Complex CKM matrix, spontaneous CP violation and generalized $\mu$-$\tau$ symmetry

TL;DR

This paper explores how a generalized $$ symmetry in multi-Higgs models can reconcile spontaneous CP violation with a complex CKM matrix, leading to observable flavor-changing effects consistent with experimental constraints.

Contribution

It introduces a generalized $$ symmetry framework that allows spontaneous CP violation and a complex CKM matrix while suppressing flavor-changing neutral currents, aligning theory with experimental data.

Findings

Hierarchical FCNC couplings with potential observable effects in B mixing.

Model accommodates light Higgs bosons around 100-150 GeV.

Predicts measurable contributions to meson mixing and CP violation.

Abstract

The multi-Higgs models having spontaneous CP violation (SPCV) 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 $\mu$-$\tau$ (called 23) symmetry in place of the discrete symmetry conventionally used to obtain NFC. If 23 symmetry is exact then the Higgs induced flavour changing neutral currents (FCNC) vanish as in case of NFC. 23 breaking introduces SPCV, a phase in $V$ and suppressed FCNC among quarks. The FCNC couplings $F_{ij}^{d,u}$ between $i$ and $j$ generations show a hierarchy $|F_{12}^{d,u}|<|F_{13}^{d,u}|<|F_{23}^{d,u}|$ with the result that the FCNC can have observable consequences in $B$ mixing without conflicting with the $K^0-\bar{K}^0$ mixing. Detailed fits to the quark masses and the CKM matrix are used to obtain the (complex) couplings $F_{ij}^d$ and $F_{ij}^u$. Combined constraints from flavour and CP violations in the $K,B_d,B_s,D$ 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 $B^0_{d,s}-\bar{B}^0_{d,s}$ mixing amplitudes and ($iii$) the $D^0-\bar{D}^0$ mixing at the current sensitivity level.