke
stroke
grestore
showpage
%%Trailer
inewidth
606.374512 123.198303 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
612.139832 123.306366 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
61165 107.250679 lineto
520.395996 106.57579 lineto
526.161316 105.948074 lineto
531.926697 105.367332 lineto
537.692017 104.833054 lineto
543.457336 104.344719 lineto
549.222168 103.901817 lineto
554.987488 103.503738 lineto
560.752869 103.149666 lineto
566.518188 102.838882 lineto
572.283508 102.570465 lineto
578.04834 102.34359 lineto
583.81366 102.157036 lineto
589.579041 102.00988 lineto
595.34436 101.900894 lineto
601.109192 101.828957 lineto
606.874512 101.792732 lineto
612.639832 101.790886 lineto
618.405212 101.822205 lineto
624.170532 101.885139 lineto
end
stroke
grestore
stroke
[] 0 setdash
0 setlinejoin
0 setgray
[] 0 setdash
2 setlinecap
0 nxsetgray
1 setlinewidth
0 setlinecap
2 setlinejoin
0 setlinecap
1 setlinewidth
179.747833 358.972565 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
185.513168 346.200012 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
191.278519 334.555817 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
197.04332 323.872742 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
202.808655 314.016296 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
208.574005 304.877716 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
214.33934 296.367371 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
220.104675 288.410339 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
225.869492 280.944305 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
231.634827 273.916382 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
237.400162 267.281281 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
243.165512 261.00058 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
248.930328 255.040985 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
254.695663 249.373352 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
260.460999 243.972412 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
266.226349 238.816254 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
271.991669 233.885208 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
277.7565 229.162109 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
283.52182 224.631622 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
289.28717 220.280304 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
295.052521 216.095886 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
300.817841 212.067749 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
306.582672 208.186035 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
312.347992 204.441956 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
318.113342 200.827866 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
323.878693 197.336655 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
329.643494 193.961807 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
335.408844 190.697678 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
341.174164 187.539154 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
346.939514 184.481445 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
352.704834 181.520416 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
358.469666 178.652115 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
364.235016 175.873154 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
370.000336 173.180557 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
375.765686 170.571472 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
381.531006 168.043335 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
387.295837 165.594086 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
393.061157 163.221695 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
398.826508 160.92421 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
404.591858 158.700287 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
410.356659 156.548645 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setlinecap
1 setlinewidth
416.122009 154.468094 moveto
1 0 rlineto
stroke
1 setlinewidth
2 setlinejoin
0 setli