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A Rephasing Invariant Formula for the Dirac CP Phase and General Perturbative Expansion: Prospects for DUNE and T2HK
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A Rephasing Invariant Formula for the Dirac CP Phase and General Perturbative Expansion: Prospects for DUNE and T2HK
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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.
Forward citations
Cited by 3 Pith papers
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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
CP phases φ1,2 in TM1,2 mixing equal rephasing invariants φ1 = -arg[U_e2 U_e3 U_μ1 U_τ1 / U_e1 det U] and φi = δ - arg[U_μi^0 U_τi^0].
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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.
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