English

Quark mixing angles and weak CP-violating phase vs quark masses: potential approach

High Energy Physics - Phenomenology 2023-06-22 v2

Abstract

It is shown that following experimentally viable expressions for quark mixing angles θ12\theta_{12}, θ23\theta_{23}, θ13\theta_{13} and CP-violating phase δ\delta: sinθ12=md/ms\sin\theta_{12} = \sqrt{m_{d} / |m_{s}|}, sinθ23=2ms/mb\sin\theta_{23} = 2 \, |m_{s}| / m_{b}, sinθ132md/mb\sin\theta_{13} \approx 2 \, m_{d} / m_{b}, tanδ=mb2mc/6mtms2\tan\delta = m_{b}^{2} \, m_{c} / 6 \, m_{t} \, m_{s}^{2} may be derived as stable points of certain 4-th power in VCKMV_{CKM} flavor-invariant potentials built with traces of 3x3 quark up and down mass matrices and the Jarlskog invariant. There is no fine-tuning, potentials' dimensionless constants are the integer numbers not above 10.

Keywords

Cite

@article{arxiv.2303.16568,
  title  = {Quark mixing angles and weak CP-violating phase vs quark masses: potential approach},
  author = {Boris Altshuler},
  journal= {arXiv preprint arXiv:2303.16568},
  year   = {2023}
}

Comments

13 pages. arXiv admin note: substantial text overlap with arXiv:2210.09780

R2 v1 2026-06-28T09:39:33.784Z