CP violation in single top quark production and decay via p(p)over-bar→t(b)over-bar+X→W+b(b)over-bar+X within the MSSM:: A possible application for measuring arg(At) at hadron colliders

CP-nonconserving effects in the reaction p (p) over bar --> t (b) over bar + X --> W(+)b (b) over bar + X, driven by the supersymmetric CP-odd phase of the top squark trilinear soft breaking term arg(A(t)), are studied. We discuss the CP-nonconserving effects in both production and the associated decay amplitudes of the top quark. We find that, within a plausible low energy scenario of the MSSM and keeping the neutron electric dipole moment below its current limit, a CP-violating cross-section asymmetry as large as 2 - 3% can arise if some of the parameters lie in a favorable range. A partial rate asymmetry originating only in the top quark decay t --> W(+)b is found to be, in general, below the 0.1% level which is somewhat smaller than previous claims. For a low tan beta of order one the decay asymmetry can reach at the most similar to 0.3%. This (few) percent level overall CP-violating signal in p (p) over bar --> t (b) over bar + X --> W(+)b (b) over bar + X might be within the reach of the future 2(4) TeV p (p) over bar Fermilab Tevatron collider that may be able to produce similar to 10000 (similar to 30000) such t (b) over bar events with an integrated luminosity of 30 fb(-1). In particular, it may be used to place an upper bound on arg(A(t)) if indeed arg(mu) --> 0, as implied from the present experimental limit on the neutron electric dipole moment. The partial rate asymmetry in the top quark decay (similar to few X 10(-3)) may also be within the reach of the CERN LHC with similar to 10(7) pairs of t (t) over bar produced, provided detector systematics are sufficiently small. We also show that if the GUT scale universality of the soft breaking trilinear A terms is relaxed, then the phases associated with arg(A(u)) and arg(A(d)) can take values up to similar to few X 10(-1) even with squarks and gluino masses of several hundred GeV's without contradicting the experimental limit on the neutron electric dipole moment.