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\begin{document}

\title{LEPTOQUARKS AND CONTACT INTERACTIONS \\ FROM A GLOBAL ANALYSIS}

\author{A. F. \.ZARNECKI}

\address{Institute of Experimental Physics, Warsaw University, \\
 Ho\.za 69, 00-681 Warszawa, Poland \\E-mail: zarnecki@fuw.edu.pl } 


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% You may repeat \author \address as often as necessary      %
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\maketitle\abstracts{
Data from HERA, LEP and the Tevatron, as well as from low energy  
experiments are used to constrain the scale of possible electron-quark 
contact interactions. 
%
Some models are found to describe the existing experimental data 
much better than the Standard Model.
%
% The effect is mostly resulting from the new data 
% on the atomic parity violation in cesium,
% but is also supported by recent LEP2 measurements 
% and results concerning CKM matrix unitarity.
%
The possibility of scalar or vector leptoquark contribution
is studied using the Buchm\"uller-R\"uckl-Wyler effective model.
%
Increase in the global probability observed for scenarios including 
$S_{1}$ or $\tilde{V}_{\circ}$
leptoquark production/exchange  
corresponds to more than a 3$\sigma$ effect.
%
Assuming that a real leptoquark signal is observed,
calculated is an allowed region in the $\lambda - M$ plane.
 }

\section{Introduction}

In the global contact interaction analysis presented
last year~\cite{gcia,dis99} data from both collider and low energy
experiments were used to constrain the mass scale of 
the possible new electron-quark contact interactions. 
%
No indication for possible deviations from the Standard 
Model predictions was found at that time.

Presented in this paper are results from the updated analysis, 
which includes new experimental data.
%
Most important are the new results from the atomic parity violation (APV)
measurements in cesium.\cite{apvnew}
%
After the theoretical uncertainties have been significantly reduced,
the measured value of the cesium weak charge is 
now 2.5$\sigma$ away from the Standard Model prediction.
%
Also the new hadronic cross-section measurements at LEP2,
for $\sqrt{s}$=192--202 GeV, are on average about 2.5\% above
the predictions.\cite{lepnew}
%
This is only about 2.3$\sigma$ effect,
but has an important influence on the analysis.

\section{Contact Interactions}
\label{sec-ci}

Four-fermion contact interactions are an effective theory, which 
allows us to describe, in the most general way, possible low energy 
effects  coming from ``new physics'' at much higher energy 
scales.
%
Vector $eeqq$ contact interactions can be represented 
as an additional term in the Standard Model Lagrangian:
%
\begin{eqnarray}
L_{CI} & = & \sum_{i,j=L,R} \eta^{eq}_{ij} (\bar{e}_{i} \gamma^{\mu} e_{i} )
              (\bar{q}_{j} \gamma_{\mu} q_{j})  \nonumber
\end{eqnarray}
where the sum runs over electron and quark helicities.
%
Couplings  $\eta^{eq}_{ij}$ describing the helicity and flavor 
structure of contact interactions can be related to the effective
mass scale $\Lambda$:
%
 $\eta = \pm 4 \pi / \Lambda^{2} $.

In the presented analysis different CI scenarios are considered.
%
The so called first-generation models assume that contact interactions 
couple only electrons to $u$ and $d$ quarks. 
%
In the three-generation model lepton universality 
($e$=$\mu$) and quark family universality ($u$=$c$=$t$ and 
$d$=$s$=$b$) is assumed.
%
Assuming $ SU(2)_{L} \times U(1)_{Y} $ gauge invariance,
there are 7 independent couplings ($\eta^{eu}_{RL}$=$\eta^{ed}_{RL}$).
%
In the most general approach different couplings are allowed to
vary independently, whereas in the so called one-parameter scenarios
only one coupling (or given combination of couplings~\cite{gcia}) 
is allowed to be non-zero.

The analysis combines relevant data from HERA, Tevatron and LEP2, 
results from low-energy $eN$, $\mu N$ and $\nu N$ scattering experiments,
constraints on the CKM matrix unitarity and electron-muon universality,
and the atomic parity violation (APV) measurements.\cite{glqa}


The best description of all data is obtained for three-generation 
model with $e_{L}d_{L}$ type coupling.
% 
Increase in the global probability ${\cal P}(\eta)$ corresponds
to 3.8$\sigma$ deviation from the Standard Model.
%
The mass scale of new interaction is  $\Lambda^{ed}_{LL} = 13.2 \pm 1.8$ TeV 
(10.3 TeV $< \; \Lambda^{ed}_{LL} \; <$ 21.9 TeV on 95\% CL).

95\% CL exclusion limits on $\eta$ are defined as minimum ($\eta^{-}$) and
maximum ($\eta^{+}$) coupling values resulting in the global probability
equal to 5\% of the Standard Model probability:
${\cal P}(\eta^{\pm}) = 0.05 \; {\cal P}(0)$. 
%
\begin{table}[t]
\caption{Mass scale limits for different contact interaction models.
         \label{tab:ci}}
\vspace{0.2cm}
\begin{center}
\footnotesize
   \begin{tabular}{|c|rr|rr|rr|rr|}
     \hline
%
  & \multicolumn{8}{c|}{95\% CL exclusion limit ~~~~ $TeV$} \\ \cline{2-9}
%
  & \multicolumn{4}{c|}{General approach} & 
    \multicolumn{4}{c|}{One-parameter models} \\ 
\cline{2-9} 
%
\raisebox{0pt}[8pt]{Coupling}
 & \multicolumn{2}{c|}{1$^{st}$ gen.} & 
               \multicolumn{2}{c|}{3 gen.} &
               \multicolumn{2}{c|}{1$^{st}$ gen.} &
               \multicolumn{2}{c|}{3 gen.} \\
\cline{2-9}
%
& \raisebox{0pt}[8pt]{$\Lambda^{-}$} & $\Lambda^{+}$ &
  $\Lambda^{-}$ & $\Lambda^{+}$ &
  $\Lambda^{-}$ & $\Lambda^{+}$ &
  $\Lambda^{-}$ & $\Lambda^{+}$ \\ 
\hline
%
 %  Limits from general fits using 1T, 3T models
 %       and 1T and 3T one parameter fits
 %  25/04/2000 12.03.37
 %
 \raisebox{0pt}[8pt]{ $\eta^{ed}_{LL}$} &
 5.3 & 4.4 &
 6.7 & 7.2 &
 28.6 & 8.4 &
 30.5 & 8.9 \\
 %
 \raisebox{0pt}[8pt]{$\eta^{ed}_{LR}$} &
 2.4 & 3.0 &
 3.6 & 3.8 &
 19.2 & 7.6 &
 19.5 & 7.5 \\
 %
 \raisebox{0pt}[8pt]{$\eta$}$^{ed}_{RL}$ &
 3.5 & 3.7 &
 4.3 & 4.2 &
 ~ & ~ &
 ~ & ~ \\
 %
 \raisebox{0pt}[8pt]{$\eta$}$^{ed}_{RR}$ &
 2.8 & 3.5 &
 4.0 & 5.9 &
 8.0 & 18.1 &
 8.8 & 17.4 \\
% \hline
 %
 \raisebox{0pt}[8pt]{$\eta$}$^{eu}_{LL}$ &
 4.9 & 4.6 &
 6.0 & 8.2 &
 12.5 & 18.7 &
 11.8 & 21.4 \\
 %
 \raisebox{0pt}[8pt]{$\eta$}$^{eu}_{LR}$ &
 4.3 & 3.4 &
 5.0 & 4.8 &
 17.4 & 7.5 &
 17.3 & 7.8 \\
 %
 \raisebox{0pt}[8pt]{$\eta$}$^{eu}_{RL}$ &
 3.5 & 3.7 &
 4.3 & 4.2 &
 ~ & ~ &
 ~ & ~ \\
 %
 \raisebox{0pt}[8pt][4pt]{$\eta$}$^{eu}_{RR}$ &
 4.0 & 3.8 &
 4.9 & 4.7 &
 6.9 & 19.7 &
 7.0 & 21.2 \\
\hline
 %
 \raisebox{0pt}[8pt]{$VV$} &
 ~ & ~ &
 ~ & ~ &
 6.5 & 11.1 &
 8.2 & 15.1 \\
 %
 $AA$ &
 ~ & ~ &
 ~ & ~ &
 5.7 & 6.3 &
 10.5 & 11.7 \\
 %
 $VA$ &
 ~ & ~ &
 ~ & ~ &
 4.5 & 4.6 &
 5.7 & 7.8 \\
 %
 %
 % Generated with dis4.kumac
 %

%
\hline
\end{tabular}
\vspace{-3mm}
\end{center}
\end{table}
%
Mass scale limits $\Lambda^{\pm}$, corresponding the coupling limits
$\eta^{\pm}$, for different contact interaction models
are presented in Table \ref{tab:ci}.




\section{Leptoquarks}

In a recent paper~\cite{glqa} available  data were also 
 used to constrain Yukawa couplings and masses
for scalar and vector leptoquarks
using the Buchm\"uller-R\"uckl-Wyler effective model.\cite{brw}
%
In the limit of very high leptoquark masses, constraints
on the coupling to the mass ratio were studied using 
the contact-interaction approximation.\cite{lqci}
%
The best description of the data is obtained for the $S_{1}$ 
and the $\tilde{V}_{\circ}$ leptoquarks~\cite{aachen} with 
$\lambda_{LQ} / M_{LQ} \sim  0.3\; {\rm TeV^{-1}}$.
%
Increase in the global probability  
corresponds to more than 3$\sigma$ deviation from the Standard Model.

Constraints on the leptoquark couplings and masses were
studied also for finite leptoquark masses, with mass effects 
correctly taken into account.
%
Shown in Figure~\ref{fig:lq} are the 95\% exclusion limits
as well as the  68\% and 95\% CL  signal limits for
$S_{1}$ and $\tilde{V}_{\circ}$ leptoquarks.
%
\begin{figure}[t]
\psfig{figure=dis2000.eps,width=\textwidth}
\vspace{-8mm}
\caption{  Signal limits on 68\% and 95\% CL for $S_{1}$ and 
           $\tilde{V}_{\circ}$ leptoquarks. Dashed lines indicate
            the 95\% CL exclusion limits. 
            For $\tilde{V}_{\circ}$ model
            a star indicates the best fit parameters.
            For  $S_{1}$  model the best fit is obtained in the contact
            interaction limit $M_{LQ} \rightarrow \infty$. \label{fig:lq}}
\end{figure}
%
The best description of the data for the $\tilde{V}_{\circ}$ model
is obtained for $M_{LQ} \; = \; 276 \pm 7$ GeV and
$\lambda_{LQ} \; = \; 0.095 \pm 0.015$. 


Table \ref{tab:lq} summarizes the results of the global 
leptoquark analysis.\cite{glqa} For all leptoquark models the 95\% CL
exclusion limits are given both for $\lambda_{LQ}/M_{LQ}$
(upper limit) and for $M_{LQ}$ (lower limit).
%
For models which describe the existing experimental data 
better than the Standard Model 
the maximum value of the global probability ${\cal P}_{max}$ 
%  (normalised to the Standard Model probability)
and  the corresponding coupling to the
mass ratio $\left( \lambda_{LQ}/M_{LQ} \right)_{max}$ 
are included.
%
% For models with  ${\cal P}_{max}>20$ signal limits on 95\% CL,
% corresponding to ${\cal P}(\lambda_{LQ},M_{LQ}) = 0.05 \;{\cal P}_{max}$, 
% are given for  $\lambda_{LQ}/M_{LQ}$ and $M_{LQ}$. 
%
95\% CL signal limits  for  $\lambda_{LQ}/M_{LQ}$ and $M_{LQ}$,
defined by the condition 
${\cal P}(\lambda_{LQ},M_{LQ}) > 0.05 \;{\cal P}_{max}$, 
are given for models with  ${\cal P}_{max}>20$.
%
\begin{table}[t]
\caption{ Results of the global leptoquark analysis:
     the 95\% CL  exclusion limits on the leptoquark coupling to the
     mass ratio $\lambda_{LQ}/M_{LQ}$ (upper limit) 
     and the leptoquark mass $M_{LQ}$ (lower limit),
    the coupling to the mass ratio
    $( \lambda_{LQ}/M_{LQ} )_{max}$
   resulting in the best description of the experimental data
   and the corresponding model probability ${\cal P}_{max}$,
   and  the 95\% CL  signal limits on $\lambda_{LQ}/M_{LQ}$ and $M_{LQ}$,
   for models with ${\cal P}_{max}>20$. 
   Global probability function is defined in such a way that 
   the Standard Model probability ${\cal P}_{SM} \equiv 1$.
   \label{tab:lq}}
\vspace{0.2cm}
\begin{center}
\footnotesize
   \begin{tabular}{|l|cc|cc|cc|}
      \hline
      &  \multicolumn{2}{c|}{95\% CL }
      &  \multicolumn{2}{c|}{best description}
      & \multicolumn{2}{c|}{95\% CL  } \\ \cline{4-5}
%
      &  \multicolumn{2}{c|}{excl. limits}
      &    & 
      & \multicolumn{2}{c|}{signal limits } \\ \cline{2-3} \cline{6-7}
%
 Model &  \raisebox{0pt}[11pt][7pt]{$\frac{\lambda_{LQ}}{M_{LQ}}$} 
       & $M_{LQ}$
      &  \raisebox{4pt}[-8pt][-8pt]{$\left(\frac{\lambda_{LQ}}{M_{LQ}}\right)_{max}$}
      & ${\cal P}_{max}$     
      &  \raisebox{0pt}[-8pt][-8pt]{$\frac{\lambda_{LQ}}{M_{LQ}}$} 
      & $M_{LQ}$ \\
%
      & $TeV^{-1}$   & $GeV$ & $TeV^{-1}$  & &$TeV^{-1}$  &  $GeV$ \\ 
\hline
%
%
%  Leptoquark limits in CI approximation
%           20/04/2000  15.48.00
%
\raisebox{0pt}[8pt]{ $S_{\circ}^L$}  &  0.27 & 213 &     &   &   &   \\  
%
$S_{\circ}^R$  &  0.25 & 242 &     &   &   &   \\
%
$\tilde{S}_{\circ}$  &  0.28 & 242 &   &   &   &  \\
%
$S_{1/2}^L$    &  0.29 & 229 &      &   &   &  \\
%
$S_{1/2}^R$    & 0.49  & 245 & 0.32 $\pm$ 0.06 &  35.8 & 0.09--0.44 & 258 \\  
%
$\tilde{S}_{1/2}$  & 0.26 & 233 &    &   &   &  \\  
%
$S_1$  & 0.41 & 245 & 0.28 $\pm$ 0.04 &  367. & 0.15--0.36 &  267 \\  
%
\hline
%
\raisebox{0pt}[8pt]{ $V_{\circ}^L$}  &  0.12 & 230 &     &   &   &  \\ 
%
$V_{\circ}^R$  & 0.44 & 231 & 0.28 $\pm$ 0.07 &  11.7 &  & \\ 
%
$\tilde{V}_{\circ}$ & 0.52 & 235 & 0.34 $\pm$ 0.06 & 122. & 0.16--0.46 & 259 \\  
%
$V_{1/2}^L$  & 0.47 & 235 & 0.30 $\pm$ 0.06 &  31.7 & 0.08--0.42 &  254 \\  
%
$V_{1/2}^R$  &  0.13 & 262 &         &    &  &  \\
%
$\tilde{V}_{1/2}$  & 0.47 & 244 & 0.30 $\pm$ 0.07 &  14.8 & &  \\
%
$V_1$  &  0.14 & 254 &    &   &   &  \\
%
\hline
\end{tabular}
\end{center}
\end{table}


\section*{Acknowledgments}
This work has been partially supported by the Polish State Committee 
for Scientific Research (grant No. 2 P03B 035 17).


\section*{References}
\begin{thebibliography}{99}

\bibitem{gcia}   % My global analysis
A.F. \.Zarnecki \Journal{\EPJC}{11}{539}{1999}. 

\bibitem{dis99}   % My DIS99 contribution
A.F. \.Zarnecki \Journal{\em Nucl. Phys. Proc. Suppl.}{79}{158}{1999}.

\bibitem{apvnew}    % New APV results
S.C. Bennett and C.E. Wieman, \Journal{\PRL}{82}{2484}{1999}.

\bibitem{lepnew}    % LEP new results
LEP Electroweak Working Group, C.Geweniger {\it et al}, LEP2FF/00-01.

\bibitem{glqa}   % My global LQ analysis
A.F. \.Zarnecki .

\bibitem{brw}   % BRW model
W.Buchm\"uller, R.R\"uckl and D.Wyler, \Journal{\PLB}{191}{442}{1987}; \\
Erratum: \Journal{\PLB}{448}{320}{1999}.

\bibitem{lqci}  % LQ in CI approximation
J.Kalinowski {\it et al},    \Journal{\ZPC}{74}{595}{1997}.

\bibitem{aachen} % Aachen notation
A.Djouadi, T.K{\"o}hler, M.Spira, J.Tutas,  \Journal{\ZPC}{46}{679}{1990}.

\end{thebibliography}

\end{document}

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