The leptonic CP phase is determined by an equation involving the PMNS matrix elements

TL;DR

This paper derives an equation involving the PMNS matrix elements that predicts the leptonic CP phase to be approximately 276 degrees, aligning with recent neutrino oscillation data, and connects it to similar quark sector symmetries.

Contribution

It introduces an equation based on matrix element equalities that predicts the leptonic CP phase, linking quark and neutrino sectors through hidden symmetries.

Findings

Predicted leptonic CP phase $oxed{ ext{276.10}^ ext{ ext{o}}}$ from the equation.

Equation yields a CKM CP phase consistent with experimental data.

Supports the hypothesis of common symmetries in quark and neutrino sectors.

Abstract

Several approximate equalities among the matrix elements of CKM and PMNS imply that hidden symmetries may exist and be common for both quark and neutrino sectors. The CP phase of the CKM matrix ($\delta_{\rm CKM}$) is involved in these equalities and can be investigated when these equalities turn into several equations. As we substitute those experimentally measured values of the three mixing angles into the equations for quarks, it is noted that one of the equations which holds exactly has a solution $\delta_{\rm CKM}=68.95^\circ$. That value accords with $(69.1^{+2.02}_{-3.85})^\circ$ determined from available data. Generalizing the scenario to the lepton sector, the same equality determines the leptonic CP phase $\delta_{\rm PMNS}$ to be $ 276.10^\circ$. Thus we predict the value of $\delta_{\rm PMNS}$ from the equation. So far there is no direct measurement on $\delta_{\rm PMNS}$ yet, but a recent analysis based on the neutrino oscillation data prefers the phase close to $270^\circ$.