Weak mixing matrix under permutation symmetry breaking

Abstract

The two-Higgs-doublet extension of the standard electroweak model is considered. A permutation symmetry-breaking scheme is proposed and used to calculate the weak mixing matrix up to second order. The CP-violation factor J and the correction to Bjorken's approximation are then given. A special case is considered.

A Two-Higgs-Doublet Model without Flavor-Changing Neutral Currents at Tree-Level

“…Theoretically, finding matrix pairs which can be diagonalized by a same U matrix simultaneously is a better way to solve the FCNC problem since that will be more general than those imposing symmetries [16][17][18][19], forbiddance [3] or zeros in mass matrices [8,9]. In usual, physicists prefer a general model applies to wider fields to special models apply only under certain conditions.…”

“…where p, q, r and s are arbitrary numbers, will also be diagonalized by the same U and free of tree-level FCNCs naturally. Besides, the derivation demonstrated above did not employ any symmetries like Z 2 in [3], S 3 in [16][17][18] or (S 3 + S 2 ) in [19] except for the only assumption of hermiticity of quark mass matrices. Such a matrix pattern is a very general one.…”

“…That can be achieved by letting either A = B = 0 or C = 0 for corresponding quark type. The S 3 pattern in Equation ( 1) can be achieved by letting x = y = 1 (firstly achieved in [16][17][18] or the case-1 in [19]). Those three patterns achieved in the (S 3 + S 2 ) model correspond to x = y = −1 (case-2), x = −y = 1 (case-3) and x = −y = −1 (case-4), respectively.…”

“…In fact, such matrix pairs do exist and the first one had been discovered in a S 3 -symmetric 2HDM [16][17][18] decades ago. The matrix pair derived there were…”

Theoretical Origin of CP Violation in a Special FCNC-Free 2HDM with $S_N$ Symmetries

“…In such a model both M 1 and M 2 are non-zero and can be diagonalized simultaneously by a same U matrix. In fact, the first such matrix pair had been discovered in a S 3 -symmetric 2HDM [14][15][16] decades ago. The matrix pair achieved there were given as…”