Can the CP asymmetries in B→ψ KS and B→ψ KL differ?

In the standard model the CP asymmetries in B --> psiK(S) and B --> psiK(L) are equal in magnitude and opposite in sign to very good approximation. We compute the order epsilon(K) corrections to each of these CP asymmetries and find that they give a deviation from sin 2beta at the half percent level, which may eventually be measurable. However, the correction to a(CP) (B --> psiK(S)) + a(CP)(B --> psiK(L)) due to epsilon(K) is further suppressed. The dominant corrections to this sum, at the few times 10(-3) level, come from the B lifetime difference, and CP violation in B-(B) over bar mixing and B --> psiK decay. New physics could induce a significant difference in the sin(Deltam (B) t) time dependence in the asymmetries if and only if the "wrong-flavor" amplitudes B --> psi(K) over bar or (B) over bar --> psiK are generated. A scale of new physics that lies well below the weak scale would be required. Potential scenarios are therefore highly constrained, and do not appear feasible. A direct test is proposed to set bounds on such effects. (C) 2002 Published by Elsevier Science B.V.