A Rephasing Invariant Formula for the Dirac CP Phase and General Perturbative Expansion: Prospects for DUNE and T2HK

TL;DR

This paper introduces a simple, rephasing-invariant formula for the Dirac CP phase in neutrino mixing, enabling precise perturbative corrections analysis relevant for upcoming experiments like DUNE and T2HK.

Contribution

It provides a novel, computationally simple formula for the Dirac CP phase and derives general perturbative corrections from charged-lepton mixing, enhancing predictions for future neutrino experiments.

Findings

The formula is less sensitive to approximations than the Jarlskog invariant.

Perturbative corrections can exceed 10 degrees, affecting experimental measurements.

Analytic expressions relate charged-lepton mixing to neutrino CP phase corrections.

Abstract

We present a formula for the Dirac CP phase $\delta = \arg ( U_{e1} U_{e2} U_{\mu 3} U_{\tau 3} / U_{e3} \det U_{\rm MNS} )$, directly derived from the lepton mixing matrix in an arbitrary basis of phases. In contrast to the numerically suppressed Jarlskog invariant, this expression is computationally simple and less sensitive to approximations. We apply the formula to derive general perturbative corrections from charged-lepton mixing $s_{ij}^{e}$ to the underlying CP phase of neutrinos $\delta_{\nu}$. A compact analytic expressions $\delta = \delta_{\nu} + s_{12}^{e} D_{12} + s_{13}^{e} D_{13} + s_{23}^{e} D_{23}$ shows that these corrections can substantially exceed $O(10^{\circ})$, potentially within the reach of future long-baseline experiments such as DUNE and T2HK.