%Paper: 
%From: MAREK@taunivm.tau.ac.il
%Date: 13 Jul 94 15:39 IST
%Date (revised): 13 Jul 94 16:00 IST


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\begin{document}

\begin{titlepage}
\begin{flushright}
CERN-TH-7324/94\\
TAUP-2178-94\\

\end{flushright}
\begin{centering}
\vspace{.1in}
{\large {\bf Determination of $\alpha_s$ and the Nucleon\\
Spin Decomposition using Recent Polarized Structure Function Data}}\\
\vspace{.4in}
{\bf John Ellis}\\
\vspace{.05in}
Theory Division, CERN, CH-1211, Geneva 23, Switzerland. \\
e-mail: johne@cernvm.cern.ch \\
\vspace{0.5cm}
and \\
\vspace{0.5cm}

\vspace{.05in}
{\bf Marek Karliner}\\

\vspace{.05in}
School of Physics and Astronomy
\\ Raymond and Beverly Sackler Faculty of Exact Sciences
\\ Tel-Aviv University, 69978 Tel-Aviv, Israel
\\ e-mail: marek@vm.tau.ac.il
\\
\vspace{.03in}
\vspace{.1in}
{\bf Abstract} \\
\vspace{.05in}
\end{centering}
{\small

New data on polarized $\mu{-}p$ and $e{-}p$
scattering permit a first determination of $\alpha_s$
using the Bjorken sum rule, as well as higher
precision in determining the nucleon spin
decomposition. Using perturbative QCD calculations
to \OIV\ for the non-singlet combination of
structure functions, we find
$\alpha_s(2.5\,\, \hbox{GeV}^2) = 0.375^{+0.062}_{-0.081}\,\,$,
corresponding to $\alpha_s(M_Z^2) =0.122^{+0.005}_{-0.009}\,\,$,
and using calculations to \OIII\ for the singlet combination
we find
$\Du = 0.83  \pm 0.03$,
$\Dd =-0.43  \pm 0.03$,
$\Ds =-0.10  \pm 0.03$,
$\Delta \Sigma \equiv \Du + \Dd + \Ds =  0.31 \pm 0.07$,
at a renormalization scale $Q^2 = 10\ \hbox{GeV}^2$.
Perturbative QCD corrections play an essential role
in reconciling the interpretations of
data taken using different targets.
We discuss higher-twist uncertainties in these determinations.
The $\Delta q$ determinations are used to update predictions for
the couplings of massive Cold Dark Matter particles and axions
to nucleons.
}
\paragraph{}
\par
\vspace{0.7in}
\begin{flushleft}
CERN-TH-7324/94\\
July 1994 \\
\end{flushleft}


\end{titlepage}
\newpage

When Bjorken first derived his sum rule for polarized deep-inelastic
scattering \cite{BjI},
he doubted whether it could be tested experimentally.
Several years later, however, he changed his mind \cite{BjII}
and an experimental programme
on polarized electron-proton scattering was launched at
SLAC \cite{oldSLACa,oldSLACb,oldSLACc}
In view of this, a sum rule for the polarized proton
and neutron
structure function $g_1^p$ was proposed \cite{EJ},
based on the dynamical
hypothesis that strange quarks and antiquarks in a polarized
nucleon would have no net polarization. However, this sum rule
was not at all rigorous, in contrast to the Bjorken sum rule
which is an inescapable prediction of
QCD \cite{Kodaira,KodairaAnomDim}.
The first round of
polarized $e$-$p$ experiments that were consistent, within their
stated errors, with the hypothesis of no net strange polarization.
However, no measurements were made on polarized $e$-$n$
scattering, so the crucial Bjorken sum rule went untested.

Several years later, following the advent of naturally-polarized
high-energy and \hbox{-intensity} muon beams at CERN, the EMC made a
second measurement of $g_1^p$ \cite{EMCPL,EMCNP}.
  This was more precise than the
earlier SLAC measurements, and extended to lower values of
$x\equiv \vert q^2 \vert/2 m_p \nu$. It indicated a disagreement
with the polarized-proton sum rule, corresponding to a non-zero
and negative net contribution \Ds\ of strange quarks and antiquarks
to the spin of the proton, and a small total contribution of the
light quarks: $\Du + \Dd + \Ds \ll 1$\quad
\cite{SmallSpinI,SmallSpinII}.
This result was surprising
from the point of view of the most \naive\ formulation of the
constituent quark model, which would suggest $\Du + \Dd \simeq 1$, and
$\Ds = 0$, and even compared with more sophisticated versions
adapted to fit measurements of $g_A = \Du - \Dd$ and the
hyperon axial-current matrix elements' $F/D$ ratio, which suggested
$\Du + \Dd \simeq 0.6$ and $\Ds \simeq 0$.

This surprise indicated that our theoretical understanding of
non-perturbative QCD was incomplete, and stimulated attempts
to remedy this defect. For example, it was pointed out
\cite{BEK} that the
EMC result could be understood qualitatively within $SU(3)_f$
topological models of the nucleon, which describe light quarks via
collective fields, incorporate the global symmetries
of non-perturbative QCD, and predict $\Du + \Dd + \Ds \ll 1$.
Alternatively, it was suggested
\cite{DeltagI,DeltagII,DeltagIII}
that the $U(1)$ axial anomaly
might play a key r\^ole, which would modify the \naive\ quark
model predictions.
It was even suggested that the ``sacred"
Bjorken sum rule might be violated \cite{BJviolation}.

In view of the interest in checking the EMC polarized
$\mu$-$p$ results and extending them to test the Bjorken sum rule,
extensive experimental programmes are under way at CERN, SLAC and
DESY. An important round of results on polarized $\mu$-$D$
scattering from CERN \cite{SMCd}
and polarized $^3$He scattering from SLAC \cite{E142} were
published in 1993, permitting for the first time an
experimental test of the Bjorken sum rule. The CERN and SLAC
data agreed within their errors on the extracted value of
$g_1^n$
and confirmed the validity of the Bjorken sum rule
with a precision of about 12\% \cite{EKBjSR},
once the then-available
higher-order perturbative QCD corrections \cite{BJcorr}
were taken into account and allowance made for higher-twist
corrections \cite{HigherTwist,BBK}.
These data also indicated $\Ds < 0$ and
$\Du + \Dd +\Ds \ll 1$.

Recently, two new sets of data with polarized proton targets have
been made available \cite{SMCp,E143}.
 In addition, order $(\alpha_s/\pi)^2$
corrections to the singlet part of structure functions
$g_1^p$ and $g_1^n$ have recently been calculated \cite{Larin}
and estimates
made of higher-order perturbative QCD corrections to
the Bjorken and singlet
sum rules \cite{EstimCorr,KataevSinglet}.
Therefore, now is an appropriate moment to reassess the
precision with which the Bjorken sum rule has been tested,
and to extract new estimates of \Du, \Dd\ and \Ds.

We find that the Bjorken sum rule is now verified with a
precision of
10\%, once all available perturbative corrections are
taken into account. As an exercise, we determine $\alpha_s$
for the first time from the polarization sum rule data,
finding
$\alpha_s(2.5\,\, \hbox{GeV}^2) = 0.375^{+0.062}_{-0.081}\,\,$,
corresponding to $\alpha_s(M_Z^2) =0.122^{+0.005}_{-0.009}\,\,$.
On the other hand, we find
a consistent pattern of violation of the
separate sum rules for proton and neutron targets \cite{EJ},
indicating that $\Ds < 0$. Encouraged by the consistency,
we extract values of $\Du + \Dd + \Ds$ from the
different data sets. These are superficially different
if the data are analyzed in the \naive\ parton model,
i.e. neglecting perturbative QCD corrections. However,
the agreement between different data sets improves
systematically as each higher order of perturbative
QCD correction is included.
Including the \OIII\ calculation \cite{BJcorr}, together with
estimates of \OIV\ effects
in the non-singlet channel \cite{EstimCorr}
and
the \OII\ calculation \cite{Larin},
together with estimates of \OIII\
effects in the singlet channel \cite{KataevSinglet},
we find
\beq
        \Du = 0.83  \pm 0.03,
 \quad \Dd =-0.43  \pm 0.03,
 \quad \Ds =-0.10  \pm 0.03,
 \quad \Delta \Sigma = 0.31 \pm 0.07
\label{finalDqs}
\eeq
at a renormalization scale $Q^2 = 10\ \hbox{GeV}^2$,
with a global $\chi^2=1.3\ $ for $5$ degrees of freedom.
As an example of relevance of these results, we present
at the end of this paper an analysis of the implications of these
determination for dark matter couplings to matter, including
the elastic scattering of supersymmetric relics and
axion couplings to nucleons.

Up to now, the prevailing attitude has been to use
polarized structure function data to test the Bjorken
sum rule, using the most complete theoretical calculations
of corrections and a world-average value of $\alpha_s$. The
conclusion last year was \cite{EKBjSR}
that the EMC/SMC and SLAC E142
data together verified the Bjorken sum rule to within
the available precision of 12\%.
Here we take a different attitude, more akin to that adopted
with regard to the Gross-Llewellyn Smith sum rule \cite{GLLSsr}.
There is no convincing theoretical evidence against the validity
of the Bjorken sum rule, which is a solid prediction of QCD.
Therefore, its validity can be assumed. Instead,
one can use the new polarized structure function
data to extract a value of $\alpha_s(Q^2)$, whose
consistency with other measurements is an {\em a posteriori} check
on the validity of the Bjorken sum rule.

As is well known, data at low $Q^2$ are particularly
sensitive to $\LamMSbar$ and hence at a premium in determining
\asMZ. As is illustrated by
$\tau$ decays, even a relatively imprecise determination
of $\alpha_s(\hbox{low}\ Q^2)_{\MSbar}$
(provided higher-order perturbative QCD and nonperturbative
uncertainties are understood) extrapolates to a
relatively precise determination of \asMZ\ \cite{alphasALEPH}.
The SLAC E142 $^3$He (i.e. $n$) data have
$\langle Q^2 \rangle \simeq 2$ GeV$^2$,
and the E143 $p$ data have
$\langle Q^2 \rangle \simeq 3$ GeV$^2$,
and are hence particularly well placed to exploit this
lever arm on $\LamMSbar$. Since they are at higher $Q^2$,
the new SMC $p$ data are less useful in this respect, though they
do provide important information about $\gIp$
at small $x$, and enter into the determination
of the $\Delta q$, as we discuss later.

We use the value of $\Gamma_1^n(Q^2{=}2\ \hbox{GeV}^2)=
-0.028 \pm 0.006 \pm 0.009$ given in ref.~\cite{EKBjSR}
and the value  $\Gamma_1^p(Q^2{=}3\ \hbox{GeV}^2)=
0.133 \pm 0.004 \pm 0.012$ given in ref.~\cite{E143}.
We emphasize that these estimates are based on polarization
asymmetry $A_1(x,Q^2)$ data taken at average values of $Q^2$
that depend on the bin in $x$, which have been converted
into values of $g_1^p(x,\langle Q^2 \rangle)$
by assuming that the $Q^2$ dependence of $A_1(x,Q^2)$
is insignificant  \cite{EKBjSR,Petratos}
and using standard parametrizations of
$F_2(x,Q^2)$ \cite{NMC} and $R(x,Q^2)$ \cite{Whitlow}
to estimate
\beq
g_1(x,Q^2) =
{A_1(x)F_2(x,Q^2)\over 2x [1 + R(x,Q^2)]}
\label{gIapprox}
\eeq
No data set indicates a significant $Q^2$ dependence of
$A_1(x,Q^2)$, and perturbative QCD calculations
\cite{ZvN,ANR,BBS,GS} lead one to expect that the
$Q^2$ dependence can be neglected at the level of
precision required here.
The estimates of $g_1^{p,n}(x,Q^2)$ also require
assumptions on $g_2^p(x,Q^2)$ that are borne out
by the latest experimental bounds \cite{SMCp},
and consistent with the latest theoretical
calculations \cite{ALNR}.
Based on the above numbers, we use in our subsequent
analysis
\beq
\Gamma_1^p - \Gamma_1^n \vert_{Q^2=2.5\ \hbox{\scriptsize GeV}^2}
=0.161 \pm 0.007 \pm 0.015
\label{Gammapn}
\eeq
for the Bjorken integral.

    The small-$x$ behaviours of $g_1^{p,n}$ have recently been
discussed \cite{BassLandshoff}
in the context of a non-perturbative model
of the Pomeron \cite{NonPertP},
which suggests that ${g_1^{p,n} \simeq
\log (1/x)}$ at small $x$,
rather than $\sim x^{\alpha}$, $-0.5 \le \alpha \le 0$
\cite{Heimann,EK}.
Although such an effect would alter the
estimates of $\Gamma_1^{p,n}$ that we use, it would cancel out in
the difference that appears in the Bjorken sum rule, since this
effect would be due to two-gluon exchange. Hence the estimate in
equation \eqref{Gammapn} would be unaltered.

Perturbative QCD corrections to the Bjorken sum rule
have been calculated up to \OIII\ \cite{BJcorr}
and an estimate was made of the \OIV\ coefficient
\cite{EstimCorr}:
\bea
\Gamma_1^p(Q^2) - \Gamma_1^n(Q^2) =
{1\over6}\vert g_A \vert
\left[ 1 - \left(\frac{\alpha_s(Q^2)}{\pi}\right)
    -3.5833 \left(\frac{\alpha_s(Q^2)}{\pi}\right)^2
\right.\nonumber\\
\label{BJpredIV}\\
\left.
-20.2153 \left(\frac{\alpha_s(Q^2)}{\pi}\right)^3
-\OO(130) \left(\frac{\alpha_s(Q^2)}{\pi}\right)^4
+ \dots \right]\nonumber
\eea
in the $\MSbar$ prescription for $N_f=3$ flavours, as
appropriate to $Q^2=2.5$ GeV$^2$. The value of
$\alpha_s(2.5\ \hbox{GeV}^2)$ extracted by comparing
\eqref{Gammapn} and \eqref{BJpredIV} depends on the
order in QCD perturbation theory which is used. As we
see in fig.~1, the extracted value decreases as one
progresses from \OI\ to higher orders, but
shows good signs of stabilizing in \OIV. We infer from
this analysis a value
\beq
\alpha_s(2.5\,\, \hbox{GeV}^2)\vert_{\MSbar, N_f=3}
 = 0.375^{+0.062}_{-0.081}
\label{aslowQeq}
\eeq
which corresponds to
\beq
\alpha_s(M_Z^2)\vert_{\MSbar,N_f=5}
 =0.122^{+0.005}_{-0.009}
\label{asmZeq}
\eeq
Note that in evaluating \eqref{asmZeq}\ we have used the
3-loop renormalization group equations \cite{ThreeLoopBeta},
and matched
values of $\alpha_s$ at the flavour thresholds
$Q=m_c, m_b$, as is appropriate
 in the $\MSbar$ scheme.
The relevant prescription is given in ref.~\cite{Bernreuther}:
${\alpha_s}_{-}(m_Q^2)=
 {\alpha_s}_{+}(m_Q^2)
\bigl[1+ a\,({\alpha_s}_{+}(m_Q^2)/\pi)
  + b\,({\alpha_s}_{+}(m_Q^2)/\pi)^2\bigr]$,
  where $a=0$, $b=7/72$.
This means that the two-loop
 ${\alpha_s}_{-}(m_Q^2)={\alpha_s}_{+}(m_Q^2)$,
but that the three-loop
 ${\alpha_s}_{-}(m_Q^2)$ and ${\alpha_s}_{+}(m_Q^2)$
are slightly different at $m_Q$.
Figure 3 compares this determination of $\alpha_s$ with
others, as compiled in \cite{Bethke}.

    We have not yet included higher-twist effects
\cite{HigherTwist}
in this analysis,
for two main reasons. One is that their coefficients appear to be
rather smaller than originally thought \cite{BBK}, and
also because the available estimates differ considerably from
one another
\cite{CloseRoberts,Ji,BI,ESM,RossRoberts,ZZ,MSS}.
For our purposes it is sufficient to take
a rough estimate,
\beq
\delta_\smallHT\, ( \Gamma_1^p - \Gamma_1^n ) \equiv
{c_{\smallHT} \over Q^2} \simeq
{( -0.02 \pm 0.01) \ \hbox{GeV}^2 \over  Q^2 }
\label{DeltaHT}
\eeq
Another reason is that it may be double counting \cite{Mueller}
to include this as
well as the higher-order perturbative QCD contributions that have
now been calculated and estimated. Including the estimate
\eqref{DeltaHT} in
a fit to the data described above, we find
\beq
\alpha_s(M_Z^2)\vert_{\MSbar,N_f=5,\smallHT}
= 0.118^{+0.007}_{-0.014}
\label{asmZhteq}
\eeq
The difference between this and the value in equation
\eqref{asmZeq} is
indicative of the theoretical systematic error.

This Bjorken sum rule determination of $\alpha_s$ is
encouragingly precise, and quite consistent with the
other determinations shown in fig.~3, though not yet
competitive with the market leaders, This consistency
means that the Bjorken sum rule is verified within
10\% precision by the SLAC E142 and E143 data alone, as well
as being verified to within 12\% precision by the SLAC
E142 and EMC/SMC data \cite{EKBjSR}.
The higher precision expected from future SLAC data might
enable this determination of $\alpha_s$ to become truly
competitive.
A good understanding of the radiative corrections will be
needed at this level \cite{Krasny}.
The optimal evaluation of the Bjorken integral will also
require data from low $x$, where the SMC data are available
and will continue to provide crucial input. Also, the very
high precision data from HERMES \cite{HERMES}
at moderate $x$ will be
very useful. The Bjorken sum rule is making the
transition from a test of QCD to a tool for
evaluating $\alpha_s$ within QCD.

Having verified that the Bjorken sum rule is well satisfied
by the latest data, we consider the sum rules for proton and neutron
targets separately. Their theoretical prediction requires an extra
assumption on the singlet axial current matrix elements
$\Delta\Sigma(Q^2)$ or, equivalently, the nucleon matrix element \Ds\ of
the $\bar{s} \gamma_\mu\gamma_5 s$ current. Alternatively, one can
regard measurements of
$\Gamma_1^{p(n)} \equiv \int_0^1 d x \, g_1^{p(n)}(x,Q^2)$
as determinations of $\Delta\Sigma(Q^2)$, or
equivalently \Ds, if one assumes the validity of the Bjorken sum rule.
This is the attitude taken here.
The fact that $\Gamma_1^p-\Gamma_1^n$ is in good agreement
with the Bjorken sum rule means that the different targets
yield consistent values of $\DSigma$, as we now show.

We use in our determinations of $\Delta\Sigma(Q^2)$ and \Ds\ the
calculated \OIII\ corrections to the Bjorken sum rule and the
estimate \cite{EstimCorr}
of the \OIV\ corrections used above.
We also use the recent calculation of the \OII\ correction
\cite{Larin} to the
singlet part of the sum rule and a recent estimate \cite{KataevSinglet}
of the
\OIII\ correction to it. If one chooses the renormalization
scale $\mu = Q$, the proton and neutron sum rules including these
corrections can be written as
\bea
\int_{0}^{1} d x g_1^{p(n)}(x,Q^2)=
\left(\pm \frac{1}{12}|g_A|+\frac{1}{36}a_8\right)\times
\phantom{aaaaaaaaaaaaaaaaaaa}
\nonumber\\
\times\left[ 1 {-} \left(\frac{\alpha_s(Q^2)}{\pi}\right)
\kern-0.2em
{-}3.5833 \left(\frac{\alpha_s(Q^2)}{\pi}\right)^{\kern-0.3em2}
\kern-0.3em
{-}20.2153 \left(\frac{\alpha_s(Q^2)}{\pi}\right)^{\kern-0.3em3 }
\kern-0.3em
{-}\OO(130)\left(\frac{\alpha_s(Q^2)}{\pi}\right)^{\kern-0.3em4}
\kern-0.3em
{+}\dots\,\right]
\phantom{}\kern-0.5cm % make TeX think this line is shorter so the next
\nonumber
\\
+\left[1 - \left(\frac{\alpha_s(Q^2)}{\pi}\right)
-1.0959 \left(\frac{\alpha_s(Q^2)}{\pi}\right)^2
-{\cal O}(6)\left(\frac{\alpha_s(Q^2)}{\pi}\right)^3
+\dots\,\,\right]
 \frac{1}{9} \Delta\Sigma(Q^2)\,.
\nonumber\\
\label{nucleonSR}
\eea
It is worth emphasizing that the
$Q^2$ dependence due to QCD in the singlet channel has
two sources, namely the anomalous dimension of the
singlet axial current, as well as the coefficient
function. However, the $Q^2$ dependence of $\DSigma(Q^2)$
is not large from the $Q^2$ range of the present data
upwards.
Note that we have not included any higher-twist contributions, but
will comment later on their possible effects.

It is interesting to note that, because of their different
$Q^2$-dependences, it would be possible in principle to
separate the $SU(3)$ octet and singlet contributions
$(a_8,\,\Delta\Sigma)$ to either $\GIp$ or $\GIn$, and avoid in
this way the use of $SU(3)$ \cite{LipkinWeak}
relations to estimate $a_8$ on the
basis of hyperon $\beta$-decay data.
Writing the square-bracket perturbative QCD correction factors
on the first and last lines of equation \eqref{nucleonSR}
as $f(\alpha_s)$ and $h(\alpha_s)$, respectively, for the
octet and singlet contributions, one can write
\bea
\nonumber\\
{f(\alpha_s)\over 36} a_8 \quad + \quad {h(\alpha_s)\over 9 }
\DSigma(Q^2)
\quad  = \quad
\Gamma_1^p(Q^2) \quad - \quad {f(\alpha_s)\over 12} g_A
\nonumber\\
\nonumber\\
{f(\alpha_s)\over 36} a_8 \quad + \quad {h(\alpha_s)\over 9 }
\DSigma(Q^2)
\quad = \quad
\Gamma_1^n(Q^2) \quad + \quad {f(\alpha_s)\over 12} g_A
\label{GpGnGdA}\\
\nonumber\\
{f(\alpha_s)\over 36} a_8 \quad + \quad {h(\alpha_s)\over 9 }
\DSigma(Q^2)
\quad = \quad
\Gamma_1^d(Q^2) \phantom{\quad + \quad {f(\alpha_s)\over 12} g_Aa}
\nonumber\\
\nonumber
\eea
where the right-hand sides are combinations of measurable and
theoretically-known quantities.
(Strictly speaking, $\Gamma_1^d$ in eq.~\eqref{GpGnGdA}
is $(\Gamma_1^p+\Gamma_1^n)/2$,
i.e. it includes nuclear corrections.)
In leading order,
$f(\alpha_s)=h(\alpha_s)=1-(\alpha_s/\pi)$, and the
different equations \eqref{GpGnGdA} are not independent.
At NLO, however, $f(\alpha_s) \neq h(\alpha_s)$, and then
\undertext{each} of the equations \eqref{GpGnGdA} allows in
principle an independent determination of $\DSigma$ and
$a_8$, provided data with sufficiently high precision are
available at different values of $Q^2$. One can also combine
data from experiments with different targets. The
current precision of the
world data does not permit a meaningful separation of $a_8$
and $\DSigma$ using this technique.

Using
the known variation of $\alpha_s(Q^2)$ and
assuming $\DSigma \sim 0.3$ in
eq.~\eqref{GpGnGdA},
one can estimate the experimental
precision required to make this approach practical.
For a range of $Q^2$ between $Q^2{=}2$ GeV$^2$
and $Q^2{=}15$ GeV$^2$
we estimate that the right-hand side of
eq.~\eqref{GpGnGdA} would have to be known with
a precision much better than $\pm0.002$, including both
statistical and systematic errors.
Currently E143 quotes
\cite{E143}
error values of
$\pm0.004$ (stat.) and
$\pm 0.012$ (syst.), so the required
improvement in precision would have to be very substantial,
especially in the systematic error, unless for some reason
the systematic error is approximately independent of
$Q^2$, in which case it would largely cancel out
when comparing the r.h.s. of eq.~\eqref{GpGnGdA}
for the various values of $Q^2$.
Pending future improvements in the experimental precision,
for the rest of this paper we assume the usual
$SU(3)$ value $a_8 = 0.601 \pm 0.038$ \cite{FoverD},
and we return now to the discussion of the existing data.

In order to combine all the data available from different
targets, we re-express the measurement on Deuteron and $^3$He
targets in terms of the corresponding values of $\GIp$,
assuming the Bjorken sum rule and incorporating all the non-singlet
perturbative corrections $f(\alpha_s)$ on the first line of
equation \eqref{nucleonSR}. The resulting values of $\GIp$
inferred from the E142  $^3$He and SMC D data are shown together
with the EMC, SMC and preliminary E143  $p$ data in fig.~4. We
see \undertext{no signs of convergence} towards the
{\naive}ly-suggested \cite{EJ} value holding if $\Ds = 0$.
This situation contrasts with what has been found previously
with the Gross - Llewelyn Smith and Bjorken sum rules, namely
\undertext{good agreement} once the available perturbative QCD
corrections are included. Also shown in fig.~4, to guide the
eye, is the prediction for $\GIp$ that would be obtained
if $\Ds = -0.10 \pm 0.04$ which is \undertext{highly consistent}
with the data. The inclusion of all available higher-order
perturbative QCD corrections is important for this consistent
picture to emerge. We plot in fig.~5 the values of $\DSigma$
that would be extracted from each experiment if one restricted
one's analysis to include only low orders of perturbative QCD.
The values of $\DSigma$ extracted using the \naive\ parton model,
i.e. \Oas{0}, are in poor agreement, particularly the E142
neutron measurement done on $^3$He. However, the agreement
improves significantly as one proceeds to \OI, \OII and
\OIII. (This last analysis includes the estimate of the
\OIV\ corrections to the Bjorken sum rule \cite{EstimCorr}
and of the \OIII\ correction \cite{KataevSinglet}
to the singlet sum rules.)
The overall $\chi^2$ of the global fit decreases systematically
as each order of perturbative QCD is included,
$\chi^2 = 12$ (\naive) $\rightarrow$ 4.2 (\OI)
$\rightarrow$ 2.4 (\OII) $\rightarrow$ 1.6 (\OIII)
$\rightarrow$ 1.3 (\OIV).
The fact that the $g_1^n$ determination of $\DSigma$
falls in increasing orders of perturbation theory,
whilst the determination from $g_1^p$
rises, is easily understood from the fact that
the higher order perturbative QCD corrections to the
Bjorken sum rule are much larger than those of the
singlet combinations of structure functions.
The main perturbative correction to the non-singlet part
comes from the isovector term $\pm g_A$ which reverses
its sign between the neutron and the proton. In the deuteron
this term is absent and the effect of the remaining
$a_8$ term is small, and therefore
 the $g_1^D$ determination does not
change much in increasing orders of perturbation theory.

We conclude that a consistent overall picture
of $\DSigma$ and $\Ds$ is emerging, which leads to the
values quoted in equation \eqref{finalDqs} at the
beginning of this paper.

    The overall consistency of the different determinations of
$\DSigma$ and ${\Delta s}$ that we find is not affected by the
possible $\log(1/x)$ behaviour \cite{BassLandshoff}
of the $g_1^{p,n}$ that
we discussed earlier, since this consistency is simply a
consequence of the data and the assumed correctness of the Bjorken
sum rule. However, such behaviour would alter the determinations
of the individual ${\Delta q}$ quoted in equation \eqref{finalDqs}.
As pointed out in \cite{CloseRobertsG1},
this could shift the experimental values of the
integrals $\Gamma_1^{p,n}$ and hence the inferred values of the
${\Delta q}$ by about one standard deviation towards a higher
value of $\DSigma$ and a lower value of $\Ds$. As also
pointed out in \cite{CloseRobertsG1},
these shifts could be much larger if the
small-$x$ behaviours of $g_1^{p,n}$ were even more singular, but
this possibility does not seem to be very well motivated theoretically.
For the reasons discussed earlier in connection with the Bjorken
sum rule, we have not yet included estimates of singlet
higher-twist effects
\beq
\delta_\smallHT\, ( \Gamma_1^p + \Gamma_1^n )_{singlet} \simeq
{( -0.02 \pm 0.01) \ \hbox{GeV}^2 \over  Q^2 }
\label{dHTsinglet}
\eeq
in the extraction of the ${\Delta q}$. If we include them in the
global fit, we find
\beq
       \Du = 0.85  \pm 0.03,
 \quad \Dd =-0.41  \pm 0.03,
 \quad \Ds =-0.08  \pm 0.03,
 \quad \Delta \Sigma = 0.37 \pm 0.07
\label{DqwithHT}
\eeq
at ${Q^2=10\ \hbox{GeV}^2}$, and
we regard the differences between these and the values in equation
\eqref{finalDqs}
as indicative of the possible theoretical systematic errors.

We cannot resist commenting that the value of $\DSigma$
that we obtain is much closer to the light current-quark
model value of zero in the large-$N_c$ and chiral
limit \cite{BEK}
than it is to the most \naive\ quark model of unity, and that
finite-$N_c$ \cite{Ryzak} and $m_s \neq 0$ corrections
\cite{BEK},\cite{SkyrmeNow} were estimated to be capable
of altering $\DSigma$ by about 0.3\ .
This picture may be reconciled with otherwise
highly-successful models based on constituent quarks, if the
latter are regarded as effective constructs that
contain non-trivial internal chiral and gluonic
structure \cite{MG,Kaplan,Fritzsch,EFHK,staticQ,Weise}.

    Finally, as an application of these results, we discuss their
implications for the couplings to nucleons of certain candidates
for non-baryonic Dark Matter. We consider first the lightest
supersymmetric particle (LSP), which we assume to be a neutralino,
i.e., some combination of neutral, non-strongly-interacting spin-1/2
partners of the $SU(2)$ gauge boson $W^0$,
the $U(1)$ gauge boson $B$,
and the neutral Higgs boson $H^0_{1,2}$ in the minimal supersymmetric
extension of the Standard Model (MSSM). Since the neutralino has
spin $1/2$, its couplings to nucleons include a spin-dependent
part that is related to the contributions ${\Delta q}$
of the different
quark species to the nucleon spin. Experiments at LEP and elsewhere
constrain the parameters of the MSSM in such a way that the LSP
cannot be an approximately pure photino or Higgsino. However, it
could be an approximately pure $U(1)$ gaugino
${\tilde B}$, in which case its
spin-dependent coupling to a proton is proportional to
\beq
a_p = 17/36 \Delta u + 5/36 ( \Delta d + \Delta s )
= ( 6 g_A + 2 a_8 + 9\DSigma )/36
\label{apDef}
\eeq
and the analogous coupling $a_n$ to the neutron is given by a
similar formula with ${\Delta u}$ and ${\Delta d}$ interchanged,
in the limit of a small momentum transfer from the LSP to the
proton and $m_{LSP} \ll m_{\tilde q}$. The couplings $a_{p,n}$
should be evaluated
using the value of the ${\DSigma}$ evolved to a renormalization
scale of order $m_{\tilde q}$,
which we take for illustration
to be 500 GeV. Using the values (and errors) of the ${\Delta q}$
given in equation \eqref{finalDqs}, we find
\bea
a_p =  \phantom{{-}}0.32 \pm 0.017   \nonumber\\
\label{apanValues} \\
a_n = {-}0.10 \pm 0.017  \nonumber
\eea
We note that the error on $a_p$ is only about 5\%, whilst the
error on $a_n$ is about 17\%. This implies that one can estimate
relatively reliably the spin-dependent coupling of the LSP to
odd-even nuclei such as $^{39}$K or $^{93}$Nb,
whose spins are carried essentially by protons, whereas
the uncertainty is somewhat larger for even-odd nuclei
such as $^{73}$Ge or $^{29}$Si, whose spins
are carried essentially by neutrons.
Predictions based on the \naive\
quark model \cite{KKR}
for the spin content of the nucleon are very
misleading, particularly for the neutron.
\pr
Next, we turn to the couplings of the axion to nucleons, which are
given by
\bea
C_{ap} = 2 \,[{-} 2.76\, \Du - 1.13\, \Dd + 0.89\, \Ds
-\cos 2 \beta \, (\Du - \Dd - \Ds) ],
\nonumber\\
\label{CapCan}\\
C_{an} = 2\, [{-} 2.76\, \Dd - 1.13\, \Du + 0.89\, \Ds
-\cos 2 \beta \, (\Dd - \Du - \Ds) ]
\phantom{,}
\nonumber
\eea
for the proton and neutron respectively. In this case, the
low-renormalization scale values of the ${\Delta q}$ are the
relevant ones, and we evaluate them at the scale $Q = 1$ GeV,
which might be appropriate for the core of a neutron star. We find
\bea
C_{ap} = ({-}3.9 \pm 0.4) - (2.68 \pm 0.06)
\cos 2 \beta
\nonumber\\
\label{Vanalogue}\\
C_{an} = (0.19 \pm 0.4) + (2.35 \pm 0.06)
\cos 2 \beta
\phantom{,}
\nonumber
\eea
which can be compared with the \naive\ quark model values given in
equation (4) of \cite{Mayle}. We see that the axion-proton
coupling is relatively well determined, except for large values of
$\tan \beta$, whilst the axion-neutron coupling
is more sensitive at intermediate values of $\tan \beta$,
to the experimental errors in the determination
of the ${\Delta q}$. As was discussed in \cite{Mayle}
and references therein, the
dominant axion emission process from the core of a neutron star
is likely to be axion bremsstrahlung in nucleon-nucleon collisions,
which is sensitive to a combination of $C_{ap}$ and $C_{an}$. The
relative weights of neutron-neutron, neutron-proton and proton-proton
bremsstrahlung processes are given roughly by
\beq
{C_{an}}^2 + 0.83 (C_{an} + C_{ap})^2 + 0.47 {C_{ap}}^2
\label{Csquares}
\eeq
One
tries to bound the axion decay constant $f_a$ by constraining the
rate of axion emission from the core of the neutron star. Using
the numbers given in equation \eqref{Vanalogue}, we find a
sensitivity
\beq
\Delta f_a / f_a = 30\% \ \hbox{to}\ 50\%
\label{fSensitivity}
\eeq
This source of error in the constraint on $f_a$ is much less than
other sources of error, in the nuclear equation of state, for
example. We conclude that our present knowledge of
the ${\Delta q}$ is adequate for the purpose of bounding $f_a$.

    We conclude that the available polarized structure function data
are in perfect agreement with QCD, once higher-order perturbative
corrections are taken into account. These are indeed essential: the
naive parton model is not adequate to describe the nucleon as viewed
through polarized lenses. The polarized structure function data
already yield an interestingly precise value of $\alpha_s$, that
future rounds of data could render highly competitive with other
determinations. The total nucleon spin fraction $\DSigma$ carried by
quarks is around 30 \%, and the strange contribution ${\Delta s
< 0}$. The dynamical mechanism that explains these findings remains
a puzzle, and the challenge to reconcile them with the \naive\
constituent quark model persists. More high-precision data would be
most welcome, in order to discriminate between the chiral soliton
and axial $U(1)$ anomaly interpretations of the data, to probe the
behaviours of $g_1^{p,n}$ at small $x$, to explore the $Q^2$-dependence
of $A_1$, and hopefully to extract higher-twist effects and $\DSigma$
from data at different values of $Q^2$.
Other experiments, for example
on elastic ${\nu N}$ scattering \cite{EK,KaplanManohar,Ahrens,nuN}
and using high-energy polarized
proton beams to measure gluon polarization directly, may also help to
disentangle the nucleon spin decomposition more completely. This is
not only a fascinating way of probing non-perturbative QCD, but also
has implications in other areas of physics, for example in searches
for Dark Matter particles, as discussed above.
{\em Floreat} nucleon spin physics!

\bigskip
\begin{flushleft}
{\bf Acknowledgements}
\end{flushleft}
We thank A. Kataev for useful conversations and for communicating
his results before publication. We also thank
S. Bethke,
M.W. Krasny and
S.~Larin
for useful discussions.
J.E. thanks the SLAC Theory Group for its
kind hospitality while this work was being completed.
The  research of M.K. was supported in part
by grant No.~90-00342 from the United States-Israel
Binational Science Foundation (BSF), Jerusalem, Israel,
and by the Basic Research Foundation administered by the
Israel Academy of Sciences and Humanities.
\bigskip
\def\etal{{\em et al.}}
\def\PL{{\em Phys. Lett.\ }}
\def\NP{{\em Nucl. Phys.\ }}
\def\PR{{\em Phys. Rev.\ }}
\def\PRL{{\em Phys. Rev. Lett.\ }}

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\newpage
\begin{flushleft}
{\Large \bf Figure Captions:}\\
\end{flushleft}
\vskip 0.5cm
Fig.~1.
Values of
$\alpha_s(Q^2=2.5\ \hbox{GeV}^2)$ extracted from the E142 $\Gamma_1^n$
and E143 $\Gamma_1^p$ measurements
using the Bjorken sum rule and increasing orders
of QCD perturbation theory.
The last point    includes    the estimate
of the 4-th order perturbative coefficient
in \cite{EstimCorr}.
\hfill\break
\vskip 0.1cm
\noindent
Fig.~2.
Values of
$\alpha_s(Q^2=2.5\ \hbox{GeV}^2)$ extracted from the E142 $\Gamma_1^n$
and E143 $\Gamma_1^p$ using the Bjorken sum rule
and assuming
a given non-zero value
of the higher twist coefficient $c_{\smallHT}$ (cf.
eq.~\eqref{DeltaHT}).
Dashed lines denote error bands corresponding
to one standard deviation with respect to the central value of
$\alpha_s$.
Vertical dotted lines denote the range of $c_{\smallHT}$
given in eq.~\eqref{DeltaHT}.
\hfill\break
\vskip 0.1cm
\noindent
Fig.~3.
The value of
$\alpha_s(Q^2=2.5\ \hbox{GeV}^2)$ from the Bjorken sum rule,
using all available
perturbative QCD corrections but neglecting possible higher-twist
effects, shown
together with a compilation of world data on $\alpha_s(Q)$
as given in ref.~\cite{Bethke}.
\hfill\break
\vskip 0.1cm
\noindent
Fig.~4.
EMC, SMC and preliminary E143  $p$ data on
$\GIp$, together with $\GIp$
inferred from the E142  $^3$He and SMC D data using the Bjorken
sum rule.
The upper continuous curve shows the
{\naive}ly-suggested \cite{EJ} value holding if $\Ds = 0$,
together with an error band plotted with dotted curves.
The lower curve shows
the prediction for $\GIp$ that would be obtained
if $\Ds = -0.10 \pm 0.04$.
\hfill\break
\vskip 0.1cm
\noindent
Fig.~5.
The values of $\DSigma(Q^2{=}10\ \hbox{GeV}^2)$
extracted from each experiment plotted as functions of the
increasing order of QCD perturbation theory
used in obtaining  $\DSigma$ from the data.
The last point    includes    the estimate
of the 4-th order perturbative coefficient
in \cite{EstimCorr}.

\end{document}

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415 378 lt
0 trot 11 tsiz 415 388 text 4 sf
(1) tsho tend
484 394 mt
484 367 lt
0 trot 11 tsiz 484 380 text 4 sf
(1) tsho tend
491 385 mt
491 376 lt
0 trot 11 tsiz 491 381 text 4 sf
(1) tsho tend
491 381 mt
491 375 lt
0 trot 11 tsiz 491 378 text 4 sf
(1) tsho tend
491 383 mt
491 377 lt
0 trot 11 tsiz 491 380 text 4 sf
(1) tsho tend
233 319 mt
233 314 lt
272 315 mt
272 314 lt
295 315 mt
295 314 lt
312 315 mt
312 314 lt
325 315 mt
325 314 lt
335 315 mt
335 314 lt
344 315 mt
344 314 lt
352 315 mt
352 314 lt
358 315 mt
358 314 lt
364 319 mt
364 314 lt
404 315 mt
404 314 lt
427 315 mt
427 314 lt
444 315 mt
444 314 lt
456 315 mt
456 314 lt
467 315 mt
467 314 lt
476 315 mt
476 314 lt
483 315 mt
483 314 lt
490 315 mt
490 314 lt
496 319 mt
496 314 lt
536 315 mt
536 314 lt
0 trot 18 tsiz 233 297 text 0 sf
(1) tsho tend
0 trot 18 tsiz 325 297 text 0 sf
(5) tsho tend
0 trot 18 tsiz 358 297 text 0 sf
(10) tsho tend
0 trot 18 tsiz 450 297 text 0 sf
(50) tsho tend
0 trot 18 tsiz 483 297 text 0 sf
(100) tsho tend
233 583 mt
233 578 lt
272 583 mt
272 581 lt
295 583 mt
295 581 lt
312 583 mt
312 581 lt
325 583 mt
325 581 lt
335 583 mt
335 581 lt
344 583 mt
344 581 lt
352 583 mt
352 581 lt
358 583 mt
358 581 lt
364 583 mt
364 578 lt
404 583 mt
404 581 lt
427 583 mt
427 581 lt
444 583 mt
444 581 lt
456 583 mt
456 581 lt
467 583 mt
467 581 lt
476 583 mt
476 581 lt
483 583 mt
483 581 lt
490 583 mt
490 581 lt
496 583 mt
496 578 lt
536 583 mt
536 581 lt
238 314 mt
233 314 lt
234 325 mt
233 325 lt
234 335 mt
233 335 lt
234 346 mt
233 346 lt
234 357 mt
233 357 lt
238 368 mt
233 368 lt
234 378 mt
233 378 lt
234 389 mt
233 389 lt
234 400 mt
233 400 lt
234 411 mt
233 411 lt
238 422 mt
233 422 lt
234 432 mt
233 432 lt
234 443 mt
233 443 lt
234 454 mt
233 454 lt
234 465 mt
233 465 lt
238 475 mt
233 475 lt
234 486 mt
233 486 lt
234 497 mt
233 497 lt
234 508 mt
233 508 lt
234 519 mt
233 519 lt
238 529 mt
233 529 lt
234 540 mt
233 540 lt
234 551 mt
233 551 lt
234 562 mt
233 562 lt
234 572 mt
233 572 lt
0 trot 18 tsiz 194 314 text 0 sf
(0.0) tsho tend
0 trot 18 tsiz 194 368 text 0 sf
(0.1) tsho tend
0 trot 18 tsiz 194 422 text 0 sf
(0.2) tsho tend
0 trot 18 tsiz 194 475 text 0 sf
(0.3) tsho tend
0 trot 18 tsiz 194 529 text 0 sf
(0.4) tsho tend
536 314 mt
530 314 lt
536 325 mt
534 325 lt
536 335 mt
534 335 lt
536 346 mt
534 346 lt
536 357 mt
534 357 lt
536 368 mt
530 368 lt
536 378 mt
534 378 lt
536 389 mt
534 389 lt
536 400 mt
534 400 lt
536 411 mt
534 411 lt
536 422 mt
530 422 lt
536 432 mt
534 432 lt
536 443 mt
534 443 lt
536 454 mt
534 454 lt
536 465 mt
534 465 lt
536 475 mt
530 475 lt
536 486 mt
534 486 lt
536 497 mt
534 497 lt
536 508 mt
534 508 lt
536 519 mt
534 519 lt
536 529 mt
530 529 lt
536 540 mt
534 540 lt
536 551 mt
534 551 lt
536 562 mt
534 562 lt
536 572 mt
534 572 lt
259 554 mt
259 478 lt
0 trot 11 tsiz 259 516 text 4 sf
(2) tsho tend
259 554 mt
259 478 lt
0 trot 9 tsiz 259 516 text 4 sf
(2) tsho tend
259 554 mt
259 478 lt
0 trot 8 tsiz 259 516 text 4 sf
(2) tsho tend
259 554 mt
259 478 lt
0 trot 8 tsiz 259 516 text 4 sf
(2) tsho tend
259 554 mt
259 478 lt
0 trot 7 tsiz 259 516 text 4 sf
(2) tsho tend
259 554 mt
259 478 lt
0 trot 6 tsiz 259 516 text 4 sf
(2) tsho tend
259 554 mt
259 478 lt
0 trot 5 tsiz 259 516 text 4 sf
(2) tsho tend
259 554 mt
259 478 lt
0 trot 5 tsiz 259 516 text 4 sf
(2) tsho tend
259 554 mt
259 478 lt
0 trot 4 tsiz 259 516 text 4 sf
(2) tsho tend
259 554 mt
259 478 lt
0 trot 3 tsiz 259 516 text 4 sf
(2) tsho tend
259 554 mt
259 478 lt
0 trot 2 tsiz 259 516 text 4 sf
(2) tsho tend
259 554 mt
259 478 lt
0 trot 2 tsiz 259 516 text 4 sf
(2) tsho tend
0 trot 14 tsiz 238 240 text 0 sf
(Bjorken sum rule) tsho tend
0 trot 14 tsiz 224 211 text 4 sf
(1 ) tsho 0 sf
(compilation of world ) tsho 1 sf
(a) tsho 0 tsubsc 0 sf
(S) tsho 1 tsubsc (\050Q\051 data by S. Bethke \0501994\051) tsho tend
0 trot 11 tsiz 256 346 text 0 sf
(QCD ) tsho 1 sf
(L) tsho 0 tsubsc 0 sf
(MS) tsho 1 tsubsc ( = ) tsho tend
0 trot 18 tsiz 293 353 text 0 sf
(_) tsho tend
0 trot 8 tsiz 287 353 text 0 sf
(\0505\051) tsho tend
0 trot 11 tsiz 319 346 text 0 sf
(250 MeV) tsho tend
0 trot 11 tsiz 319 357 text 0 sf
(350 MeV) tsho tend
0 trot 11 tsiz 319 335 text 0 sf
(150 MeV) tsho tend
0 trot 11 tsiz 319 325 text 0 sf
(100 MeV) tsho tend
364 346 mt
404 346 lt
364 357 mt
365 357 lt
370 357 mt
371 357 lt
376 357 mt
377 357 lt
381 357 mt
383 357 lt
387 357 mt
388 357 lt
393 357 mt
394 357 lt
399 357 mt
400 357 lt
404 357 mt
364 335 mt
369 335 lt
373 335 mt
378 335 lt
383 335 mt
387 335 lt
392 335 mt
396 335 lt
401 335 mt
404 335 lt
364 325 mt
365 325 lt
371 325 mt
371 325 lt
377 325 mt
388 325 lt
394 325 mt
395 325 lt
400 325 mt
401 325 lt
404 325 mt
256 522 mt
261 511 lt
266 500 lt
272 490 lt
276 484 lt
280 478 lt
285 472 lt
288 468 lt
292 464 lt
295 460 lt
298 457 lt
301 454 lt
304 451 lt
307 449 lt
309 447 lt
312 444 lt
314 443 lt
316 441 lt
319 439 lt
321 437 lt
323 436 lt
325 435 lt
326 433 lt
328 432 lt
330 431 lt
332 430 lt
333 429 lt
335 428 lt
337 427 lt
338 427 lt
340 426 lt
341 425 lt
342 424 lt
344 424 lt
345 423 lt
346 422 lt
348 422 lt
349 421 lt
350 420 lt
352 420 lt
353 419 lt
354 419 lt
355 418 lt
356 418 lt
357 417 lt
358 417 lt
359 416 lt
360 416 lt
361 415 lt
362 415 lt
363 414 lt
364 414 lt
365 414 lt
366 413 lt
367 413 lt
368 412 lt
369 412 lt
370 412 lt
371 411 lt
373 410 lt
375 410 lt
378 409 lt
381 407 lt
383 406 lt
386 405 lt
389 405 lt
391 404 lt
393 403 lt
396 402 lt
398 401 lt
400 401 lt
402 400 lt
404 400 lt
406 399 lt
408 398 lt
409 398 lt
411 397 lt
413 397 lt
414 396 lt
416 396 lt
417 396 lt
419 395 lt
420 395 lt
422 394 lt
423 394 lt
424 394 lt
426 393 lt
427 393 lt
428 393 lt
430 392 lt
431 392 lt
432 392 lt
433 391 lt
434 391 lt
435 391 lt
436 391 lt
437 390 lt
439 390 lt
440 390 lt
441 389 lt
442 389 lt
443 389 lt
444 389 lt
444 389 lt
445 388 lt
446 388 lt
447 388 lt
448 388 lt
449 388 lt
450 387 lt
451 387 lt
451 387 lt
452 387 lt
453 387 lt
454 386 lt
455 386 lt
455 386 lt
456 386 lt
457 386 lt
458 386 lt
459 385 lt
459 385 lt
460 385 lt
461 385 lt
461 385 lt
462 385 lt
463 385 lt
463 384 lt
464 384 lt
465 384 lt
465 384 lt
466 384 lt
467 384 lt
467 384 lt
468 383 lt
469 383 lt
469 383 lt
470 383 lt
470 383 lt
471 383 lt
472 383 lt
472 383 lt
473 382 lt
473 382 lt
474 382 lt
474 382 lt
475 382 lt
476 382 lt
476 382 lt
477 382 lt
477 382 lt
478 382 lt
478 381 lt
479 381 lt
479 381 lt
480 381 lt
480 381 lt
481 381 lt
481 381 lt
482 381 lt
482 381 lt
483 381 lt
483 380 lt
484 380 lt
484 380 lt
485 380 lt
485 380 lt
485 380 lt
486 380 lt
486 380 lt
487 380 lt
487 380 lt
488 380 lt
488 380 lt
489 380 lt
489 379 lt
489 379 lt
490 379 lt
490 379 lt
491 379 lt
491 379 lt
492 379 lt
492 379 lt
492 379 lt
493 379 lt
493 379 lt
494 379 lt
494 379 lt
494 378 lt
495 378 lt
495 378 lt
496 378 lt
496 378 lt
256 573 mt
256 572 lt
257 568 mt
258 567 lt
259 562 mt
259 561 lt
261 557 mt
261 556 lt
261 556 lt
262 551 mt
263 550 lt
264 546 mt
264 545 lt
266 540 mt
266 540 lt
266 539 lt
268 535 mt
268 534 lt
270 530 mt
270 529 lt
272 524 mt
272 523 lt
272 523 lt
274 519 mt
275 518 lt
276 514 mt
276 514 mt
277 513 lt
279 509 mt
279 508 lt
280 506 mt
282 504 mt
282 503 lt
284 499 mt
285 498 lt
285 497 mt
287 494 mt
288 493 lt
288 492 mt
290 489 mt
291 488 lt
292 486 mt
293 484 mt
294 483 lt
295 481 mt
297 479 mt
297 478 lt
298 477 mt
300 475 mt
301 474 lt
301 473 mt
303 470 mt
304 469 lt
304 469 mt
307 466 mt
307 466 mt
308 465 lt
309 463 mt
311 462 mt
312 461 lt
312 461 mt
314 458 mt
315 457 mt
316 457 lt
316 456 mt
319 454 mt
319 453 mt
320 453 lt
321 452 mt
323 450 mt
323 449 mt
324 449 lt
325 448 mt
326 447 mt
328 446 mt
328 445 lt
328 445 lt
330 444 mt
332 443 mt
332 443 mt
333 442 lt
333 442 mt
335 440 mt
337 439 mt
337 439 mt
338 439 lt
338 438 mt
340 437 mt
341 436 mt
342 436 mt
342 435 lt
343 435 lt
344 435 mt
345 434 mt
346 433 mt
346 433 lt
347 432 lt
348 432 mt
349 431 mt
350 431 mt
351 430 mt
352 430 lt
352 429 lt
353 429 mt
354 429 mt
355 428 mt
356 427 mt
356 427 mt
357 427 lt
357 427 lt
358 426 mt
359 426 mt
360 425 mt
361 425 mt
361 425 lt
362 424 lt
362 424 lt
363 423 mt
364 423 mt
365 423 mt
366 422 mt
366 422 mt
367 422 lt
367 421 lt
368 421 mt
369 421 mt
370 420 mt
371 419 mt
372 419 mt
373 419 lt
373 419 mt
375 418 mt
377 417 mt
378 417 lt
378 417 lt
381 415 mt
382 415 mt
383 414 lt
383 414 mt
386 413 mt
387 412 mt
388 412 lt
389 412 mt
391 411 mt
392 410 mt
393 410 lt
394 410 lt
396 409 mt
398 408 mt
398 408 lt
399 408 lt
400 407 mt
402 407 mt
403 406 mt
404 406 lt
404 406 lt
406 405 mt
408 405 mt
409 404 mt
409 404 lt
410 404 lt
411 403 mt
413 403 mt
414 402 mt
414 402 lt
415 402 lt
416 402 mt
417 401 mt
419 401 mt
419 401 mt
420 400 lt
420 400 lt
422 400 mt
423 400 mt
424 399 mt
425 399 mt
426 399 lt
426 399 lt
427 398 mt
428 398 mt
430 398 mt
430 397 mt
431 397 lt
431 397 lt
432 397 mt
433 397 mt
434 396 mt
435 396 mt
436 396 mt
436 396 lt
437 395 lt
437 395 mt
439 395 mt
440 395 mt
441 394 mt
441 394 mt
442 394 lt
442 394 lt
443 394 mt
444 394 mt
444 393 mt
445 393 mt
446 393 mt
447 393 mt
447 393 lt
448 392 lt
448 392 mt
449 392 mt
450 392 mt
451 392 mt
451 392 mt
452 391 mt
452 391 mt
453 391 lt
453 391 lt
454 391 mt
455 391 mt
455 391 mt
456 390 mt
457 390 mt
458 390 mt
458 390 mt
459 390 lt
459 390 lt
459 390 mt
460 389 mt
461 389 mt
461 389 mt
462 389 mt
463 389 mt
463 389 mt
463 389 mt
464 388 lt
465 388 lt
465 388 mt
465 388 mt
466 388 mt
467 388 mt
467 388 mt
468 388 mt
469 387 mt
469 387 mt
469 387 lt
470 387 lt
470 387 lt
470 387 mt
471 387 mt
472 387 mt
472 387 mt
473 387 mt
473 386 mt
474 386 mt
474 386 mt
475 386 mt
475 386 lt
476 386 lt
476 386 lt
476 386 mt
477 386 mt
477 386 mt
478 385 mt
478 385 mt
479 385 mt
479 385 mt
480 385 mt
480 385 mt
480 385 lt
481 385 lt
481 385 lt
481 385 lt
482 385 mt
482 384 mt
483 384 mt
483 384 mt
484 384 mt
484 384 mt
485 384 mt
485 384 mt
485 384 mt
486 384 mt
486 384 lt
486 384 lt
487 384 lt
487 383 lt
487 383 mt
488 383 mt
488 383 mt
489 383 mt
489 383 mt
489 383 mt
490 383 mt
490 383 mt
491 383 mt
491 383 mt
491 383 mt
492 383 lt
492 382 lt
492 382 lt
493 382 lt
493 382 mt
493 382 mt
494 382 mt
494 382 mt
494 382 mt
495 382 mt
495 382 mt
496 382 mt
496 382 mt
256 476 mt
259 472 lt
261 469 mt
262 469 mt
265 465 lt
267 463 mt
268 462 mt
271 458 lt
272 457 mt
274 455 mt
276 453 lt
277 452 lt
280 449 mt
281 449 lt
284 446 lt
285 445 mt
287 443 mt
288 442 lt
291 440 lt
292 439 mt
295 437 mt
295 437 lt
298 435 lt
298 435 lt
301 433 mt
302 432 mt
304 431 lt
306 430 lt
307 429 mt
309 427 mt
310 427 mt
312 426 lt
314 425 lt
314 425 mt
316 423 mt
318 422 mt
319 422 lt
321 421 lt
322 420 lt
323 420 mt
325 419 mt
326 418 mt
326 418 lt
328 417 lt
330 416 lt
330 416 mt
332 415 mt
333 415 mt
334 414 mt
335 414 lt
337 413 lt
338 413 lt
338 413 lt
340 412 mt
341 411 mt
342 411 mt
343 411 mt
344 410 lt
345 410 lt
346 409 lt
347 409 lt
348 409 mt
349 408 mt
350 408 mt
351 408 mt
352 407 lt
353 407 lt
354 407 lt
355 406 lt
355 406 lt
356 406 mt
357 405 mt
358 405 mt
359 405 mt
360 404 mt
360 404 lt
361 404 lt
362 404 lt
363 403 lt
364 403 lt
364 403 mt
365 403 mt
366 402 mt
367 402 mt
368 402 mt
368 402 mt
369 401 lt
370 401 lt
371 401 lt
373 400 lt
373 400 mt
375 400 mt
377 399 mt
378 399 lt
381 398 lt
381 397 lt
383 397 mt
386 396 mt
386 396 lt
389 395 lt
390 395 lt
391 395 mt
393 394 mt
395 394 mt
396 393 lt
398 393 lt
399 393 lt
400 392 mt
402 392 mt
403 391 mt
404 391 lt
406 391 lt
408 390 lt
408 390 lt
409 390 mt
411 390 mt
412 389 mt
413 389 lt
414 389 lt
416 388 lt
417 388 lt
417 388 mt
419 388 mt
420 387 mt
421 387 mt
422 387 lt
423 387 lt
424 386 lt
426 386 lt
426 386 mt
427 386 mt
428 386 mt
430 385 mt
430 385 mt
431 385 lt
432 385 lt
433 385 lt
434 384 lt
435 384 lt
435 384 mt
436 384 mt
437 384 mt
439 383 mt
439 383 mt
440 383 lt
441 383 lt
442 383 lt
443 383 lt
444 382 lt
444 382 lt
444 382 mt
445 382 mt
446 382 mt
447 382 mt
448 382 mt
448 382 mt
449 381 lt
450 381 lt
451 381 lt
451 381 lt
452 381 lt
453 381 lt
453 381 mt
454 380 mt
455 380 mt
455 380 mt
456 380 mt
457 380 mt
457 380 mt
458 380 lt
459 380 lt
459 380 lt
460 379 lt
461 379 lt
461 379 lt
462 379 lt
462 379 mt
463 379 mt
463 379 mt
464 379 mt
465 379 mt
465 378 mt
466 378 mt
466 378 mt
467 378 lt
467 378 lt
468 378 lt
469 378 lt
469 378 lt
470 378 lt
470 378 lt
471 378 lt
471 377 mt
472 377 mt
472 377 mt
473 377 mt
473 377 mt
474 377 mt
474 377 mt
475 377 mt
475 377 mt
476 377 lt
476 377 lt
477 377 lt
477 376 lt
478 376 lt
478 376 lt
479 376 lt
479 376 lt
480 376 lt
480 376 mt
480 376 mt
481 376 mt
481 376 mt
482 376 mt
482 376 mt
483 376 mt
483 375 mt
484 375 mt
484 375 mt
484 375 mt
485 375 lt
485 375 lt
485 375 lt
486 375 lt
486 375 lt
487 375 lt
487 375 lt
488 375 lt
488 375 lt
489 375 lt
489 375 lt
489 375 mt
489 375 mt
490 374 mt
490 374 mt
491 374 mt
491 374 mt
492 374 mt
492 374 mt
492 374 mt
493 374 mt
493 374 mt
493 374 mt
494 374 lt
494 374 lt
494 374 lt
495 374 lt
495 374 lt
496 374 lt
496 374 lt
256 452 mt
256 452 lt
260 448 mt
261 448 lt
261 448 mt
265 444 mt
267 443 lt
272 438 lt
274 437 lt
276 435 mt
279 434 mt
279 433 lt
281 432 mt
284 430 mt
285 430 lt
285 430 mt
288 427 mt
289 427 mt
292 425 lt
295 423 lt
298 422 lt
299 421 lt
301 420 mt
304 418 mt
304 418 mt
305 418 lt
307 417 mt
309 416 mt
310 416 mt
310 415 lt
312 415 mt
314 414 mt
316 413 mt
316 412 lt
319 411 lt
321 411 lt
323 410 lt
325 409 lt
326 408 lt
326 408 mt
328 407 mt
330 407 mt
331 406 mt
332 406 lt
332 406 lt
333 406 mt
335 405 mt
337 404 mt
337 404 mt
338 404 lt
338 404 mt
340 403 mt
341 403 mt
342 402 mt
343 402 mt
344 402 lt
345 402 lt
346 401 lt
348 401 lt
349 400 lt
350 400 lt
352 400 lt
353 399 lt
354 399 lt
354 399 lt
355 398 mt
356 398 mt
357 398 mt
358 397 mt
359 397 mt
360 397 mt
360 397 lt
360 397 mt
361 397 mt
362 396 mt
363 396 mt
364 396 mt
365 395 mt
366 395 mt
366 395 lt
366 395 lt
367 395 mt
368 395 mt
369 394 mt
370 394 mt
371 394 mt
372 394 mt
373 393 lt
375 393 lt
378 392 lt
381 391 lt
383 391 lt
383 391 mt
386 390 mt
388 389 mt
389 389 lt
389 389 lt
391 389 mt
393 388 mt
395 388 mt
395 388 lt
396 388 mt
398 387 mt
400 387 mt
401 387 mt
402 386 lt
404 386 lt
406 386 lt
408 385 lt
409 385 lt
411 384 lt
412 384 lt
413 384 mt
414 384 mt
416 383 mt
417 383 mt
417 383 mt
418 383 lt
419 383 mt
420 382 mt
422 382 mt
423 382 mt
424 382 mt
424 382 lt
424 382 mt
426 381 mt
427 381 mt
428 381 mt
430 381 mt
430 381 mt
431 380 lt
432 380 lt
433 380 lt
434 380 lt
435 380 lt
436 379 lt
437 379 lt
439 379 lt
440 379 lt
441 379 lt
441 379 lt
442 379 mt
443 378 mt
444 378 mt
444 378 mt
445 378 mt
446 378 mt
447 378 mt
447 378 lt
447 378 lt
448 377 mt
449 377 mt
450 377 mt
451 377 mt
451 377 mt
452 377 mt
453 377 mt
453 377 lt
453 377 lt
454 376 mt
455 376 mt
455 376 mt
456 376 mt
457 376 mt
458 376 mt
459 376 mt
459 376 mt
459 376 lt
460 375 lt
461 375 lt
461 375 lt
462 375 lt
463 375 lt
463 375 lt
464 375 lt
465 375 lt
465 375 lt
466 375 lt
467 374 lt
467 374 lt
468 374 lt
469 374 lt
469 374 lt
470 374 lt
470 374 lt
470 374 mt
471 374 mt
472 374 mt
472 374 mt
473 374 mt
473 373 mt
474 373 mt
474 373 mt
475 373 mt
476 373 mt
476 373 mt
476 373 lt
477 373 lt
477 373 mt
477 373 mt
478 373 mt
478 373 mt
479 373 mt
479 373 mt
480 373 mt
480 372 mt
481 372 mt
481 372 mt
482 372 mt
482 372 mt
482 372 mt
483 372 lt
483 372 lt
483 372 mt
484 372 mt
484 372 mt
485 372 mt
485 372 mt
485 372 mt
486 372 mt
486 372 mt
487 372 mt
487 371 mt
488 371 mt
488 371 mt
488 371 mt
489 371 lt
489 371 lt
489 371 lt
490 371 lt
490 371 lt
491 371 lt
491 371 lt
492 371 lt
492 371 lt
492 371 lt
493 371 lt
493 371 lt
494 371 lt
494 371 lt
494 371 lt
495 370 lt
495 370 lt
496 370 lt
496 370 lt
0 trot 14 tsiz 225 237 text 4 sf
(2) tsho tend
0 trot 13 tsiz 225 237 text 4 sf
(2) tsho tend
0 trot 12 tsiz 225 237 text 4 sf
(2) tsho tend
0 trot 11 tsiz 225 237 text 4 sf
(2) tsho tend
0 trot 11 tsiz 225 237 text 4 sf
(2) tsho tend
0 trot 10 tsiz 225 237 text 4 sf
(2) tsho tend
0 trot 9 tsiz 225 237 text 4 sf
(2) tsho tend
0 trot 8 tsiz 225 237 text 4 sf
(2) tsho tend
0 trot 8 tsiz 225 237 text 4 sf
(2) tsho tend
0 trot 7 tsiz 225 237 text 4 sf
(2) tsho tend
0 trot 6 tsiz 225 237 text 4 sf
(2) tsho tend
0 trot 5 tsiz 225 237 text 4 sf
(2) tsho tend
0 trot 5 tsiz 225 237 text 4 sf
(2) tsho tend
0 trot 4 tsiz 225 237 text 4 sf
(2) tsho tend
0 trot 3 tsiz 225 237 text 4 sf
(2) tsho tend
0 trot 2 tsiz 225 237 text 4 sf
(2) tsho tend
en
%%Page:4 4
star
3 slw
0 trot 22 tsiz 270 602 text 0 sf
(Ellis-Jaffe sum rule vs. Q) tsho 2 tsubsc (2) tsho 3 tsubsc tend
0 trot 22 tsiz 62 451 text 1 sf
(G) tsho 0 tsubsc 0 sf
(1) tsho 1 tsubsc 2 thskip 4 thskip 1 tvskip 2 tsubsc (p) tsho 3 tsubsc tend
0 trot 19 tsiz 295 161 text 0 sf
(Q) tsho 2 tsubsc (2) tsho 3 tsubsc ( \050GeV) tsho 2 tsubsc (2) tsho 3 tsubsc
 (\051) tsho tend
0 trot 15 tsiz 221 118 text 4 sf
(1 ) tsho 0 sf
(E142, ) tsho 4 sf
(4 ) tsho 0 sf
(E143, ) tsho 4 sf
(2 ) tsho 0 sf
(SMC-d, ) tsho 4 sf
(3 ) tsho 0 sf
(SMC-p, ) tsho 4 sf
(5 ) tsho 0 sf
(EMC) tsho tend
0 trot 15 tsiz 221 88 text 0 sf
(n and d data converted to p using Bjorken) tsho tend
0 trot 15 tsiz 483 88 text 0 sf
(sum rule) tsho tend
0 trot 17 tsiz 623 542 text 1 sf
(D) tsho 0 sf
(S=0) tsho tend
0 trot 17 tsiz 623 481 text 1 sf
(D) tsho 0 sf
(S=-0.10+0.04) tsho tend
0 trot 17 tsiz 688 481 text 0 sf
(_) tsho tend
0 trot 17 tsiz 688 482 text 0 sf
(_) tsho tend
0 trot 19 tsiz 585 57 text 0 sf
(Fig. 4) tsho tend
154 582 mt
154 199 lt
154 199 mt
614 199 lt
614 199 mt
614 582 lt
614 582 mt
154 582 lt
154 200 mt
154 199 lt
173 204 mt
173 199 lt
192 200 mt
192 199 lt
212 200 mt
212 199 lt
231 200 mt
231 199 lt
251 200 mt
251 199 lt
270 204 mt
270 199 lt
289 200 mt
289 199 lt
309 200 mt
309 199 lt
328 200 mt
328 199 lt
347 200 mt
347 199 lt
367 204 mt
367 199 lt
386 200 mt
386 199 lt
405 200 mt
405 199 lt
425 200 mt
425 199 lt
444 200 mt
444 199 lt
464 204 mt
464 199 lt
483 200 mt
483 199 lt
502 200 mt
502 199 lt
522 200 mt
522 199 lt
541 200 mt
541 199 lt
560 204 mt
560 199 lt
580 200 mt
580 199 lt
599 200 mt
599 199 lt
0 trot 19 tsiz 173 181 text 0 sf
(2) tsho tend
0 trot 19 tsiz 270 181 text 0 sf
(4) tsho tend
0 trot 19 tsiz 367 181 text 0 sf
(6) tsho tend
0 trot 19 tsiz 464 181 text 0 sf
(8) tsho tend
0 trot 19 tsiz 554 181 text 0 sf
(10) tsho tend
154 582 mt
154 580 lt
173 582 mt
173 577 lt
192 582 mt
192 580 lt
212 582 mt
212 580 lt
231 582 mt
231 580 lt
251 582 mt
251 580 lt
270 582 mt
270 577 lt
289 582 mt
289 580 lt
309 582 mt
309 580 lt
328 582 mt
328 580 lt
347 582 mt
347 580 lt
367 582 mt
367 577 lt
386 582 mt
386 580 lt
405 582 mt
405 580 lt
425 582 mt
425 580 lt
444 582 mt
444 580 lt
464 582 mt
464 577 lt
483 582 mt
483 580 lt
502 582 mt
502 580 lt
522 582 mt
522 580 lt
541 582 mt
541 580 lt
560 582 mt
560 577 lt
580 582 mt
580 580 lt
599 582 mt
599 580 lt
159 199 mt
154 199 lt
155 219 mt
154 219 lt
155 239 mt
154 239 lt
155 259 mt
154 259 lt
155 279 mt
154 279 lt
159 299 mt
154 299 lt
155 320 mt
154 320 lt
155 340 mt
154 340 lt
155 360 mt
154 360 lt
155 380 mt
154 380 lt
159 400 mt
154 400 lt
155 421 mt
154 421 lt
155 441 mt
154 441 lt
155 461 mt
154 461 lt
155 481 mt
154 481 lt
159 501 mt
154 501 lt
155 521 mt
154 521 lt
155 542 mt
154 542 lt
155 562 mt
154 562 lt
155 582 mt
154 582 lt
0 trot 19 tsiz 101 199 text 0 sf
(0.00) tsho tend
0 trot 19 tsiz 101 299 text 0 sf
(0.05) tsho tend
0 trot 19 tsiz 101 400 text 0 sf
(0.10) tsho tend
0 trot 19 tsiz 101 501 text 0 sf
(0.15) tsho tend
614 199 mt
608 199 lt
614 219 mt
612 219 lt
614 239 mt
612 239 lt
614 259 mt
612 259 lt
614 279 mt
612 279 lt
614 299 mt
608 299 lt
614 320 mt
612 320 lt
614 340 mt
612 340 lt
614 360 mt
612 360 lt
614 380 mt
612 380 lt
614 400 mt
608 400 lt
614 421 mt
612 421 lt
614 441 mt
612 441 lt
614 461 mt
612 461 lt
614 481 mt
612 481 lt
614 501 mt
608 501 lt
614 521 mt
612 521 lt
614 542 mt
612 542 lt
614 562 mt
612 562 lt
614 582 mt
612 582 lt
154 499 mt
154 499 lt
156 500 lt
158 501 lt
161 503 lt
163 504 lt
166 505 lt
168 506 lt
171 507 lt
173 508 lt
175 509 lt
178 510 lt
180 511 lt
183 511 lt
185 512 lt
188 513 lt
190 513 lt
192 514 lt
195 515 lt
197 515 lt
200 516 lt
202 516 lt
204 517 lt
207 517 lt
209 518 lt
212 518 lt
214 519 lt
217 519 lt
219 520 lt
221 520 lt
224 521 lt
226 521 lt
229 521 lt
231 522 lt
234 522 lt
236 522 lt
238 523 lt
241 523 lt
243 523 lt
246 524 lt
248 524 lt
251 524 lt
253 525 lt
255 525 lt
258 525 lt
260 525 lt
263 526 lt
265 526 lt
267 526 lt
270 526 lt
272 527 lt
275 527 lt
277 527 lt
280 527 lt
282 528 lt
284 528 lt
287 528 lt
289 528 lt
292 528 lt
294 529 lt
297 529 lt
299 529 lt
301 529 lt
304 529 lt
306 530 lt
309 530 lt
311 530 lt
313 530 lt
316 530 lt
318 530 lt
321 531 lt
323 531 lt
326 531 lt
328 531 lt
330 531 lt
333 531 lt
335 531 lt
338 532 lt
340 532 lt
343 532 lt
345 532 lt
347 532 lt
350 532 lt
352 532 lt
355 533 lt
357 533 lt
359 533 lt
362 533 lt
364 533 lt
367 533 lt
369 533 lt
372 533 lt
374 534 lt
376 534 lt
379 534 lt
381 534 lt
384 534 lt
386 534 lt
389 534 lt
391 534 lt
393 534 lt
396 535 lt
398 535 lt
401 535 lt
403 535 lt
405 535 lt
408 535 lt
410 535 lt
413 535 lt
415 535 lt
418 535 lt
420 535 lt
422 536 lt
425 536 lt
427 536 lt
430 536 lt
432 536 lt
435 536 lt
437 536 lt
439 536 lt
442 536 lt
444 536 lt
447 536 lt
449 537 lt
452 537 lt
454 537 lt
456 537 lt
459 537 lt
461 537 lt
464 537 lt
466 537 lt
468 537 lt
471 537 lt
473 537 lt
476 537 lt
478 537 lt
481 537 lt
483 538 lt
485 538 lt
488 538 lt
490 538 lt
493 538 lt
495 538 lt
498 538 lt
500 538 lt
502 538 lt
505 538 lt
507 538 lt
510 538 lt
512 538 lt
514 538 lt
517 538 lt
519 539 lt
522 539 lt
524 539 lt
527 539 lt
529 539 lt
531 539 lt
534 539 lt
536 539 lt
539 539 lt
541 539 lt
544 539 lt
546 539 lt
548 539 lt
551 539 lt
553 539 lt
556 539 lt
558 539 lt
560 539 lt
563 540 lt
565 540 lt
568 540 lt
570 540 lt
573 540 lt
575 540 lt
577 540 lt
580 540 lt
582 540 lt
585 540 lt
587 540 lt
590 540 lt
592 540 lt
594 540 lt
594 540 mt
597 540 lt
599 540 lt
602 540 lt
604 540 lt
607 540 lt
609 540 lt
611 541 lt
614 541 lt
614 541 lt
156 520 mt
158 520 mt
158 520 lt
159 521 lt
161 521 mt
163 522 mt
163 522 lt
164 522 lt
166 523 mt
168 523 mt
168 523 mt
169 523 lt
171 524 mt
173 524 mt
174 524 mt
174 525 lt
175 525 mt
178 525 mt
179 526 mt
179 526 lt
180 526 mt
183 526 mt
184 527 mt
185 527 lt
185 527 mt
188 527 mt
189 528 mt
190 528 lt
190 528 mt
192 528 mt
194 528 mt
195 529 lt
195 529 lt
197 529 mt
200 529 mt
200 529 lt
200 529 lt
202 530 mt
204 530 mt
205 530 mt
205 530 lt
207 530 mt
209 531 mt
210 531 mt
211 531 lt
212 531 mt
214 531 mt
215 532 mt
216 532 lt
217 532 mt
219 532 mt
221 532 mt
221 532 lt
221 532 mt
224 533 mt
226 533 mt
226 533 lt
227 533 lt
229 533 mt
231 534 mt
231 534 mt
232 534 lt
234 534 mt
236 534 mt
236 534 mt
237 534 lt
238 534 mt
241 535 mt
242 535 mt
242 535 lt
243 535 mt
246 535 mt
247 535 mt
248 535 lt
248 535 mt
251 536 mt
252 536 mt
253 536 lt
253 536 mt
255 536 mt
258 536 mt
258 536 lt
258 536 lt
260 536 mt
263 537 mt
263 537 mt
263 537 lt
265 537 mt
267 537 mt
268 537 mt
269 537 lt
270 537 mt
272 537 mt
273 538 mt
274 538 lt
275 538 mt
277 538 mt
279 538 mt
279 538 lt
280 538 mt
282 538 mt
284 538 mt
284 538 lt
285 538 lt
287 538 mt
289 539 mt
289 539 mt
290 539 lt
292 539 mt
294 539 mt
295 539 mt
295 539 lt
297 539 mt
299 539 mt
300 539 mt
301 539 lt
301 539 mt
304 540 mt
305 540 mt
306 540 lt
306 540 mt
309 540 mt
311 540 mt
311 540 lt
311 540 lt
313 540 mt
316 540 mt
316 540 lt
316 540 lt
318 540 mt
321 541 mt
321 541 mt
322 541 lt
323 541 mt
326 541 mt
326 541 mt
327 541 lt
328 541 mt
330 541 mt
332 541 mt
332 541 lt
333 541 mt
335 541 mt
337 541 mt
338 541 lt
338 541 mt
340 542 mt
342 542 mt
343 542 lt
343 542 lt
345 542 mt
347 542 mt
348 542 mt
348 542 lt
350 542 mt
352 542 mt
353 542 mt
354 542 lt
355 542 mt
357 542 mt
358 542 mt
359 543 lt
359 543 mt
362 543 mt
364 543 mt
364 543 lt
364 543 mt
367 543 mt
369 543 mt
369 543 lt
369 543 lt
372 543 mt
374 543 mt
374 543 mt
375 543 lt
376 543 mt
379 543 mt
380 543 mt
380 543 lt
381 543 mt
384 544 mt
385 544 mt
385 544 lt
386 544 mt
389 544 mt
390 544 mt
391 544 lt
391 544 mt
393 544 mt
395 544 mt
396 544 lt
396 544 lt
398 544 mt
401 544 mt
401 544 mt
401 544 lt
403 544 mt
405 544 mt
406 544 mt
407 544 lt
408 544 mt
410 545 mt
411 545 mt
412 545 lt
413 545 mt
415 545 mt
417 545 mt
417 545 lt
418 545 mt
420 545 mt
422 545 mt
422 545 lt
423 545 lt
425 545 mt
427 545 mt
427 545 lt
428 545 lt
430 545 mt
432 545 mt
433 545 mt
433 545 lt
435 545 mt
437 545 mt
438 545 mt
438 545 lt
439 545 mt
442 546 mt
443 546 mt
444 546 lt
444 546 mt
447 546 mt
448 546 mt
449 546 lt
449 546 mt
452 546 mt
454 546 mt
454 546 lt
454 546 lt
456 546 mt
459 546 mt
459 546 mt
460 546 lt
461 546 mt
464 546 mt
464 546 mt
465 546 lt
466 546 mt
468 546 mt
470 546 mt
470 546 lt
471 546 mt
473 546 mt
475 546 mt
476 547 lt
476 547 mt
478 547 mt
480 547 mt
481 547 lt
481 547 lt
483 547 mt
485 547 mt
486 547 mt
486 547 lt
488 547 mt
490 547 mt
491 547 mt
492 547 lt
493 547 mt
495 547 mt
496 547 mt
497 547 lt
498 547 mt
500 547 mt
502 547 mt
502 547 lt
502 547 mt
505 547 mt
507 547 mt
507 547 lt
507 547 lt
510 547 mt
512 547 mt
512 547 mt
513 547 lt
514 547 mt
517 548 mt
517 548 mt
518 548 lt
519 548 mt
522 548 mt
523 548 mt
523 548 lt
524 548 mt
527 548 mt
528 548 mt
529 548 lt
529 548 mt
531 548 mt
533 548 mt
534 548 lt
534 548 lt
536 548 mt
539 548 mt
539 548 mt
539 548 lt
541 548 mt
544 548 mt
544 548 mt
545 548 lt
546 548 mt
548 548 mt
549 548 mt
550 548 lt
551 548 mt
553 548 mt
555 548 mt
555 548 lt
556 548 mt
558 548 mt
560 548 mt
560 548 lt
561 548 lt
563 549 mt
565 549 mt
565 549 lt
566 549 lt
568 549 mt
570 549 mt
571 549 mt
571 549 lt
573 549 mt
575 549 mt
576 549 mt
576 549 lt
577 549 mt
580 549 mt
581 549 mt
582 549 lt
582 549 mt
585 549 mt
586 549 mt
587 549 lt
587 549 mt
590 549 mt
592 549 mt
592 549 lt
592 549 lt
594 549 mt
594 549 mt
597 549 mt
597 549 mt
598 549 lt
599 549 mt
602 549 mt
602 549 mt
603 549 lt
604 549 mt
607 549 mt
608 549 mt
608 549 lt
609 549 mt
611 549 mt
613 549 mt
614 549 lt
614 549 mt
156 480 mt
157 481 mt
158 482 lt
158 482 mt
161 484 mt
161 485 mt
162 485 lt
163 486 mt
166 488 mt
166 488 lt
166 488 lt
168 489 mt
170 490 mt
171 490 lt
171 491 lt
173 492 mt
175 493 mt
175 493 lt
175 493 lt
178 494 mt
180 495 mt
180 495 lt
180 495 lt
183 496 mt
185 497 mt
185 497 lt
185 497 lt
188 498 mt
190 499 mt
190 499 lt
190 499 lt
192 500 mt
195 501 mt
195 501 lt
195 501 lt
197 502 mt
200 502 mt
200 502 mt
200 503 lt
202 503 mt
204 504 mt
205 504 mt
205 504 lt
207 504 mt
209 505 mt
210 505 mt
210 505 lt
212 506 mt
214 506 mt
215 506 mt
216 507 lt
217 507 mt
219 507 mt
220 508 mt
221 508 lt
221 508 mt
224 508 mt
225 509 mt
226 509 lt
226 509 mt
229 509 mt
231 510 mt
231 510 lt
231 510 lt
234 510 mt
236 511 mt
236 511 lt
236 511 lt
238 511 mt
241 512 mt
241 512 mt
242 512 lt
243 512 mt
246 512 mt
246 512 mt
247 513 lt
248 513 mt
251 513 mt
252 513 mt
252 513 lt
253 513 mt
255 514 mt
257 514 mt
257 514 lt
258 514 mt
260 514 mt
262 515 mt
263 515 lt
263 515 lt
265 515 mt
267 515 mt
267 515 lt
268 515 lt
270 516 mt
272 516 mt
273 516 mt
273 516 lt
275 516 mt
277 516 mt
278 517 mt
279 517 lt
280 517 mt
282 517 mt
283 517 mt
284 517 lt
284 517 mt
287 517 mt
289 518 mt
289 518 lt
289 518 mt
292 518 mt
294 518 mt
294 518 lt
294 518 lt
297 518 mt
299 519 mt
299 519 mt
300 519 lt
301 519 mt
304 519 mt
304 519 mt
305 519 lt
306 519 mt
309 520 mt
310 520 mt
310 520 lt
311 520 mt
313 520 mt
315 520 mt
316 520 lt
316 520 mt
318 520 mt
320 520 mt
321 520 lt
321 521 lt
323 521 mt
326 521 mt
326 521 lt
326 521 lt
328 521 mt
330 521 mt
331 521 mt
331 521 lt
333 521 mt
335 522 mt
336 522 mt
337 522 lt
338 522 mt
340 522 mt
341 522 mt
342 522 lt
343 522 mt
345 522 mt
347 522 mt
347 522 lt
347 522 mt
350 523 mt
352 523 mt
352 523 lt
353 523 lt
355 523 mt
357 523 mt
357 523 mt
358 523 lt
359 523 mt
362 523 mt
363 523 mt
363 523 lt
364 523 mt
367 524 mt
368 524 mt
369 524 lt
369 524 mt
372 524 mt
373 524 mt
374 524 lt
374 524 mt
376 524 mt
379 524 mt
379 524 lt
379 524 lt
381 524 mt
384 524 mt
384 524 mt
384 524 lt
386 525 mt
389 525 mt
389 525 mt
390 525 lt
391 525 mt
393 525 mt
394 525 mt
395 525 lt
396 525 mt
398 525 mt
400 525 mt
400 525 lt
401 525 mt
403 525 mt
405 525 mt
405 525 lt
406 525 lt
408 526 mt
410 526 mt
410 526 lt
411 526 lt
413 526 mt
415 526 mt
416 526 mt
416 526 lt
418 526 mt
420 526 mt
421 526 mt
422 526 lt
422 526 mt
425 526 mt
426 526 mt
427 526 lt
427 526 mt
430 527 mt
432 527 mt
432 527 lt
432 527 lt
435 527 mt
437 527 mt
437 527 lt
437 527 lt
439 527 mt
442 527 mt
442 527 mt
443 527 lt
444 527 mt
447 527 mt
447 527 mt
448 527 lt
449 527 mt
452 527 mt
453 527 mt
453 527 lt
454 527 mt
456 528 mt
458 528 mt
459 528 lt
459 528 mt
461 528 mt
463 528 mt
464 528 lt
464 528 lt
466 528 mt
468 528 mt
469 528 mt
469 528 lt
471 528 mt
473 528 mt
474 528 mt
475 528 lt
476 528 mt
478 528 mt
479 528 mt
480 528 lt
481 528 mt
483 528 mt
485 528 mt
485 528 lt
485 528 mt
488 529 mt
490 529 mt
490 529 lt
491 529 lt
493 529 mt
495 529 mt
495 529 mt
496 529 lt
498 529 mt
500 529 mt
501 529 mt
501 529 lt
502 529 mt
505 529 mt
506 529 mt
506 529 lt
507 529 mt
510 529 mt
511 529 mt
512 529 lt
512 529 mt
514 529 mt
516 529 mt
517 529 lt
517 529 lt
519 529 mt
522 530 mt
522 530 mt
522 530 lt
524 530 mt
527 530 mt
527 530 mt
528 530 lt
529 530 mt
531 530 mt
532 530 mt
533 530 lt
534 530 mt
536 530 mt
538 530 mt
538 530 lt
539 530 mt
541 530 mt
543 530 mt
544 530 lt
544 530 lt
546 530 mt
548 530 mt
548 530 lt
549 530 lt
551 530 mt
553 530 mt
554 530 mt
554 530 lt
556 530 mt
558 530 mt
559 530 mt
560 530 lt
560 531 mt
563 531 mt
564 531 mt
565 531 lt
565 531 mt
568 531 mt
570 531 mt
570 531 lt
570 531 mt
573 531 mt
575 531 mt
575 531 lt
575 531 lt
577 531 mt
580 531 mt
580 531 mt
581 531 lt
582 531 mt
585 531 mt
585 531 mt
586 531 lt
587 531 mt
590 531 mt
591 531 mt
591 531 lt
592 531 mt
594 531 mt
594 531 mt
596 531 mt
597 531 lt
597 531 mt
599 531 mt
601 531 mt
602 531 lt
602 531 lt
604 531 mt
607 532 mt
607 532 mt
607 532 lt
609 532 mt
611 532 mt
612 532 mt
613 532 lt
614 532 mt
221 493 mt
221 441 lt
2 slw
0 trot 19 tsiz 221 467 text 4 sf
(4) tsho tend
3 slw
594 503 mt
594 410 lt
2 slw
0 trot 19 tsiz 594 457 text 4 sf
(5) tsho tend
3 slw
560 504 mt
560 442 lt
2 slw
0 trot 19 tsiz 560 473 text 4 sf
(3) tsho tend
3 slw
173 508 mt
173 443 lt
2 slw
0 trot 19 tsiz 173 475 text 4 sf
(1) tsho tend
3 slw
299 484 mt
299 374 lt
2 slw
0 trot 19 tsiz 299 429 text 4 sf
(2) tsho tend
3 slw
154 442 mt
154 442 lt
156 443 lt
158 444 lt
161 445 lt
163 446 lt
166 447 lt
168 448 lt
171 449 lt
173 450 lt
175 451 lt
178 452 lt
180 452 lt
183 453 lt
185 454 lt
188 454 lt
190 455 lt
192 455 lt
195 456 lt
197 457 lt
200 457 lt
202 458 lt
204 458 lt
207 458 lt
209 459 lt
212 459 lt
214 460 lt
217 460 lt
219 461 lt
221 461 lt
224 461 lt
226 462 lt
229 462 lt
231 462 lt
234 463 lt
236 463 lt
238 463 lt
241 464 lt
243 464 lt
246 464 lt
248 464 lt
251 465 lt
253 465 lt
255 465 lt
258 465 lt
260 466 lt
263 466 lt
265 466 lt
267 466 lt
270 466 lt
272 467 lt
275 467 lt
277 467 lt
280 467 lt
282 468 lt
284 468 lt
287 468 lt
289 468 lt
292 468 lt
294 468 lt
297 469 lt
299 469 lt
301 469 lt
304 469 lt
306 469 lt
309 469 lt
311 470 lt
313 470 lt
316 470 lt
318 470 lt
321 470 lt
323 470 lt
326 470 lt
328 471 lt
330 471 lt
333 471 lt
335 471 lt
338 471 lt
340 471 lt
343 471 lt
345 471 lt
347 472 lt
350 472 lt
352 472 lt
355 472 lt
357 472 lt
359 472 lt
362 472 lt
364 472 lt
367 472 lt
369 473 lt
372 473 lt
374 473 lt
376 473 lt
379 473 lt
381 473 lt
384 473 lt
386 473 lt
389 473 lt
391 473 lt
393 474 lt
396 474 lt
398 474 lt
401 474 lt
403 474 lt
405 474 lt
408 474 lt
410 474 lt
413 474 lt
415 474 lt
418 474 lt
420 474 lt
422 475 lt
425 475 lt
427 475 lt
430 475 lt
432 475 lt
435 475 lt
437 475 lt
439 475 lt
442 475 lt
444 475 lt
447 475 lt
449 475 lt
452 475 lt
454 476 lt
456 476 lt
459 476 lt
461 476 lt
464 476 lt
466 476 lt
468 476 lt
471 476 lt
473 476 lt
476 476 lt
478 476 lt
481 476 lt
483 476 lt
485 476 lt
488 476 lt
490 476 lt
493 477 lt
495 477 lt
498 477 lt
500 477 lt
502 477 lt
505 477 lt
507 477 lt
510 477 lt
512 477 lt
514 477 lt
517 477 lt
519 477 lt
522 477 lt
524 477 lt
527 477 lt
529 477 lt
531 477 lt
534 477 lt
536 478 lt
539 478 lt
541 478 lt
544 478 lt
546 478 lt
548 478 lt
551 478 lt
553 478 lt
556 478 lt
558 478 lt
560 478 lt
563 478 lt
565 478 lt
568 478 lt
570 478 lt
573 478 lt
575 478 lt
577 478 lt
580 478 lt
582 478 lt
585 478 lt
587 478 lt
590 479 lt
592 479 lt
594 479 lt
594 479 mt
597 479 lt
599 479 lt
602 479 lt
604 479 lt
607 479 lt
609 479 lt
611 479 lt
614 479 lt
614 479 lt
156 473 mt
157 473 mt
157 473 lt
158 474 mt
161 475 mt
162 475 mt
163 475 lt
163 475 mt
166 476 mt
167 476 mt
168 477 lt
168 477 mt
171 478 mt
172 478 mt
173 478 lt
173 478 mt
175 479 mt
177 479 mt
178 479 lt
178 479 mt
180 480 mt
182 481 mt
183 481 lt
183 481 lt
185 481 mt
188 482 mt
188 482 mt
188 482 lt
190 482 mt
192 483 mt
193 483 mt
193 483 lt
195 483 mt
197 484 mt
198 484 mt
199 484 lt
200 484 mt
202 485 mt
203 485 mt
204 485 lt
204 485 mt
207 485 mt
208 486 mt
209 486 lt
209 486 mt
212 486 mt
214 486 mt
214 486 lt
214 486 lt
217 487 mt
219 487 mt
219 487 lt
220 487 lt
221 488 mt
224 488 mt
224 488 mt
225 488 lt
226 488 mt
229 488 mt
230 489 mt
230 489 lt
231 489 mt
234 489 mt
235 489 mt
235 489 lt
236 489 mt
238 490 mt
240 490 mt
241 490 lt
241 490 mt
243 490 mt
245 490 mt
246 490 lt
246 490 lt
248 491 mt
251 491 mt
251 491 mt
251 491 lt
253 491 mt
255 491 mt
256 491 mt
256 492 lt
258 492 mt
260 492 mt
261 492 mt
262 492 lt
263 492 mt
265 492 mt
266 492 mt
267 492 lt
267 493 mt
270 493 mt
272 493 mt
272 493 lt
272 493 lt
275 493 mt
277 493 mt
277 493 lt
278 493 lt
280 494 mt
282 494 mt
282 494 mt
283 494 lt
284 494 mt
287 494 mt
288 494 mt
288 494 lt
289 494 mt
292 494 mt
293 494 mt
294 495 lt
294 495 mt
297 495 mt
298 495 mt
299 495 lt
299 495 mt
301 495 mt
304 495 mt
304 495 lt
304 495 lt
306 495 mt
309 496 mt
309 496 mt
309 496 lt
311 496 mt
313 496 mt
314 496 mt
315 496 lt
316 496 mt
318 496 mt
319 496 mt
320 496 lt
321 496 mt
323 496 mt
325 496 mt
325 497 lt
326 497 mt
328 497 mt
330 497 mt
330 497 lt
331 497 lt
333 497 mt
335 497 mt
335 497 mt
336 497 lt
338 497 mt
340 497 mt
341 497 mt
341 497 lt
343 497 mt
345 498 mt
346 498 mt
347 498 lt
347 498 mt
350 498 mt
351 498 mt
352 498 lt
352 498 mt
355 498 mt
357 498 mt
357 498 lt
357 498 lt
359 498 mt
362 498 mt
362 498 lt
362 498 lt
364 498 mt
367 499 mt
367 499 mt
368 499 lt
369 499 mt
372 499 mt
372 499 mt
373 499 lt
374 499 mt
376 499 mt
378 499 mt
378 499 lt
379 499 mt
381 499 mt
383 499 mt
384 499 lt
384 499 mt
386 499 mt
388 499 mt
389 499 lt
389 499 lt
391 500 mt
393 500 mt
394 500 mt
394 500 lt
396 500 mt
398 500 mt
399 500 mt
400 500 lt
401 500 mt
403 500 mt
404 500 mt
405 500 lt
405 500 mt
408 500 mt
410 500 mt
410 500 lt
410 500 mt
413 500 mt
415 500 mt
415 500 lt
416 500 lt
418 501 mt
420 501 mt
420 501 mt
421 501 lt
422 501 mt
425 501 mt
426 501 mt
426 501 lt
427 501 mt
430 501 mt
431 501 mt
431 501 lt
432 501 mt
435 501 mt
436 501 mt
437 501 lt
437 501 mt
439 501 mt
441 501 mt
442 501 lt
442 501 lt
444 501 mt
447 501 mt
447 501 mt
447 501 lt
449 502 mt
452 502 mt
452 502 mt
453 502 lt
454 502 mt
456 502 mt
457 502 mt
458 502 lt
459 502 mt
461 502 mt
463 502 mt
463 502 lt
464 502 mt
466 502 mt
468 502 mt
468 502 lt
469 502 lt
471 502 mt
473 502 mt
473 502 lt
474 502 lt
476 502 mt
478 502 mt
479 502 mt
479 502 lt
481 502 mt
483 502 mt
484 502 mt
484 502 lt
485 502 mt
488 503 mt
489 503 mt
490 503 lt
490 503 mt
493 503 mt
495 503 mt
495 503 lt
495 503 lt
498 503 mt
500 503 mt
500 503 lt
500 503 lt
502 503 mt
505 503 mt
505 503 mt
506 503 lt
507 503 mt
510 503 mt
510 503 mt
511 503 lt
512 503 mt
514 503 mt
516 503 mt
516 503 lt
517 503 mt
519 503 mt
521 503 mt
522 503 lt
522 503 mt
524 503 mt
526 503 mt
527 503 lt
527 503 lt
529 504 mt
531 504 mt
532 504 mt
532 504 lt
534 504 mt
536 504 mt
537 504 mt
538 504 lt
539 504 mt
541 504 mt
542 504 mt
543 504 lt
544 504 mt
546 504 mt
548 504 mt
548 504 lt
548 504 mt
551 504 mt
553 504 mt
553 504 lt
553 504 lt
556 504 mt
558 504 mt
558 504 mt
559 504 lt
560 504 mt
563 504 mt
564 504 mt
564 504 lt
565 504 mt
568 504 mt
569 504 mt
569 504 lt
570 504 mt
573 504 mt
574 504 mt
575 504 lt
575 504 mt
577 504 mt
579 505 mt
580 505 lt
580 505 lt
582 505 mt
585 505 mt
585 505 mt
585 505 lt
587 505 mt
590 505 mt
590 505 mt
591 505 lt
592 505 mt
594 505 mt
594 505 mt
595 505 mt
596 505 lt
597 505 mt
599 505 mt
601 505 mt
601 505 lt
602 505 mt
604 505 mt
606 505 mt
607 505 lt
607 505 lt
609 505 mt
611 505 mt
611 505 lt
612 505 lt
614 505 mt
156 413 mt
156 413 lt
156 413 lt
158 415 mt
160 416 mt
161 416 lt
161 416 lt
163 417 mt
165 418 mt
166 419 lt
166 419 mt
168 420 mt
170 421 mt
170 421 lt
171 421 mt
173 422 mt
175 423 mt
175 423 lt
175 423 mt
178 424 mt
180 424 mt
180 425 lt
180 425 lt
183 425 mt
185 426 mt
185 426 lt
185 426 lt
188 427 mt
190 428 mt
190 428 lt
190 428 lt
192 428 mt
195 429 mt
195 429 mt
196 429 lt
197 429 mt
200 430 mt
200 430 mt
201 430 lt
202 431 mt
204 431 mt
205 431 mt
206 431 lt
207 432 mt
209 432 mt
211 432 mt
211 433 lt
212 433 mt
214 433 mt
216 433 mt
216 433 lt
217 433 mt
219 434 mt
221 434 mt
221 434 lt
222 434 lt
224 435 mt
226 435 mt
226 435 mt
227 435 lt
229 435 mt
231 436 mt
232 436 mt
232 436 lt
234 436 mt
236 436 mt
237 437 mt
237 437 lt
238 437 mt
241 437 mt
242 437 mt
243 437 lt
243 437 mt
246 438 mt
247 438 mt
248 438 lt
248 438 mt
251 438 mt
253 439 mt
253 439 lt
253 439 lt
255 439 mt
258 439 mt
258 439 mt
258 439 lt
260 439 mt
263 440 mt
263 440 mt
264 440 lt
265 440 mt
267 440 mt
268 440 mt
269 440 lt
270 440 mt
272 440 mt
274 441 mt
274 441 lt
275 441 mt
277 441 mt
279 441 mt
280 441 lt
280 441 lt
282 441 mt
284 442 mt
284 442 lt
285 442 lt
287 442 mt
289 442 mt
290 442 mt
290 442 lt
292 442 mt
294 442 mt
295 442 mt
296 442 lt
297 442 mt
299 443 mt
300 443 mt
301 443 lt
301 443 mt
304 443 mt
306 443 mt
306 443 lt
306 443 mt
309 443 mt
311 443 mt
311 443 lt
311 443 lt
313 444 mt
316 444 mt
316 444 mt
317 444 lt
318 444 mt
321 444 mt
321 444 mt
322 444 lt
323 444 mt
326 444 mt
327 444 mt
327 444 lt
328 444 mt
330 445 mt
332 445 mt
333 445 lt
333 445 mt
335 445 mt
337 445 mt
338 445 lt
338 445 lt
340 445 mt
343 445 mt
343 445 mt
343 445 lt
345 445 mt
347 445 mt
348 445 mt
349 446 lt
350 446 mt
352 446 mt
353 446 mt
354 446 lt
355 446 mt
357 446 mt
359 446 mt
359 446 lt
359 446 mt
362 446 mt
364 446 mt
364 446 lt
364 446 lt
367 446 mt
369 446 mt
369 446 lt
370 447 lt
372 447 mt
374 447 mt
374 447 mt
375 447 lt
376 447 mt
379 447 mt
380 447 mt
380 447 lt
381 447 mt
384 447 mt
385 447 mt
386 447 lt
386 447 mt
389 447 mt
390 447 mt
391 447 lt
391 447 mt
393 447 mt
396 448 mt
396 448 lt
396 448 lt
398 448 mt
401 448 mt
401 448 mt
402 448 lt
403 448 mt
405 448 mt
406 448 mt
407 448 lt
408 448 mt
410 448 mt
412 448 mt
412 448 lt
413 448 mt
415 448 mt
417 448 mt
417 448 lt
418 448 mt
420 448 mt
422 448 mt
422 448 lt
423 448 lt
425 449 mt
427 449 mt
428 449 mt
428 449 lt
430 449 mt
432 449 mt
433 449 mt
433 449 lt
435 449 mt
437 449 mt
438 449 mt
439 449 lt
439 449 mt
442 449 mt
443 449 mt
444 449 lt
444 449 mt
447 449 mt
449 449 mt
449 449 lt
449 449 lt
452 449 mt
454 449 mt
454 449 mt
455 449 lt
456 449 mt
459 450 mt
459 450 mt
460 450 lt
461 450 mt
464 450 mt
465 450 mt
465 450 lt
466 450 mt
468 450 mt
470 450 mt
471 450 lt
471 450 mt
473 450 mt
475 450 mt
476 450 lt
476 450 lt
478 450 mt
481 450 mt
481 450 mt
481 450 lt
483 450 mt
485 450 mt
486 450 mt
486 450 lt
488 450 mt
490 450 mt
491 450 mt
492 450 lt
493 450 mt
495 450 mt
497 451 mt
497 451 lt
498 451 mt
500 451 mt
502 451 mt
502 451 lt
502 451 lt
505 451 mt
507 451 mt
507 451 lt
508 451 lt
510 451 mt
512 451 mt
512 451 mt
513 451 lt
514 451 mt
517 451 mt
518 451 mt
518 451 lt
519 451 mt
522 451 mt
523 451 mt
524 451 lt
524 451 mt
527 451 mt
528 451 mt
529 451 lt
529 451 mt
531 451 mt
534 451 mt
534 451 lt
534 451 lt
536 451 mt
539 451 mt
539 451 mt
540 451 lt
541 451 mt
544 452 mt
544 452 mt
545 452 lt
546 452 mt
548 452 mt
550 452 mt
550 452 lt
551 452 mt
553 452 mt
555 452 mt
555 452 lt
556 452 mt
558 452 mt
560 452 mt
560 452 lt
561 452 lt
563 452 mt
565 452 mt
566 452 mt
566 452 lt
568 452 mt
570 452 mt
571 452 mt
571 452 lt
573 452 mt
575 452 mt
576 452 mt
577 452 lt
577 452 mt
580 452 mt
581 452 mt
582 452 lt
582 452 mt
585 452 mt
587 452 mt
587 452 lt
587 452 lt
590 452 mt
592 452 mt
592 452 mt
593 452 lt
594 452 mt
594 452 mt
597 452 mt
597 452 mt
598 453 lt
599 453 mt
602 453 mt
603 453 mt
603 453 lt
604 453 mt
607 453 mt
608 453 mt
609 453 lt
609 453 mt
611 453 mt
613 453 mt
614 453 lt
en
%%Page:5 5
star
4 slw
0 trot 19 tsiz 143 597 text 0 sf
(Proton spin fraction carried by quarks) tsho tend
0 trot 19 tsiz 449 597 text 0 sf
(vs. order of QCD pert. theory) tsho tend
0 trot 14 tsiz 232 150 text 4 sf
(1 ) tsho 0 sf
(E142, ) tsho 4 sf
(4 ) tsho 0 sf
(E143, ) tsho 4 sf
(2 ) tsho 0 sf
(SMC-d, ) tsho 4 sf
(3 ) tsho 0 sf
(SMC-p, ) tsho 4 sf
(5 ) tsho 0 sf
(EMC) tsho tend
0 trot 14 tsiz 275 126 text 0 sf
(all ) tsho 1 sf
(DS ) tsho 0 sf
(values evolved to Q) tsho 2 tsubsc (2) tsho 3 tsubsc (=1O GeV) tsho 2 tsubsc
 (2) tsho 3 tsubsc tend
0 trot 22 tsiz 126 393 text 1 sf
(DS) tsho tend
207 563 mt
207 223 lt
207 223 mt
647 223 lt
647 223 mt
647 563 lt
647 563 mt
207 563 lt
212 223 mt
207 223 lt
209 242 mt
207 242 lt
209 262 mt
207 262 lt
209 281 mt
207 281 lt
209 301 mt
207 301 lt
212 320 mt
207 320 lt
209 339 mt
207 339 lt
209 359 mt
207 359 lt
209 378 mt
207 378 lt
209 398 mt
207 398 lt
212 417 mt
207 417 lt
209 437 mt
207 437 lt
209 456 mt
207 456 lt
209 475 mt
207 475 lt
209 495 mt
207 495 lt
212 514 mt
207 514 lt
209 534 mt
207 534 lt
209 553 mt
207 553 lt
0 trot 18 tsiz 168 223 text 0 sf
(0.0) tsho tend
0 trot 18 tsiz 168 320 text 0 sf
(0.2) tsho tend
0 trot 18 tsiz 168 417 text 0 sf
(0.4) tsho tend
0 trot 18 tsiz 168 514 text 0 sf
(0.6) tsho tend
647 223 mt
642 223 lt
647 242 mt
645 242 lt
647 262 mt
645 262 lt
647 281 mt
645 281 lt
647 301 mt
645 301 lt
647 320 mt
642 320 lt
647 339 mt
645 339 lt
647 359 mt
645 359 lt
647 378 mt
645 378 lt
647 398 mt
645 398 lt
647 417 mt
642 417 lt
647 437 mt
645 437 lt
647 456 mt
645 456 lt
647 475 mt
645 475 lt
647 495 mt
645 495 lt
647 514 mt
642 514 lt
647 534 mt
645 534 lt
647 553 mt
645 553 lt
3 slw
239 517 mt
239 427 lt
2 slw
0 trot 18 tsiz 239 472 text 4 sf
(1) tsho tend
3 slw
245 325 mt
245 223 lt
2 slw
0 trot 18 tsiz 245 271 text 4 sf
(4) tsho tend
3 slw
251 373 mt
251 223 lt
2 slw
0 trot 18 tsiz 251 256 text 4 sf
(2) tsho tend
3 slw
257 355 mt
257 223 lt
2 slw
0 trot 18 tsiz 257 287 text 4 sf
(3) tsho tend
3 slw
263 352 mt
263 223 lt
2 slw
0 trot 18 tsiz 263 251 text 4 sf
(5) tsho tend
3 slw
324 509 mt
324 404 lt
2 slw
0 trot 18 tsiz 324 456 text 4 sf
(1) tsho tend
3 slw
330 399 mt
330 278 lt
2 slw
0 trot 18 tsiz 330 338 text 4 sf
(4) tsho tend
3 slw
336 396 mt
336 223 lt
2 slw
0 trot 18 tsiz 336 267 text 4 sf
(2) tsho tend
3 slw
342 411 mt
342 264 lt
2 slw
0 trot 18 tsiz 342 338 text 4 sf
(3) tsho tend
3 slw
348 408 mt
348 223 lt
2 slw
0 trot 18 tsiz 348 299 text 4 sf
(5) tsho tend
3 slw
409 492 mt
409 383 lt
2 slw
0 trot 18 tsiz 409 438 text 4 sf
(1) tsho tend
3 slw
415 427 mt
415 302 lt
2 slw
0 trot 18 tsiz 415 364 text 4 sf
(4) tsho tend
3 slw
421 400 mt
421 223 lt
2 slw
0 trot 18 tsiz 421 270 text 4 sf
(2) tsho tend
3 slw
427 426 mt
427 277 lt
2 slw
0 trot 18 tsiz 427 352 text 4 sf
(3) tsho tend
3 slw
433 423 mt
433 223 lt
2 slw
0 trot 18 tsiz 433 312 text 4 sf
(5) tsho tend
3 slw
494 480 mt
494 364 lt
2 slw
0 trot 18 tsiz 494 422 text 4 sf
(1) tsho tend
3 slw
500 443 mt
500 314 lt
2 slw
0 trot 18 tsiz 500 378 text 4 sf
(4) tsho tend
3 slw
506 402 mt
506 223 lt
2 slw
0 trot 18 tsiz 506 271 text 4 sf
(2) tsho tend
3 slw
512 432 mt
512 283 lt
2 slw
0 trot 18 tsiz 512 357 text 4 sf
(3) tsho tend
3 slw
518 428 mt
518 223 lt
2 slw
0 trot 18 tsiz 518 318 text 4 sf
(5) tsho tend
3 slw
579 472 mt
579 348 lt
2 slw
0 trot 18 tsiz 579 410 text 4 sf
(1) tsho tend
3 slw
585 455 mt
585 322 lt
2 slw
0 trot 18 tsiz 585 389 text 4 sf
(4) tsho tend
3 slw
591 403 mt
591 223 lt
2 slw
0 trot 18 tsiz 591 272 text 4 sf
(2) tsho tend
3 slw
597 436 mt
597 285 lt
2 slw
0 trot 18 tsiz 597 360 text 4 sf
(3) tsho tend
3 slw
603 431 mt
603 223 lt
2 slw
0 trot 18 tsiz 603 321 text 4 sf
(5) tsho tend
3 sls
207 376 mt
647 376 lt
1 sls
207 342 mt
647 342 lt
207 410 mt
647 410 lt
4 sls
4 slw
0 trot 18 tsiz 678 393 text 0 sf
(average:) tsho tend
0 trot 18 tsiz 678 369 text 0 sf
(0.31 + 0.07) tsho tend
0 trot 18 tsiz 715 368 text 0 sf
(_) tsho tend
0 trot 18 tsiz 678 271 text 1 sf
(c) tsho 2 tsubsc 0 sf
(2) tsho 3 tsubsc ( = 1.3) tsho tend
0 trot 18 tsiz 610 77 text 0 sf
(Fig. 5) tsho tend
0 trot 14 tsiz 241 213 text 0 sf
(naive) tsho tend
0 trot 14 tsiz 237 199 text 0 sf
(parton) tsho tend
0 trot 14 tsiz 237 184 text 0 sf
(model) tsho tend
0 trot 18 tsiz 326 199 text 0 sf
(O\050) tsho 1 sf
(a) tsho 0 tsubsc 0 sf
(s) tsho 1 tsubsc 1 thskip 1 thskip (\051) tsho tend
0 trot 18 tsiz 411 199 text 0 sf
(O\050) tsho 1 sf
(a) tsho 0 tsubsc 0 sf
(s) tsho 1 tsubsc 0 thskip 2 tsubsc (2) tsho 3 tsubsc 1 thskip (\051) tsho tend
0 trot 18 tsiz 496 199 text 0 sf
(O\050) tsho 1 sf
(a) tsho 0 tsubsc 0 sf
(s) tsho 1 tsubsc 0 thskip 2 tsubsc (3) tsho 3 tsubsc 1 thskip (\051) tsho tend
0 trot 18 tsiz 581 199 text 0 sf
(O\050) tsho 1 sf
(a) tsho 0 tsubsc 0 sf
(s) tsho 1 tsubsc 0 thskip 2 tsubsc (4) tsho 3 tsubsc 1 thskip (\051) tsho tend
en
%%Trailer
%%DocumentFonts: Times-BoldItalic Symbol PlotSymbol
%%Pages: 5


