Correlations among new CP violating effects in ΔF=2 observables

We point out that the observed CP violation in B-d-(B) over bar (d) mixing, taking into account the measured ratio Delta M-d/Delta M-s, the recently decreased lattice value of the nonperturbative parameter B boolean AND(K) and an additional effective suppression factor kappa(epsilon)similar or equal to 0.92 in epsilon(K) neglected so far in most analyses, may be insufficient to describe the measured value of epsilon(K) within the standard model (SM), thus hinting at new CP violating contributions to the K-(K) over bar and/or B-d-(B) over bar (d) systems. Furthermore, assuming that Delta M-d/Delta M-s is SM-like, the signs and the magnitudes of new-physics effects in epsilon(K) and in the CP asymmetries S-psi Ks and S-psi phi may turn out to be correlated. For example, in a scenario with new CP phases in B-d and B-s mixings being approximately equal and negative, a common new phase approximate to-5 degrees could remove the tension between epsilon(K) and S-psi Ks present in the SM and simultaneously accommodate, at least partly, the recent claim of S-psi phi being much larger than the SM expectation. We emphasize the importance of precise determinations of V-cb, B boolean AND(K), F-K, and xi(s), to which the parameter epsilon(K) and its correlation with the CP violation in the B-d-(B) over bar (d) system are very sensitive.