The CKM CP phase is expressed as a fourth-order rephasing invariant constructed from the down-quark mass matrix and its inverse via perturbative singular value decomposition.
A Rephasing Invariant Formula for the Dirac CP Phase and General Perturbative Expansion: Prospects for DUNE and T2HK
3 Pith papers cite this work. Polarity classification is still indexing.
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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.
fields
hep-ph 3years
2026 3representative citing papers
TM1,2 mixing phases φ1,2 equal specific rephasing-invariant phase combinations of the PMNS matrix and satisfy exact sum rules with the Dirac phase δ.
Under the approximations U13^e = 0 and U23^e = 0, the Fritzsch-Xing CP phase equals the sum of the neutrino-intrinsic phase and the relative phase between the first two generations.
citing papers explorer
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Perturbative determination of CP phase in CKM matrix using rephasing invariants of hierarchical mass matrices and their inverses
The CKM CP phase is expressed as a fourth-order rephasing invariant constructed from the down-quark mass matrix and its inverse via perturbative singular value decomposition.
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Rephasing invariant CP phases and sum rules in TM$_{1,2}$ mixing
TM1,2 mixing phases φ1,2 equal specific rephasing-invariant phase combinations of the PMNS matrix and satisfy exact sum rules with the Dirac phase δ.
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Rephasing invariant structure of CP phase for simplified mixing matrices in Fritzsch--Xing parametrization
Under the approximations U13^e = 0 and U23^e = 0, the Fritzsch-Xing CP phase equals the sum of the neutrino-intrinsic phase and the relative phase between the first two generations.