%Paper: 
%From: Rey Soo Jong <sjrey@phyb.snu.ac.kr>
%Date: Tue, 5 Apr 94 19:49:13 KST

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\documentstyle[preprint,aps]{revtex}
\begin{document}
\draft
\preprint{\vbox
{\hbox{SNUTP 94-08} \hbox \hbox{March 1994} }}
\title{Instanton Contribution to \\
        $B \rightarrow X_u e \bar \nu $ Decay}
\author{Junegone Chay\footnote{E-mail address:
\tt chay@kupt.korea.ac.kr}
and Soo-Jong Rey\footnote{E-mail address:
\tt sjrey@phyb.snu.ac.kr}}
\address{Physics Department, Korea University, Seoul 136-701,
Korea${}^*$ \\
  Physics Department and Center for Theoretical Physics \\
  Seoul National University, Seoul 151-752, Korea${}^\dagger$ }

\date{\today}
\maketitle

\begin{abstract}
We study instanton effects on inclusive semileptonic
$b \rightarrow u$ decay using the heavy quark effective
field theory and the operator product expansion.
The effect contributes not only to the hadronic matrix element
but also to
the coefficient functions in the operator product expansion.
We find that the
coefficient function is singular near the boundaries of the phase
space.
In order to use perturbative QCD reliably, it is necessary to
introduce smearing near the boundary.
However the instanton contribution to $b \rightarrow c$ decay seems
negligibly small.
\end{abstract}
\pacs{12.15.Ji, 12.38.Lg, 13.20.Jf, 14.40.Jz}
\narrowtext
\section {Introduction}
The Cabibbo-Kobayashi-Maskawa matrix element $V_{ub}$ may
be extracted from the shape of electron energy spectrum in
inclusive semileptonic $B$ decay.
In order to avoid large $b \rightarrow c$ decay background,
we have to
look at the endpoint region of ${\cal O}(300 {\rm MeV})$.
However this is precisely the regime in which theoretical
prediction is
least understood due to various low-energy QCD effects. Therefore
experimental data have been compared mainly with phenomenological
models such as ACCMM~\cite{accmm} or ISGW~\cite{isgw}.

Recently there has been important theoretical progress in
inclusive semileptonic $B$ decay. The first model-independent QCD
approach
has been formulated using the heavy quark effective field
theoy(HQEFT) and the operator product expansion(OPE).
Chay, Georgi and Grinstein~\cite{chayetal} have shown that the
weak decay of
$B$ mesons can be described by a systematic expansion in
inverse powers of
$m_b$, in which the leading contribution reproduces the
parton-model result (See also Ref.~\cite{bigietal}.).
Using the OPE, Chay et.al. have shown that next-order
corrections are of order $(\Lambda /m_b)^2$,
where $\Lambda$ is the QCD scale, hence expected to be small.
Mannel~\cite{mannel}, Manohar and Wise~\cite{manoharwise}
have analyzed these corrections and concluded that these
corrections are singular at the boundaries
of the Dalitz plot, which necessitates some smearing prescription
before comparing with experimental data.

There are also radiative QCD corrections to the decay
rate~\cite{corboetal}.
In the leading log approximation, double logarithms are
summed to provide the Sudakov factor.
In $b \rightarrow u$ decay, this changes significantly
the shape of the electron spectrum near the endpoint.
Falk, Jenkins, Manohar and Wise~\cite{falketal}
have considered the validity of this resummation near the
endpoint of electron energy.
By studying the pattern of the summation of subleading logarithms,
they have reached a conclusion that a smearing is necessary for
the validity of the leading log approximation.
Bigi et.al.~\cite{bigiope} have reached essentially
the same conclusion but with a careful study of running
$\alpha_s (k^2)$.

The idea of using the OPE in the approach of Ref.~\cite{chayetal}
is that it factorizes the short-distance and the long-distance
physics in terms of the product of the Wilson coefficient
functions and the matrix elements of local operators.
So far the main focus of recent discussions has been on the
systematic analysis  of nonperturbative hadronic matrix elements.
However the coefficient functions may be affected by
nonperturbative effects as well.
One of the examples is an instanton contribution.

In this paper we investigate the effect of instantons on the
coefficient functions in $B$ decay.
Due to asymptotic freedom $\alpha_s (Q^2) \sim 1 / \ln Q^2$
as $Q^2 \rightarrow \infty$, we expect that the strength of
a single instanton is of order $\exp(-2 \pi / \alpha_s (Q^2))$.
At large momenta this is negligible compared to perturbative
QCD corrections.
However the characteristic scale for $\alpha_s$ is not $m_b$
but the momentum transfer to final hadrons.
Therefore near the endpoint of electron energy spectrum
where $\alpha_s$ becomes large, it is likely that instanton
effects on the decay rate may grow sizably.
For large momentum transfer $Q^2$ to final hadrons,
we expect that small instantons of size $\rho
\mathrel{\rlap{\lower3pt\hbox{\hskip0pt$\sim$}}\raise1pt\hbox{$<$}}
1/|Q|$ are most relevant.
We study their effect by calculating one instanton
(+ anti-instanton) corrections to the inclusive semileptonic
$b$ decay rate.
We find that the effect is negligible in most of the
the phase space except near the boundaries of the Dalitz plot.
At the boundaries we find that the instanton contribution
becomes singular.
Therefore the decay rate has to be smeared in such a way that
the instanton contribution remains small compared to the
parton-model result.

In this estimate we use the dilute gas approximation since the
main contribution comes from small instantons.
Instantons contribute not only to the hadronic matrix elements
but also to the coefficient functions.
We emphasize that we have neither attempted to calculate QCD
radiative corrections in the realistic instanton background
nor other nonperturbative effects such as multi-instantons or
renormalons.
It is possible that any of these give bigger contributions
than a single instanton contribution.
Even in this case our estimate may still characterize a typical
size of nonperturbative effects in the coefficient functions.
After all the dilute instantons are the only known
calculable nonperturbative effect in QCD.

This paper is organized as follows. In Section 2 we discuss
the kinematics relevant to the inclusive semileptonic $B$ decay.
In Section 3 we recapitulate the OPE and summarize the general
structure of local operators and their coefficient functions.
In Section 4 we compute the instanton contribution to the
coefficient functions in the forward Compton scattering amplitude.
In Section 5 we discuss numerical estimate of the results of
Section 4.
We conclude in Section 6  and also comment on the nonperturbative
effects in other cases.

\section{Kinematics}
The semileptonic $b \rightarrow u $ decay is described by the weak
Hamiltonian
\begin{eqnarray}
\displaystyle
H_W & = & \frac{G_F}{\sqrt{2}} V_{ub} {\overline u} \gamma^{\mu}
(1+\gamma_5 )b \cdot {\overline e}\gamma_{\mu} (1+\gamma_5) \nu_e
\nonumber \\
& = & \frac{G_F}{\sqrt{2}} V_{ub} \, J_u^{\mu} J_{e \mu}^{\dagger},
\label{ham}
\end{eqnarray}
where $J^\mu_u = \bar u (1 + \gamma_5) b$ and
$J^\mu_e = \bar \nu_e \gamma^\mu (1 + \gamma_5) e$.
For $b \rightarrow c$ decay the Hamiltonian is obtained from
Eq.~(\ref{ham}) by replacing $u$ and $V_{ub}$ by $c$ and
$V_{cb}$ respectively.
The inclusive decay rate is related to the hadronic tensor
defined by
\begin{equation}
W^{\mu \nu} = (2\pi)^3 \sum_X \delta^4 (p_B -q - p_X) \langle B |
J_u^{\mu \dagger} |X\rangle \langle X | J_u^{\nu} |B\rangle,
\label{wmunu}
\end{equation}
where $X$ denotes all possible hadronic final states.
Let $k^\mu_e$ be the electron momentum, $k^\mu_{\bar \nu}$ be the
antineutrino momentum, and $p^\mu_B = M_B v^\mu$ be the momentum
of the $B$ meson.
Then the hadronic tensor $W_{\mu \nu}$ depends on the timelike
vector $q^{\mu} = k^{\mu}_e + k^{\mu}_{\bar \nu}$.
In this paper we do not distinguish the $B$ meson mass $M_B$ and
the $b$ quark mass $m_b$.
This difference may be incorporated into the kinematics as
discussed in Refs.~\cite{bigietal,manoharwise}.

The differential decay rate of the $B$ meson is given by
\begin{equation}
d\Gamma = \frac{G_F^2}{4 m_b} |V_{ub}|^2 W^{\mu \nu} L_{\mu \nu}
d({\rm {PS} }),
\label{differential}
\end{equation}
where $L_{\mu\nu}$ is the leptonic tensor given by
\begin{equation}
L^{\mu \nu} = 8 (k^{\mu}_e k^{\nu}_{\bar \nu} +
k^{\nu}_e k^{\mu}_{\bar \nu} -g^{\mu \nu} k_e \cdot k_{\bar \nu}
-i{\epsilon^{\mu\nu}}_{\alpha\beta} k^{\alpha}_e
k^{\beta}_{\bar \nu} ).
\label{lmunu}
\end{equation}
We can express the phase space integral in terms of the three
independent
kinematic variables $ y = 2 E_e / m_b$, $\hat q^2 = q^2/m_b^2$
and $v \cdot \hat q = v \cdot q / m_b$ as
\begin{equation}
d ( {\rm PS})
= {d^3 k \over (2 \pi)^3 2 E_e} {d^3 k' \over (2 \pi)^3 2 E_\nu}
= {m^4_b \over 2^7 \pi^4} \,\, d v \!\cdot\!\hat q \,\,dy\,\,
d \hat q^2.
\label{psint}
\end{equation}

In the complex $v \cdot \hat q$ plane with $\hat q^2$ fixed,
$W^{\mu \nu}$ is related to the discontinuity of the forward
Compton scattering amplitude $T^{\mu \nu}$ across a physical cut as
\begin{equation}
W^{\mu\nu} = 2 \, {\rm Im} \, T^{\mu\nu},
\end{equation}
where
\begin{equation}
T^{\mu\nu} (q, v) = -i \! \int d^4x \, e^{i q \cdot x} \,
\langle B | T\{J_u^{\mu}(x)^{\dagger} J_u^{\nu}(0)\} |B \rangle.
\label{tmunu}
\end{equation}

To evaluate the decay rate it is necessary to examine the
analytic structure
of $T^{\mu \nu}(q, v)$ ~\cite{chayetal,manoharwise}.
In the complex $v\cdot\hat q$ plane, a ``physical cut'' relevant
to the decay is located on the real axis between
$\sqrt{\hat q^2} \le v\cdot \hat q \le (1 + \hat q^2 -\rho )/2$
where $\rho \equiv m_u^2 / m_b^2$ is the mass ratio-squared of
the $u$ quark to the $b$ quark.
Discontinuity of $T^{\mu \nu}$ across this physical cut
yields $W^{\mu\nu}$ for semileptonic $B$ decay. There are also
other cuts for $v\cdot \hat q \le -\sqrt{\hat q^2}$ and
$v \cdot \hat q \ge \frac{1}{2} ((2 + \sqrt \rho)^2 - \hat q^2 -1)$
but they correspond to other physical processes.
In Fig.1 we show the analytic structure of $T^{\mu \nu}$ in
$v \cdot\hat q$ plane.
As $v\cdot \hat q$ approaches $(1 + \hat q^2- \rho^2)/2$ the
final hadron reaches a resonance region.
There we expect significant nonperturbative QCD effects.
Chay et.al.~\cite{chayetal} have observed that one can calculate
the decay rate even in this limit perturbatively by choosing
the integration contour away from the resonance region.
This should provide a good approach to $b \rightarrow c$
inclusive decay.
Since $m_c^2 \gg \Lambda^2$, the other cut on the right-hand
side in Fig.1 always stays away from the physical cut.

However this is no longer true in $b \rightarrow u$ decay.
In this case we cannot choose a contour away from the resonance
region without enclosing some of the unphysical cut.
When $\hat q^2 \rightarrow 1$ and $\rho \rightarrow 0$,
the physical cut and the right-hand side cut in Fig.1 pinch
together. This is in fact the origin of large logarithms of
lepton energy found in Ref.~\cite{corboetal}.
Since the charm threshold lies at $y = 1 - \rho \sim 0.9$,
we have to deal with this problem.
For the moment we consider $q^2 \ll m_b^2 $ but
$(m_b v - q)^2 \gg \Lambda^2$ in order to calculate the decay
distribution reliably using perturbative QCD.
In the end we are interested in how far the result may be
extended to the endpoint region.

The total decay rate is given by
\begin{equation}
\Gamma = {G_F^2 m_b^5 \over 2^9 \pi^4} |V_{ub}|^2 \int_0^1 d y \,
\int_0^y \! d \hat q^2
\int_{{y \over 2} + {\hat q^2 \over 2 y}}^{{1 + \hat q^2 \over 2}}
\!\! d \hat v \cdot q \, {W^{\mu \nu} L_{\mu \nu} \over m_b^2}.
 \label {total1}
\end{equation}
Note that the interval of $v \cdot \hat q $ integration in
Eq.~(\ref{total1}) does not coincide with the physical cut.
{}From the kinematics the minimum of
$v \cdot \hat q$ is at point $P$ in Fig.1 where
$v \cdot \hat q = y / 2 + \hat q^2 / 2 y$.
In Eq.~(\ref{total1}) $W^{\mu \nu} L_{\mu \nu}$ is evaluated from
the discontinuity of $T^{\mu \nu} L_{\mu \nu}$ along the contour
$C^{\prime}$ in Fig.1.
Using Cauchy's theorem this is related to the contour integral
along the contour $C$ in the complex $v \cdot \hat q$ plane.
The integral along $C$ is reliably evaluated using perturbative
QCD as long as $(m_b v - q)^2 \gg \Lambda^2$.
Then the double differential decay rate can be expressed as
\begin{equation}
{d^2 \Gamma \over d \hat q^2 d y} = - {G_F^2 m_b^5 \over 2^8 \pi^4}
|V_{ub}|^2
\int_C \! d v \cdot \hat q \,\, {T^{\mu \nu} L_{\mu \nu} \over m_b^2}
\label{doublerate}
\end{equation}
The contour $C$ is shown in Fig.1. Care must be taken in
choosing the contour $C$ in Eq.~(\ref{doublerate}).
For example if $T^{\mu \nu}$ contains poles only,
any contour enclosing the poles gives the right
answer~\cite{chayetal,manoharwise}.
On the other hand if $T^{\mu \nu}$ has cuts, the contour has to be
chosen in such a way to cover the correct $v \cdot \hat q$
integration interval determined by kinematics.
We therefore have chosen the contour $C$ in
Eq.~(\ref{doublerate}) as
a circle of radius $z  = (y - \hat q^2) ( 1 - y) / y$ centered at
$v \cdot \hat q = (1 + \hat q^2 )/2$.
The contribution of the contour integral near the point $P$,
$ v \cdot \hat q = y/2 + \hat q^2 / 2y$
is negligibly small as long as  $z \gg \Lambda / m_b$.

Near the boundaries of the Dalitz plot $\hat q^2 \rightarrow y$ or
$y \rightarrow 1$, $z$ shrinks to zero and we are in the
resonance region.
This is where nonperturbative effects dominate.
This limits the extent of our theoretical prediction of the decay
rate to which the experimental data can be compared.
Therefore it is necessary to introduce a smearing in order to use
perturbation theory reliably~\cite{pqw}.
The size of the smearing is determined by requiring that the
nonperturbative effects be smaller than the parton-model result.

\section{Operator Product Expansion}
For processes involving $b$-quark decay,
it is appropriate to use the HQEFT.
In the HQEFT, the full QCD $b$ field is expressed in terms of
$b_v$ for $b$ quark velocity $v$.
The $b_v$ field is defined by
\begin{equation}
b_v = \frac{1+ v \hskip -.215cm / }{2} e^{im_b v \cdot x} b + \cdots,
\end{equation}
where the ellipses denote terms suppressed by powers of $1/m_b$.
The equation of motion for $b_v$ is $v \hskip-0.215cm / b_v = b_v$.
We can apply the techniques of the OPE to expand $T^{\mu \nu}$
in terms of matrix elements of local operators involving $b_v$ fields
\begin{eqnarray}
\displaystyle
T^{\mu \nu}
& = & -i \int d^4x e^{i q \cdot x}
\langle B | T\{J_u^{\mu}(x)^{\dagger} J_u^{\nu}(0)\} | B \rangle
\nonumber  \\
& = & \sum_{n,v} C_n^{\mu\nu} (v, q) \,
\langle B | {\cal O}_v^{(n)} | B \rangle.
\label{ope}
\end{eqnarray}
Here ${\cal O}_v^{(n)}$ are local operators involving
$\bar b_v b_v$ bilinears.
The coefficient functions $C^{\mu \nu}_n$ depend explicitly on
$q$ and $v$ because of the $v$ dependence of ${\cal O}_v^{(n)}$.
All large momenta are contained in the coefficient functions
while the matrix elements describe low-energy physics.

In this scheme $T^{\mu \nu}$ is expanded as a double series
in powers of $\alpha_s$ and $1 / m_b$.
To leading order in $\alpha_s$ and $1 / m_b$
\widetext
\begin{eqnarray}
T^{\mu\nu}  &=& -i \int \! d^4x \, e^{i (m_b v -q) \cdot x} \,
\langle B|T\{ {\overline b}_v(x) \gamma^{\mu}(1+\gamma_5 ) u(x)
{\overline u}(0) \gamma^{\nu} (1+\gamma_5)b_v (0) \} |B \rangle
\nonumber \\
 &=& -i \int \! d^4x \, e^{i (m_b v - q)  \cdot x} \,
 \langle B| T\{{\overline b}_v(x)
 \gamma^{\mu}(1+\gamma_5) S_0 (x) \gamma^{\nu} (1+\gamma_5)b_v(0)\}
 |B\rangle,
\label{tstart}
\end{eqnarray}
\narrowtext
\noindent where $S_0 (x)$ denotes a free $u$ quark propagator.
In momentum space Eq.~(\ref{tstart}) is proportional to
\begin{equation}
\gamma^{\mu} {{\cal Q} \hskip -.22cm / +k \hskip -.22cm /
\over ({\cal Q} +k)^2 } \gamma^\nu (1 + \gamma_5),
\label{uprop}
\end{equation}
where ${\cal Q} = m_b v - q $ is the momentum transferred to
the $u$ quark and $k^\mu$ is a small residual momentum of the
$b_v$ field of order $\Lambda$.

When $ \Lambda^2 \ll {\cal Q}^2 \ll m_b^2$,
it is sufficient to keep the terms at leading order in
$1 / m_b$ only and expand Eq.~(\ref{uprop}) in powers of
$k / |{\cal Q}|$. This generates coefficient functions and
local operators in which $k$ is replaced by the derivatives
acting on the $b_v$ fields.
The leading term independent of $k$ gives the parton-model result.
Contracting the leading term with $L_{\mu \nu}$ we find
\begin{eqnarray}
T^{\mu \nu}_0 L_{\mu \nu} & = &
64 {k_e \cdot {\cal Q} \over {\cal Q}^2} k_{\bar \nu}^{\mu}
\langle B | \bar b_v \gamma_\mu (1 + \gamma_5) b_v | B \rangle
\nonumber \\
&= & 128 m_b {k_e \cdot {\cal Q} k_{\bar \nu} \cdot v \over
{\cal Q}^2 },
\label{partonresult}
\end{eqnarray}
where $T^{\mu \nu}_0$ is $T^{\mu \nu}$ at leading order in
$k/|{\cal Q}|$.
The second line in Eq.~(\ref{partonresult})
follows from the normalization
$\langle B | \bar b_v b_v | B \rangle = 2 m_b$.

The next-order correction to  Eq.~(\ref{partonresult})
is suppressed by at least $(\Lambda / {\cal Q})^2$~\cite{chayetal}.
Corrections to $T^{\mu \nu}$ from higher dimensional operators
involving $\overline b_v b_v$ bilinears have been studied
systematically~\cite{bigietal,mannel,manoharwise}.
Furthermore Neubert~\cite{neubert} has resummed these
corrections to get a ``shape function''.
He has observed that the shape function
is universal independent of the final quark flavor.

Usually the coefficient functions are calculated perturbatively.
In addition there could be nonperturbative correction to the
coefficient functions as well~\cite{shifman}.
In the next section we calculate how instantons affect the
coefficient function of the leading term, Eq.~(\ref{partonresult}),
in the OPE.
The instantons contribute not only to the matrix elements but
also to the coefficient functions.
If there is an infrared divergence due to large instantons we
attribute it to the contribution to the matrix elements.
For infrared-finite parts we interpret them as the correction to
the coefficient functions.

\section{Instanton Contribution}
We now compute the contribution of instantons to the coefficient
functions.
In estimating the contribution we start from the Euclidean
region where ${\cal Q}^2$ is large enough to use the OPE reliably.
We expect that the main contribution comes from small instantons
of size $\rho
\mathrel{\rlap{\lower3pt\hbox{\hskip0pt$\sim$}}\raise1pt\hbox{$<$}}
{1 /|{\cal Q}|}$, hence we use the dilute gas approximation
in what follows.
More specifically we calculate the instanton correction to the
decay rate at leading order in both $\alpha_s$ and $k$ in the OPE.
This is the instanton correction to the parton model result
Eq.~(\ref{partonresult}).

In the background of an instanton ($+$ anti-instanton) of size $\rho$
and instanton orientation $U$ located at the origin, the Euclidean
fermion propagator may be expanded in small fermion masses
as~\cite{andreigross}
\begin{eqnarray}
\displaystyle
S_\pm (x, &y;& \rho_\pm; U_\pm)  =
- {1 \over m} \psi_0 (x) \psi^\dagger_0 (y)
+ S^{(1)}_\pm (x, y; \rho_\pm; U_\pm) \nonumber \\
&+& m \int d^4 w S^{(1)}_\pm (x, w; \rho_\pm; U_\pm)
S^{(1)}_\pm (w, y; \rho_\pm; U_\pm)
\nonumber \\
&+& {\cal O}(m^2),
\label{propexp}
\end{eqnarray}
where $\pm$ denotes instanton, anti-instanton.
$\psi_0$ is the fermion zero mode eigenfunction  and
$S^{(1)}_\pm = \sum_{E>0} {1 \over E} \Psi_{E \pm} (x)
\Psi^\dagger_{E \pm} (y)$ is the Green's function of fermion
nonzero modes.

In evaluating the forward Compton scattering amplitude
$T^{\mu \nu}$, Eq.~(\ref{tmunu}),
we should use the propagator in Eq.~(\ref{propexp})
instead of $S_0$. $T^{\mu \nu}$ can be written as
\begin{equation}
T^{\mu \nu}  = T^{\mu \nu}_0  + T^{\mu \nu}_{\rm inst.},
\label{tdecomp}
\end{equation}
where the first term is the parton-model amplitude.
The second term is the amplitude due to instantons of all
orientation $U$, position $z$ and size $\rho$.
A schematic configuration of an instanton or anti-instanton is
shown in Fig.2.
After averaging over instanton orientations $T^{\mu \nu}_{\rm inst}$
is given by
\widetext
\begin{equation}
T^{\mu \nu}_{\rm inst.}   =  \int \! d^4 \Delta \,
e^{i {\cal Q} \cdot \Delta } \sum_{a = \pm} \!\! \int
\! d^4 z_a \, d \rho_a D(\rho_a)
 \langle B | \bar b_v (x) \gamma^\mu (1+\gamma_5) \{ {\cal S}_a
(X, Y; \rho_a) -S_0 (\Delta)\} \gamma^\nu (1 + \gamma_5) b_v (y)
| B \rangle,
\label{insttmunu}
\end{equation}
\narrowtext
\noindent where $D(\rho)$ is the instanton density,
$\Delta = x - y, \,\,\, X = x - z$ and $Y = y - z$.
In Eq.~(\ref{insttmunu}), ${\cal S}_\pm (X, Y; \rho_\pm)$ is the
fermion propagator averaged over instanton (anti-instanton)
orientations centered at $z$.
Using the ${\overline {\rm MS}}$ scheme with $n_f$
flavors of light fermions, $D(\rho)$ is given by~\cite{bernard}
\begin{equation}
\displaystyle
D(\rho)  =  K \, \Lambda^5 \, (\rho \Lambda)^{6 + {n_f \over 3}}
      \, \biggl( \ln{1 \over \rho^2 \Lambda^2}
      \biggr)^{45-5 n_f \over 33 - 2 n_f},
      \label{density}
\end{equation}
where
\begin{eqnarray}
      \displaystyle
      K  & = & \biggl( \prod_i {\hat m_i \over \Lambda} \biggr) \,
2^{12 n_f \over 33 - 2n_f} \, \biggl({33 - 2n_f \over 12} \biggr)^6
      \nonumber \\
& \times & {2 \over \pi^2} \,
\exp\bigl[{1 \over 2} - \alpha (1) + 2 (n_f -1)
\alpha ({1 \over 2}) \bigr]
      \label{ddensity}
\end{eqnarray}
in which the $\beta$ function at two loops and the running mass
at one loop are used and $\hat m_i$ are the
renormalization-invariant quark masses.
In Eq.~(\ref{ddensity}) $\alpha(1) = 0.443307$ and
$\alpha(1/2) = 0.145873$.
{}From now on we replace the logarithmic
term in $D(\rho)$ by its value for $\rho = 1/|{\cal Q}|$.
Corrections to this replacement are
negligible since they are logarithmically suppressed.

Inserting Eq.~(\ref{propexp}) to Eq.~(\ref{insttmunu}),
the leading contribution comes from the mass-independent part
${\cal S}_\pm^{(1)}$ due to the chiral structure of the
left-handed weak currents.
The chirality-conserving part of ${\cal S}^{(1)}_\pm$
in singular gauge~\cite{andreigross} is written as
\widetext
\begin{eqnarray}
\displaystyle
\sum_{a = \pm} {\cal S}^{(1)}_a (X, Y; \rho) & = &
-{1 \over \pi^2} {\Delta \hskip-0.23cm / \over \Delta^{4}}
(X^2 Y^2 + \rho^2 X \cdot Y)[X^2 Y^2 (X^2 + \rho^2)
(Y^2 + \rho^2)]^{-{1 \over 2}} \nonumber \\
    && - {\rho^2  \over 4 \pi^2} {\Delta \hskip-0.23cm /
    \over \Delta^{2}}
    ( X^2 [X^2 Y^2 (X^2 + \rho^2)^3 (Y^2 + \rho^2)]^{-{1 \over 2}}
   + (X \leftrightarrow Y) ) \nonumber \\
    && + {\rho^2 \over 4 \pi^2} ( X \hskip-0.24cm / \,
    [X^2 Y^2 (X^2 + \rho^2)^3 (Y^2  + \rho^2)]^{-{1 \over 2}} -
    (X \leftrightarrow Y) ).
    \label{prop1}
    \end{eqnarray}
{}From Eq.~(\ref{prop1}) ${\cal S}_\pm(X, Y; \rho) - S_0(\Delta)$
can be written as
\begin{eqnarray}
\displaystyle
\sum_{a = \pm}
\bigl({\cal S}_a (X, Y; \rho)  - S_0 (\Delta) \bigr) &  \approx &
-{\rho^4 \over 8 \pi^2} {\Delta \hskip-0.23cm / \over \Delta^{4}}
   (X^2 - Y^2)^2 [X^2 Y^2 (X^2 + \rho^2)
   (Y^2 + \rho^2)]^{-1} \nonumber \\
   && + {\rho^4 \over 2 \pi^2} {\Delta \hskip-0.23cm / \over
   \Delta^{2}}
   \biggl({1 \over X^2 + \rho^2} + {1 \over Y^2 + \rho^2}\biggr)
 [X^2 Y^2 (X^2 + \rho^2)(Y^2 + \rho^2)]^{-{1 \over 2}} \nonumber \\
   &&
   + {\rho^2 \over 4 \pi^2} \biggl({{X \hskip -0.23cm /}
   \over X^2 + \rho^2} - {{Y \hskip -0.23cm /}
   \over Y^2 + \rho^2} \biggr)
   [X^2 Y^2 (X^2 + \rho^2 ) (Y^2 + \rho^2)]^{-{1 \over 2}},
\label{prop}
\end{eqnarray}
\narrowtext
\noindent
where $S_0 (\Delta) = -\Delta \hskip-0.23cm / / 2 \pi^2 \Delta^4$
is the free quark propagator.
In deriving Eq.~(\ref{prop}) we move $-\rho^2(X^2 + Y^2)/2$
proportional-part of the first line to the second line in
Eq.~(\ref{prop1}) using
$\rho^2 X \cdot Y = \rho^2 ((X+Y)^2 - X^2- Y^2)/2$.
We also approximate the remaining terms to get the first line in
Eq.~(\ref{prop})
so that exact analytic calculation is possible while leaving
small instanton contribution essentially unaltered.
Plugging Eq.~(\ref{prop}) into Eq.~(\ref{insttmunu}),
we integrate over the instanton center $z$,
the instanton size $\rho$, and finally make a Fourier
transform over $\Delta$.
Note that the integral over $z$ is convergent as
$|z| \rightarrow \infty$.

We notice that the integration over $\rho$ is convergent for small
instantons. On the other hand large instanton part is divergent.
However since the integrand is analytic for large $\rho$
(See Appendix.),
 there are only a finite number of divergent terms when
 $T^{\mu \nu}_{\rm inst}$ is expanded in $1 / \rho$.
 We interpret these infrared divergent terms as the instanton
 contribution to the matrix elements of operators in the
 OPE~\cite{balietal}. The remaining terms are infrared convergent
 and are interpreted that they contribute to the coefficient
 functions.
 In order to calculate finite
 terms any convenient regularization prescription will do.
To this end we analytically continue the exponent of $\rho$ in the
instanton density so that $D(\rho) \propto
\rho^{M-4}$~\cite{porrati} and the spacetime dimensions to
$d = 4 + 2 \epsilon$.
In the end we let $M \rightarrow 11$ for $n_f = 3$ and
$\epsilon \rightarrow 0$ to get the final answer.

After some algebra which we show in the Appendix,
the contribution to $T_{\rm inst}^{\mu \nu} L_{\mu \nu}$ from
the first line of Eq.~(\ref{prop}) consists of two pieces.
The contribution of the first piece is  written as
\begin{eqnarray}
&& K \! \int \! d \rho \, \rho^4 D(\rho) \int \!
{d^4 w \over w^2 (w^2 + \rho^2)} \nonumber \\
& \times &  2^6 \,
{k_e \cdot {\cal Q} \over {\cal Q}^2 } k^\mu_{\bar \nu}
\langle B | \overline b_v \gamma_\mu ( 1 + \gamma_5) b_v
| B \rangle.
\label{divterm1}
\end{eqnarray}
The integration over $\rho$ is  divergent as we take the
physical value $M = 11$.
This is interpreted as the large-instanton contribution to
the matrix element $\overline b_v \gamma^\mu b_v$.

The contribution from the second piece is regular as
$M \rightarrow 11$, $\epsilon \rightarrow 0$ and is given by
\begin{eqnarray}
\displaystyle
 && K \, {2^{10} \over 35}\, \pi^2 \Gamma^2 (6) \,
\, \biggl({\Lambda^2 \over {\cal Q}^2} \biggr)^6 \,
\biggl( \ln {{\cal Q}^2 \over \Lambda^2} \biggr)^{10 / 9}
\nonumber \\
& \times & 2^6 \,
{k_e \cdot {\cal Q} \over {\cal Q}^2 } k^\mu_{\bar \nu}
\langle B | \overline b_v \gamma_\mu ( 1 + \gamma_5) b_v
| B \rangle.
\label{convterm1}
\end{eqnarray}
The contribution from the second and the third lines
in~Eq.(\ref{prop})
to $T^{\mu \nu}_{\rm inst} L_{\mu \nu}$  vanishes,
as explained in the Appendix.
Therefore Eq.~(\ref{convterm1}) is the overall finite contribution.

It is now straightforward to evaluate the instanton contribution
to the differential decay rate.
So far we have worked in Euclidean spacetime.
We now make a naive analytic continuation to Minkowski spacetime
with timelike ${\cal Q}^2 = (m_b v - q)^2$ to evaluate the
differential decay rate.
Then $T^{\mu \nu}_{\rm inst}L_{\mu \nu}$ is written as
\begin{eqnarray}
\displaystyle
T^{\mu \nu}_{\rm inst} L_{\mu \nu} & = & - {5 \over 4} A m_b^2 \,
{(v \cdot \hat q - {y \over 2}) (y - \hat q^2) \over
(v \cdot \hat q - {1 + \hat q^2 \over 2} )^7} \nonumber \\
 & \times & \biggl[\ln {-2 m_b^2 \over \Lambda^2}
\bigl( v \cdot \hat q - {1 + \hat q^2 \over 2} \bigr) \biggr]^{10/9},
\label{timunu}
\end{eqnarray}
where
\begin{equation}
A = {2^{11} \pi^2 \over 175} \, \Gamma^2(6) \, K
\biggl({\Lambda \over m_b} \biggr)^{12}.
\label{a}
\end{equation}
Eq.~(\ref{timunu}) has a branch cut emanating from the
resonance point $v \cdot \hat q = {1 + \hat q^2} / 2$,
which we have shown in Fig.1.

To get the double differential decay rate
$d^2 \Gamma / d\hat q^2 d y$,
we integrate  Eq.~(\ref{timunu}) over
$v \cdot \hat q$ along $C$ in Fig.1 as described in Section 2.
The differential decay rate is written as
\begin{eqnarray}
\displaystyle
{1 \over \Gamma_0} {d \Gamma_{\rm inst} \over  d \hat q^2 d y}
& = & {15 \over 32 \pi} A \,
\int_C  d v \cdot \hat q \, {(y - \hat q^2)
(v \cdot \hat q - {y \over 2})
\over ( v \cdot \hat q - {1 + \hat q^2 \over 2})^7} \nonumber \\
& \times & \biggl[\ln {-2 m_b^2 \over \Lambda^2}
\bigl( v \cdot \hat q - {1 + \hat q^2 \over 2} \bigr)
\biggr]^{10/9},
\label{ddrate}
\end{eqnarray}
where $\Gamma_0 = G_F^2 |V_{ub}|^2 m_b^5 / 192 \pi^3$.
The exponent of the logarithm is almost unity and we replace $
10/9$ by $1$. We expect that it does not change the result much.
We finally get
\begin{equation}
\displaystyle
{1 \over \Gamma_0} {d^2 \Gamma_{\rm inst} \over d \hat q^2 d y} =
A \, y^5 \,
{ 5 \hat q^2 - (1-y) (y-\hat q^2) \over (1 - y)^{6}
(y - \hat q^2)^{5}}.
\label{ddrate2}
\end{equation}
The instanton effect is suppressed at $y \sim 0$.
However it become singular near the boundaries of the phase space
at $y \sim 1$ and $y \sim \hat q^2$.
At these boundaries the final quark approaches the resonance region.
As there are large instanton contributions near the resonance point,
it is necessary to introduce a smearing to define sensible
decay rate in perturbative QCD.
We discuss this in detail in the next section.

\section{Numerical Analysis}
We have calculated the instanton effect on the inclusive
semileptonic $b$ decay.
As we have observed in the previous section the effect is
singular at the boundaries of the phase space.
In order to use perturbative expansions
reliably a smearing prescription has to be introduced.

As a simple prescription we first consider the smeared single
differential decay rate
\begin{equation}
\langle {d \Gamma_{\rm inst} \over d y} \rangle_\delta
= \int_0^y d \hat q^2 \, \theta( y - \hat q^2 - \delta)
{d \Gamma_{\rm inst} \over d y}
\label{singsmear}
\end{equation}
in which we restrict the phase space so that the singular region
$y = \hat q^2$ is avoided by $\delta$.
The size of smearing $\delta$ is determined by the requirement
that the smeared instanton contribution to
the single differential decay rate be smaller than that in
the parton model
$d \Gamma_0 / d y = 2 y^2 (3 - 2 y) \Gamma_0$.
Eq.(\ref{singsmear}) is given by
\begin{eqnarray}
\langle {d \Gamma_{\rm inst} \over d y} \rangle_\delta
& = & \bigl({d \Gamma_0 \over d y} \big)
{ A \over 24} {1 \over (1-y)^6 (3 - 2y)}
\nonumber \\
& \times & \bigl[9 - 4 y - 24({y \over \delta})^3 + 15
({y \over \delta})^4 + 4 ({y^4 \over \delta^3}) \bigr].
\label{singsmear2}
\end{eqnarray}

The ratio $R(y, \delta) = \langle d \Gamma_{\rm inst}
/ dy \rangle_\delta / (d \Gamma_0 / dy)$
is plotted in Fig.3 for three different values of
$\delta$ = 0.15, 0.17, 0.19 with $\Lambda = 400$ MeV and
$m_b = 5$ GeV.
The numerical value of $A$ is given by
\begin{equation}
A = \biggl({19.2 {\rm GeV} \over m_b} \biggr)^3 \,
\biggl({\Lambda \over m_b} \biggr)^9,
\label{numa}
\end{equation}
in which we set $n_f = 3$ and the renormalization-invariant
quark masses as~\cite{quarkmass}
 \begin{eqnarray}
 \hat m_u & =& 8.2 \pm 1.5 {\rm MeV}, \nonumber \\
 \hat m_d & = & 14.4 \pm 1.5 {\rm MeV}, \nonumber \\
 \hat m_s & = & 288 \pm 48 {\rm MeV}.
 \end{eqnarray}
We see that for these choices of $\delta$, $R (y, \delta)$
grows rapidly for $y
\mathrel{\rlap{\lower4pt\hbox{\hskip1pt$\sim$}}\raise1pt\hbox{$>$}}
0.84$. From Fig.3 we see that a smearing of
$ \delta \approx 0.16 \sim 0.20$ at the boundary
$y = \hat q^2$ of the phas space is needed to extract a
reliable electron spectrum from the single differential decay rate.

We have also examined the behavior of $R(y, \delta)$ as we increase
$\delta$.
The position at which $R(y, \delta)$ grows like a brick wall
does not shift much from $y \sim 0.84$. Because of this singular
behavior we need another smearing near $y = 1$.
For simplicity we cut off the region near $y = 1$ by the
same smearing width $\delta$ as in Eq.~(\ref{singsmear}).

Instanton contribution to the total decay rate after such a smearing
prescription is given by
\begin{eqnarray}
\displaystyle
\langle  \Gamma_{\rm inst} \rangle_\delta & =&
\! \int_0^1 \! d y \! \int_0^y \! d \hat q^2
\theta(y-\hat q^2 -\delta) \theta(1 - y - \delta)
{d^2 \Gamma_{\rm inst} \over d \hat q^2 d y} \nonumber \\
& = &  \Gamma_0 \, {A \over 24}
\, {1 \over \delta^9}
( \, 6 - 53 \delta + 198 \delta^2 - 420 \delta^3
+ 612 \delta^4  \nonumber \\
&& - 354 \delta^5 + 16 \delta^6 - 4 \delta^7 - \delta^9
+ 180 \delta^5 \ln \delta).
\label{totsmear}
\end{eqnarray}
The ratio $R(\delta) = \langle \Gamma \rangle_\delta / \Gamma_0$
is plotted in Fig.4 for three different values of $\Lambda =
350, 400, 450$ MeV and for $m_b = 5$ GeV.
We see that the ratio $R (\delta)$ also rises sharply like
a brick wall as $\delta$ decreases.
When $\delta$ is large, say $\delta
\mathrel{\rlap{\lower4pt \hbox{\hskip1pt$\sim$}}\raise1pt\hbox{$>$}}
0.15$, $R (\delta)$ is
insensitive to the choice of $\Lambda / m_b$. However, for small
$\delta$, say $ \delta \approx 0.12$, $R(\delta)$ is sensitive to
the value of $\Lambda / m_b$. If we require $R (\delta )$ be less
than 20\%,
the size of the smearing is roughly at least $ 0.12 \sim 0.15$
for our choices of $\Lambda$.

Our results Eqs.~(\ref{singsmear2}),~(\ref{totsmear}) are
sensitive to the precise value of $\Lambda$.
This is what we expect from the instanton effect.
Nevertheless, as emphasized in Introduction, our results may
still represent a typical size of nonperturbative effects.

\section{Conclusion}
In this paper we have studied instanton effects on the decay rate of
the inclusive semileptonic $b \rightarrow u$ decay.
In particular we have estimated the instanton correction to the
coefficient function at leading order.
We have found that the correction is singular at the boundaries
of the phase space.
Because of the large instanton contribution to the
coefficient function,
we have found that it is necessary to introduce a smearing near the
boundaries of the phase space.
For the single differential decay rate a smearing of size
$\delta \approx 0.16 \sim 0.2$ is needed taking into account
of the correlation of the
smearing sizes at the two boundaries $ y = 1$ and $ y = \hat q^2$.
For the total decay rate the smearing size is
$\delta \approx 0.12 \sim 0.15$. Note that $d \Gamma_0 / d y$ is
appreciable for all $y$ while $d \Gamma_{\rm inst} / d y$ is
negligible except at the boundaries of the Dalitz plot.
Therefore the smearing size for the total decay rate is smaller
than that for the single differential decay rate.

Precise theoretical prediction in the endpoint region is important
for the extraction of $V_{ub}$.
Singular nature of various corrections indicates we need some
smearing before comparing with data.
Manohar and Wise~\cite{manoharwise} have studied the smearing
necessary for the effects of matrix elements of higher
dimensional operators.
They have concluded that the size of smearing should be
$\epsilon \sim 0.2$.
Neubert ~\cite{neubert} has suggested an idea to measure
the universal shape function from $b \rightarrow c$ decay and
apply it to $b \rightarrow u$ decay.
He has proposed this as a promising way to a precise extraction
of $V_{ub}$.

Falk et.al.~\cite{falketal} have studied the smearing for the
validity of the leading log approximation and have found
the smearing size should be roughly $0.1$ or less.
The instanton effect is another source of corrections to $B$ decays.
While it is negligible for $b \rightarrow c$ decay the
effect is significant in $b \rightarrow u$ decay.
Our analysis shows that the smearing has to be about
$\delta \approx 0.12 \sim 0.16$.
This is comparable to the difference in the endpoints of the
$b \rightarrow c$ and $b \rightarrow u$ decays.
Therefore it is perhaps difficult to eliminate a model
dependence in extracting $V_{ub}$ from inclusive semileptonic
$b \rightarrow u$ decay.

We can similarly consider the instanton effect in inclusive
semileptonic $c$ decay.
As we can infer from the quark mass dependence in Eq.~(\ref{a})
we expect the effect is much larger in this case because
$m_c \ll m_b$.
Therefore the decay rate near the endpoint is strongly
model-dependent due to large uncertainties from radiative
corrections and nonperturbative effects~\cite{manoharwise}
including instantons.
We may also consider the instanton effect on inclusive
$b \rightarrow c$ decay.
Because ${\cal Q}^2
\mathrel{\rlap{\lower4pt\hbox{\hskip1pt$\sim$}}\raise1pt\hbox{$>$}}
m_c^2$ the instanton effect is finite even at the boundaries
of the phase space.
The numerical value is negligibly small since it is proportional to
high powers $(\Lambda / m_c)^n$ where $n$ may be determined from the
instanton density Eq.~(\ref{density}) for $n_f = 4$.

\section*{Acknowledgements}
SJR thanks M. Luke, M. Peskin, J. Preskill, H. Quinn, M. Shifman and
M.B. Wise for useful discussions.
This work was supported in part by KOSEF-SRC program (SJR, JGC),
KOSEF Grant`94 (JGC), Ministry of Education through SNU-RIBS (SJR)
and BSRI-93-218 (JGC), KRF-Nondirected Research Grant`93 (SJR).

\section*{Appendix: Instanton Integrations}
There are three integrations [See Eq.~(\ref{prop}).]
we have to perform.
The integrals of Eq.~(\ref{prop}) over $\rho, z$
and Fourier transform of $\Delta$ after a suitable change of
variables are expressed as
\begin{eqnarray}
\displaystyle
&& K \biggl(\ln {{\cal Q}^2 \over \Lambda^2} \biggr)^{10/9}
\int_0^\infty d \rho \, \rho^{M-4} \int d^d t \, d^d u {\rho^2
\over 4 \pi^2}
\nonumber \\
&\times& \biggl[ \biggl( {i \partial \over {\partial {\cal Q}
   \hskip-0.23cm / }} {e^{i {\cal Q} \cdot t} \over t^4} \biggr)
  \biggl(
  {\rho^2 \over u^2 (u^2 + \rho^2)} -
  { \rho^2 \over u^2 ((t-u)^2 + \rho^2)}
  \biggr)  \label{first}  \\
&-&
\biggl( {i \partial \over {\partial {\cal Q} \hskip-0.23cm / }}
{e^{i {\cal Q} \cdot t} \over t^2} \biggr) \,
{2 \rho^2 \over \sqrt{u^2 (u^2 + \rho^2)
(t-u)^2 ((t-u)^2 + \rho^2)^3}}
\label{second} \\
&-& \,\,
\biggl(2 {i \partial \over {\partial {\cal Q} \hskip-0.23cm / }}
{e^{i {\cal Q} \cdot t} \over \sqrt{t^2 (t^2 + \rho^2)^3}}
\biggr) \,\,
 {e^{i{\cal Q}\cdot u} \over \sqrt{u^2 (u^2 + \rho^2)}} \,\, \biggr],
\label{third}
\end{eqnarray}
where ${\partial / \partial {\cal Q} \hskip-0.23cm / }
= \gamma_\mu {\partial / \partial {\cal Q}^\mu}$.
At small $\rho$, the $\rho$ integral is convergent while  at
large $\rho$ it is divergent.
However for large $\rho$ the integrand may be expanded in powers of
$1 / \rho$.
We can see clearly that there are only a finite number of
divergent terms at the physical value $M=11$ for $n_f=3$.
These divergent terms are interpreted as the instanton contribution
to the matrix elements of operators in the OPE~\cite{balietal}.
Since the remaining terms are finite we may evaluate them by any
convenient methods. We have analytically continued $M$ and
the spacetime dimensions $d = 4 + 2 \epsilon$.
We set $M = 11$ and $d=4$ in the end.

The first term in Eq.~(\ref{first}) is divergent and we interpret
it as a contribution to the hadronic matrix
elements~\cite{balietal}.
In evaluating the second term in Eq.~(\ref{first})
we first integrate over $u$ and then over $\rho$.
Finally we make a Fourier transform with respect to $t$.
The result turns out to be regular as $\epsilon \rightarrow 0$.
Setting $\epsilon =0$ the second term in  Eq.~(\ref{first})
is given by
\begin{eqnarray}
&& K \, 2^{M-1}\pi^2 \frac{M+1}{M+3}
\Gamma^2 \biggl(\frac{M+1}{2} \biggr)
\frac{\Gamma(-\frac{1+M}{2})}{\Gamma(-\frac{M-3}{2})} \nonumber \\
&& \times \frac{i{\cal Q}
\hskip -0.24cm /}{{\cal Q}^{M+3}}\,
\biggl( \ln {{\cal Q}^2 \over \Lambda^2} \biggr)^{10/9}.
\label{term1int}
\end{eqnarray}
In getting Eq.~(\ref{term1int}) we have analytically continued
$M$ in such a way that the integral becomes convergent.
However the result can be extended to $M=11$ as it is
convergent for any positive $M \ge 3$.
The final result is
\begin{equation}
K \, \frac{2^{M+1}\pi^2}{(M+3)(M-1)}
\Gamma^2 \biggl(\frac{M+1}{2} \biggr)
\frac{i{\cal Q}\hskip -0.22cm /}{{\cal Q}^{M+3}}
\,  \biggl(\ln {{\cal Q}^2 \over \Lambda^2} \biggr)^{10/9}.
\end{equation}
Putting $M=11$ yields
\begin{equation}
 4.16\times 10^6 \,K\, \frac{i{\cal Q}\hskip -0.22cm /}
 {{\cal Q}^{14}}
 \,  \biggl( \ln {{\cal Q}^2 \over \Lambda^2} \biggr)^{10/9}.
\label{result1}
\end{equation}

Eq.~(\ref{second}) is regular as $\epsilon \rightarrow 0$.
Setting $\epsilon = 0$ and after some calculation it is written as
\begin{eqnarray}
\displaystyle
&& K \,  2^{M-2}\pi^2 \frac{1+M}{1-M}\Gamma^2
\biggl(\frac{M+1}{2} \biggr)
\frac{i{\cal Q}\hskip -0.24cm /}{{\cal Q}^{M+3}}
\, \biggl( \ln {{\cal Q}^2 \over \Lambda^2} \biggr)^{10/9}
\nonumber \\
&\times& \! \int \!\! \int_0^1 \! dx \,dy \,
x^{-(M+2)/2} (1-x)^{-1/2} y^{1/2} (1-y)^{-1/2}
\nonumber \\
& \times & F \bigl(\frac{M+1}{2}, \frac{M+3}{2};M+2;
1-\frac{y}{x} \bigr),
\label{term2int}
\end{eqnarray}
where $F \equiv \, _2F_1$ is the hypergeometric function.
Here $x$ and $y$ are Feynman parameters introduced in
integrating over the instanton position.
Eq.~(\ref{term2int}) is also regular as
$M\rightarrow 11$, hence we can set $M=11$.
We can expand the hypergeometric function as a series of $(y/x)^n$
for $n\geq 0$. The $y$ integral is of the form
\begin{equation}
\int_0^1 dy y^{n+1/2}(1-y)^{-1/2},
\end{equation}
which is finite for all $n\geq 0$.
On the other hand the $x$ integral is of the form
\begin{equation}
\int_0^1 dx x^{-M/2-n-1}(1-x)^{-1/2},
\label{xint}
\end{equation}
which is zero for odd $M$ and infinity for even $M$.
Therefore for $M=11$ the integral vanishes.

Similarly Eq.~(\ref{third}) is regular as
$\epsilon\rightarrow 0$ and $M \rightarrow 11$.
After some calculation the result with $\epsilon=0$, $M=11$
is written as
\begin{eqnarray}
\displaystyle
&& K \, 2^{12} { \Gamma(7) \Gamma^2(6) \Gamma(5) \over \Gamma(12)}
\, \frac{i{\cal Q}\hskip -0.24cm /}{{\cal Q}^{14}}
 \, \biggl( \ln {{\cal Q}^2 \over \Lambda^2} \biggr)^{10/9}
 \nonumber \\
&\times& \int_0^1 dx dy x^{-11/2}(1-x)^{-1/2}y^{-1/2}(1-y)^{1/2}
\nonumber \\
& \times & F \bigl(5,6;12;1-\frac{y}{x} \bigr).
\end{eqnarray}
Again the hypergeometric function can be expanded as a
series of $(y/x)^n$ for $n \ge 0$.
The $y$ integral is finite but the $x$ integral vanishes for
the same reason as in Eq.~(\ref{xint}).
Therefore it turns out that Eqs.~(\ref{second}), (\ref{third})
vanish and the only finite contribution is Eq.~(\ref{result1}).

\begin{references}
\bibitem{accmm}
G. Altarelli, N. Cabibbo, G. Corbo, L. Maiani and G. Martinelli,
Nucl. Phys. \bf B208 \rm, 365 (1982).

\bibitem{isgw} B. Grinstein, N. Isgur and M.B. Wise,
Phys. Rev. Lett. \bf 56 \rm, 258 (1986);
N. Isgur, D. Scora, B. Grinstein and M.B. Wise,
Phys. Rev. \bf D39 \rm, 799 (1989).

\bibitem{chayetal} J. Chay, H. Georgi and B. Grinstein,
Phys. Lett. \bf 247B \rm, 399 (1990).

\bibitem{bigietal}
I.I. Bigi, M.A. Shifman, N.G. Uraltsev and A.I. Vainshtein,
Phys. Rev. Lett. \bf 71 \rm, 496 (1993);
B. Blok, L. Koyrakh, M. Shifman and A.I. Vainshtein,
NSF-ITP 93-68 preprint, 1993 (unpublished).

\bibitem{mannel} T. Mannel, Nucl. Phys. \bf B413 \rm, 396 (1994).

\bibitem{manoharwise} A.V. Manohar and M.B. Wise,
CALT-68-1883 preprint, 1993 (unpublished).

\bibitem{corboetal} N. Cabbibo, G. Corb\'o and L. Maiani,
Nucl. Phys. \bf B155 \rm, 93 (1979);
G. Corbo, Nucl. Phys. \bf B212 \rm, 99 (1983);
A. Ali and E. Pietarinen, Nucl. Phys. \bf B154 \rm, 519 (1979).

\bibitem{falketal}
A.F. Falk, E. Jenkins, A.V. Manohar, and M.B. Wise,
CALT-68-1910 preprint, 1993 (unpublished).

\bibitem{bigiope} I.I. Bigi, M.A. Shifman, N.G. Uraltsev and
A.I. Vainshtein, TPI-MINN-93/60-T preprint, 1993 (unpublished).

\bibitem{pqw} E.C. Poggio, H.R. Quinn and S. Weinberg,
Phys. Rev. \bf D13 \rm, 1958 (1976).

\bibitem{neubert} M. Neubert,
CERN-TH.7087/93 preprint, 1993 (unpublished).

\bibitem{shifman}
V.A. Novikov, M.A. Shifman, A.I. Vainshtein and V.I. Zakharov,
Nucl. Phys. \bf B174 \rm, 378 (1980).

\bibitem{andreigross} N. Andrei and D. Gross,
Phys. Rev. \bf D18 \rm, 468 (1978).

\bibitem{bernard} G. 't Hooft, Phys. Rev. \bf D14 \rm, 3432 (1976);
G. 't Hooft, Phys. Rep. \bf 142\rm, 357 (1986);
C. Bernard, Phys. Rev. \bf D19 \rm, 3013 (1979).

\bibitem{balietal}
L. Balieu, J. Ellis, M.K. Gaillard and W.J. Zakrzewski,
Phys. Lett. \bf 77B \rm, 290 (1978).

\bibitem{porrati}
I.I. Balitskii, M. Beneke and V.M. Braun, Phys. Lett.
\bf 318B \rm, 371 (1993);
P. Nason and M. Porrati,
CERN-TH.6787/93 preprint, 1993 (unpublished).

\bibitem{quarkmass} C.A. Dominguez and E. de Rafael,
Ann. Phys. \bf 174 \rm, 372 (1987).
\end{references}

\begin{figure}
\caption{Anaytic structure of $T^{\mu \nu}$ in the complex
$ v \cdot \hat q$ plane.
The point $P$ is the minimum of $v \cdot \hat q$ at
$y/2 + \hat q^2 / 2y$ for $b \rightarrow u$ decay.
The contour integral along $C^{\prime}$ is related to the
contour integral along $C$.}
\label{fig1}
\end{figure}

\begin{figure}
\caption{Schematic diagram of an instanton configuration with
size $\rho$ located at $z_\mu$ contributing to the forward
Compton amplitude.}
\label{fig2}
\end{figure}

\begin{figure}
\caption{$R(y, \delta)$ for $\delta$= 0.15, 0.17, 0.19 with
$\Lambda=400$ MeV and $m_b$=5 GeV.}
\label{fig3}
\end{figure}

\begin{figure}
\caption{$R(\delta)$ for $\Lambda$= 350, 400, 450 MeV with
$m_b$= 5 GeV.}
\label{fig4}
\end{figure}

\end{document}

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 3634 349 9 rps
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411
 3640 414 9 rps
 3683 355 3680 352 3683 349 3686 352 3 rcs

 3723 414 3714 411 3711 405 3711 395 3714 389 3723 386 3736 386 3745 389 3748
395
 3748 405 3745 411 3736 414 11 rcs

 3723 414 3717 411 3714 405 3714 395 3717 389 3723 386 5 rps
 3736 386 3742 389 3745 395 3745 405 3742 411 3736 414 5 rps
 3723 386 3714 383 3711 380 3708 374 3708 361 3711 355 3714 352 3723 349 3736
349
 3745 352 3748 355 3751 361 3751 374 3748 380 3745 383 3736 386 15 rps
 3723 386 3717 383 3714 380 3711 374 3711 361 3714 355 3717 352 3723 349 7 rps
 3736 349 3742 352 3745 355 3748 361 3748 374 3745 380 3742 383 3736 386 7 rps
 3770 414 3770 395 1 rps
 3770 402 3773 408 3779 414 3785 414 3801 405 3807 405 3810 408 3813 414 7 rps
 3773 408 3779 411 3785 411 3801 405 3 rps
 3813 414 3813 405 3810 395 3798 380 3795 374 3792 364 3792 349 6 rps
 3810 395 3795 380 3792 374 3788 364 3788 349 4 rps
 594 463 594 2449 1 rps
 593 462 593 2450 1 rps
 592 461 592 2451 1 rps
 591 460 591 2452 1 rps
 590 459 590 2453 1 rps
 3714 463 3714 2449 1 rps
 3715 462 3715 2450 1 rps
 3716 461 3716 2451 1 rps
 3717 460 3717 2452 1 rps
 3718 459 3718 2453 1 rps
 594 463 630 463 1 rps
 3714 463 3678 463 1 rps
 594 794 612 794 1 rps
 3714 794 3696 794 1 rps
 594 1125 630 1125 1 rps
 3714 1125 3678 1125 1 rps
 594 1456 612 1456 1 rps
 3714 1456 3696 1456 1 rps
 594 1787 630 1787 1 rps
 3714 1787 3678 1787 1 rps
 594 2118 612 2118 1 rps
 3714 2118 3696 2118 1 rps
 594 2449 630 2449 1 rps
 3714 2449 3678 2449 1 rps
 512 496 503 493 496 484 493 468 493 459 496 443 503 434 512 431 518 431
 527 434 533 443 537 459 537 468 533 484 527 493 518 496 15 rcs

 512 496 506 493 503 490 499 484 496 468 496 459 499 443 503 437 506 434
 512 431 9 rps
 518 431 524 434 527 437 530 443 533 459 533 468 530 484 527 490 524 493
 518 496 9 rps
 503 1146 509 1149 518 1158 518 1093 3 rps
 515 1155 515 1093 1 rps
 503 1093 530 1093 1 rps
 496 1808 499 1804 496 1801 493 1804 493 1808 496 1814 499 1817 509 1820 521
1820
 530 1817 533 1814 537 1808 537 1801 533 1795 524 1789 509 1783 503 1780
 496 1774 493 1764 493 1755 19 rps
 521 1820 527 1817 530 1814 533 1808 533 1801 530 1795 521 1789 509 1783 7 rps
 493 1761 496 1764 503 1764 518 1758 527 1758 533 1761 537 1764 6 rps
 503 1764 518 1755 530 1755 533 1758 537 1764 537 1770 5 rps
 496 2470 499 2466 496 2463 493 2466 493 2470 496 2476 499 2479 509 2482 521
2482
 530 2479 533 2473 533 2463 530 2457 521 2454 512 2454 14 rps
 521 2482 527 2479 530 2473 530 2463 527 2457 521 2454 5 rps
 521 2454 527 2451 533 2445 537 2439 537 2429 533 2423 530 2420 521 2417 509
2417
 499 2420 496 2423 493 2429 493 2432 496 2436 499 2432 496 2429 15 rps
 530 2448 533 2439 533 2429 530 2423 527 2420 521 2417 5 rps
 [20 20] 0 setdash
 594 500 611 501 668 504 726 507 783 510 840 513 898 517 955 520 1012 524
 1070 529 1127 533 1184 538 1241 544 1299 550 1356 556 1413 563 1471 570
 1528 578 1585 587 1643 597 1700 607 1757 618 1814 630 1872 643 1929 658
 1986 673 2044 690 2101 709 2158 729 2216 751 2273 775 2330 801 2387 830
 2445 862 2502 897 2559 935 2617 977 2674 1023 2731 1074 2789 1130 2846 1191
 2903 1260 2960 1335 3018 1419 3075 1511 3132 1614 3190 1728 3247 1855 3304
1996
 3362 2154 3419 2330 3453 2449 51 rps
 [] 0 setdash
 594 484 611 485 668 487 726 488 783 490 840 492 898 494 955 496 1012 498
 1070 501 1127 504 1184 506 1241 510 1299 513 1356 517 1413 521 1471 525
 1528 530 1585 535 1643 540 1700 546 1757 553 1814 560 1872 567 1929 576
 1986 585 2044 594 2101 605 2158 617 2216 630 2273 644 2330 659 2387 676
 2445 694 2502 714 2559 736 2617 761 2674 788 2731 817 2789 850 2846 885
 2903 925 2960 969 3018 1017 3075 1071 3132 1131 3190 1197 3247 1271 3304 1353
 3362 1445 3419 1548 3476 1663 3533 1791 3591 1935 3648 2097 3705 2280 3714
2311
 56 rps
 [80 20] 0 setdash
 594 476 611 476 668 477 726 478 783 479 840 481 898 482 955 483 1012 484
 1070 486 1127 488 1184 489 1241 491 1299 493 1356 496 1413 498 1471 501
 1528 504 1585 507 1643 510 1700 514 1757 518 1814 522 1872 527 1929 532
 1986 537 2044 543 2101 550 2158 557 2216 565 2273 573 2330 583 2387 593
 2445 604 2502 617 2559 630 2617 645 2674 662 2731 680 2789 700 2846 722
 2903 746 2960 773 3018 803 3075 836 3132 872 3190 913 3247 958 3304 1009
 3362 1065 3419 1128 3476 1199 3533 1278 3591 1366 3648 1466 3705 1578 3714
1597
 56 rps
 [] 0 setdash
 2122 222 2126 228 2132 235 2142 235 2145 231 2145 222 2139 202 2139 196 2145
189
 8 rps
 2139 235 2142 231 2142 222 2135 202 2135 196 2139 192 2145 189 2152 189 2158
192
 2165 199 2171 212 10 rps
 2181 235 2168 189 2165 179 2158 170 2148 166 2139 166 2132 170 2129 173 2129
176
 2132 179 2135 176 2132 173 11 rps
 2178 235 2165 189 2161 179 2155 170 2148 166 4 rps
 256 1319 324 1300 1 rps
 256 1323 324 1303 1 rps
 256 1310 256 1345 259 1355 266 1358 272 1358 282 1355 285 1352 288 1342 288
1313
 8 rps
 256 1345 259 1352 266 1355 272 1355 282 1352 285 1349 288 1342 6 rps
 288 1329 292 1336 295 1339 321 1342 324 1345 324 1352 318 1355 314 1355 7 rps
 295 1339 318 1345 321 1349 321 1352 318 1355 4 rps
 324 1290 324 1313 1 rps
 243 1404 249 1397 259 1391 272 1384 288 1381 301 1381 318 1384 331 1391 340
1397
 347 1404 9 rps
 249 1397 262 1391 272 1388 288 1384 301 1384 318 1388 327 1391 340 1397 7 rps
 292 1417 285 1420 279 1427 279 1436 282 1440 292 1440 311 1433 318 1433 324
1440
 8 rps
 279 1433 282 1436 292 1436 311 1430 318 1430 321 1433 324 1440 324 1446 321
1453
 314 1459 301 1466 10 rps
 279 1475 324 1462 334 1459 344 1453 347 1443 347 1433 344 1427 340 1423 337
1423
 334 1427 337 1430 340 1427 11 rps
 279 1472 324 1459 334 1456 344 1449 347 1443 4 rps
 324 1498 321 1495 318 1498 321 1501 327 1501 334 1498 337 1495 6 rps
 282 1556 278 1550 278 1542 282 1532 292 1526 302 1522 312 1522 318 1526 322
1530
 324 1536 324 1542 322 1552 312 1560 302 1562 292 1562 286 1560 268 1546
 262 1542 256 1542 252 1546 252 1552 256 1560 262 1566 22 rps
 278 1542 282 1536 292 1530 302 1526 316 1526 322 1530 5 rps
 324 1542 322 1550 312 1556 302 1560 288 1560 282 1556 272 1550 266 1546 260
1546
 256 1550 256 1556 262 1566 11 rps
 243 1586 249 1593 259 1599 272 1606 288 1609 301 1609 318 1606 331 1599 340
1593
 347 1586 9 rps
 249 1593 262 1599 272 1602 288 1606 301 1606 318 1602 327 1599 340 1593 7 rps
 992 1914 968 1846 1 rps
 992 1914 1016 1846 1 rps
 992 1904 1012 1846 1 rps
 962 1846 982 1846 1 rps
 1002 1846 1022 1846 1 rps
 1037 1885 1096 1885 1 rps
 1037 1865 1096 1865 1 rps
 1148 1908 1148 1846 1 rps
 1151 1914 1151 1846 1 rps
 1151 1914 1115 1865 1167 1865 2 rps
 1138 1846 1161 1846 1 rps
 1203 1914 1193 1911 1187 1901 1183 1885 1183 1875 1187 1859 1193 1849 1203
1846 1209 1846
 1219 1849 1226 1859 1229 1875 1229 1885 1226 1901 1219 1911 1209 1914 15 rcs

 1203 1914 1196 1911 1193 1908 1190 1901 1187 1885 1187 1875 1190 1859 1193
1852 1196 1849
 1203 1846 9 rps
 1209 1846 1216 1849 1219 1852 1222 1859 1226 1875 1226 1885 1222 1901 1219
1908 1216 1911
 1209 1914 9 rps
 1268 1914 1258 1911 1252 1901 1248 1885 1248 1875 1252 1859 1258 1849 1268
1846 1274 1846
 1284 1849 1291 1859 1294 1875 1294 1885 1291 1901 1284 1911 1274 1914 15 rcs

 1268 1914 1261 1911 1258 1908 1255 1901 1252 1885 1252 1875 1255 1859 1258
1852 1261 1849
 1268 1846 9 rps
 1274 1846 1281 1849 1284 1852 1287 1859 1291 1875 1291 1885 1287 1901 1284
1908 1281 1911
 1274 1914 9 rps
 1320 1914 1320 1846 1 rps
 1323 1914 1343 1856 1 rps
 1320 1914 1343 1846 1 rps
 1365 1914 1343 1846 1 rps
 1365 1914 1365 1846 1 rps
 1369 1914 1369 1846 1 rps
 1310 1914 1323 1914 1 rps
 1365 1914 1378 1914 1 rps
 1310 1846 1330 1846 1 rps
 1356 1846 1378 1846 1 rps
 1398 1872 1437 1872 1437 1878 1434 1885 1430 1888 1424 1891 1414 1891 1404
1888 1398 1882
 1395 1872 1395 1865 1398 1856 1404 1849 1414 1846 1421 1846 1430 1849 1437
1856
 16 rps
 1434 1872 1434 1882 1430 1888 2 rps
 1414 1891 1408 1888 1401 1882 1398 1872 1398 1865 1401 1856 1408 1849 1414
1846 7 rps
 1456 1914 1479 1846 1 rps
 1460 1914 1479 1856 1 rps
 1502 1914 1479 1846 1 rps
 1450 1914 1469 1914 1 rps
 1489 1914 1508 1914 1 rps
 1528 1846 1525 1849 1528 1852 1531 1849 1531 1843 1528 1836 1525 1833 6 rps
 1575 1878 1578 1885 1585 1891 1595 1891 1598 1888 1598 1882 1595 1869 1588
1846 7 rps
 1591 1891 1595 1888 1595 1882 1591 1869 1585 1846 4 rps
 1595 1869 1601 1882 1608 1888 1614 1891 1621 1891 1627 1888 1630 1885 1630
1878 1621 1846
 8 rps
 1621 1891 1627 1885 1627 1878 1617 1846 3 rps
 1627 1869 1634 1882 1640 1888 1647 1891 1653 1891 1660 1888 1663 1885 1663
1878 1656 1859
 1656 1849 1660 1846 10 rps
 1653 1891 1660 1885 1660 1878 1653 1859 1653 1849 1656 1846 1666 1846 1673
1852 1676 1859
 8 rps
 1699 1885 1689 1853 1689 1846 1691 1839 1694 1836 4 rps
 1701 1885 1691 1853 1 rps
 1691 1853 1694 1861 1699 1866 1703 1868 1708 1868 1713 1866 1716 1863 1718
1858 1718 1851
 1716 1844 1711 1836 1703 1834 1699 1834 1694 1836 1691 1844 14 rcs

 1713 1866 1716 1861 1716 1851 1713 1844 1708 1836 1703 1834 5 rps
 1691 1885 1701 1885 1 rps
 1738 1885 1796 1885 1 rps
 1738 1866 1796 1866 1 rps
 1826 1915 1819 1882 1 rps
 1819 1882 1826 1889 1835 1892 1845 1892 1855 1889 1861 1882 1865 1872 1865
1866 1861 1856
 1855 1850 1845 1847 1835 1847 1826 1850 1822 1853 1819 1859 1819 1863 1822
1866
 1826 1863 1822 1859 18 rps
 1845 1892 1852 1889 1858 1882 1861 1872 1861 1866 1858 1856 1852 1850 1845
1847 7 rps
 1826 1915 1858 1915 1 rps
 1826 1911 1842 1911 1858 1915 2 rps
 1930 1905 1933 1895 1933 1915 2 rcs

 1930 1905 1923 1911 1913 1915 1907 1915 1897 1911 1891 1905 1887 1898 1884
1889 1884 1872
 1887 1863 1891 1856 1897 1850 1907 1847 1913 1847 1923 1850 1930 1856 15 rps
 1907 1915 1900 1911 1894 1905 1891 1898 1887 1889 1887 1872 1891 1863 1894
1856 1900 1850
 1907 1847 9 rps
 1930 1872 1930 1847 1 rps
 1933 1872 1933 1847 1 rps
 1920 1872 1943 1872 1 rps
 1962 1872 2001 1872 2001 1879 1998 1885 1995 1889 1988 1892 1978 1892 1969
1889 1962 1882
 1959 1872 1959 1866 1962 1856 1969 1850 1978 1847 1985 1847 1995 1850 2001
1856
 16 rps
 1998 1872 1998 1882 1995 1889 2 rps
 1978 1892 1972 1889 1965 1882 1962 1872 1962 1866 1965 1856 1972 1850 1978
1847 7 rps
 2021 1915 2043 1847 1 rps
 2024 1915 2043 1856 1 rps
 2066 1915 2043 1847 1 rps
 2014 1915 2034 1915 1 rps
 2053 1915 2073 1915 1 rps
 [20 20] 0 setdash
 1111 1636 1384 1636 1 rps
 [] 0 setdash
 1517 1644 1511 1648 1503 1648 1493 1644 1487 1634 1483 1624 1483 1614 1487
1608 1491 1604
 1497 1602 1503 1602 1513 1604 1521 1614 1523 1624 1523 1634 1521 1640 1507
1658
 1503 1664 1503 1670 1507 1674 1513 1674 1521 1670 1527 1664 22 rps
 1503 1648 1497 1644 1491 1634 1487 1624 1487 1610 1491 1604 5 rps
 1503 1602 1511 1604 1517 1614 1521 1624 1521 1638 1517 1644 1511 1654 1507
1660 1507 1666
 1511 1670 1517 1670 1527 1664 11 rps
 1550 1641 1609 1641 1 rps
 1550 1622 1609 1622 1 rps
 1651 1670 1641 1667 1635 1657 1631 1641 1631 1631 1635 1615 1641 1605 1651
1602 1657 1602
 1667 1605 1674 1615 1677 1631 1677 1641 1674 1657 1667 1667 1657 1670 15 rcs

 1651 1670 1644 1667 1641 1664 1638 1657 1635 1641 1635 1631 1638 1615 1641
1609 1644 1605
 1651 1602 9 rps
 1657 1602 1664 1605 1667 1609 1670 1615 1674 1631 1674 1641 1670 1657 1667
1664 1664 1667
 1657 1670 9 rps
 1703 1609 1700 1605 1703 1602 1706 1605 3 rcs

 1739 1657 1745 1661 1755 1670 1755 1602 3 rps
 1752 1667 1752 1602 1 rps
 1739 1602 1768 1602 1 rps
 1800 1670 1794 1638 1 rps
 1794 1638 1800 1644 1810 1648 1820 1648 1830 1644 1836 1638 1839 1628 1839
1622 1836 1612
 1830 1605 1820 1602 1810 1602 1800 1605 1797 1609 1794 1615 1794 1618 1797
1622
 1800 1618 1797 1615 18 rps
 1820 1648 1826 1644 1833 1638 1836 1628 1836 1622 1833 1612 1826 1605 1820
1602 7 rps
 1800 1670 1833 1670 1 rps
 1800 1667 1817 1667 1833 1670 2 rps
 1111 1527 1384 1527 1 rps
 1517 1535 1511 1539 1503 1539 1493 1535 1487 1525 1483 1515 1483 1505 1487
1499 1491 1495
 1497 1493 1503 1493 1513 1495 1521 1505 1523 1515 1523 1525 1521 1531 1507
1549
 1503 1555 1503 1561 1507 1565 1513 1565 1521 1561 1527 1555 22 rps
 1503 1539 1497 1535 1491 1525 1487 1515 1487 1501 1491 1495 5 rps
 1503 1493 1511 1495 1517 1505 1521 1515 1521 1529 1517 1535 1511 1545 1507
1551 1507 1557
 1511 1561 1517 1561 1527 1555 11 rps
 1550 1532 1609 1532 1 rps
 1550 1513 1609 1513 1 rps
 1651 1561 1641 1558 1635 1548 1631 1532 1631 1522 1635 1506 1641 1496 1651
1493 1657 1493
 1667 1496 1674 1506 1677 1522 1677 1532 1674 1548 1667 1558 1657 1561 15 rcs

 1651 1561 1644 1558 1641 1555 1638 1548 1635 1532 1635 1522 1638 1506 1641
1500 1644 1496
 1651 1493 9 rps
 1657 1493 1664 1496 1667 1500 1670 1506 1674 1522 1674 1532 1670 1548 1667
1555 1664 1558
 1657 1561 9 rps
 1703 1500 1700 1496 1703 1493 1706 1496 3 rcs

 1739 1548 1745 1552 1755 1561 1755 1493 3 rps
 1752 1558 1752 1493 1 rps
 1739 1493 1768 1493 1 rps
 1794 1561 1794 1542 1 rps
 1794 1548 1797 1555 1804 1561 1810 1561 1826 1552 1833 1552 1836 1555 1839
1561 7 rps
 1797 1555 1804 1558 1810 1558 1826 1552 3 rps
 1839 1561 1839 1552 1836 1542 1823 1526 1820 1519 1817 1509 1817 1493 6 rps
 1836 1542 1820 1526 1817 1519 1813 1509 1813 1493 4 rps
 [80 20] 0 setdash
 1111 1418 1384 1418 1 rps
 [] 0 setdash
 1517 1425 1511 1429 1503 1429 1493 1425 1487 1415 1483 1405 1483 1395 1487
1389 1491 1385
 1497 1383 1503 1383 1513 1385 1521 1395 1523 1405 1523 1415 1521 1421 1507
1439
 1503 1445 1503 1451 1507 1455 1513 1455 1521 1451 1527 1445 22 rps
 1503 1429 1497 1425 1491 1415 1487 1405 1487 1391 1491 1385 5 rps
 1503 1383 1511 1385 1517 1395 1521 1405 1521 1419 1517 1425 1511 1435 1507
1441 1507 1447
 1511 1451 1517 1451 1527 1445 11 rps
 1550 1422 1609 1422 1 rps
 1550 1403 1609 1403 1 rps
 1651 1451 1641 1448 1635 1438 1631 1422 1631 1412 1635 1396 1641 1386 1651
1383 1657 1383
 1667 1386 1674 1396 1677 1412 1677 1422 1674 1438 1667 1448 1657 1451 15 rcs

 1651 1451 1644 1448 1641 1445 1638 1438 1635 1422 1635 1412 1638 1396 1641
1390 1644 1386
 1651 1383 9 rps
 1657 1383 1664 1386 1667 1390 1670 1396 1674 1412 1674 1422 1670 1438 1667
1445 1664 1448
 1657 1451 9 rps
 1703 1390 1700 1386 1703 1383 1706 1386 3 rcs

 1739 1438 1745 1442 1755 1451 1755 1383 3 rps
 1752 1448 1752 1383 1 rps
 1739 1383 1768 1383 1 rps
 1836 1429 1833 1419 1826 1412 1817 1409 1813 1409 1804 1412 1797 1419 1794
1429 1794 1432
 1797 1442 1804 1448 1813 1451 1820 1451 1830 1448 1836 1442 1839 1432 1839
1412
 1836 1399 1833 1393 1826 1386 1817 1383 1807 1383 1800 1386 1797 1393 1797
1396
 1800 1399 1804 1396 1800 1393 27 rps
 1813 1409 1807 1412 1800 1419 1797 1429 1797 1432 1800 1442 1807 1448 1813
1451 7 rps
 1820 1451 1826 1448 1833 1442 1836 1432 1836 1412 1833 1399 1830 1393 1823
1386 1817 1383
 8 rps
 grestore showpage
%Trailer
%EOF
%%%%%%%%%% CUT HERE %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%% fig4.eps %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%!PS-Adobe-2.0 EPSF-1.2
%%BoundingBox: 0 0 468 360
%%%%DocumentFonts: /Helvetica
%%Title: Axum PostScript file
%%Creator: TriMetrix, Inc.
%%Pages: 1
%%EndComments
% Copyright 1988-1991 by TriMetrix, Inc. All rights reserved.
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 1114 463 1114 499 1 rps
 1114 2449 1114 2413 1 rps
 1374 463 1374 481 1 rps
 1374 2449 1374 2431 1 rps
 1634 463 1634 499 1 rps
 1634 2449 1634 2413 1 rps
 1894 463 1894 481 1 rps
 1894 2449 1894 2431 1 rps
 2154 463 2154 499 1 rps
 2154 2449 2154 2413 1 rps
 2414 463 2414 481 1 rps
 2414 2449 2414 2431 1 rps
 2674 463 2674 499 1 rps
 2674 2449 2674 2413 1 rps
 2934 463 2934 481 1 rps
 2934 2449 2934 2431 1 rps
 3194 463 3194 499 1 rps
 3194 2449 3194 2413 1 rps
 3454 463 3454 481 1 rps
 3454 2449 3454 2431 1 rps
 3714 463 3714 499 1 rps
 3714 2449 3714 2413 1 rps
 510 413 501 410 494 400 491 384 491 374 494 358 501 348 510 345 517 345
 527 348 533 358 536 374 536 384 533 400 527 410 517 413 15 rcs

 510 413 504 410 501 407 497 400 494 384 494 374 497 358 501 352 504 348
 510 345 9 rps
 517 345 523 348 527 352 530 358 533 374 533 384 530 400 527 407 523 410
 517 413 9 rps
 562 352 559 348 562 345 566 348 3 rcs

 598 400 605 404 614 413 614 345 3 rps
 611 410 611 345 1 rps
 598 345 627 345 1 rps
 663 400 670 404 679 413 679 345 3 rps
 676 410 676 345 1 rps
 663 345 692 345 1 rps
 1030 413 1021 410 1014 400 1011 384 1011 374 1014 358 1021 348 1030 345 1037
345
 1047 348 1053 358 1056 374 1056 384 1053 400 1047 410 1037 413 15 rcs

 1030 413 1024 410 1021 407 1017 400 1014 384 1014 374 1017 358 1021 352 1024
348
 1030 345 9 rps
 1037 345 1043 348 1047 352 1050 358 1053 374 1053 384 1050 400 1047 407 1043
410
 1037 413 9 rps
 1082 352 1079 348 1082 345 1086 348 3 rcs

 1118 400 1125 404 1134 413 1134 345 3 rps
 1131 410 1131 345 1 rps
 1118 345 1147 345 1 rps
 1177 400 1180 397 1177 394 1173 397 1173 400 1177 407 1180 410 1190 413 1203
413
 1212 410 1216 407 1219 400 1219 394 1216 387 1206 381 1190 374 1183 371
 1177 365 1173 355 1173 345 19 rps
 1203 413 1209 410 1212 407 1216 400 1216 394 1212 387 1203 381 1190 374 7 rps
 1173 352 1177 355 1183 355 1199 348 1209 348 1216 352 1219 355 6 rps
 1183 355 1199 345 1212 345 1216 348 1219 355 1219 361 5 rps
 1550 413 1541 410 1534 400 1531 384 1531 374 1534 358 1541 348 1550 345 1557
345
 1567 348 1573 358 1576 374 1576 384 1573 400 1567 410 1557 413 15 rcs

 1550 413 1544 410 1541 407 1537 400 1534 384 1534 374 1537 358 1541 352 1544
348
 1550 345 9 rps
 1557 345 1563 348 1567 352 1570 358 1573 374 1573 384 1570 400 1567 407 1563
410
 1557 413 9 rps
 1602 352 1599 348 1602 345 1606 348 3 rcs

 1638 400 1645 404 1654 413 1654 345 3 rps
 1651 410 1651 345 1 rps
 1638 345 1667 345 1 rps
 1697 400 1700 397 1697 394 1693 397 1693 400 1697 407 1700 410 1710 413 1723
413
 1732 410 1736 404 1736 394 1732 387 1723 384 1713 384 14 rps
 1723 413 1729 410 1732 404 1732 394 1729 387 1723 384 5 rps
 1723 384 1729 381 1736 374 1739 368 1739 358 1736 352 1732 348 1723 345 1710
345
 1700 348 1697 352 1693 358 1693 361 1697 365 1700 361 1697 358 15 rps
 1732 378 1736 368 1736 358 1732 352 1729 348 1723 345 5 rps
 2070 413 2061 410 2054 400 2051 384 2051 374 2054 358 2061 348 2070 345 2077
345
 2087 348 2093 358 2096 374 2096 384 2093 400 2087 410 2077 413 15 rcs

 2070 413 2064 410 2061 407 2057 400 2054 384 2054 374 2057 358 2061 352 2064
348
 2070 345 9 rps
 2077 345 2083 348 2087 352 2090 358 2093 374 2093 384 2090 400 2087 407 2083
410
 2077 413 9 rps
 2122 352 2119 348 2122 345 2126 348 3 rcs

 2158 400 2165 404 2174 413 2174 345 3 rps
 2171 410 2171 345 1 rps
 2158 345 2187 345 1 rps
 2243 407 2243 345 1 rps
 2246 413 2246 345 1 rps
 2246 413 2210 365 2262 365 2 rps
 2233 345 2256 345 1 rps
 2590 413 2581 410 2574 400 2571 384 2571 374 2574 358 2581 348 2590 345 2597
345
 2607 348 2613 358 2616 374 2616 384 2613 400 2607 410 2597 413 15 rcs

 2590 413 2584 410 2581 407 2577 400 2574 384 2574 374 2577 358 2581 352 2584
348
 2590 345 9 rps
 2597 345 2603 348 2607 352 2610 358 2613 374 2613 384 2610 400 2607 407 2603
410
 2597 413 9 rps
 2642 352 2639 348 2642 345 2646 348 3 rcs

 2678 400 2685 404 2694 413 2694 345 3 rps
 2691 410 2691 345 1 rps
 2678 345 2707 345 1 rps
 2740 413 2733 381 1 rps
 2733 381 2740 387 2750 391 2759 391 2769 387 2776 381 2779 371 2779 365 2776
355
 2769 348 2759 345 2750 345 2740 348 2737 352 2733 358 2733 361 2737 365
 2740 361 2737 358 18 rps
 2759 391 2766 387 2772 381 2776 371 2776 365 2772 355 2766 348 2759 345 7 rps
 2740 413 2772 413 1 rps
 2740 410 2756 410 2772 413 2 rps
 3110 413 3101 410 3094 400 3091 384 3091 374 3094 358 3101 348 3110 345 3117
345
 3127 348 3133 358 3136 374 3136 384 3133 400 3127 410 3117 413 15 rcs

 3110 413 3104 410 3101 407 3097 400 3094 384 3094 374 3097 358 3101 352 3104
348
 3110 345 9 rps
 3117 345 3123 348 3127 352 3130 358 3133 374 3133 384 3130 400 3127 407 3123
410
 3117 413 9 rps
 3162 352 3159 348 3162 345 3166 348 3 rcs

 3198 400 3205 404 3214 413 3214 345 3 rps
 3211 410 3211 345 1 rps
 3198 345 3227 345 1 rps
 3292 404 3289 400 3292 397 3296 400 3296 404 3292 410 3286 413 3276 413 3266
410
 3260 404 3257 397 3253 384 3253 365 3257 355 3263 348 3273 345 3279 345
 3289 348 3296 355 3299 365 3299 368 3296 378 3289 384 3279 387 3276 387
 3266 384 3260 378 3257 368 27 rps
 3276 413 3270 410 3263 404 3260 397 3257 384 3257 365 3260 355 3266 348 3273
345
 8 rps
 3279 345 3286 348 3292 355 3296 365 3296 368 3292 378 3286 384 3279 387 7 rps
 3630 413 3621 410 3614 400 3611 384 3611 374 3614 358 3621 348 3630 345 3637
345
 3647 348 3653 358 3656 374 3656 384 3653 400 3647 410 3637 413 15 rcs

 3630 413 3624 410 3621 407 3617 400 3614 384 3614 374 3617 358 3621 352 3624
348
 3630 345 9 rps
 3637 345 3643 348 3647 352 3650 358 3653 374 3653 384 3650 400 3647 407 3643
410
 3637 413 9 rps
 3682 352 3679 348 3682 345 3686 348 3 rcs

 3718 400 3725 404 3734 413 3734 345 3 rps
 3731 410 3731 345 1 rps
 3718 345 3747 345 1 rps
 3773 413 3773 394 1 rps
 3773 400 3777 407 3783 413 3790 413 3806 404 3812 404 3816 407 3819 413 7 rps
 3777 407 3783 410 3790 410 3806 404 3 rps
 3819 413 3819 404 3816 394 3803 378 3799 371 3796 361 3796 345 6 rps
 3816 394 3799 378 3796 371 3793 361 3793 345 4 rps
 594 463 594 2449 1 rps
 593 462 593 2450 1 rps
 592 461 592 2451 1 rps
 591 460 591 2452 1 rps
 590 459 590 2453 1 rps
 3714 463 3714 2449 1 rps
 3715 462 3715 2450 1 rps
 3716 461 3716 2451 1 rps
 3717 460 3717 2452 1 rps
 3718 459 3718 2453 1 rps
 594 463 630 463 1 rps
 3714 463 3678 463 1 rps
 594 652 612 652 1 rps
 3714 652 3696 652 1 rps
 594 842 630 842 1 rps
 3714 842 3678 842 1 rps
 594 1031 612 1031 1 rps
 3714 1031 3696 1031 1 rps
 594 1221 630 1221 1 rps
 3714 1221 3678 1221 1 rps
 594 1410 612 1410 1 rps
 3714 1410 3696 1410 1 rps
 594 1600 630 1600 1 rps
 3714 1600 3678 1600 1 rps
 594 1789 612 1789 1 rps
 3714 1789 3696 1789 1 rps
 594 1979 630 1979 1 rps
 3714 1979 3678 1979 1 rps
 594 2168 612 2168 1 rps
 3714 2168 3696 2168 1 rps
 594 2359 630 2359 1 rps
 3714 2359 3678 2359 1 rps
 509 497 500 494 493 484 490 468 490 458 493 442 500 432 509 429 516 429
 526 432 532 442 535 458 535 468 532 484 526 494 516 497 15 rcs

 509 497 503 494 500 491 496 484 493 468 493 458 496 442 500 436 503 432
 509 429 9 rps
 516 429 522 432 526 436 529 442 532 458 532 468 529 484 526 491 522 494
 516 497 9 rps
 500 863 506 867 516 876 516 808 3 rps
 513 873 513 808 1 rps
 500 808 529 808 1 rps
 493 1242 496 1239 493 1236 490 1239 490 1242 493 1249 496 1252 506 1255 519
1255
 529 1252 532 1249 535 1242 535 1236 532 1229 522 1223 506 1216 500 1213
 493 1207 490 1197 490 1187 19 rps
 519 1255 526 1252 529 1249 532 1242 532 1236 529 1229 519 1223 506 1216 7 rps
 490 1194 493 1197 500 1197 516 1190 526 1190 532 1194 535 1197 6 rps
 500 1197 516 1187 529 1187 532 1190 535 1197 535 1203 5 rps
 493 1621 496 1618 493 1615 490 1618 490 1621 493 1628 496 1631 506 1634 519
1634
 529 1631 532 1625 532 1615 529 1608 519 1605 509 1605 14 rps
 519 1634 526 1631 529 1625 529 1615 526 1608 519 1605 5 rps
 519 1605 526 1602 532 1595 535 1589 535 1579 532 1573 529 1569 519 1566 506
1566
 496 1569 493 1573 490 1579 490 1582 493 1586 496 1582 493 1579 15 rps
 529 1599 532 1589 532 1579 529 1573 526 1569 519 1566 5 rps
 519 2007 519 1945 1 rps
 522 2013 522 1945 1 rps
 522 2013 487 1965 539 1965 2 rps
 509 1945 532 1945 1 rps
 496 2393 490 2361 1 rps
 490 2361 496 2367 506 2371 516 2371 526 2367 532 2361 535 2351 535 2345 532
2335
 526 2328 516 2325 506 2325 496 2328 493 2332 490 2338 490 2341 493 2345
 496 2341 493 2338 18 rps
 516 2371 522 2367 529 2361 532 2351 532 2345 529 2335 522 2328 516 2325 7 rps
 496 2393 529 2393 1 rps
 496 2390 513 2390 529 2393 2 rps
 [20 20] 0 setdash
 594 691 655 666 783 625 911 593 1038 568 1166 548 1294 532 1421 519 1549 509
 1677 501 1804 494 1932 489 2059 484 2187 481 2315 478 2442 475 2570 473
 2698 472 2825 470 2953 469 3081 468 3208 467 3336 467 3463 466 3591 466
 3714 466 25 rps
 [] 0 setdash
 594 1223 655 1139 783 1004 911 898 1038 814 1166 747 1294 694 1421 651 1549
617
 1677 590 1804 567 1932 549 2059 534 2187 522 2315 512 2442 504 2570 497
 2698 492 2825 487 2953 483 3081 480 3208 478 3336 475 3463 473 3591 472
 3714 472 25 rps
 [80 20] 0 setdash
 645 2449 655 2412 783 2023 911 1716 1038 1475 1166 1282 1294 1129 1421 1006
1549 908
 1677 828 1804 764 1932 711 2059 669 2187 634 2315 605 2442 582 2570 562
 2698 546 2825 533 2953 522 3081 513 3208 505 3336 499 3463 493 3591 489
 3714 486 25 rps
 [] 0 setdash
 2164 227 2158 231 2150 231 2140 227 2134 217 2130 207 2130 197 2134 191 2138
187
 2144 185 2150 185 2160 187 2168 197 2170 207 2170 217 2168 223 2154 241
 2150 247 2150 253 2154 257 2160 257 2168 253 2174 247 22 rps
 2150 231 2144 227 2138 217 2134 207 2134 193 2138 187 5 rps
 2150 185 2158 187 2164 197 2168 207 2168 221 2164 227 2158 237 2154 243 2154
249
 2158 253 2164 253 2174 247 11 rps
 252 1369 320 1350 1 rps
 252 1373 320 1353 1 rps
 252 1360 252 1395 255 1405 262 1408 268 1408 278 1405 281 1402 284 1392 284
1363
 8 rps
 252 1395 255 1402 262 1405 268 1405 278 1402 281 1399 284 1392 6 rps
 284 1379 288 1386 291 1389 317 1392 320 1395 320 1402 314 1405 310 1405 7 rps
 291 1389 314 1395 317 1399 317 1402 314 1405 4 rps
 320 1340 320 1363 1 rps
 239 1454 245 1447 255 1441 268 1434 284 1431 297 1431 314 1434 327 1441 336
1447
 343 1454 9 rps
 245 1447 258 1441 268 1438 284 1434 297 1434 314 1438 323 1441 336 1447 7 rps
 278 1506 274 1500 274 1492 278 1482 288 1476 298 1472 308 1472 314 1476 318
1480
 320 1486 320 1492 318 1502 308 1510 298 1512 288 1512 282 1510 264 1496
 258 1492 252 1492 248 1496 248 1502 252 1510 258 1516 22 rps
 274 1492 278 1486 288 1480 298 1476 312 1476 318 1480 5 rps
 320 1492 318 1500 308 1506 298 1510 284 1510 278 1506 268 1500 262 1496 256
1496
 252 1500 252 1506 258 1516 11 rps
 239 1535 245 1542 255 1548 268 1555 284 1558 297 1558 314 1555 327 1548 336
1542
 343 1535 9 rps
 245 1542 258 1548 268 1552 284 1555 297 1555 314 1552 323 1548 336 1542 7 rps
 2662 1878 2665 1885 2672 1891 2682 1891 2685 1888 2685 1882 2682 1869 2675
1846 7 rps
 2678 1891 2682 1888 2682 1882 2678 1869 2672 1846 4 rps
 2682 1869 2688 1882 2695 1888 2701 1891 2708 1891 2714 1888 2717 1885 2717
1878 2708 1846
 8 rps
 2708 1891 2714 1885 2714 1878 2704 1846 3 rps
 2714 1869 2721 1882 2727 1888 2734 1891 2740 1891 2747 1888 2750 1885 2750
1878 2743 1859
 2743 1849 2747 1846 10 rps
 2740 1891 2747 1885 2747 1878 2740 1859 2740 1849 2743 1846 2753 1846 2760
1852 2763 1859
 8 rps
 2786 1885 2776 1853 2776 1846 2778 1839 2781 1836 4 rps
 2788 1885 2778 1853 1 rps
 2778 1853 2781 1861 2786 1866 2791 1868 2795 1868 2800 1866 2803 1863 2805
1858 2805 1851
 2803 1844 2798 1836 2791 1834 2786 1834 2781 1836 2778 1844 14 rcs

 2800 1866 2803 1861 2803 1851 2800 1844 2795 1836 2791 1834 5 rps
 2778 1885 2788 1885 1 rps
 2825 1885 2884 1885 1 rps
 2825 1866 2884 1866 1 rps
 2913 1915 2906 1882 1 rps
 2906 1882 2913 1889 2923 1892 2932 1892 2942 1889 2949 1882 2952 1872 2952
1866 2949 1856
 2942 1850 2932 1847 2923 1847 2913 1850 2910 1853 2906 1859 2906 1863 2910
1866
 2913 1863 2910 1859 18 rps
 2932 1892 2939 1889 2945 1882 2949 1872 2949 1866 2945 1856 2939 1850 2932
1847 7 rps
 2913 1915 2945 1915 1 rps
 2913 1911 2929 1911 2945 1915 2 rps
 3017 1905 3020 1895 3020 1915 2 rcs

 3017 1905 3010 1911 3001 1915 2994 1915 2984 1911 2978 1905 2975 1898 2971
1889 2971 1872
 2975 1863 2978 1856 2984 1850 2994 1847 3001 1847 3010 1850 3017 1856 15 rps
 2994 1915 2988 1911 2981 1905 2978 1898 2975 1889 2975 1872 2978 1863 2981
1856 2988 1850
 2994 1847 9 rps
 3017 1872 3017 1847 1 rps
 3020 1872 3020 1847 1 rps
 3007 1872 3030 1872 1 rps
 3049 1872 3088 1872 3088 1879 3085 1885 3082 1889 3075 1892 3066 1892 3056
1889 3049 1882
 3046 1872 3046 1866 3049 1856 3056 1850 3066 1847 3072 1847 3082 1850 3088
1856
 16 rps
 3085 1872 3085 1882 3082 1889 2 rps
 3066 1892 3059 1889 3053 1882 3049 1872 3049 1866 3053 1856 3059 1850 3066
1847 7 rps
 3108 1915 3131 1847 1 rps
 3111 1915 3131 1856 1 rps
 3153 1915 3131 1847 1 rps
 3101 1915 3121 1915 1 rps
 3140 1915 3160 1915 1 rps
 [20 20] 0 setdash
 2411 1636 2684 1636 1 rps
 [] 0 setdash
 2807 1670 2783 1602 1 rps
 2807 1670 2831 1602 1 rps
 2807 1660 2827 1602 1 rps
 2777 1602 2797 1602 1 rps
 2817 1602 2837 1602 1 rps
 2852 1641 2911 1641 1 rps
 2852 1622 2911 1622 1 rps
 2937 1657 2940 1654 2937 1651 2933 1654 2933 1657 2937 1664 2940 1667 2950
1670 2963 1670
 2972 1667 2976 1661 2976 1651 2972 1644 2963 1641 2953 1641 14 rps
 2963 1670 2969 1667 2972 1661 2972 1651 2969 1644 2963 1641 5 rps
 2963 1641 2969 1638 2976 1631 2979 1625 2979 1615 2976 1609 2972 1605 2963
1602 2950 1602
 2940 1605 2937 1609 2933 1615 2933 1618 2937 1622 2940 1618 2937 1615 15 rps
 2972 1635 2976 1625 2976 1615 2972 1609 2969 1605 2963 1602 5 rps
 3005 1670 2998 1638 1 rps
 2998 1638 3005 1644 3015 1648 3024 1648 3034 1644 3041 1638 3044 1628 3044
1622 3041 1612
 3034 1605 3024 1602 3015 1602 3005 1605 3002 1609 2998 1615 2998 1618 3002
1622
 3005 1618 3002 1615 18 rps
 3024 1648 3031 1644 3037 1638 3041 1628 3041 1622 3037 1612 3031 1605 3024
1602 7 rps
 3005 1670 3037 1670 1 rps
 3005 1667 3021 1667 3037 1670 2 rps
 3083 1670 3073 1667 3067 1657 3063 1641 3063 1631 3067 1615 3073 1605 3083
1602 3089 1602
 3099 1605 3106 1615 3109 1631 3109 1641 3106 1657 3099 1667 3089 1670 15 rcs

 3083 1670 3076 1667 3073 1664 3070 1657 3067 1641 3067 1631 3070 1615 3073
1609 3076 1605
 3083 1602 9 rps
 3089 1602 3096 1605 3099 1609 3102 1615 3106 1631 3106 1641 3102 1657 3099
1664 3096 1667
 3089 1670 9 rps
 3135 1670 3135 1602 1 rps
 3138 1670 3158 1612 1 rps
 3135 1670 3158 1602 1 rps
 3180 1670 3158 1602 1 rps
 3180 1670 3180 1602 1 rps
 3184 1670 3184 1602 1 rps
 3125 1670 3138 1670 1 rps
 3180 1670 3193 1670 1 rps
 3125 1602 3145 1602 1 rps
 3171 1602 3193 1602 1 rps
 3213 1628 3252 1628 3252 1635 3249 1641 3245 1644 3239 1648 3229 1648 3219
1644 3213 1638
 3210 1628 3210 1622 3213 1612 3219 1605 3229 1602 3236 1602 3245 1605 3252
1612
 16 rps
 3249 1628 3249 1638 3245 1644 2 rps
 3229 1648 3223 1644 3216 1638 3213 1628 3213 1622 3216 1612 3223 1605 3229
1602 7 rps
 3271 1670 3294 1602 1 rps
 3275 1670 3294 1612 1 rps
 3317 1670 3294 1602 1 rps
 3265 1670 3284 1670 1 rps
 3304 1670 3323 1670 1 rps
 2411 1527 2684 1527 1 rps
 2807 1561 2783 1493 1 rps
 2807 1561 2831 1493 1 rps
 2807 1551 2827 1493 1 rps
 2777 1493 2797 1493 1 rps
 2817 1493 2837 1493 1 rps
 2852 1532 2911 1532 1 rps
 2852 1513 2911 1513 1 rps
 2963 1555 2963 1493 1 rps
 2966 1561 2966 1493 1 rps
 2966 1561 2930 1513 2982 1513 2 rps
 2953 1493 2976 1493 1 rps
 3018 1561 3008 1558 3002 1548 2998 1532 2998 1522 3002 1506 3008 1496 3018
1493 3024 1493
 3034 1496 3041 1506 3044 1522 3044 1532 3041 1548 3034 1558 3024 1561 15 rcs

 3018 1561 3011 1558 3008 1555 3005 1548 3002 1532 3002 1522 3005 1506 3008
1500 3011 1496
 3018 1493 9 rps
 3024 1493 3031 1496 3034 1500 3037 1506 3041 1522 3041 1532 3037 1548 3034
1555 3031 1558
 3024 1561 9 rps
 3083 1561 3073 1558 3067 1548 3063 1532 3063 1522 3067 1506 3073 1496 3083
1493 3089 1493
 3099 1496 3106 1506 3109 1522 3109 1532 3106 1548 3099 1558 3089 1561 15 rcs

 3083 1561 3076 1558 3073 1555 3070 1548 3067 1532 3067 1522 3070 1506 3073
1500 3076 1496
 3083 1493 9 rps
 3089 1493 3096 1496 3099 1500 3102 1506 3106 1522 3106 1532 3102 1548 3099
1555 3096 1558
 3089 1561 9 rps
 3135 1561 3135 1493 1 rps
 3138 1561 3158 1503 1 rps
 3135 1561 3158 1493 1 rps
 3180 1561 3158 1493 1 rps
 3180 1561 3180 1493 1 rps
 3184 1561 3184 1493 1 rps
 3125 1561 3138 1561 1 rps
 3180 1561 3193 1561 1 rps
 3125 1493 3145 1493 1 rps
 3171 1493 3193 1493 1 rps
 3213 1519 3252 1519 3252 1526 3249 1532 3245 1535 3239 1539 3229 1539 3219
1535 3213 1529
 3210 1519 3210 1513 3213 1503 3219 1496 3229 1493 3236 1493 3245 1496 3252
1503
 16 rps
 3249 1519 3249 1529 3245 1535 2 rps
 3229 1539 3223 1535 3216 1529 3213 1519 3213 1513 3216 1503 3223 1496 3229
1493 7 rps
 3271 1561 3294 1493 1 rps
 3275 1561 3294 1503 1 rps
 3317 1561 3294 1493 1 rps
 3265 1561 3284 1561 1 rps
 3304 1561 3323 1561 1 rps
 [80 20] 0 setdash
 2411 1418 2684 1418 1 rps
 [] 0 setdash
 2807 1451 2783 1383 1 rps
 2807 1451 2831 1383 1 rps
 2807 1441 2827 1383 1 rps
 2777 1383 2797 1383 1 rps
 2817 1383 2837 1383 1 rps
 2852 1422 2911 1422 1 rps
 2852 1403 2911 1403 1 rps
 2963 1445 2963 1383 1 rps
 2966 1451 2966 1383 1 rps
 2966 1451 2930 1403 2982 1403 2 rps
 2953 1383 2976 1383 1 rps
 3005 1451 2998 1419 1 rps
 2998 1419 3005 1425 3015 1429 3024 1429 3034 1425 3041 1419 3044 1409 3044
1403 3041 1393
 3034 1386 3024 1383 3015 1383 3005 1386 3002 1390 2998 1396 2998 1399 3002
1403
 3005 1399 3002 1396 18 rps
 3024 1429 3031 1425 3037 1419 3041 1409 3041 1403 3037 1393 3031 1386 3024
1383 7 rps
 3005 1451 3037 1451 1 rps
 3005 1448 3021 1448 3037 1451 2 rps
 3083 1451 3073 1448 3067 1438 3063 1422 3063 1412 3067 1396 3073 1386 3083
1383 3089 1383
 3099 1386 3106 1396 3109 1412 3109 1422 3106 1438 3099 1448 3089 1451 15 rcs

 3083 1451 3076 1448 3073 1445 3070 1438 3067 1422 3067 1412 3070 1396 3073
1390 3076 1386
 3083 1383 9 rps
 3089 1383 3096 1386 3099 1390 3102 1396 3106 1412 3106 1422 3102 1438 3099
1445 3096 1448
 3089 1451 9 rps
 3135 1451 3135 1383 1 rps
 3138 1451 3158 1393 1 rps
 3135 1451 3158 1383 1 rps
 3180 1451 3158 1383 1 rps
 3180 1451 3180 1383 1 rps
 3184 1451 3184 1383 1 rps
 3125 1451 3138 1451 1 rps
 3180 1451 3193 1451 1 rps
 3125 1383 3145 1383 1 rps
 3171 1383 3193 1383 1 rps
 3213 1409 3252 1409 3252 1416 3249 1422 3245 1425 3239 1429 3229 1429 3219
1425 3213 1419
 3210 1409 3210 1403 3213 1393 3219 1386 3229 1383 3236 1383 3245 1386 3252
1393
 16 rps
 3249 1409 3249 1419 3245 1425 2 rps
 3229 1429 3223 1425 3216 1419 3213 1409 3213 1403 3216 1393 3223 1386 3229
1383 7 rps
 3271 1451 3294 1383 1 rps
 3275 1451 3294 1393 1 rps
 3317 1451 3294 1383 1 rps
 3265 1451 3284 1451 1 rps
 3304 1451 3323 1451 1 rps
 grestore showpage
%Trailer
%EOF



