A lower bound on sin 2 beta from minimal flavour violation

We point out that there exists an absolute lower bound on sin2 beta in all models with minimal flavour violation (MFV), that do not have any new opera tors beyond those present in the Standard Model and in which all flavour ch anging transitions are governed by the CKM matrix with no new phases beyond the KM phase. This bound depends only on \V-cb\, \V-ub/V-cb\ and the hadro nic parameters (B) over cap (K), F(Bd)root(B) over cap (d) and xi relevant for the CP violating parameter epsilon and the B-d,s(0)-(B) over bar (0)(d, s) mixings. Performing a simple scanning over the present ranges of these p arameters we find sin2 beta greater than or equal to 0.34. We illustrate ho w this bound could become stronger when our knowledge of the parameters in question improves and when the upper bound on the B-s(0)-(B) over bar (0)(s ) mixing ((DeltaM)(s)) will be experimentally known. Provided the future ac curate measurements of sin2 beta through the CP asymmetry in B-d(0)((B) ove r bar (0)(d)) --> psiK(S) will confirm the low values recently reported by BaBar and Belie, there is a likely possibility that this class of models wi ll be excluded. This would firmly imply the necessity of new CP violating p hases and/or new effective operators in the weak effective Hamiltonians for K-0-(K) over bar (0) and B-d,s(0)-(K) over bar (0)(d,s) mixings. We also p oint out that within the MFV models there exists also an absolute lower bou nd on the angle gamma. We find sin gamma greater than or equal to 0.24. Thi s lower bound could become stronger in the future. (C) 2001 Elsevier Scienc e B.V. All rights reserved.