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\begin{document}
\section{The case for RHIC Spin}
\subsection{Future plans/ideas at RHIC}
\subsubsection{Physics beyond the Standard Model (M.J.Tannenbaum)}
At RHIC, the standard model parity violating effects are large. 
In inclusive single jet production, the leading strong interaction 
process, the two-spin parity violating asymmetry, $A_{LL}^{PV}$,  due to the interference of gluon and 
$W$ exchange is $\sim 1$\%  at $\sqrt{s}=500$ GeV    
(see Fig.~\ref{fig:pvlambda} SM). 
Of course, a more spectacular effect at RHIC concerns the direct production of 
the Weak Bosons, $W^{\pm}$ and $Z^0$, visible through their di-jet or di-lepton decay.  The peak from $W\rightarrow$~Jets is 
evident in Fig.~\ref{fig:pvlambda}. 
\begin{figure}[htb] 
\centerline{\psfig{file=TaxilVireyALLPV.eps,height=4.0in}}
\caption[]{ Prediction~\cite{Virey} for $A_{LL}^{PV}$ in inclusive jet 
production at RHIC. Solid curve is standard model (SM), with error bars corresponding to sensitivity with $L=0.80$ fb$^{-1}$ integrated luminosity. Dot-dash curves are contact model of quark compositeness with $\Lambda_c=1.6$ TeV.} 
\label{fig:pvlambda}
\end{figure}
	Flavor-identified structure function measurements using $W^{\pm}$ production are discussed elsewhere in this document. Here we concentrate on the physics beyond the standard model that is opened up by searches for parity violating effects at RHIC.  A typical example of such a possibility is quark compositeness or substructure~\cite{MJT85}. 
	Composite models of quarks and leptons~\cite{eichten} 
generally violate parity, since the scale of compositeness 
$\Lambda_c \gg M_W$. 
Without the Parity Violating Asymmetry ($PVA$) handle, detectors at the Tevatron are limited to searching 
for substructure by deviations of jet production from QCD predictions 
at large values of $p_T$. It is difficult to prove that a 
small deviation is really due to something new. However a few \% 
parity-violation effect would be {\bf a clear 
indication of new physics}. The experimental limit is 
presently~\cite{CDFLambda}  $\Lambda_c\cong 1.6$ TeV. The estimate of sensitivity to compositeness at RHIC~\cite{Virey} with this value of $\Lambda_c$ is shown on 
Fig.~\ref{fig:pvlambda}. The error bars shown on the standard model correspond to  
$L=0.80$ fb$^{-1}$ integrated 
luminosity.  Structure function uncertainties 
can be calibrated out using the $PVA$ in $W\rightarrow$~Jet (inclusive) which 
is clearly visible on the plot. 
The limits of 
sensitivity for $\Lambda_c$ in the contact model of quark compositeness~\cite{TaxilVirey} are 
tabulated in Table~\ref{T:1} for the standard $L\sim 1$ fb$^{-1}$ integrated 
luminosity 
of the original RHIC-spin run plan. 
\begin {table}[h]
\begin{center}
\begin{tabular}{|c|c|c|}
\hline
$\sqrt{s}$ GeV & $L$(fb$^{-1}$) & $\Lambda_c$ (TeV) \\
\hline
500 & 1  & 3.3\\
500 & 10 & 5.5\\
500 & 100 &7.5\\
650 & 1& 3.8\\
650 & 10& 6.3\\
650 & 100& 8.8\\
\hline
\end{tabular}
\end{center}
\caption[]{Limits on $\Lambda(\epsilon=-1)$ at 95\% CL, P=0.7,  
$\Delta\eta=1$, 10\% systematic error in Asymmetry~\cite{TaxilVirey}.}
\label{T:1}
\end{table}
The limits increase siginificantly 
with factors of 10 and 100 increase in luminosity (but for this reaction, 
are not much improved with increasing c.m. energy). For comparison, at the 
Tevatron, sensitivity is $\Lambda_c\sim 4$ TeV for $L=$2 fb$^{-1}$ (Run II) and 
5 TeV for 30 fb$^{-1}$ (Run III) and $\Lambda_c\sim$ 20-30 TeV at the LHC for $L=10-100$ fb$^{-1}$. Of course, even if an anomaly were found at either the Tevatron or the LHC, only RHIC will be able to provide polarization information on the anomaly to determine what its chiral properties are and whether it is a new interaction, a supersymmetric particle, or   anything with a non-standard-model spin signature.    
\begin{thebibliography}{99}
\bibitem{MJT85} F.~Paige and M.~J.~Tannenbaum, cited in R.~Ruckl, {\it J. de Phys.} {\bf 46}, \ C2-55\ (1985) and T.~L.~Trueman, {\it ibid.}, C2-721. 
\bibitem{eichten}  E.~J.~Eichten, K.~D.~Lane and M.~E.~Peskin, 
{\it Phys. Rev. Lett.} {\bf 50},\ 811\ (1983). 
\bibitem{CDFLambda} CDF Collaboration, F.~Abe, {\it et al., 
Phys. Rev. Lett.} {\bf 68},\ 1104\ (1992); {\it ibid.} {\bf 77},\ 438\ (1996). 
See also New York Times, Feb 8, 1996.  
\bibitem{Virey} J.-M.~Virey, in {\em Beyond the Desert 1997, Proceedings of 
1st International Conference on Particle Physics Beyond the Standard
Model}, 8-14 Jun 1997, Castle Ringberg, Germany, hep-ph/9707470. See also, J. Soffer, {\it Acta Phys. Polon.} {\bf B29}, \ 1303\ (1998). 
\bibitem{TaxilVirey} P.~Taxil and J.~M.~Virey, {\it Phys. Rev.} {\bf D 55}, 4480\ (1997); {\it Phys. Lett. } {\bf B522},\ 89\ (2001).   
\end{thebibliography}
\end{document}
\begin{table}
\begin{center} 
\begin{tabular}{|c|cc|ccc|cc|}
\hline
%\topline
 & RHIC & & &TEVATRON  & &LHC & \\
%\midline
$L$ ($fb^{-1}$) & 0.8 & 3.2 & 1. & 10. & 100. & 10. & 100. \\
\hline
%\midline
$\epsilon = -1$ & 3.30 & 4.40 & 3.20 & 3.70 & 4.10 & 25.5 & 33.0 \\
\hline
%\midline
$\epsilon = +1$ & 3.25 & 4.35 & 2.90 & 3.35 & 3.75 & 16.0 & 19.5 \\
\hline
%\bottomline
\end{tabular}\\ 
\end{center}
%\vspace{-0.5cm}
\caption[]{Limits on $\Lambda$ in TeV at 95\% CL.}
\end{table}