Complex CKM matrix, spontaneous CP violation and generalized μ–τμ–τ symmetry

The multi-Higgs models having spontaneous CP violation (SPCPV) and natural flavor conservation (NFC) lead to a real CKM matrix V contradicting current evidence in favour of a complex V  . This contradiction can be removed by using a generalized μ–τμ–τ (called 23) symmetry in place of the discrete symmetry conventionally used to obtain NFC. If the 23 symmetry is exact then the Higgs induced flavour changing neutral currents (FCNC) vanish as in the case of NFC. 23 breaking introduces SPCPV, a phase in V   and suppressed FCNC among quarks. The FCNC couplings Fijd,u between i and j   generations show a hierarchy |F12d,u|<|F13d,u|<|F23d,u| with the result that the FCNC can have observable consequences in B   mixing without conflicting with the K0–K¯0 mixing. Detailed fits to the quark masses and the CKM matrix are used to obtain the (complex) couplings Fijd and Fiju. Combined constraints from flavour and CP violations in the K  , BdBd, BsBs, D   mesons are analyzed within the model. They allow (i) relatively light Higgs, 100–150 GeV (ii) measurable extra contributions to the magnitudes and phases of the Bd,s0–B¯d,s0 mixing amplitudes and (iii) the D0–D¯0 mixing at the current sensitivity level.