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We demonstrate that in the class of models with Constrained Minimal FlavourViolation (CMFV), in which the CKM matrix is the only source of CP violationand B^0_q-\bar B^0_q mixings (q=d,s) are described by a single operator (\bar bq)_{V-A} (\bar b q)_{V-A}, the lower bounds on the mass differences DeltaM_{s,d} are simply given by their Standard Model values (Delta M_{s,d})_SM withtwo possible exceptions that we identify. Our proof involves all possiblecharged gauge boson, Goldstone boson and physical charged and neutral scalarexchanges and assumes that the masses of new charge +2/3 singlet heavy fermionsT_i that mix with the top quark have all to be larger than m_t, which is chosenby nature. Similarly, the additional charged gauge bosons have to satisfyM_i>M_W, while no such bound needs to be set on the charged and neutral scalarmasses. The two possible exceptions arise in the presence of U(1) neutral gaugebosons and Majorana fermions in box diagrams with flavour violating couplings.However in the case of the MSSM with CMFV and low tan beta our bound issatisfied in spite of gluino and neutralino contributions.Comment: 18 pages, 4 figures. v2: Discussion of neutral particle contributions  added, conclusions unchanged. v3: Discussion of Majorana fermion  contributions improved, conclusions unchange

Lower bounds on ΔMs,dfrom constrained minimal flavour violation

Lower bounds on ΔM_s,dfrom constrained minimal flavour violation