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\begin{document}

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\begin{titlepage}

\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 & & &
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,width=2.cm} \\[.2em] \hline
\multicolumn{4}{l}{{\bf
                31st International Conference 
                on High Energy Physics, ICHEP02},
                July~24,~2002,~Amsterdam} \\
                 & Abstract:        & {\bf 301}    &\\
                 & Parallel Session & {\bf 3, 6}   &\\ \hline
 & \multicolumn{3}{r}{\footnotesize {\it
    www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em]
\end{tabular}
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\vspace*{2cm}

\begin{center}
  \Large
  {\bf 
    Search for Compositeness, Leptoquarks \\  
    and Large Extra Dimensions \\ 
%    in {\boldmath $e q$} Contact Interactions at HERA}
    in {\boldmath $e^- q$} and {\boldmath $e^+ q$}
    Contact Interactions at HERA}

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

\begin{abstract}

\noindent
Deep-inelastic $e^\pm p$ scattering at high momentum transfer $Q^2$  
is used to search for $eq$ contact interactions associated to scales 
not directly accessible at HERA. 
The cross section measurements $\rm d \sigma / \rm d Q^2$,
corresponding to luminosities of $15.2~\pb^{-1}$ of $e^-p$ data
and $35.6~\pb^{-1}$ of $e^+p$ data,
%do not show significant deviations from the Standard Model and 
are analysed to derive limits on new phenomena.
For conventional contact interactions lower bounds can be set on
$eq$ compositeness scales $\Lambda^\pm$ at $1.5 - 6.4~\TeV$
and on leptoquarks with a ratio mass over coupling $M/\lambda$
of order $1~\TeV$.  
A search for low scale gravitational effects through the exchange of
Kaluza-Klein excitations of gravitons in models with large extra 
dimensions results in lower limits on the effective Planck scale $M_S$ 
around $0.7~\TeV$.
\end{abstract}


\end{titlepage}

\pagestyle{plain}

\section{Introduction}

Deep inelastic neutral current scattering $e p \rightarrow e X$ at very high 
squared momentum transfer $Q^2$ allows 
to study the structure of $e q$ interactions at short distances and 
to search for new phenomena beyond the Standard Model.
A convenient tool is the concept of four-fermion contact interaction,
investigating the interference of a new point-like particle with the 
$\gamma$ and $Z$ fields.
This paper investigates conventional contact interactions, 
such as general models of compositeness and the exchange of heavy leptoquarks,
as well as low scale quantum gravity effects, which may be mediated
via %Kaluza-Klein excitations of 
gravitons coupling to Standard Model particles
and propagating into large extra spatial dimensions.

The preliminary results presented here are based on recent $e^-p$ 
cross section measurements and are combined with results of a previous 
contact term analysis of $e^+p$ scattering~\cite{h1ci}. 



\section{Data and analysis method}

The data have been collected with the H1 detector at {\sc Hera} and correspond 
altogether to integrated luminosities of $15.2~\pb^{-1}$ of $e^-p$ interactions 
at $\sqrt{s} = 318~\GeV$ and $35.6~\pb^{-1}$ of $e^+p$ scattering at 
$\sqrt{s} = 300~\GeV$.
Details of the cross section measurements can be found
elsewhere~\cite{h1xsece-p, h1xsece+p}.

The present contact interaction analysis uses the same methods 
%and investigates the same phenomenological models
as described in ref.~\cite{h1ci}.
The differential cross section ${\rm d}\sigma / {\rm d}Q^2$
is compared to the Standard Model prediction and deviations expressed in terms
of model parameters are searched for. 
The experimental and theoretical uncertainties, in particular the impact of 
different parton distributions, are properly considered in the $\chi^2$ analysis
and the derivation of scale limits.
The cross section ${\rm d}\sigma (e^-p \rightarrow e^-X) / {\rm d}Q^2$,
shown in figure~\ref{cismxsec}, is well described by the Standard Model in
the range of $Q^2 = 200 - 30,000~\GeV^2$ and does not show evidence for
new physics.
The phenomenological models under investigation and their analytical treatment
are discussed in ref.~\cite{h1ci}.


\section{Compositeness}

The most general chiral invariant Lagrangian for neutral current vector-like  
contact interactions can be written in the form~\cite{elpr,haberl}
\begin{eqnarray}
  {\cal L}_V  &=& %\sum_{q \, = \, u,\, d} 
  \sum_{a,\,b\, =\, L,\,R}
  \eta^q_{ab}\, (\bar{e}_a\gamma_\mu e_a)(\bar{q}_b\gamma^\mu q_b) \ .
 \label{lcontact}
\end{eqnarray}
For each quark flavour $q = u,\,d$ there are four coupling coefficients 
$\eta^q_{ab} = \epsilon (g/\Lambda^q_{ab})^2$,
where $a$ and $b$ indicate the $L,\, R$ fermion helicities,
$g$ is the overall coupling strength, $\Lambda^q_{ab}$ is a scale parameter
and $\epsilon$
determines the interference sign with the Standard Model currents.
In the study of possible fermion compositeness or substructure it is convenient
to choose a coupling of $g^2 = 4\,\pi$ and to assume a common scale $\Lambda$ for 
all quarks. Various scenarios of chiral structures are selected by the choice of
$\epsilon = \pm 1$ or $0$.

Lower limits on compositeness scale parameters $\Lambda^\pm$,
associated to positive or negative interference,
are summarised in table~\ref{etafits}.
As an example fits of the $e^-p$ cross section to the $VV$ model are shown in 
figure~\ref{cixsec}.
The $e^-p$ analysis exhibits for some models,
{\em e.g.} $LL^+$, $RR^+$ and $AA^+$, a higher sensitivity than the $e^+p$
data and both lepton polarities nicely complement each other. 
A combined analysis of both data sets yields improved lower limits on 
compositeness scale parameters.
The results are listed in table~\ref{etafits}
and displayed in figure~\ref{cieta}.
Limits on $\Lambda^+$ range between 3.1 and 6.4~GeV and
on $\Lambda^-$ between 1.5 and 3.8~GeV depending on the chiral structure.
The results of direct searches for $(e q)$ compositeness are compatible 
with those of other experiments at {\sc Hera}~\cite{zeusci}, 
{\sc Lep~\cite{lepci}} and {\sc Tevatron}~\cite{tevatronci}.


\section{Leptoquarks}

Leptoquarks couple to lepton--quark pairs and appear in extensions of the
Standard Model which try to establish a connection between leptons 
and quarks. 
They are colour triplet scalar or vector bosons, carrying 
lepton ($L$) and baryon ($B$) number. 
A fermion number $F = L + 3\,B$ is preserved, which takes {\em e.g.}
values of $F  = 2$ for $e^- q$ and $F=0$ for $e^+ q$ states.
One therefore expects different sensitivities to particular leptoquark types
from both lepton beam polarities.
The leptoquark mass $M_{LQ}$ and its coupling $\lambda$ are related to the
contact interaction coefficients via $g/\Lambda = \lambda/M_{LQ}$. 
The notation and the couplings to
$u$ and $d$ quarks are given in table~\ref{lqfits}.

As an example figure~\ref{cilqxsec} shows the possible contributions of the
leptoquarks $S^L_1$ and $V^L_1$ to the $e^-p$ cross section measurements,
both having $LL$ couplings to $u$ and $d$ quarks with different strength and
sign.
Limits on the ratio $M_{LQ}/\lambda$ of all leptoquark species are summarised in 
table~\ref{lqfits}. 
In some cases the $e^-p$ data considerably improve the previous
results from $e^+p$ scattering, {\em e.g.} for $S^L_0$ and $V^L_1$. 
The combined analysis helps to further constrain the lower leptoquark bounds
reaching values of $M_{LQ}/\lambda \sim {\cal O}(1~\TeV)$.
It should be emphasised that upper bounds on the coupling strength $\lambda$
can only be set for leptoquark masses exceeding the accessible center of mass
energy of {\sc Hera}.
Masses far above 300~GeV are excluded for almost all types of 
leptoquarks with a coupling of $\lambda \gtrsim 1$. 
These results complement the direct leptoquark searches~\cite{h1lq}. 
They are also compatible with limits derived in $e^+e^-$ experiments~\cite{lepci}.


\section{Large extra dimensions}

It has recently been suggested that the gravitational scale in $4+n$ dimensional
string theory may be as low as the electroweak scale~\cite{add}.
%leading to measurable effects of virtual graviton exchange~\cite{add}. 
In models with large extra dimensions the spin 2 graviton 
propagates into the extra spatial dimensions and
appears in the 4-dimensional world as a spectrum of massive Kaluza-Klein states.
The exchange of a whole Kaluza-Klein tower between Standard Model particles
leads to an effective contact interaction with a coupling coefficient
$\eta_G = \lambda/M^4_S$~\cite{giudice}.
By convention the coupling strength is set to $\lambda = \pm 1$.

Possible effects of Kaluza-Klein graviton exchange on the cross section 
measurement are shown in figure~\ref{graveffect}.
Lower limits on the scale parameter $M_S$, derived from fits to the
${\rm d}\sigma / {\rm d}Q^2$ distribution including gravitational effects, 
are summarised in table~\ref{ledfits}.
For the $e^-p$ data stronger bounds are obtained for positive coupling
than for negative coupling. The opposite behaviour is observed in $e^+p$
scattering. Again, both lepton polarities complement each other and a
combined analysis yields almost symmetric limits on $M_S$ of
$0.67~\TeV \ (\lambda = +1)$ and $0.73~\TeV \ (\lambda = -1)$.
Similar investigations of virtual graviton effects in $e^+e^-$ annihilation
provide comparable limits~\cite{leped}.


\section{Conclusions}

Neutral current deep inelastic $e^-p$ and $e^+p$
cross section measurements
are analysed to search for new phenomena mediated through 
$(\bar{e} e)(\bar{q} q)$ contact interactions.
No significant signal for compositeness, virtual leptoquark or graviton exchange 
is observed.
Both data sets provide complementary information
and a combined analysis yields improved limits on scales of new physics.


Limits on $(e q)$ compositeness scale parameters $\Lambda^\pm$
are derived within a model independent analysis.
They range between $1.5~\TeV$ and $6.4~\TeV$ 
depending on the chiral structure of the model.

A study of virtual leptoquark exchange yields lower limits on 
the ratio $M_{LQ}/\lambda$ between $0.27~\TeV$ and $1.1~\TeV$.
%which exceed the collider
%center of mass energy and reach about $1~\TeV$ for vector leptoquarks.
These measurements extend the direct leptoquark searches at 
{\sc Hera} to high masses $M_{LQ} > \sqrt{s}$.

Possible effects of low scale quantum gravity with gravitons coupling to
Standard Model particles and propagating into extra spatial dimensions
are searched for.
Lower limits on the effective Planck scale $M_S$ of $0.67~\TeV$ and
$0.73~\TeV$ for positive and negative coupling, respectively, are found.


%
%   References for Contact Interaction paper
%
\begin{thebibliography}{99}

% H1 CI paper
\bibitem{h1ci} H1 collaboration, C.~Adloff {\em et al.},
               Phys. Lett. B~479 (2000) 358.

\bibitem{h1xsece-p} H1 collaboration, 
                    contributed paper 971 to ICHEP~2000, Osaka, Japan.
                    %$e^-p$ NC  cross section at high $Q^2$

\bibitem{h1xsece+p} H1 collaboration, C.~Adloff {\em et al.},
                    Eur. Phys. J. C~13 (2000) 609.

% CI phenomenology
\bibitem{elpr} E.J.~Eichten, K.D.~Lane and M.E.~Peskin,
               Phys. Rev. Lett. 50 (1983) 811; \\
               R.~R\"uckl, Phys. Lett. B~129 (1983) 363 and
               Nucl. Phys. B~234 (1984) 91.

\bibitem{haberl} P.~Haberl, F.~Schrempp and H.-U.~Martyn,
                 Proc. Workshop {\em `Physics at HERA'}, 
                 eds. W.~Buchm\"uller and G.~Ingelman,
                 DESY, Hamburg (1991), vol. 2, p. 1133.
% contact interaction experiments
\bibitem{zeusci} ZEUS collaboration, J.~Breitweg {\em et al.},
                 %DESY~99-058 [hep-ex/9905039].
                 Eur. Phys. J. C~14 (2000) 239.
\bibitem{lepci} OPAL collaboration, G.~Abbiendi {\em et al.},
                %Eur. Phys. J. C~6 (1999) 1 and 
                %CERN-EP/99-097 [hep-ex/9908008], 
                Eur. Phys. J. C~13 (2000) 533; \\
                ALEPH collaboration, R.~Barate {\em et al.},
                Eur. Phys. J. C 12 (2000) 183; \\
                %and ALEPH 99-018; \\
                DELPHI collaboration, P.~Abreu {\em et al.},
                Eur. Phys. J. C~11 (1999) 383; \\
                L3 collaboration, 
                CERN-EP/2000-061 [hep-ex/0005028].
                %L3 Note 2402 (1999), contribution to EPS-HEP~99.
                %M.~Acciarri {\em et al.}, Phys. Lett. B 433 (1998) 163.

\bibitem{tevatronci} CDF collaboration, F.~Abe {\em et al.},
                     Phys. Rev. Lett. 79 (1997) 2192; \\
                     D0 collaboration, B.~Abbott {\em et al.},
                     Phys. Rev.  Lett. 82 (1999) 4769.

% leptoquarks
\bibitem{h1lq} H1 collaboration, C.~Adloff {\em et al.}, %Leptoquark search
               Eur. Phys. J. C~11 (1999) 447.

% quantum gravity
\bibitem{add} N.~Arkani-Hamed, S.~Dimopolous and G.~Dvali,
              Phys. Lett. B~429 (1998) 263 and
              Phys. Rev. D~59 (1999) 086004.

\bibitem{giudice} G.F.~Giudice, R.~Rattazzi and J.D.~Wells,
                  Nucl. Phys. B 544 (1999) 3;
                  %and erratum to appear; 
                  see also hep-ph/9811291
                  revised v2: 13 Mar 2000.

\bibitem{leped} OPAL collaboration, G.~Abbiendi {\em et al.},
                %CERN-EP/99-097 [hep-ex/9908008], 
                Eur. Phys. J. C~13 (2000) 533; \\
                L3 collaboration, M.~Acciarri {\em et al.},
                % Phys. Lett. B~464 (1999) 135 and
                Phys. Lett. B~470 (1999) 281. %; \\
                %ALEPH collaboration, ALEPH CONF 99-027.
          
\end{thebibliography}


%\clearpage
\vspace{3cm}

% compositeness scales
\begin{table}[htb]
\begin{center}
{\bf\Large\bf H1 preliminary}

\begin{tabular}{l c c c c}
   \hdick \\[-1.5ex]
          & \multicolumn{2}{c}{$e^-p$ data}  
          & \multicolumn{2}{c}{$e^+ p$ \& $e^- p$ data } \\ %[-0.5ex]
 coupling & \ $\Lambda^+~[\TeV]$ \ & \ $\Lambda^-~[\TeV]$ \ 
          & \ $\Lambda^+~[\TeV]$ \ & \ $\Lambda^-~[\TeV]$ \ \\[1ex]
   \hdick \\[-1.5ex]
 $LL$ & 3.1 & 1.4  & 3.6 & 1.5 \\[.4em]
 $LR$ & 1.7 & 1.4  & 3.5 & 1.6\\[.4em]
 $RL$ & 1.7 & 1.4  & 3.5 & 1.7\\[.4em]
 $RR$ & 3.0 & 1.5  & 3.5 & 1.5\\[.4em]
 $VV$ & 4.5 & 2.6  & 6.4 & 3.1\\[.4em]
 $AA$ & 4.0 & 1.7  & 3.9 & 3.8\\[.4em]
 $VA$ & 2.7 & 2.5  & 3.1 & 3.1\\[.4em]
 $LL+RR$ & 4.2 & 2.2  & 4.8 & 2.1\\[.4em]
 $LR+RL$ & 2.2 & 1.6  & 4.8 & 1.9\\[.4em]
 \hline
\end{tabular}
\end{center}
\caption{
  Compositeness scale parameters 
  $\Lambda^\pm$ (95\%~CL lower limits) for various chiral structures.
  Limits are given for the $e^-p$ data alone and for a combined $e^+p$ and 
  $e^-p$ analysis.}
\label{etafits}
\end{table}


\begin{table}[htb]
\begin{center}
{\bf\Large\bf H1 preliminary}\vspace{2mm}

\begin{tabular}{c c c c c c}
  \hdick \\[-1.5ex]
    &         &  &  & $e^-p$ data &  $e^+ p$ \& $e^-p$ \\[.5ex]
   LQ  & \ coupling to $u$ quark \ & \ coupling to $d$ quark \
    & \ $F$ \ & $M_{LQ}/\lambda$ & $M_{LQ}/\lambda$ \\[.5ex]
    &  &  & & $[ \GeV ]$ &  $[ \GeV ]$ \\[1ex]
  \hdick \\[-1.5ex]
   $S_0^L$ & 
    \ $\eta^u_{LL} = +\frac{1}{2}\ (\lambda/M_{LQ})^2$ \ & & 2 & 720 & 870 \\[.2em]
   $S_0^R$ & 
    \ $\eta^u_{RR} = +\frac{1}{2}\ (\lambda/M_{LQ})^2$ \ & & 2 & 650 & 780 \\[.2em]
   $\tilde{S}_0^R$ & &
    \ $\eta^d_{RR} = +\frac{1}{2}\ (\lambda/M_{LQ})^2$ \   & 2 & 270 & 270 \\[.2em]
   $S_{1/2}^L$ &
    \ $\eta^u_{LR} = -\frac{1}{2}\ (\lambda/M_{LQ})^2$ \ & & 0 & 280 & 370 \\[.2em]
   $S_{1/2}^R$ &
    \ $\eta^u_{RL} = -\frac{1}{2}\ (\lambda/M_{LQ})^2$ \   &
    \ $\eta^d_{RL} = -\frac{1}{2}\ (\lambda/M_{LQ})^2$ \   & 0 & 280 & 330 \\[.2em]
   $\tilde{S}_{1/2}^L$ & &
    \ $\eta^d_{LR} = -\frac{1}{2}\ (\lambda/M_{LQ})^2$ \   & 0 & 270 & 460 \\[.2em]
   $S_1^L$ &
    \ $\eta^u_{LL} = +\frac{1}{2}\ (\lambda/M_{LQ})^2$ \   &
    \ $\eta^d_{LL} = +1\ (\lambda/M_{LQ})^2$               & 2 & 580 & 610 \\[1ex]
  \hline \\[-1.5ex]
   $V_0^L$ & &
    \ $\eta^d_{LL} = -1\ (\lambda/M_{LQ})^2$ \   & 0 & 640 & 820 \\[.2em]
   $V_0^R$ & & 
    \ $\eta^d_{RR} = -1\ (\lambda/M_{LQ})^2$ \   & 0 & 540 & 660 \\[.2em]
   $\tilde{V}_0^R$ & 
    \ $\eta^u_{RR} = -1\ (\lambda/M_{LQ})^2$ \ & & 0 & 550 & 550 \\[.2em]
   $V_{1/2}^L$ & &
    \ $\eta^d_{LR} = +1\ (\lambda/M_{LQ})^2$ \   & 2 & 320 & 400\\[.2em]
   $V_{1/2}^R$ & 
    \ $\eta^u_{RL} = +1\ (\lambda/M_{LQ})^2$ \ &
    \ $\eta^d_{RL} = +1\ (\lambda/M_{LQ})^2$ \   & 2 & 490 & 1000 \\[.2em]
   $\tilde{V}_{1/2}^L$ &
    \ $\eta^u_{LR} = +1\ (\lambda/M_{LQ})^2$ \ & & 2 & 500 & 1100\\[.2em]
   $V_1^L$ &
    \ $\eta^u_{LL} = -2\ (\lambda/M_{LQ})^2$ \ &
    \ $\eta^d_{LL} = -1\ (\lambda/M_{LQ})^2$ \   & 0 & 740 & 720 \\[1ex]
  \hline
\end{tabular}
\end{center}
\caption{Coupling coefficients $\eta^q_{ab}$, fermion number $F$ 
  and 95\%~CL lower limits on $M_{LQ}/\lambda$ for scalar (S) and vector (V) 
  leptoquarks, 
  including systematics from different parton distributions. 
  Limits are given for
  the $e^-p$ data alone and the combined $e^+p$ and $e^-p$ data.
  The notation indicates the lepton chirality {\em L, R} 
  and weak isospin $I = 0,\ 1/2,\ 1$.
  $\tilde{S}$ and $\tilde{V}$ differ by two units of hypercharge from $S$ and $V$.
  By convention the quantum numbers and helicities are given for
  $e^-q$ and $e^-\bar{q}$ states.
  Limits on the coupling $\lambda$ are only meaningful for 
  leptoquark masses $M_{LQ}>\sqrt{s}$.}
\label{lqfits}
\end{table}

\vspace{2cm}
\begin{table}[htb]
\begin{center}
%{\bf\Large\bf H1 preliminary}

\begin{tabular}{l c c}
   & & \\
   \hdick \\[-1.5ex]
          & $\lambda = +1$ & $\lambda = -1$ \\
 data set & \ $M_S~[\TeV]$ \ & \ $M_S~[\TeV]$ \ \\[1ex]
   \hdick \\[-1.5ex]
 $e^- p$  preliminary & 0.68 & 0.48 \\[.4em]
 $e^+ p$  & 0.48 & 0.72 \\[.4em]
 $e^+ p$  \& $e^- p$  preliminary & 0.67 & 0.73 \\[.4em]
 \hline
\end{tabular}
\end{center}
\caption{
     Lower limits (95\%~CL) on the effective gravitational scale $M_S$
     for positive ($\lambda = +1$) and negative ($\lambda = -1$)
     coupling.}
\label{ledfits}
\end{table}


\clearpage
% \input{figures}

% Data Analysis
%
\begin{figure}[p] 
  \begin{center}
%    \epsfig{file=/h1/psfiles/figures/d00-181f21.eps,width=16cm}
    \epsfig{file=h1.eps,width=16cm}
  \end{center}
  \caption{Differential cross section 
    ${\rm d}\sigma / {\rm d}E_T^2$ for the production of six jets,
four of which contain $D^*$ candidates, with a proton detected in
the leading proton spectrometer.
H1 data are compared with the predictions of the 
leading order Monte Carlo model RAPGAP and with the results of
a next-to-leading order QCD fit to the data. The inner error
bars show the statistical uncertainties. The outer error bars
show the statistical and systematic uncertainties added in
quadrature. }
  \label{cismxsec}
\end{figure} 

\end{document}

