$R$--Parity Violating SUSY or Leptoquarks: Virtual Effects in Dilepton Production

In the Standard Model (SM), dilepton production in hadron--hadron collisions proceeds through the conventional Drell--Yan mechanism $q \bar{q} \rightarrow l^+ l^-$ with the exchange of a gauge boson. Some extensions of the SM contain a quark--lepton contact interaction {\it via} a $q l \phi$ Yukawa coupling, where $\phi$ is a scalar. Theories with scalar leptoquarks and $R$--parity violating SUSY models are the most important examples of such extensions. These Yukawa couplings induce a different dynamical configuration compared to the SM ($t$-channel vs. $s$-channel) in the $q\bar{q} \rightarrow l^+l^-$ process and thus offer the possibility of being identifiable upon imposition of suitable kinematic cuts. We discuss these effects in the context of the dilepton production in the CDF experiment, and explore consequences in the forthcoming Large Hadron Collider (LHC).