Can the CP asymmetries in B→ψKS and B→ψKL differ?

In the standard model the CP asymmetries in B→ψKS and B→ψKL are equal in magnitude and opposite in sign to very good approximation. We compute the order ϵK corrections to each of these CP asymmetries and find that they give a deviation from sin2β at the half percent level, which may eventually be measurable. However, the correction to aCP(B→ψKS)+aCP(B→ψKL) due to ϵK 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 mixing and B→ψK decay. New physics could induce a significant difference in the sin(ΔmB t) time dependence in the asymmetries if and only if the “wrong-flavor” amplitudes B→ψK or B→ψK 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.