Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 21 min ago
PreprintarXiv licencearXiv

Perturbative determination of quark CP phase and rephasing invariants of hierarchical mass matrices using their inverses

  • Masaki J. S. Yang
Open at sourcePDFDOICite

Abstract

In this paper, we derive approximate expressions for the CP phase δ in the CKM matrix by a perturbative singular value decomposition for hierarchical mass matrices of quarks mu,d. The diagonalization is achieved through a seesaw-like procedure in which the heavier generations are successively integrated out, naturally leading to mixing matrices expressed in terms of the mass matrices and their inverses mu,d−1. As a result, in the basis where the up-type quark mass matrix is diagonal, δ is reduced to a fourth-order invariant δ≃ arg [ − m−1d12 md23 / m−1d11 md13 ]. Furthermore, in the Kobayashi--Maskawa parametrization, the CP phase is likewise expressed by an invariant δKM ≃ arg [ m−1d13 md33 / m−1d11 md13 ] ≃ π/2 in the same basis. Since the next-to-leading-order corrections are suppressed at second order in the perturbation, the accuracy of these expressions is typically of order O(λ2) ∼ 4 %.

Related

  1. The non-perturbative topological string: from resurgence to wall-crossing of DT invariants
    Simon Douaud, Amir-Kian Kashani-Poor
    Journal of High Energy PhysicsPeer-reviewedCC BY 4.0Full textMathematical physicsHigh-energy & particle physicsHAL
  2. Electron Rephasing in a Truncated Tunable Plasma Channel
    Arujash Mohanty, Santhosh Krishnamurthy, Yinren Shou +6
    arXivPreprintarXiv licenceFull textApplied physics & instrumentationOptics & photonicsarXiv
  3. Instanton liquid framework for non-perturbative QCD in light hadrons
    Wei-Yang Liu
    Nuclear Physics BPeer-reviewedCC BY 4.0Full textHigh-energy & particle physicsCrossref
  4. Practical approach to perturbative corrections to few-body observables
    Sourav Mondal, Martin Schäfer, Mirko Bagnarol +3
    Phys.Rev.CPeer-reviewedLicence not statedNuclear physicsHAL
  5. Quantum Residues and the Geometry of Perturbative/Non-perturbative Relations
    Can Kozçaz
    arXivPreprintCC BY 4.0Full textHigh-energy & particle physicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{yang2026perturbative,
  title = {{Perturbative determination of quark CP phase and rephasing invariants of hierarchical mass matrices using their inverses}},
  author = {Masaki J. S. Yang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.06985},
  eprint = {2607.06985},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.06985},
}
RIS
TY  - UNPB
TI  - Perturbative determination of quark CP phase and rephasing invariants of hierarchical mass matrices using their inverses
AU  - Masaki J. S. Yang
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2607.06985
UR  - https://arxiv.org/abs/2607.06985
AB  - In this paper, we derive approximate expressions for the CP phase δ in the CKM matrix by a perturbative singular value decomposition for hierarchical mass matrices of quarks m_u,d. The diagonalization is achieved through a seesaw-like procedure in which the heavier generations are successively integrated out, naturally leading to mixing matrices expressed in terms of the mass matrices and their inverses m_u,d^−1. As a result, in the basis where the up-type quark mass matrix is diagonal, δ is reduced to a fourth-order invariant δ≃ arg [ − m^−1_d12 m_d23^ / m^−1_d11 m_d13^ ]. Furthermore, in the Kobayashi--Maskawa parametrization, the CP phase is likewise expressed by an invariant δ_KM ≃ arg [ m^−1_d13 m_d33^ / m^−1_d11 m_d13^ ] ≃ π/2 in the same basis. Since the next-to-leading-order corrections are suppressed at second order in the perturbation, the accuracy of these expressions is typically of order O(λ^2) ∼ 4 %.
ER  -