Resolving a discrete ambiguity in the CKM angle β through Bu,d→J/ψ K∗ and Bs→J/ψ φ decays

It is well known that sin(2β), where β is one of the angles of the unitarity triangle of the CKM matrix, can be determined in a theoretically clean way by measuring mixing-induced CP violation in the decay Bd→J/ψ KS. Another clean extraction of this CKM angle is provided by the time-dependent angular distribution for the decay products of Bd→J/ψ(→l+l−) K∗0(→π0KS), where we have more observables at our disposal than in the case of Bd→J/ψ KS, so that in addition to sin(2β) also cos(2β) can be probed in a direct way. Unfortunately a sign ambiguity remains in cos(2β). If it could be resolved, a discrete ambiguity in the extraction of the CKM angle β could be resolved as well, which would allow a more incisive test of the CKM model of CP violation. This note shows that detailed time-dependent studies of Bu,d→J/ψ K∗ and Bs→J/ψ φ decay processes can determine the sign of cos(2β), thereby removing the corresponding ambiguity in the extraction of the CKM angle β.