%Title: Charge asymmetry of top production at hadron colliders
%Author: J.H. K\"uhn and G. Rodrigo
%Published:     <EM> Proceedings of the XXXIIIrd Rencontres de Moriond</EM> Les Arcs, France. 
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\begin{document}
\vspace*{4cm}
\title{CHARGE ASYMMETRY OF TOP PRODUCTION AT HADRON COLLIDERS}

\author{G.~Rodrigo and J.H.~K\"uhn}

\address{ Institut f\"ur Theoretische Teilchenphysik,
    Universit\"at Karlsruhe,\\ D-76128 Karlsruhe, Germany}

\maketitle\abstracts{
A sizeable difference in the differential production cross section
of top and antitop quarks, respectively, is predicted for 
hadronically produced heavy quarks.
It is of order $\alpha_s$ and arises from the 
interference between charge odd and even amplitudes respectively.
For the TEVATRON it amounts up to 15\% for the differential 
distribution in suitable chosen kinematical regions.
The resulting integrated forward-backward asymmetry of 
4--5\% could be measured in the next round of experiments.
At the LHC the asymmetry can be studied by selecting 
appropriately chosen kinematical regions.
}

Top quark production at hadron colliders has become one of the
central issues of theoretical~\cite{Catani:1997rn}
and experimental~\cite{Tipton:1996}
research. The investigation and understanding of the production 
mechanism is crucial for the determination of the top quark 
couplings, its mass and the search for new physics involving the top
system. 
A lot of effort has been invested in the prediction of the total 
cross section and, more recently, of inclusive transverse
momentum distributions~\cite{Catani:1997rn}. 

In this work we point to a different aspect of the hadronic
production process, which can be studied with a 
fairly modest sample of quarks.
Top quarks produced through light quark-antiquark annihilation 
exhibit a sizeable charge asymmetry -- an excess of 
top versus antitop quarks in specific kinematic regions --
induced through the interference of the final-state
with initial-state radiation 
and the interference of the box with the lowest-order-diagram.
The asymmetry is thus of order $\alpha_s$ relative to the 
dominant production process.

Top production at the TEVATRON is dominated by quark-antiquark
annihilation, hence the charge asymmetry will be reflected
not only in the partonic rest frame but also in the center 
of mass system of proton and antiproton. The situation 
is more intricate for proton-proton collisions at the LHC, 
where no preferred direction is at hand in the laboratory frame. 
Nevertheless it is also in this case possible to pick 
kinematical configurations which allow the study of the charge
asymmetry~\cite{KR}.

The charge asymmetry has also been investigated in~\cite{Halzen:1987xd}
for a top mass of $45$ GeV. There, however, only the contribution 
from real gluon emission was considered requiring the 
introduction of a physical cutoff on the gluon energy and 
rapidity to avoid infrared and collinear singularities.
Experimentally, however, only inclusive top-antitop production has been 
studied to date, and the separation of an additional soft 
gluon will in general be difficult. 
In this work, we  include virtual corrections and 
consider inclusive distributions only.
The sign of the asymmetry we found is opposite to the one 
given for the $t\bar{t}g$ process in~\cite{Halzen:1987xd}.
The charge asymmetry of heavy flavour production in quark-antiquark
annihilation to bottom quarks was also discussed
in~\cite{Ellis:1986ba,Nason:1989zy,Beenakker:1991ma} where its contribution 
to the forward-backward asymmetry in proton-antiproton collisions
was shown to be very small.
In addition there is also a slight difference between the 
distribution of top and antitop quarks in the reaction 
$g q \to t \bar{t}q$. At the 
TEVATRON its contributions is bellow~$10^{-4}$. 

At the partonic level the QCD asymmetry is related to the 
corresponding QED asymmetry~\cite{Berends:1973}
through  the replacement of $\alpha_{QED} Q Q'$ by the factor 
$\frac{1}{2}\alpha_s (d_{abc}/4)^2 = \alpha_s \cdot 5/12$.
The asymmetry can in principle be studied experimentally in 
the partonic restframe, as a function of $\hat{s}$, by 
measuring the invariant mass of the $t \bar{t}$ system 
plus an eventually radiated gluon. It is, however, also instructive
to study the asymmetry in the laboratory frame by folding 
the angular distribution with the structure
functions~\cite{Martin:1996as}.
For the total charge asymmetry in the laboratory frame we predict~\cite{KR0}
\beq
\bar{A} = 
\frac{N_t(\cos \theta \geq 0)
    - N_{\bar{t}}(\cos \theta \geq 0)}
     {N_t(\cos \theta \geq 0)
    + N_{\bar{t}}(\cos \theta \geq 0)} = 4.3 - 4.6 \%~,
\eeq
where different choices of the structure function and 
different choices of the factorization scale, $\mu = \sqrt{\hat{s}}$
and $\mu = \sqrt{\hat{s}}/2$, have been considered.
We defined $\cos \theta$ as the top quark production angle in 
the $p \bar{p}$ restframe and $N(\cos \theta) =
d\sigma/d\Omega (\cos \theta)$.

In principle one might expect that cuts on the top quark or its
decay products at large rapidities could affect the asymmetry.
Nevertheless, the rapidity distribution shows that the 
asymmetry approaches its maximal value already for 
$y_{cut}=1$, indicating that also cuts on the top decay products 
$W$ and $b$ jets with rapidities, say, larger than 2 will not lead
to a significant reduction of the asymmetry.
We would also like to mention that event generators which do not 
include the full NLO matrix
elements~\cite{Marchesini:1991ch,Sjostrand:1994yb} cannot 
predict the asymmetry.


\section*{Acknowledgments}
We would like to acknowledge useful discussions with R.K.~Ellis,
T.~Sj\"ostrand and M.~Seymour.
Work supported by BMBF under Contract 057KA92P 
and DFG under Contract Ku 502/8-1.



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

\bibitem{Catani:1997rn}
R.~K. Ellis {\it these Proceedings}.

\bibitem{Tipton:1996}
M.~Strovink {\it these Proceedings}.

\bibitem{KR}
J.~H. K{\"u}hn and R.~Rodrigo {\em In preparation}.

\bibitem{Halzen:1987xd}
F.~Halzen, P.~Hoyer, and C.~S. Kim {\em Phys. Lett.} {\bf 195B} (1987) 74.

\bibitem{Ellis:1986ba}
R.~K. Ellis {\em in Strong Interactions and Gauge Theories, ed. J.~Tran Thanh
  Van (Editions Fronti\`ere, Gif-sur-Yvette) pg.339} (1986).

\bibitem{Nason:1989zy}
P.~Nason, S.~Dawson, and R.~K. Ellis {\em Nucl. Phys.} {\bf B327} (1989) 49.

\bibitem{Beenakker:1991ma}
W.~Beenakker {\em et.~al.} {\em Nucl. Phys.} {\bf B351} (1991) 507.

\bibitem{Berends:1973}
F.~A. Berends {\em et.~al.} {\em Nucl. Phys.} {\bf B63}
  (1973) 381; {\em Acta Phys. Polon.} {\bf B14} (1983) 413.

\bibitem{Martin:1996as}
A.~D. Martin, R.~G. Roberts, and W.~J. Stirling {\em Phys. Lett.} {\bf B387}
  (1996) 419.

\bibitem{KR0}
J.~H. K{\"u}hn and R.~Rodrigo, {{\tt hep-ph/9802268}}.

\bibitem{Marchesini:1991ch}
G.~Marchesini {\em et.~al.} {\em Comput. Phys. Commun.} {\bf 67} (1992) 465.

\bibitem{Sjostrand:1994yb}
T.~Sj{\"o}strand {\em Comput. Phys. Commun.} {\bf 82} (1994) 74.

\end{thebibliography}

\end{document}

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