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% MW defs
\def\be{\begin{equation}}

\def\eequ{\end{equation}}
\def\endeq{\end{equation}}

\def\bea{\begin{eqnarray}}
\def\eea{\end{eqnarray}}
%
\def\bit{\begin{itemize}}
\def\eit{\end{itemize}}
%
\def\cm{\,{\rm cm}}
\def\GeV{\,{\rm GeV}}
\def\xbj{x_{\rm Bj}}
\def\ycut{y_{\rm cut}}
\def\kperp{k_\perp}
%\def\mjj{M_{jj}}
\def\mjj{M_{\rm jj}}
\def\mjj{M_{\sf jj}}
\def\sumet{\sum E_{T,{\rm \, Breit}}}
\def\avet{\overline{E}_{T}}
\def\avetsq{\overline{E}_T^{\,2}}
\def\etjet{E_{T,{\rm \, jet}}}
\def\etbreit{E_{T,{\rm \, Breit}}}
\def\etaflab{\eta_{\rm forw,\, lab}}
\newcommand{\alps}{\alpha_s}
\newcommand{\alpsq}{\mbox{$\alpha_s^2$ }}
\newcommand{\alpset}{\alpha_s(E_T)}
\newcommand{\alpsmz}{\alpha_s(M_Z)}
\newcommand{\alpsmu}{\alpha_s(\mu_r)}
\newcommand{\alpsqmu}{\alpha_s^2(\mu_r)$}
\newcommand{\ord}{{\cal O}}
\newcommand{\ordalps}{{\cal O}(\alps)}
\newcommand{\ordalpsq}{{\cal O}(\alps^2)}
\newcommand{\epem}{e^+e^-}
\newcommand{\pbarp}{\bar{p}p}
\newcommand{\cndof}{\chi^2 / {\rm n.d.f.}}


%===============================title page=============================

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\newcommand{\TeV}{\rm TeV}
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\begin{document}

\pagestyle{empty}
\begin{titlepage}

\noindent
% {\bf H-UM \& JS: version of \today} \\[.3em] 
Submitted to the 30th International Conference on 
High-Energy Physics ICHEP2000, \\ 
Osaka, Japan, July 2000

%\noindent
%Date: July 13, 2000              \\
%Editors: T. Carli, M. Wobisch   \\
%Referees:  J.B. Dainton, H.-C. Schultz-Coulon \\

\vspace*{3cm}

\begin{center}
  \Large
  {\bf  \boldmath
A Simultaneous, Direct Determination of $\alpha_s$
and the Gluon Density in the Proton in a QCD Fit to DIS Jet Data }

  \vspace*{1cm}
    {\Large H1 Collaboration} 
\end{center}

\begin{abstract}
\noindent
We present the results of a QCD fit to different cross sections
measured in deep-inelastic scattering with the H1 detector 
at HERA.
In a combined fit to inclusive DIS cross sections
and to dijet and inclusive jet cross sections measured in the 
Breit frame, we determine the strong coupling constant
$\alpsmz$ simultaneously with the gluon and the quark densities
in the proton.
%
The result shows a large anticorrelation between $\alpsmz$
and the value of the gluon density at fixed values of the 
momentum fraction $x$.
%
\end{abstract}


\vfill
\begin{flushleft}
  {\bf Abstract: 1000 } \\
  {\bf Parallel session: 3} \\
  {\bf Plenary talk: 11}
\end{flushleft}

\end{titlepage}

\pagestyle{plain}


\section*{Introduction}
\noindent
Deep-inelastic lepton-proton scattering (DIS) experiments
have played a fundamental role in the understanding 
of the structure of the proton and in establishing 
Quantum-Chromodynamics (QCD) as the theory of the strong 
interaction.
%
The inclusive lepton-proton cross section is directly sensitive 
to the quark densities in the proton, but 
gives only indirect information
on the gluon content and on the strong coupling constant $\alps$
via scaling violations of the structure functions.
Observables which are directly sensitive both to $\alps$ and to
the gluon density in the proton are 
the production rates of events in which the final state contains
more than one hard jet (besides the proton remnant).
These multi-jet cross sections can be used to test 
the predictions of perturbative QCD (pQCD)
and allow a direct determination of $\alps$ and the gluon density.



The large center-of-mass energy $\sqrt{s}$ of $300\GeV$ at HERA
allows multi-jet production in DIS to be studied over large regions
of phase space.
The H1 collaboration has presented preliminary measurements of 
the dijet cross section~\cite{wobisch98c,h1glueichep98} 
and the inclusive jet 
cross section~\cite{wobisch99a,h1incljetseps99} in the Breit frame
at large four-momentum transfers
$150 < Q^2 < 5\,000\GeV^2$.
In a QCD fit to the inclusive jet cross section we have 
determined $\alps$ as a function of the transverse jet 
energy $E_T$ in the Breit frame~\cite{h1incljetseps99} 
using parton density parameterizations obtained in global 
fits~\cite{cteq5,mrst99}.
A consistent determination of the  quark and the gluon
densities in the proton has been obtained in a simultaneous 
fit to the dijet cross section~\cite{h1glueichep98} and
the inclusive DIS cross section~\cite{h1highq2} in which
$\alpsmz$ has been taken to be the world average value.







In this paper we present a simultaneous determination
of $\alps$, the gluon and the quark densities in
the proton from a QCD fit to the dijet and the inclusive 
jet cross section and to the inclusive DIS cross section.
We give a brief description of the assumptions and 
methods used in the QCD fit and present the result
as a correlation plot between $\alpsmz$ and the gluon
density at fixed values of $x$.




\section*{Strategy}


% *********************************************************************
% *********************************************************************
%\subsubsection*{The Structure of Jet Cross Sections in perturbative QCD}


In perturbative QCD (pQCD) the cross section of any process 
in deep-inelastic lepton-proton scattering
can be written as a convolution of (process specific) 
perturbative coefficients $c_{a,n}$ with (universal) 
parton density functions $f_{a/p}$ of the proton
%\begin{equation}
\be
\sigma  \, = \,  
\sum_{a,n}  
\; \int_0^1 {\rm d}x \; \alpha_s^n(\mu_r) \;
 c_{a,n}\left(\frac{\xbj}{x}, \mu_r, \mu_f \right) \; f_{a/h}(x,\mu_f) \; .
\label{eq:directint}
%\ee
\end{equation}
%
The sum runs over all parton flavors $a$ and all orders $n$ 
considered in the perturbative expansion.
The integration is carried out over all fractional parton 
momenta $x$.
%
The coefficients $c_{a,n}$ are predicted by pQCD.
They are currently known to next-to-leading order in the
strong coupling constant for the inclusive DIS cross section 
($n=0,1$) and for the dijet and the inclusive jet cross 
section ($n=1,2$)~\cite{zijlstra92}. 
%
%The truncation of the perturbative expansion at a fixed order
%introduces a dependence of the cross section on the choice of 
%the renormalization scale $\mu_r$ and the factorization 
%scale $\mu_f$.
%
In the regions of sufficiently large transverse jet energies
and not too large values of $Q^2$ ($Q^2 < 5\,000\GeV^2$)
the effects from quark masses and from $Z^\circ$ exchange can 
safely be neglected~\cite{wobisch2000a}.
In the approximation of photon induced processes and for massless 
quarks, in each order of $\alps$ the perturbative coefficients 
of the quarks fulfill the relations 
\begin{equation}
c_u = c_c = c_t \; = \; c_{\bar{u}} =  c_{\bar{c}} =  c_{\bar{t}} 
\hskip6mm  \mbox{\small and} \hskip6mm 
c_d = c_s = c_b \; = \; c_{\bar{d}} =  c_{\bar{s}} =  c_{\bar{b}}  \; .
\label{eq:coeff_relation}
\end{equation}
Therefore only three coefficients 
are independent and
the cross section can be described by three independent
parton density functions\footnote{We do not explicitly display 
the dependence on the factorization scale.} 
$xG(x)$, $x\Delta(x)$ and $x\Sigma(x)$ with coefficients
$c_G$, $c_\Delta$ and $c_\Sigma$,
which have to be defined such that
\be
 c_g g(x) \, +\, \sum_a  c_a q_a(x)
\; = \; 
c_G \, G(x) \: +\: c_\Sigma \,\Sigma(x)\: +\: c_\Delta\,\Delta(x) \: .
\end{equation}
%
%We chose these as\footnote{We do not explicitly display here 
%the dependence on the factorization scale.}
We chose these three parton density functions as
\begin{eqnarray}
\mbox{Gluon:} \hskip7mm
  x \, G(x) & \equiv & x \, g(x) \, , \nonumber \\
\mbox{Sigma:} \hskip7mm
  x \, \Sigma(x)  & \equiv & x \, \sum_a \, ( q_a(x) + \bar{q}_a(x) ) \, ,
\nonumber \\
\mbox{Delta:} \hskip7mm
  x \, \Delta(x) & \equiv & x \, 
\sum_a  e_a^2 \; ( q_a(x) + \bar{q}_a(x) ) \, ,
\label{eq:def_pdf}
\end{eqnarray}
where the sums run over all quark flavors $a$ and $e_a$ denotes the 
electrical charge of the corresponding quark.
The three corresponding coefficients are given by linear 
combinations of the single flavor coefficients
%
%\footnote{Using (\ref{eq:coeff_relation}) and 
%the definitions (\ref{eq:def_pdf}) and
%(\ref{eq:def_coeff}) it can easily be verified that
%$
%c_G \, G(x) \: +\: c_\Sigma \,\Sigma(x)\: +\: c_\Delta\,\Delta(x) 
%\; = \; 
% c_g g(x) \, +\, \sum_a  c_a q_a(x)$.}
%
\be
c_G  =  c_{\rm gluon}               \hskip11mm
c_\Sigma  =  1/3 \; (4\, c_d - c_u) \hskip11mm
c_\Delta  =  3 \; (c_u - c_d)   \; .
\label{eq:def_coeff}
\end{equation}


At orders ${\cal O}(\alpha_s^0)$ and ${\cal O}(\alpha_s^1)$
the contributions from different quark flavors are
proportional to their electrical charge squared
(i.e.\  $c_u = 4\, c_d$).
Therefore
the coefficient $c_\Sigma$ in (\ref{eq:def_coeff}) vanishes 
%
%therefore
%at orders ${\cal O}(\alpha_s^0)$ and ${\cal O}(\alpha_s^1)$,
%
and the only quark contributions to the cross sections come from 
$x\Delta(x)$.
The gluon gives contributions 
% to the DIS cross section 
at order ${\cal O}(\alps)$ and higher.
%
$x\Sigma(x)$ starts to contribute at order 
${\cal O}(\alpha_s^2)$ and does therefore not contribute to the 
inclusive DIS cross section up to next-to-leading order.
Table~\ref{tab:pdforders} gives an overview of the orders 
in which the parton densities contribute to the different 
processes (up to NLO).
%
\begin{table}[b]
\centering
%\begin{center}
\begin{tabular}{|l|c|c|}
\hline 
      & \sf LO & \sf NLO \\ 
\hline
$\sigma_{\rm incl.\ DIS}$ & $x\Delta(x)$ & $x\Delta(x), \; xG(x)$ \\
$\sigma_{\rm jets}$  & \,\,  $xG(x), \; x\Delta(x)$ \,\, & 
\,\, $xG(x), \; x\Delta(x), \; x\Sigma(x) $ \,\, \\
\hline
\end{tabular}
%\end{center}
\caption{Overview of the orders at which the parton
density functions contribute to different cross 
sections\label{tab:pdforders}}
\end{table}
%
$x\Sigma(x)$ enters only the jet cross sections via the 
next-to-leading order corrections.
At large $Q^2$ these contributions are, however, small
(4.5\% for the dijet cross section at $150 < Q^2 < 200\GeV^2$,
decreasing to 2\% at $600 < Q^2 < 5000\GeV^2$).
%
In the following we use the parameterization CTEQ5M1 to 
determine this contribution which is not regarded 
as a degree of freedom in the analysis.
This is, however, only a weak assumption which will 
(due to the smallness of the contribution)
not bias any result.

With this approximation
the inclusive DIS cross section and the jet cross section
now depend on three quantities which will be determined
in this analysis:
$\alps$, the gluon density $xG(x)$ and the 
quark density $x\Delta(x)$.
%
To demonstrate the basic sensitivity we write the leading
order cross sections in the symbolic form
%
\bea
\mbox{inclusive DIS cross section:} \hskip8mm 
\sigma_{\rm incl.\, DIS} & \propto &  \Delta    \nonumber \\
\mbox {jet cross sections in DIS:} \hskip20.5mm 
\sigma_{\rm jet} & \propto & 
\alps \cdot ( c_G  \, G \; + \; c_\Delta \, \Delta  )      \, .
\label{eq:fiteq}
\eea
%
These relations make clear
that in DIS a direct determination of either $\alps$ or the 
gluon density can never be performed without considering
the correlation with the other quantity.
The quark densities
are directly constrained by the inclusive DIS cross section.
Using the jet cross section we can then determine either 
% one of
the gluon density or $\alps$.
For a simultaneous determination of both additional information
is needed, e.g.\   a measurement of the jet cross section in a 
different kinematic region where the perturbative prediction is 
given by
\be
\sigma'_{\rm jet} \; \propto \; 
\alps \cdot ( c'_g  \, g \; + \; c'_\Delta \, \Delta )      \hskip15mm
\mbox{with} \hskip15mm  \frac{c'_g}{c'_\Delta} \; \neq \; 
\frac{c_g}{c_\Delta} \, .
\label{eq:fiteq2}
\end{equation}
This is in fact the case for the inclusive jet and the
dijet cross section in different regions of $Q^2$, since 
the gluon induced fraction of the cross section 
decreases towards higher $Q^2$.




% *********************************************************************
% *********************************************************************
\section*{Fitting Technique}

%\subsubsection*{Data Sets and Theoretical Choices}

A determination of theoretical parameters can only be performed
in phase space regions where theoretical predictions are reliable.
We therefore  restrict the QCD analysis to the region where 
NLO corrections to the jet cross sections are reasonably small
with $k$-factors below $1.4$.
This is the region of $Q^2 > 150\GeV^2$.
The QCD analysis is using the inclusive jet cross section
presented in~\cite{h1incljetseps99} and the dijet cross section 
presented in~\cite{h1glueichep98}.
%
We include data on the (reduced) inclusive DIS cross section 
to exploit their sensitivity to the quark densities in the proton.
We use a subsample of our recently published 
measurement~\cite{h1highq2} in the range 
$150 \le Q^2 \le 1\,000\GeV^2$.
Since the present analysis uses the same experimental techniques
the effects of the point to point correlated experimental 
uncertainties can be fully taken into account.


The fit of the theoretical parameters is performed in a $\chi^2$ 
minimization using the program MINUIT~\cite{minuit}.
%
The definition of $\chi^2$~\cite{zomer95} fully takes into 
account all correlations of experimental uncertainties 
between the data points and the correlations of uncertainties 
between the theoretical predictions.
This $\chi^2$ definition has also been used in 
recent global data analyses~\cite{botje99,zomer99} and
in a previous H1 publication~\cite{h1compositeness99}.

In the fitting procedure the perturbative QCD predictions
in NLO for the inclusive DIS cross section are directly compared
to the data, 
while the NLO predictions for the jet cross sections are
divided by the hadronization corrections before they are compared 
to the jet data
\begin{eqnarray}
\sigma^{\rm H1}_{\rm incl. \,DIS}  & \longleftrightarrow &
          \sigma^{\rm NLO}_{\rm incl. \,DIS}  \nonumber \\
\sigma^{\rm H1}_{\rm jet}  & \longleftrightarrow &
          \sigma^{\rm NLO}_{\rm jet} \cdot
c^{-1}_{\rm hadronization}
 \hskip10mm \mbox{with}  \hskip5mm 
c_{\rm hadronization} = 
\frac{\sigma_{\rm jet}^{\rm parton}}{\sigma_{\rm jet}^{\rm hadron}}
 \; .  \nonumber 
\end{eqnarray}
The hadronization corrections are determined as described
in~\cite{h1glueichep98,h1incljetseps99}     
using the average value from
the model predictions by HERWIG, LEPTO and ARIADNE.
The uncertainty from the model and the parameter dependence
of these predictions is always below 3\%~\cite{wobisch99b}.
We take the uncertainty in the matching of the parton level
(parton cascade and NLO calculation)
into account by increasing the quoted uncertainty in those regions
where the hadronization corrections are large.
In detail, we define the uncertainty of the hadronization 
correction for each bin of the jet cross sections to be half 
the size of the correction, but at least 3\%.
This uncertainty is assumed to be correlated between the
theoretical predictions for all data points.


The renormalization scale $\mu^2_r$ in the NLO calculation
is identified with the process specific hard scales in both 
processes.
The inclusive DIS cross section is evaluated at $\mu^2_r = Q^2$ 
and the jet cross sections are evaluated at $\mu^2_r = E^2_T$
(the transverse jet energy in the Breit frame).
The strong coupling constant $\alps(\mu_r^2)$ is parameterized 
in terms of its value at the scale $\mu^2_r = M^2_Z$ using the 
numerical solution of the renormalization group equation 
in 4-loop accuracy\footnote{It has been checked
% It has been demonstrated~\cite{wobisch2000a} 
that in the range of scales considered in this analysis 
$7\GeV < \mu_r < M_Z$ the differences
between the 2-, 3- and 4-loop solutions are always 
below 3 per mil.}~\cite{4loop,4loopmatch}.



In principle, the arguments invoked in the choice of the 
renormalization scale $\mu_r$ also apply to the 
factorization scale $\mu_f$ for the inclusive DIS cross section 
and for the jet cross section.
However, we make a different choice for the following reasons.
%
We have combined the different parton flavors into
three independent parton density functions $xG(x,\mu_f)$, $x\Delta(x,\mu_f)$ 
and $x\Sigma(x,\mu_f)$.
These three parton densities are, however, only independent as 
long as no evolution between different scales $\mu_f$ is performed.
The evolution of the gluon density is coupled to the evolution of 
$x\Sigma(x,\mu_f)$.
Furthermore, since $x\Delta(x,\mu_f)$ is not an eigenstate of the DGLAP 
evolution operators the evolution requires its decomposition into a
non-singlet and a singlet (i.e.\  $x\Sigma(x,\mu_f)$).
This introduces an additional dependence between the 
quark densities.
%
To avoid mixing between the different parton densities
we do not evolve the parton distributions to different scales
but perform the perturbative calculations at a fixed value of the 
factorization scale $\mu^2_f = \mu^2_0$.
%
The jet cross sections are sensitive to the parton distributions
in the $x$-range of  $0.008 \lesssim x \lesssim 0.3$.
In this $x$-range the factorization scale dependence of the parton 
density functions is small.
In a next-to-leading order calculation
the remaining $\mu^2_f$ dependence given by the DGLAP 
evolution equations is largely compensated by
a corresponding term 
% $\propto \alpha_s \ln(\mu^2_f/\mu^2_0)$
in the perturbative coefficients. 
The perturbative cross sections therefore depend only weakly
on the choice of the factorization scale.
The difference between using a fixed factorization scale $\mu^2_0$
and performing the full DGLAP evolution at a scale $\mu^2_f$
is of higher order in $\alps$. 
%and enters through terms of order 
%${\cal O}(\alpha^2_s \ln^2(\mu^2_f/\mu^2_0)$.


If the scale $\mu^2_f$ is close to the fixed scale 
$\mu^2_0$ (such that $\ln(\mu^2_f/\mu^2_0) \lesssim 1$)
these higher order terms are small.
%
We therefore decide to use a fixed value of the factorization scale
of the order of the average transverse jet energies
in the dijet and the inclusive jet cross section
$\mu^2_f = \mu^2_0 = 200\GeV^2 \simeq \langle E^2_T \rangle$.
The subsample of the (reduced) inclusive DIS cross section
$150 \le Q^2 \le 1\,000\GeV^2$ has been chosen such that
the four-momentum transfer squared is also approximately
of the same size $Q^2 \simeq \mu^2_0 = 200\GeV^2$.

The renormalization and the factorization scale dependence
of the cross sections is considered as a correlated
theoretical uncertainty.
Both scales are (separately) varied by a factor $x_\mu$ 
around their nominal values $\mu^2_0$ in the range 
$x_\mu= \{ \frac{1}{4},4\}$ and the ratios
$\frac{\sigma_{\rm NLO}(x_\mu \cdot \mu_0^2) }{\sigma_{\rm NLO}(\mu^2_0)}$
are taken as the corresponding uncertainties.
Together with the uncertainty from the hadronization
corrections they constitute the quoted theoretical 
uncertainty of the fit result.


During the $\chi^2$ minimization procedure in the fit the 
NLO calculations of the jet cross sections have to be performed 
iteratively for different values of $\alpsmz$ and for different 
parton density functions (the number of calculations
used to obtain the present results and to study
their stability is in the order of one million).
%
% -> to remember: 96 points on contour = 54093 iterations!
%
Since standard computations of NLO jet cross sections are time 
consuming we use the method~\cite{wobisch2000a} of 
pre-convoluting the perturbative coefficients with suitably 
defined functions which can then be folded with 
the parton densities and $\alps$ for the 
fast computation of the NLO cross section.
The perturbative coefficients are calculated using the
the program DISENT~\cite{disent}.
The NLO calculations are performed in the $\overline{\rm MS}$
scheme for $n_f =5$.




% ********************************************************************
% ********************************************************************
\section*{QCD Fit}




A complete description of jet production in DIS in terms of our present
 quantitative level of understanding of hadronic physics, namely NLO pQCD,
 is only obtained if the cross sections can be used to determine
 simultaneously {\em both} the appropriate QCD parameters (in this case
 $\alpha_s$) {\em and} the inherently incalculable proton pdfs. 
 We have attempted such a determination, and thereby demonstrated the
 extent to which such an approach can be used.
%
%In the previous two parts of the QCD analysis we have either determined
%$\alpsmz$ or the gluon density while the respective other parameter was 
%fixed and taken from external input (world average or global fits).
We perform a simultaneous fit of the parton densities
and $\alpsmz$ using 
the inclusive DIS cross section, the inclusive jet cross section
${\rm d}^2 \sigma_{\rm jet} / {\rm d}E_T {\rm d}Q^2$ and the dijet cross 
section ${\rm d}^2 \sigma_{\rm dijet} / {\rm d}\xi {\rm d}Q^2$
(both measured with the inclusive $\kperp$ algorithm).
%
The gluon and the quark distributions are parameterized by
\be
xP(x)  = A \; x^b \; (1-x)^c \; (1+dx)      \label{eq:pdfpara}
\end{equation}
where $xP(x)$ stands for $xG(x)$ or $x\Delta(x)$. 
%
The simultaneous fit yields $\cndof = 61.10/104$ and a result
for the quark distributions identical to the one obtained in 
the fit of the gluon density with a constrained 
$\alpsmz$ (presented in~\cite{h1glueichep98}).
The results of this simultaneous fit are displayed in 
Fig.~\ref{fig:contour} as a
correlation plot between $\alpsmz$ and the gluon density 
evaluated at four different values of $x=0.01,\,0.02,\,0,04,\,0.1$
which lie in the range where the jet cross sections are sensitive.
The central fit result is indicated by the full marker
and the error ellipse is the contour along which
the $\chi^2$ of the fit is by one larger than the minimum 
(including experimental and theoretical uncertainties).
The ellipticity of the contours indicate that our data
%The contour is of a narrow and prolate shape
%indicating that our data 
are very sensitive to the product
$\alps \cdot xg(x)$ but do not yet allow a determination
of both parameters simultaneously with useful precision.


Also included in Fig.~\ref{fig:contour} are the results 
from global fits.
All of these results are within the contour
except for GRV98~\cite{grv98} (at $x<0.04$) which use
a relatively small value of $\alpsmz = 0.114$.


The stability of the results in  Fig.~\ref{fig:contour} 
has been tested by using different parameterizations
of the parton density functions (involving five parameters).
Fits have been performed excluding either the low
($Q^2 < 200\GeV^2$) or the high ($Q^2>600\GeV^2$) 
$Q^2$  data.
Although the fits give consistent central results, the 
high $Q^2$ data is needed to make a stable determination
of the contour of the ellipsoid.
%Furthermore fits to subsets of the data have been performed 
%where data are excluded, either at $Q^2 < 200\GeV^2$
%or $Q^2>600\GeV^2$.
%While both fits give consistent central results, the latter
%fit is not stable when performing the exact calculation of 
%the points along the contour of the ellipsoid.
This indicates that the data at high $Q^2$ are of special 
importance in this combined fit, due to their smaller
theoretical uncertainties.


\clearpage
\pagestyle{empty}




\begin{figure}
\centering
\epsfig{file=H1prelim-00-134.fig1.eps,width=12.5cm}
\caption{The correlation of the fit results for $\alpha_s(M_Z)$ 
and the gluon density at four different values of $x$,
determined in a simultaneous QCD fit to the inclusive
DIS cross section, the inclusive jet cross section and 
the dijet cross section. 
The jet cross sections are measured using the inclusive 
$\kperp$ jet algorithm.
The error ellipses include the experimental and the 
theoretical uncertainties.}
\label{fig:contour}
\end{figure}


\clearpage


%\bibliography{mawo}

\begin{thebibliography}{10}

\bibitem{wobisch98c}
{M.~Wobisch}{,}
\newblock proceedings of the 6th International Workshop on Deep Inelastic
  Scattering and QCD (DIS98), Brussels (1998).

\bibitem{h1glueichep98}
{H1 Collaboration}{,}
\newblock Measurement of Dijet Cross Sections in Deep-Inelastic Scattering at
  HERA and a Direct Determination of the Gluon Density in the Proton,
  Contributed paper 520 to the 29th International Conference on High-Energy
  Physics (ICHEP 98), Vancouver, Canada, 23-29 July (1998) \\
  http://www-h1.desy.de/psfiles/confpap/vancouver98/abstracts/520-carli-paper.%
ps.

\bibitem{wobisch99a}
{M.~Wobisch}{,}
\newblock proceedings of the 7th International Workshop on Deep Inelastic
  Scattering and QCD (DIS99), Nucl. Phys. B (Proc. Suppl) 79 (1999) 478.

\bibitem{h1incljetseps99}
{H1 Collaboration}{,}
\newblock Determination of the Strong Coupling Constant from the Inclusive Jet
  Cross Section in Deep-Inelastic Positron Proton Collisions at HERA,
  Contributed paper 157 to the International Europhysics Conference on High
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\end{document}

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