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.
Interplay between exactµ-τreflection symmetries, four-zero texture and universal texture
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
In this letter, we consider exact $\mu-\tau$ reflection symmetries for quarks and leptons. Fermion mass matrices are assumed to be four-zero textures for charged fermions $f = u,d,e$ and a symmetric matrix for neutrinos $\nu_{L}$. By a bi-maximal transformation, all the mass matrices lead to $\mu-\tau$ reflection symmetric forms, which seperately satisfy $T_{u} \, m_{u,\nu}^{*} \, T_{u} = m_{u,\nu}$ and $T_{d} \, m_{d,e}^{*} \, T_{d} = m_{d,e}$. Reconciliation between the $\mu-\tau$ reflection symmetries and observed $\sin \theta_{13}$ predicts $\delta_{CP} \simeq 203^{\circ}$. Moreover, imposition of universal texture $(m_{f})_{11} = 0$ for $f=u,d,\nu,e$ predicts the normal hierarchy with the lightest neutrino mass $|m_{1}| = 6.26$ or $2.54$ meV.
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hep-ph 3years
2026 3representative citing papers
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.
A model with μ-τ reflection symmetry from A4 predicts sin²θ12 ≳ 0.335 which is disfavored by JUNO results, leaving a surviving scenario with testable correlations to model parameters.
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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 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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Fate of $\theta_{12}$ under $\mu-\tau$ Reflection Symmetry in Light of the First JUNO Results
A model with μ-τ reflection symmetry from A4 predicts sin²θ12 ≳ 0.335 which is disfavored by JUNO results, leaving a surviving scenario with testable correlations to model parameters.