%================================================================ % LaTeX file with preferred layout for the contributed papers to % the ICHEP Conference 98 in Vancouver % process with: latex hep98.tex % dvips -D600 hep98 %================================================================ \documentclass[12pt]{article} \usepackage{epsfig} \usepackage{amsmath} \usepackage{hhline} \usepackage{amssymb} \usepackage{times} \renewcommand{\topfraction}{1.0} \renewcommand{\bottomfraction}{1.0} \renewcommand{\textfraction}{0.0} \newlength{\dinwidth} \newlength{\dinmargin} \setlength{\dinwidth}{21.0cm} \textheight23.5cm \textwidth16.0cm \setlength{\dinmargin}{\dinwidth} \setlength{\unitlength}{1mm} \addtolength{\dinmargin}{-\textwidth} \setlength{\dinmargin}{0.5\dinmargin} \oddsidemargin -1.0in \addtolength{\oddsidemargin}{\dinmargin} \setlength{\evensidemargin}{\oddsidemargin} \setlength{\marginparwidth}{0.9\dinmargin} \marginparsep 8pt \marginparpush 5pt \topmargin -42pt \headheight 12pt \headsep 30pt \footskip 24pt \parskip 3mm plus 2mm minus 2mm %===============================title page============================= % Some useful tex commands % \newcommand{\GeV}{\rm GeV} \newcommand{\TeV}{\rm TeV} \newcommand{\pb}{\rm pb} \newcommand{\cm}{\rm cm} \newcommand{\hdick}{\noalign{\hrule height1.4pt}} \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 \vspace*{3cm} \begin{center} \Large {\bf Search for Compositeness, Leptoquarks \\ and Large Extra Dimensions \\ 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 $81.5~\pb^{-1}$ of $e^+p$ data, are well described by the Standard Model and are analysed to set constraints on new phenomena. For conventional contact interactions lower bounds can be set on $eq$ compositeness scales $\Lambda^\pm$ at $1.6 - 9.2~\TeV$ and on leptoquarks with a ratio mass over coupling $M/\lambda$ of $0.3 - 1.7~\TeV$. 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 $M_S$ of $0.63~\TeV$ and $0.93~\TeV$ for positive and negative coupling, respectively. \end{abstract} \vfill \begin{flushleft} {\bf Abstract: 951, 952 } \\ {\bf Parallel session: 11, 3} \\ {\bf Plenary talk: 7~b } \end{flushleft} \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 to investigate the interference of a new point-like particle with the $\gamma$ and $Z$ fields is the concept of four-fermion contact interaction. This paper considers 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 gravitons coupling to Standard Model particles and propagating into large extra spatial dimensions. The preliminary results presented here are based on recent $e^-p$ and $e^+p$ cross section measurements and are combined with 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 $e^-p$ collisions taken in 1998/99 at $\sqrt{s} = 318~\GeV$, $45.9~\pb^{-1}$ of $e^+p$ collisions taken in 1999/2000 at $\sqrt{s} = 318~\GeV$, and $35.6~\pb^{-1}$ of $e^+p$ scattering recorded during 1994/97 at a lower center of mass energy $\sqrt{s} = 300~\GeV$. Details of the cross section measurements can be found elsewhere~\cite{h1xsec}. The present contact interaction analysis uses the same methods 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 sections ${\rm d}\sigma (e^-p \rightarrow e^-X) / {\rm d}Q^2$ and ${\rm d}\sigma (e^+p \rightarrow e^-X) / {\rm d}Q^2$ of the new data, shown in figure~\ref{cismxsec}, are well described by the Standard Model in the range of $Q^2 = 200 - 30,000~\GeV^2$. %and do not show evidence for new physics. Fits to the Standard Model expectation yield $\chi^2 = 14.5/16~{\rm dof}$ with a normalisation $f_n = 1.010$ for the $e^-p$ data and $\chi^2 = 13.2/16~{\rm dof}$ with $f_n = 0.991$ for the $e^+p$ data. The phenomenological models under investigation and their analytical treatment are discussed in ref.~\cite{h1ci}. In the combined analysis all three data sets are treated as independent samples with individual normalisation and measurement uncertainties. \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 example fits of the $e^-p$ and $e^+p$ cross sections to the $VV$ model are shown in figure~\ref{cixsec}. The $e^-p$ data exhibit despite the lower luminosity for some models, {\em e.g.} $AA^+$, a higher sensitivity than the $e^+p$ data and both lepton polarities complement each other. A combined analysis of all $e^\pm p$ data sets yields a substantial improvement on lower limits of compositeness scale parameters compared to the previous publication~\cite{h1ci}. The results are listed in table~\ref{etafits} and displayed in figure~\ref{cieta}. Limits on $\Lambda^+$ range between 3.5 and 9.2~GeV and on $\Lambda^-$ between 1.6 and 5.8~GeV depending on the chiral structure. The results of direct searches for $(e q)$ compositeness are competitive 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 example figure~\ref{cilqxsec} shows possible contributions of the leptoquarks $S^L_1$ and $V^L_1$ to the $e^-p$ cross section and of the leptoquarks $S^R_{1/2}$ and $V^R_{1/2}$ to the $e^+p$ cross section. Each pair of leptoquarks couples with the same chiral structure but different strength and sign to $u$ and $d$ quarks. Limits on the ratio $M_{LQ}/\lambda$ of all leptoquark species are summarised in table~\ref{lqfits}. In some cases, {\em e.g.} $S^L_1$ and $V^L_1$, the $e^-p$ data give more restrictive results than $e^+p$ scattering despite the lower luminosity. The combined analysis of all $e^\pm p$ data sets helps to further constrain the leptoquark bounds reaching values of $M_{LQ}/\lambda \simeq 1.7~\TeV$. 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 all types of leptoquarks (except $\tilde{S}^R_0$) with a coupling of $\lambda \gtrsim 1$. These results complement the direct leptoquark searches at {\sc Hera}~\cite{h1lq} and are competitive 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 measurements 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 of all $e^\pm p$ data yields limits on $M_S$ of $0.63~\TeV $ for positive coupling $\lambda = +1$ and $0.93~\TeV $ for negative coupling $\lambda = -1$. The effect of a common gravitational scale $M_S$ on the combined $e^+p$ and the $e^-p$ scattering data is illustrated in figure~\ref{ledeffect}. Similar investigations of virtual graviton exchange 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 lepton charges 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 $1.6~\TeV$ and $9.2~\TeV$ depending on the chiral structure and sign of interference. A study of virtual leptoquark exchange yields lower limits on the ratio $M_{LQ}/\lambda$ between $0.3~\TeV$ and $1.7~\TeV$. 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 $0.63~\TeV$ and $0.93~\TeV$ 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{h1xsec} H1 collaboration, C.~Adloff {\em et al.}, Eur. Phys. J. C~13 (2000) 609; \\ contributed papers 971 and 975 to ICHEP~2000, Osaka, Japan. %{\em `Measurement of cross sections % in $e^-p$ collisions at HERA'} %{\em `Inclusive measurement of DIS at high $Q^2$ % in $e^+p$ collisions at HERA'} %\bibitem{h1xsece+p} H1 collaboration, C.~Adloff {\em et al.}, % Eur. Phys. J. C~13 (2000) 609; \\ and % contributed paper 975 to ICHEP~2000, Osaka, Japan. % 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{2cm} \bigskip\bigskip % compositeness scales \begin{table}[htb] \caption{ Compositeness scale parameters $\Lambda^\pm$ (95\%~CL lower limits) for various chiral structures. Preliminary results are given for $e^-p$ data at $\sqrt{s} = 318\,\GeV$, for $e^+p$ data at $\sqrt{s} = 318\,\GeV$ and for a combined analysis also including $e^+p$ data at $\sqrt{s} = 300\,\GeV$ from~\cite{h1ci}.} \label{etafits} \begin{center} \begin{tabular}{l c c c c c c} \hdick \\[-1.5ex] & \multicolumn{2}{c}{$e^-p$ $(318\,\GeV)$} & \multicolumn{2}{c}{$e^+p$ $(318\,\GeV)$} & \multicolumn{2}{c}{all $e^+ p$ \& $e^- p$ } \\ coupling & \ $\Lambda^+~[\TeV]$ & $\Lambda^-~[\TeV]$ \ & \ $\Lambda^+~[\TeV]$ & $\Lambda^-~[\TeV]$ \ \ & \ $\Lambda^+~[\TeV]$ & $\Lambda^-~[\TeV]$ \ \\[1ex] \hdick \\[-1.5ex] $LL$ & 3.1 & 1.4 & 3.0 & 1.5 & 4.3 & 1.6 \\[.2em] $LR$ & 1.7 & 1.4 & 4.7 & 1.9 & 5.4 & 1.8 \\[.2em] $RL$ & 1.7 & 1.4 & 4.6 & 1.9 & 5.4 & 1.9 \\[.2em] $RR$ & 3.0 & 1.5 & 3.1 & 1.5 & 4.3 & 1.6 \\[.2em] $VV$ & 4.5 & 2.6 & 7.4 & 2.4 & 9.2 & 3.0 \\[.2em] $AA$ & 4.0 & 1.7 & 2.5 & 5.4 & 3.5 & 5.8 \\[.2em] $VA$ & 2.7 & 2.5 & 3.6 & 3.8 & 3.9 & 4.0 \\[.2em] $LL+RR$ & 4.2 & 2.2 & 4.1 & 1.6 & 5.9 & 2.0 \\[.2em] $LR+RL$ & 2.2 & 1.6 &6.4 & 2.1 & 7.4 & 2.1 \\[.2em] \hline \end{tabular} \end{center} \end{table} % leptoquarks \begin{table}[htb] \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. Preliminary results are given for $e^-p$ data at $\sqrt{s} = 318~\GeV$, $e^+p$ data at $\sqrt{s} = 318~\GeV$ and for a combined analysis also including $e^+p$ data at $\sqrt{s} = 300~\GeV$ from~\cite{h1ci}. 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} \begin{center} \begin{tabular}{l c c c c c c c} \hdick \\[-1.5ex] & & & & $e^-p$ $(318~\GeV)$ & $e^+p$ $(318~\GeV)$ & all $e^+ p$ \& $e^-p$ \\[.5ex] LQ & $\eta^u$ & $\eta^d$ & $F$ & $M_{LQ}/\lambda$ & $M_{LQ}/\lambda$ & $M_{LQ}/\lambda$\\[.5ex] & $[\lambda^2/M_{LQ}^2]$ & $[\lambda^2/M_{LQ}^2]$ & & $[ \GeV ]$ & $[ \GeV ]$ & $[ \GeV ]$\\[1ex] \hdick \\[-1.5ex] $S_0^L$ & \ $\eta^u_{LL} = +\frac{1}{2}$ \ & & 2 & 720 & 760 &1070 \\[.2em] $S_0^R$ & \ $\eta^u_{RR} = +\frac{1}{2}$ \ & & 2 & 650 & 690 & 960 \\[.2em] $\tilde{S}_0^R$ & & \ $\eta^d_{RR} = +\frac{1}{2}$ \ & 2 & 270 & 260 & 290 \\[.2em] $S_{1/2}^L$ & \ $\eta^u_{LR} = -\frac{1}{2}$ \ & & 0 & 280 & 350 & 380 \\[.2em] $S_{1/2}^R$ & \ $\eta^u_{RL} = -\frac{1}{2}$ \ & \ $\eta^d_{RL} = -\frac{1}{2}$ \ & 0 & 280 & 390 & 380 \\[.2em] $\tilde{S}_{1/2}^L$ & & \ $\eta^d_{LR} = -\frac{1}{2}$ \ & 0 & 270 & 570 & 650 \\[.2em] $S_1^L$ & \ $\eta^u_{LL} = +\frac{1}{2}$ \ & \ $\eta^d_{LL} = +1$ \ & 2 & 580 & 520 & 690 \\[1ex] \hline \\[-1.5ex] $V_0^L$ & & \ $\eta^d_{LL} = -1$ \ & 0 & 640 & 780 &1030 \\[.2em] $V_0^R$ & & \ $\eta^d_{RR} = -1$ \ & 0 & 540 & 640 & 810 \\[.2em] $\tilde{V}_0^R$ & \ $\eta^u_{RR} = -1$ \ & & 0 & 550 & 410 & 530 \\[.2em] $V_{1/2}^L$ & & \ $\eta^d_{LR} = +1$ \ & 2 & 320 & 480 & 480 \\[.2em] $V_{1/2}^R$ & \ $\eta^u_{RL} = +1$ \ & \ $\eta^d_{RL} = +1$ \ & 2 & 490 &1310 &1510 \\[.2em] $\tilde{V}_{1/2}^L$ & \ $\eta^u_{LR} = +1$ \ & & 2 & 500 &1460 &1690 \\[.2em] $V_1^L$ & \ $\eta^u_{LL} = -2$ \ & \ $\eta^d_{LL} = -1$ \ & 0 & 740 & 520 & 680 \\[1ex] \hline \end{tabular} \end{center} \end{table} %\clearpage % large extra dimensions \begin{table} \caption{Preliminary results of lower limits (95\%~CL) on the gravitational scale $M_S$ with %assuming positive ($\lambda = +1$) and negative ($\lambda = -1$) coupling for $e^-p$ data at $\sqrt{s} = 318~\GeV$, $e^+p$ data at $\sqrt{s} = 318~\GeV$ and a combined analysis also including $e^+p$ data at $\sqrt{s} = 300~\GeV$ from~\cite{h1ci}.} \label{ledfits} \begin{center} \begin{tabular}{l c c c} \hdick \\[-1.5ex] & \ $e^- p$ $(318~\GeV)$ \ & \ $e^+ p$ $(318~\GeV)$ \ & \ all $e^+ p$ \& $e^- p$ \\ coupling \ \ & \ $M_S~[\TeV]$ \ & \ $M_S~[\TeV]$ \ & \ $M_S~[\TeV]$ \ \\[1ex] \hline \\[-1.5ex] $\lambda = +1$ & 0.68 & 0.50 & 0.63 \\[.2em] $\lambda = -1$ & 0.48 & 0.89 & 0.93 \\[.2em] \hline \end{tabular} \end{center} \end{table} \clearpage % Data Analysis % \begin{figure}[p] \begin{center} \vspace*{-.5cm} \epsfig{file=figure1a.eps,width=.85\textwidth} \\[1em] \epsfig{file=figure1b.eps,width=.85\textwidth} \end{center} \vspace*{-.3cm} \caption{Differential cross sections ${\rm d}\sigma / {\rm d}Q^2$ at $\sqrt{s} = 318~\GeV$ for $e^-p \rightarrow e^-X$ (top) and $e^+p \rightarrow e^+X$ (bottom) scattering. H1 data %($\bullet$) are compared with Standard Model expectations %(---) using CTEQ5D parton distributions. The errors include statistics and uncorrelated experimental systematics. The normalisation uncertainties are 3\% ($e^-p$ data) and 1.5\% ($e^+p$ data).} \label{cismxsec} \end{figure} % Compositeness Scales (Limits e- & e+ combined) % \begin{figure}[htb] \begin{center} \epsfig{file=figure2.eps,width=\textwidth} \end{center} \caption{Analysis results of the parameter $\epsilon/\Lambda^2$ for compositeness models using the combined $e^+ p$ (${\cal L} = 81.5~\pb^{-1}$) and $e^- p$ (${\cal L} = 15.2~\pb^{-1}$) data. The thick hori\-zontal bars indicate the 95\%~CL limits on $\Lambda^+$ and $\Lambda^-$ including parton distribution uncertainties; values outside these regions are excluded. The corresponding thin horizontal bars show the fit results for $\epsilon/\Lambda^2$ using CTEQ5D parton distributions; inner and outer error bars represent one and two standard deviations respectively. The scale for $\epsilon\,\Lambda$ is shown for convenience.} \label{cieta} \end{figure} % illustration of VV model sensitivity % \begin{figure}[htb] \begin{center} \mbox{ \epsfig{file=figure3a.eps,width=.5\textwidth} \epsfig{file=figure3b.eps,width=.5\textwidth} } \end{center} %\vspace*{-.3cm} \caption{NC cross section ${\rm d}\sigma / {\rm d}Q^2$ at $\sqrt{s} = 318~\GeV$ normalised to the Standard Model expectation using CTEQ5D parton distributions. H1 data of $e^-p$ and $e^+p$ scattering are compared with fits to VV compositeness models corresponding to 95\%~CL exclusion limits of $\Lambda^+$ and $\Lambda^-$. The errors represent statistics and uncorrelated experimental systematics.} \label{cixsec} \end{figure} % Leptoquarks % \begin{figure}[htb] \begin{center} \mbox{ \epsfig{file=figure4a.eps,width=.5\textwidth} \epsfig{file=figure4b.eps,width=.5\textwidth} } \end{center} %\vspace*{-.3cm} \caption{NC cross section ${\rm d}\sigma / {\rm d}Q^2$ at $\sqrt{s} = 318~\GeV$ normalised to the Standard Model expectation using CTEQ5D parton distributions. H1 data compared with 95\%~CL exclusion limits of leptoquarks: $e^-p$ scattering with $S^L_{1}$ %(---) and $V^L_{1}$ %$(- -)$ and $e^+p$ scattering with $S^R_{1/2}$ %(---) and $V^R_{1/2}$. %$(- -)$. The errors represent statistics and uncorrelated experimental systematics.} \label{cilqxsec} \end{figure} % Large Extra Dimensions % \begin{figure}[t] \begin{center} \mbox{ \epsfig{file=figure5a.eps,width=.5\textwidth} \epsfig{file=figure5b.eps,width=.5\textwidth} } \end{center} %\vspace*{-.3cm} \caption{NC cross section ${\rm d}\sigma / {\rm d}Q^2$ at $\sqrt{s} = 318~\GeV$ normalised to the Standard Model expectation using CTEQ5D parton distributions. H1 data of $e^-p$ and $e^+p$ scattering are compared to gravitational effects of large extra dimensions at scales $M_S$ (95\%~CL lower limits) with positive ($\lambda = +1$) and negative ($\lambda = -1$) coupling. The errors represent statistics and uncorrelated experimental systematics.} \label{graveffect} \end{figure} % \begin{figure}[p] \begin{center} \epsfig{file=figure6.eps,width=.75\textwidth} \end{center} \caption{NC cross sections ${\rm d}\sigma / {\rm d}Q^2$ normalised to the Standard Model expectation %using CTEQ5D parton distributions. for the combined $e^+p$ and the $e^-p$ scattering data. The curves show the effects of graviton exchange in large extra dimensions given by a common fit to the scale $M_S$ (95\%~CL lower limits) with couplings $\lambda = +1$ and $\lambda = -1$. The errors represent statistics and uncorrelated experimental systematics.} \label{ledeffect} \end{figure} \end{document}