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\noindent
\begin{center}
%{\it {\large version of \today}} \\[.3em] 
\begin{small}
\begin{tabular}{llrr}
%Submitted to & \multicolumn{3}{r}{\footnotesize Electronic Access: {\it http://www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em] \hline 
%Submitted to & \multicolumn{3}{r}{\footnotesize {\it www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em] \hline 
Submitted to & & &
\epsfig{file=/h1/www/images/H1logo_bw_small.epsi
,width=2.cm} \\[.2em] \hline
                & & & \\
\multicolumn{4}{l}{{\bf
                International Europhysics Conference 
                on High Energy Physics, EPS03},
                July~17-23,~2003,~Aachen} \\
                (Abstract {\bf 111} & Parallel Session & {\bf 4}) & \\
                & & & \\
\multicolumn{4}{l}{{\bf
                XXI International Symposium on
                Lepton and Photon Interactions, LP03},
                August~11-16,~2003,~Fermilab} \\
                & & & \\
                \hline
 & \multicolumn{3}{r}{\footnotesize {\it
    www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em]
\end{tabular}
\end{small}
\end{center}
\vspace*{2cm}

\begin{center}
  \Large
  {\bf 
Two-Jet and Three-Jet Differential Event Shapes in Deep-Inelastic
Scattering
}

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

\begin{abstract}
\noindent
Deep-inelastic $ep$ scattering data, taken with the H1 detector at HERA and
corresponding to an integrated luminosity of $112~\pb^{-1}$, are used to study
the differential distributions of event shape variables. These include
two-jet event shapes (thrust, jet broadening, jet mass and the $C$-parameter),
three-jet event shapes (out-of-event-plane momentum and azimuthal correlation)
as well as two, three and four jet rates. The four-momentum
transfer $Q$ is taken to be the relevant energy scale and ranges 
between $14~\GeV$
and $200~\GeV$. Fits are performed to the two-jet event shape distributions 
using next-to-leading order QCD predictions, matched to a
leading logarithmic resummation and power law corrections to account for
hadronisation effects. The three-jet event shapes and jet rates are compared
with QCD calculations and Monte Carlo models. 

\end{abstract}

\end{titlepage}

\pagestyle{plain}

\section{Introduction}
Event shapes are designed to study QCD by measuring properties of the flow of hadronic energy-momentum.
Measurements of mean values and differential distributions have been carried out at $ep$ \cite{Adloff:1997gq,Adloff:1999gn}
 as well at $e^+e^-$ \cite{MovillaFernandez:1999yn,Abdallah:2002xz} colliders. 
The description of these infrared-collinear safe observables with fixed order calculations faces two difficulties. Firstly, 
non-perturbative hadronization effects can be large, even at formally perturbative scales. These effects can be addressed with
power corrections proportional to $1/Q$\cite{Dokshitzer:1997ew}. Secondly, 
the convergence of the perturbative series at low values of the event shape variables is very poor,
making a resummation to all orders in $\alpha_s$ necessary.

Results on the analysis of mean 
values of event shape variables have been published by the H1 Collaboration
\cite{Adloff:1999gn}. These results give support to the concept of power corrections in the approach by Dokshitzer, Webber et al.
 However, a large spread in the fitted values for $\alpha_s$ lead to the conclusion that higher order QCD corrections are needed.

Resummed NLL calculations, matched to NLO, have recently become available for many of the studied observables\cite{Dasgupta:2002dc}. Here, we
 revisit the topic with a larger data sample and improved data reconstruction and correction techniques. Moreover it is now possible to study
the whole spectra instead of only the mean values.
 Additional event shape variables are investigated, which are sensitive to 3-jet production, and where resummed, matched calculations
are near to completion\cite{Banfi:2001ci}. Therefore in total ten event shape variables are studied. 
A QCD analysis is presented, based on the five variables for which resummed and matched calculations are available.

\section{Event Shape Variables}
Hadronic final states in deep-inelastic $ep$ scattering offer excellent possibilities for the study of the predictions of 
QCD over a wide range of momentum transfer $Q$ in a single experiment.
A suitable frame in DIS is the Breit frame, which divides the event into hemispheres corresponding to the proton remnant and the hadronic final state evolving from 
the struck parton. The definitions of the event shapes treat the hadrons as massless.

Two kinds of 1-thrust,  $\tau$ and $\tau_c$, the jet broadening $B$, the jet mass $\rho$ and the $C$ parameter are
defined for the particles in the current hemisphere (CH) alone, corresponding to a cut on the pseudorapidity in the Breit frame of $\eta<0$.
 The energy in the current hemisphere has to exceed 10\% of the total hadronic energy to ensure infrared safety.
The definitions of $\tau$ and $B$ make explicit use of the virtual boson axis, while the others do not, as is the case for 
their counterparts in $e^+e^-$ reactions. The exact definitions of these event shapes can be found in \cite{Adloff:1997gq}.

From the point of view of a fixed order calculation, all five of these event shape variables may be labelled ``2-jet variables'' because, when 
neglecting hadronization, at least two partons in the final state are needed to obtain non-trivial values.
Therefore programs like DISENT and
DISASTER++, which calculate 2-jet cross sections to next to leading order in $\alpha_s$, are suitable for making predictions 
 for this class of event shapes.

In the case of 3-jet event shapes, at least two emissions in addition to the struck quark are needed before 
these observables can be greater than zero. Examples of  3-jet event shapes for which matched resummed calculations are soon expected
are the out-of-event-plane
momentum $K_{\textrm{out}}$ and the azimuthal correlation $\chi$. These observables exhibit a rich colour and geometry dependence\cite{Banfi:2001ci}.
The definition of $K_{\textrm{out}}$ is taken from \cite{Banfi:2001ci}, the definition of $\chi$ from \cite{Banfi:2002vw}.

The out-of-event plane momentum is defined as
\begin{displaymath}
K_{\textrm{out}}={\sum_h}' |p_h^{\textrm{out}}|.
\end{displaymath}
Here $p_h^{\textrm{out}}$ is the out-of-plane momentum of the hadron $h$ with the event plane formed by the proton
momentum $\vec P$ in the Breit frame and the unit vector $\vec n$ which enters the definition of thrust major:
 \begin{displaymath}
T_M=\max_{\vec n}\frac{1}{Q}{\sum_h}' |\vec p_h\cdot \vec n|,\qquad \vec n\cdot \vec P=0 \ .
\end{displaymath}
To avoid measurements in the beam region, the sum indicated by ${\sum_h}'$ extends over all hadrons with pseudo-rapidity  $\eta$ in the Breit frame
 less than 3. The restriction to only the current hemisphere ($\eta<0$), as for the 2-jet shapes, would be too restrictive in this case, because of the
 extended phase space available for three partons. For the reasons
discussed in \cite{Banfi:2001ci}, only events with $p_t\sim Q$ should be selected, which is accomplished by a cut on the (2+1)-jet
resolution $y_2$ defined by the $k_t$ clustering algorithm: $0.1<y_2<2.5$.
Results are presented in terms of $K_{\textrm{out}}/Q$. 

The azimuthal correlation between the hadrons labelled $h$ and $i$ is defined as
\begin{displaymath}
\chi=\pi-|\phi_h-\phi_i| \ ,
\end{displaymath}
where the observable is constructed by summing over all hadron pairs with a weight
\begin{displaymath}
w=\frac{p_{th}p_{ti}}{Q^2} \ .
\end{displaymath}
The azimuth in the Breit frame of hadron $h$ is denoted by $\phi_h$.
This is the only variable
studied which is not a simple differential cross section. 
In this case a single event contributes not only one value $\chi$ to the differential distribution, but instead every pair of hadrons enters with a weight $w$.

Another class of event shapes, the jet rates,  makes use of a jet algorithm. The jet definition used is the $k_t$ clustering algorithm \cite{Catani:1992zp}.
The jet rate $y_n$ is then defined as the value of the cut parameter $y_{\textrm{cut}}$, introduced
in the jet algorithm, at which the transition from ($n$ +1)-jets to ($n$)-jets takes place.
Since the proton remnant is explicitly treated by the jet algorithm, all hadrons of both hemispheres enter the calculation. 
Logarithms of the jet rates $y_2$, $y_3$ and $y_4$ are presented here.
Up to now no resummed calculations and no power corrections are available. However, jet rates are typically subject to only small hadronization
corrections. These corrections have been estimated with the RAPGAP event generator and, in the case of $y_2$ and $y_3$,  applied on top of a
NLO calculation carried out with NLOJET++, to allow for the comparison with the data.

\section{Data Sample and Analysis Methods}
The analysis is based on an inclusive neutral current DIS data sample.
The data cover a large kinematic phase space of \mbox{$14~\GeV<Q<200~\GeV$} in 4-momentum transfer and \mbox{$0.1<y<0.7$} in the inelasticity $y$. 
Seven bins in $Q$ are defined,see table~\ref{bintable}.
\begin{table}[htb]
\begin{center}
\begin{tabular}{|l||l|l|l|l|l|l|l|}
\hline
\# of $Q$ bin &1&2&3&4&5&6&7\\
\hline
lower bound [$\GeV$]&14&16&20&30&50&70&100\\
\hline
upper bound [$\GeV$]&16&20&30&50&70&100&200\\
\hline
\end{tabular}
\end{center}
\caption{Definition of the binning in momemtum transfer $Q$.}
\label{bintable}
\end{table}
A Bayesian unfolding algorithm\cite{D'Agostini:1994zf} is used to account for detector effects, while 
QED radiation corrections are applied using HERACLES\cite{Kwiatkowski:1990es}.
This data correction procedure is performed separately for three data samples:
\begin{itemize}
\item[1] $p_P=820~\GeV$, $\sqrt{s}\simeq 300~\GeV$, $\ell=e^+$, $\mathcal{L}_{\textrm{int}}=33~\pb^{-1}$
\item[2] $p_P=920~\GeV$, $\sqrt{s}\simeq 318~\GeV$, $\ell=e^-$, $\mathcal{L}_{\textrm{int}}=13~\pb^{-1}$
\item[3] $p_P=920~\GeV$, $\sqrt{s}\simeq 318~\GeV$, $\ell=e^+$, $\mathcal{L}_{\textrm{int}}=66~\pb^{-1}$
\end{itemize}
with $p_P$ being the proton beam momentum and $\ell$ the lepton type.
The unfolded distributions from the three samples are all compatible with each other within errors. Sets 1 and 3 are
 combined by calculating for all bins of the unfolded distributions
 the luminosity weighted averages. 
% This way the resulting mean values of $Q$ and $x$ for the seven Q bins are slightly modified.
%The effective $ep$ centre-of-mass energy of the combined set is then $\sqrt{s}=313~\GeV$.

One is then left with two data sets, one for each lepton charge,
 which make up the basic result of the experimental measurement. In general, small differences
in the event shape distributions between these two data sets are expected, because of weak contributions to the cross section.
The different quark coupling of the $Z^0$ compared to the photon can be thought of as modifying the correlation 
betweeen the propagator 
``direction'' and the quark directions\cite{privsalam}.
Unfortunately, the full calculation of these effects has not yet been carried out. Hence we can only perform QCD fits with calculations for photon
exchange. The  $e^+$ and $e^-$ results are thus averaged, appropriately 
weighted such that part of the
$Z^0$ contribution cancels.
 The much smaller integrated luminosity of the $e^-$ data enlarges the statistical error of the result
due to the cross section weighting. However, for the higher $Q$-bins, which are statistically limited, this effect is partly cancelled because of
the higher inclusive cross section for $e^-p$ scattering. 
The  mean values of $Q$ and $x$ are slightly modified by the combination procedure, giving the final values listed in table~\ref{xQtable}. The effective centre-of-mass energy of 
\begin{table}[htb]
\begin{center}
\begin{tabular}{|c||l|l|l|l|l|l|l|}
\hline
\# of $Q$ bin &1&2&3&4&5&6&7\\
\hline
$\mean{Q}/\GeV$&14.92& 17.74& 23.76& 36.85& 57.58& 80.52&115.57\\
\hline
$\mean{x}$&0.00841&0.0118&0.0209&0.0491&0.116&0.199&0.323\\
\hline
\end{tabular}
\end{center}
\caption{Mean momentum transfer $Q$ and Bjorken $x$ for the seven $Q$ bins of the final distributions.}
\label{xQtable}
\end{table}
the final combined set is $\sqrt{s}=316~\GeV$.

To estimate the experimental systematic error, several studies are carried out. The energy scales of the calorimeters are shifted,
the fraction of the recontructed hadronic energy contributed by the tracking devices is varied and two different Monte Carlo models are used for unfolding.
In addition, an estimate of an intrinsic bias in the Bayesian unfolding is determined. The errors from the different contributions are
added in quadrature.  

\section{Theoretical Calculations and Fits for 2-jet Variables}
A sample of $10^9$ DISASTER++ events was generated with the DISPATCH\cite{Dasgupta:2002dc} program, making use of the CTEQ5M1\cite{Lai:1999wy} 
parton density functions. The resummation, matched to NLO and the power corrections, is applied with DISRESUM\cite{Dasgupta:2002dc}.
The matching scheme for each variable is chosen to result in the lowest $\chi^2$ in the fits to the data.
Thus for the jet broadening and the $C$-parameter, ln~$R$ matching is utilized, whereas for both versions of thrust and the jet mass, the modified  
ln~$R$ matching is used. For an explanation of the matching see\cite{Dasgupta:2002dc}.

The distributions depend on two free parameters: $\alpha_s(m_{Z})$ the strong coupling constant at the $Z^0$ mass and $\bar \alpha_0(m_I=2~\GeV)$,
the effective coupling of the power correction at an infrared matching scale, chosen to be $2~\GeV$ by convention.
Both parameters are simultaneously fitted for an event shape variable.
Bins for which the theoretical calculations are expected to be questionable
are omitted from the fit.  
The definition of $\chi^2$ for the fit takes into account the bin migrations due to limited detector resolution by using a correlation matrix
which is calculated by the Bayesian unfolding algorithm. The experimental systematic errors are treated as uncorrelated between the data points.\\

\section{Results}
The corrected measured distributions for thrust, jet broadening, 
the $C$-parameter and jet mass are shown in figures~\ref{tau}-\ref{Rhoe},
together with the fitted theory prediction. The theoretical predictions are
marked with dashed lines for bins which were not included in the fit.
A good description of the data by the QCD prediction is evident for the higher values of $Q$, while for lower
$Q$ the distributions are not always well described.

The results for $\bar \alpha_0$ and $\alpha_s$ in the form of 1$\sigma$ contours 
are given in fig.~\ref{ellipses}.
For comparison a determination of the world
average value and error of $\alpha_s$\cite{Bethke:2000ai} is shown as a band.
A negative correlation coefficient between $\alpha_s$ and $\alpha_0$ is found for all variables. The universal non-perturbative
parameter $\bar \alpha_0$ is confirmed to be 0.5 at the 10\% level, in agreement with 
previous analysis in $ep$ scattering\cite{Adloff:1999gn},  which used only the mean values of the event shape variables.
In comparison to earlier analyses of mean values in DIS, a smaller spread in $\alpha_s$ is observed.
The 1$\sigma$ contours correspond to the statistical and experimental systematic uncertainties. In addition, the  theoretical error is sizeable,
mainly due to uncertainty of the renormalization scale. This theoretical error is typically around 5\% for
both $\bar \alpha_0$ and $\alpha_s$ and is therefore at least as large as the experimental error.

Figures~\ref{Y2}-\ref{Y4} show the distributions of the 2-jet, 3-jet and 4-jet rate, figures \ref{Chi} and \ref{Kout} the distributions
of the 3-jet event shapes $K_{\textrm{out}}$ and $\chi$. 
For the jet rates and the 3-jet event shapes, no fits were performed up to now.
Results from NLOJET++ give a good description of $y_2$ and $y_3$ for higher values of $Q$.
The jet rate $y_4$ and the 3-jet event shapes are well described by the RAPGAP Monte Carlo event generator using LO matrix elements with parton showers. 

\section{Conclusion}
It has been shown earlier\cite{Adloff:1999gn} that power corrections are applicable in the describtion of the non-perturbative hadronization
of event shape mean values.
With the present analysis we extend the analysis to the whole differential distributions. 
Theory predictions based on resummed terms matched with fixed order calculations and power corrections, which are presented
for  thrust, jet broadening, the $C$-parameter and jet mass, describe the data well. Fits of the free parameters of these calculations,
 $\alpha_s$ and $\bar \alpha_0$  lead to consistent results.
The completion of the generalized resummation program, which is currently underway\cite{Banfi:2003je}, is eagerly awaited for
the $y_2$, $y_3$, $K_{\textrm{out}}$ and $\chi$ variables.


% \cleardoublepage
\begin{thebibliography}{99}

%\cite{Adloff:1997gq}
\bibitem{Adloff:1997gq}
C.~Adloff {\it et al.}  [H1 Collaboration],
%``Measurement of event shape variables in deep inelastic e p scattering,''
Phys.\ Lett.\ B {\bf 406} (1997) 256
[hep-ex/9706002].
%%CITATION = HEP-EX 9706002;%%


%\cite{Adloff:1999gn}
\bibitem{Adloff:1999gn}
C.~Adloff {\it et al.}  [H1 Collaboration],
%``Investigation of power corrections to event shape variables measured in  deep-inelastic scattering,''
Eur.\ Phys.\ J.\ C {\bf 14} (2000) 255. 
Erratum-ibid.\ C {\bf 18} (2000) 417
[hep-ex/9912052].
%%CITATION = HEP-EX 9912052;%%

%\cite{MovillaFernandez:1999yn}
\bibitem{MovillaFernandez:1999yn}
P.~A.~Movilla Fernandez, O.~Biebel and S.~Bethke,
%``Tests of power corrections to event shape distributions from e+ e-  annihilation,''
[hep-ex/9906033].
%%CITATION = HEP-EX 9906033;%%

%\cite{Abdallah:2002xz}
\bibitem{Abdallah:2002xz}
J.~Abdallah {\it et al.}  [DELPHI Collaboration],
%``A study of the energy evolution of event shape distributions and their means with the DELPHI detector at LEP,''
CERN-EP-2002-082.
%\href{http://www.slac.stanford.edu/spires/find/hep/www?r=cern-ep-2002-082}{SPIRES entry}

%\cite{Dokshitzer:1997ew}
\bibitem{Dokshitzer:1997ew}
Y.~L.~Dokshitzer and B.~R.~Webber,
%``Power corrections to event shape distributions,''
Phys.\ Lett.\ B {\bf 404} (1997) 321
[hep-ph/9704298].
%%CITATION = HEP-PH 9704298;%%

%\cite{Kwiatkowski:1990es}
\bibitem{Kwiatkowski:1990es}
A.~Kwiatkowski, H.~Spiesberger and H.~J.~Mohring,
%``Heracles: An Event Generator For E P Interactions At Hera Energies Including Radiative Processes: Version 1.0,''
Comput.\ Phys.\ Commun.\  {\bf 69} (1992) 155.
%%CITATION = CPHCB,69,155;%%



%\cite{Dasgupta:2002dc}
\bibitem{Dasgupta:2002dc}
M.~Dasgupta and G.~P.~Salam,
%``Resummed event-shape variables in DIS,''
JHEP {\bf 0208} (2002) 032
[hep-ph/0208073].
%%CITATION = HEP-PH 0208073;%%

%\cite{Banfi:2001ci}
\bibitem{Banfi:2001ci}
A.~Banfi, G.~Marchesini, G.~Smye and G.~Zanderighi,
%``Out-of-plane QCD radiation in DIS with high p(t) jets,''
JHEP {\bf 0111} (2001) 066
[hep-ph/0111157].
%%CITATION = HEP-PH 0111157;%%

%\cite{Banfi:2002vw}
\bibitem{Banfi:2002vw}
A.~Banfi, G.~Marchesini and G.~Smye,
%``Azimuthal correlation in DIS,''
JHEP {\bf 0204} (2002) 024
[hep-ph/0203150].
%%CITATION = HEP-PH 0203150;%%

%\cite{Catani:1992zp}
\bibitem{Catani:1992zp}
S.~Catani, Y.~L.~Dokshitzer and B.~R.~Webber,
%``The K-perpendicular clustering algorithm for jets in deep inelastic scattering and hadron collisions,''
Phys.\ Lett.\ B {\bf 285} (1992) 291.
%%CITATION = PHLTA,B285,291;%%

%\cite{D'Agostini:1994zf}
\bibitem{D'Agostini:1994zf}
G.~D'Agostini,
%``A Multidimensional unfolding method based on Bayes' theorem,''
Nucl.\ Instrum.\ Meth.\ A {\bf 362} (1995) 487.
%%CITATION = NUIMA,A362,487;%%

%\cite{Bethke:2000ai}
\bibitem{Bethke:2000ai}
S.~Bethke,
%``Determination of the QCD coupling alpha(s),''
J.\ Phys.\ G {\bf 26} (2000) R27
[hep-ex/0004021].
%%CITATION = HEP-EX 0004021;%%

%\cite{Graudenz:1997gv}
\bibitem{Graudenz:1997gv}
D.~Graudenz,
%``DISASTER++ version 1.0,''
[hep-ph/9710244].
%%CITATION = HEP-PH 9710244;%%

%\cite{Lai:1999wy}
\bibitem{Lai:1999wy}
H.~L.~Lai {\it et al.}  [CTEQ Collaboration],
%``Global {QCD} analysis of parton structure of the nucleon: CTEQ5 parton  distributions,''
Eur.\ Phys.\ J.\ C {\bf 12} (2000) 375
[hep-ph/9903282].
%%CITATION = HEP-PH 9903282;%%

%\cite{Banfi:2003je}
\bibitem{Banfi:2003je}
A.~Banfi, G.~P.~Salam and G.~Zanderighi,
%``Generalized resummation of QCD final-state observables,''
hep-ph/0304148.
%%CITATION = HEP-PH 0304148;%%


\bibitem{privsalam}
M.~Dasgupta, G.~P.~Salam,
private communication.

\end{thebibliography}
\pagebreak
%\begin{figure}[p] 
%\vspace{20cm}
%\end{figure} 
%\pagebreak
%\cleardoublepage


\begin{figure}[p] 
  \begin{center}
\vspace{-1cm}
    \epsfig{file=H1prelim-03-033.fig1.eps,height=22cm}
\vspace{-1cm}
  \end{center}
  \caption{Measured values of $1 -$ thrust, $\tau$, averaged over $e^+$ and $e^-$ data. The data are compared with the results of a fit based 
 on NLO QCD including resummation and power corrections. The fit predictions are shown with dashed lines for those data points which were not
included in the fit. 
}
\label{tau}
\end{figure} 

\begin{figure}[p] 
  \begin{center}
 \vspace{-1cm}
   \epsfig{file=H1prelim-03-033.fig2.eps,height=22cm}
\vspace{-1cm}
  \end{center}
  \caption{Measured values of jet broadening $B$, averaged over $e^+$ and $e^-$ data. The data are compared with the results of a fit based 
 on NLO QCD including resummation and power corrections. The fit predictions are shown with dashed lines for those data points which were not
included in the fit. 
}
\label{Bp}
\end{figure} 

\begin{figure}[p] 
  \begin{center}
 \vspace{-1cm}
    \epsfig{file=H1prelim-03-033.fig3.eps,height=22cm}
\vspace{-1cm}
  \end{center}
  \caption{Measured values of $1-$ thrust, $\tau_c$, averaged over $e^+$ and $e^-$ data. The data are compared with the results of a fit based 
 on NLO QCD including resummation and power corrections. The fit predictions are shown with dashed lines for those data points which were not
included in the fit. 
}
\label{tauc}
\end{figure} 

\begin{figure}[p] 
  \begin{center}
 \vspace{-1cm}
    \epsfig{file=H1prelim-03-033.fig4.eps,height=22cm}
\vspace{-1cm}
  \end{center}
  \caption{Measured values of the $C$-parameter, averaged over $e^+$ and $e^-$ data. The data are compared with the results of a fit based 
 on NLO QCD including resummation and power corrections. The fit predictions are shown with dashed lines for those data points which were not
included in the fit. 
}
\label{Cp}
\end{figure} 

\begin{figure}[p] 
  \begin{center}
 \vspace{-1cm}
    \epsfig{file=H1prelim-03-033.fig5.eps,height=22cm}
 \vspace{-1cm}
  \end{center}
  \caption{Measured values of jet mass $\rho_0$, averaged over $e^+$ and $e^-$ data. The data are compared with the results of a fit based 
 on NLO QCD including resummation and power corrections. The fit predictions are shown with dashed lines for those data points which were not
included in the fit. 
}
\label{Rhoe}
\end{figure} 

\begin{figure}[p] 
  \begin{center}
    \epsfig{file=H1prelim-03-033.fig6.eps,width=15cm}
  \end{center}
  \caption{1-$\sigma$ contours in the $(\alpha_s,\alpha_0)$ plane from fits to the 2 jet event shape differential distributions. The $\alpha_s$ band is taken from \cite{Bethke:2000ai}.
}
\label{ellipses}
\end{figure} 

\begin{figure}[p] 
  \begin{center}
 \vspace{-1cm}
    \epsfig{file=H1prelim-03-033.fig7.eps,height=22cm}
 \vspace{-1cm}
  \end{center}
  \caption{Measured values of the jet rate $y_2$, averaged over $e^+$ and $e^-$ data. The data are compared to NLO QCD with hadronization corrections.
}
\label{Y2}
\end{figure} 

\begin{figure}[p] 
  \begin{center}
 \vspace{-1cm}
    \epsfig{file=H1prelim-03-033.fig8.eps,height=22cm}
 \vspace{-1cm}
  \end{center}
  \caption{Measured values of the jet rate $y_3$, averaged over $e^+$ and $e^-$ data. The data are compared to NLO QCD with hadronization corrections.
}
\label{Y3}
\end{figure} 

\begin{figure}[p] 
  \begin{center}
 \vspace{-1cm}
    \epsfig{file=H1prelim-03-033.fig9.eps,height=22cm}
 \vspace{-1cm}
  \end{center}
  \caption{Measured values of the jet rate $y_4$, averaged over $e^+$ and $e^-$ data. The data are compared with results from the RAPGAP Monte Carlo event generator.
}
\label{Y4}
\end{figure} 

\begin{figure}[p] 
  \begin{center}
 \vspace{-1cm}
    \epsfig{file=H1prelim-03-033.fig10.eps,height=22cm}
 \vspace{-1cm}
  \end{center}
  \caption{Measured values of azimuthal correlation $\chi$, averaged over $e^+$ and $e^-$ data. The data are compared with results from the RAPGAP Monte Carlo event generator.
}
\label{Chi}
\end{figure} 

\begin{figure}[p] 
  \begin{center}
 \vspace{-1cm}
    \epsfig{file=H1prelim-03-033.fig11.eps,height=22cm}
 \vspace{-1cm}
  \end{center}
  \caption{Measured values of out-of-plane momentum $K_{\textrm out}$,
divided by $Q$ and averaged over $e^+$ and $e^-$ data. The data are compared with results from the RAPGAP Monte Carlo event generator.
}
\label{Kout}
\end{figure} 

\end{document}

