T Violation Induced by Supersymmetry in tt̄ and W + W −

T -odd correlations of polarizations and momenta provide a promising testing ground for new physics beyond the standard model. We estimate the contribution of the minimal supersymmetric extension of the standard model to two such observables: in the production of tt̄, we look for a term proportional to Jt · ( pq × pt ) —where Jt is the polarization of the t quark and pq,t are the momenta of the initial and final particles—and find that it is of the order of 10 × (αs/π). In the production of WW, we look for a term proportional to EW · ( pq × pW ) ( pq · EW ) —where EW is the transverse polarization of W— to find that it can be as large as 10×(αw/π). CERN-TH.6751/92 Revised version, May 1993. 1. Observables which, in a given cross section, are made out of an odd number of momenta and polarizations change sign under time reversal. If we assume that CPT invariance holds, such a T -odd correlation can arise either because of final state interactions [1] or because of a violation of CP invariance. The former is a consequence of the unitarity of the S matrix and carries no new dynamical information. It is a background that can be subtracted by taking the difference between the process we are interested in and its CP conjugate [2]. This way, the truly (that is, CP -odd) time-reversal-violating observable is isolated. Such observables are negligible in the standard model—where the only possible CP -odd source of such a T -odd correlation is in the Kobayashi-Maskawa quarkmixing matrix, the effect of which is, however, suppressed by the unitarity of the matrix itself—and, for this reason, they provide a promising testing ground for physics beyond the standard model [3, 4, 5]. New physics may be unveiled either because some of the final states are made of new particles or because of its effects in the radiative corrections to the amplitude of the process. We follow this latter path and include one-loop corrections in the framework of the minimal supersymmetric extension of the standard model [6]. This model is of interest here inasmuch as time reversal invariance can be violated to a larger degree than in the standard model because of the presence of coupling strengths that cannot be made real by a suitable redefinition of the particle fields. We consider two processes which should give rise to measurable T -odd and CP violating observables. The first one is the production of tt̄ pairs in hadron qq̄ collisions and in ee annihilation: eē → tt̄ , (1) in which we look for terms in the cross section proportional to Jt · (k × p) |k × p| , (2) where Jt is the polarization vector of one of the produced t quarks, k and p are two vectors characterizing the scattering plane—hereafter chosen to be k, the center-ofmass momentum of the colliding pair, and p, the momentum of the final t quark. Other CP -odd observables have been recently computed within the minimal supersymmetric extension of the standard model [7].