Hidden Symmetry of the CKM and Neutrino Mapping Matrices

TL;DR

This paper introduces a model linking small quark masses to T violation, using hidden symmetry and phase breaking, to explain the CKM matrix and neutrino mixing with consistent results.

Contribution

It presents a novel framework connecting quark masses, T violation, and the CKM matrix through hidden symmetry and phase breaking, also extending the approach to leptons.

Findings

Derived a relation for J_{CKM} in terms of quark masses and model parameters.

Estimated light quark masses consistent with experimental values.

Showed neutrino mixing matrix aligns with experimental data.

Abstract

We propose that the smallness of the light quark masses is related to the smallness of the T violation in hadronic weak interactions. Accordingly, for each of the two quark sectors ("upper" and "lower") we construct a 3\times 3 mass matrix in a bases of unobserved quark states, such that the "upper"and "lower" basis states correspond exactly via the $W^\pm$ transitions in the weak interaction. In the zeroth approximation of our formulation, we assume T conservation by making all matrix elements real. In addition, we impose a "hidden symmetry" (invariance under simultaneous translations of all three basis quark states in each sector), which ensures a zero mass eigenstate in each sector. Next, we simultaneously break the hidden symmetry and T invariance by introducing a phase factor e^{i\chi} in the interaction for each sector. The Jarlskog invariant J_{CKM}, as well as the light quark masses are evaluated in terms of the parameters of the model. We find a simple relation with J_{CKM}=(m_dm_s/m_b^2)^{1/2}A\lambda^3\cos(\chi/2), with A and \lambda the Wolfenstein parameters. Setting J_{CKM}=3.08 \times 10^{-5}, m_b=4.7GeV, m_s=95MeV, A=0.818 and \lambda=0.227, we find m_d\cos^2(\chi/2) \simeq 2.4MeV, consistent with the accepted value m_d=3-7MeV. We make a parallel proposal for the lepton sectors. With the hidden symmetry and in the approximation of T invariance, both the masses of e and \nu_1 are zero. The neutrino mapping matrix V_\nu is shown to be of the same Harrison-Scott form which is in agreement with experiments. We also examine the correction due to T violation, and evaluate the corresponding Jarlskog invariant {\cal J}_\nu.