English

Leptonic CP Conservation and the Quark CP Phase from Octonionic Flavor Structure

High Energy Physics - Phenomenology 2026-06-26 v1

Abstract

One generation of standard-model fermions can be realized on the complexified octonions through the Clifford algebra Cl(6)\mathcal{C}l(6); the octonionic unification programme extends this to three generations, with generation transport implemented by G2G_2 automorphisms or by rotors built from the ladder operators. We prove a localization theorem for the CP-violating phases of this structure, using only the Cl(6)\mathcal{C}l(6) construction and the stated three-generation representatives, independently of the wider programme. For quarks, the first-to-second generation step is the occupation flip of one ladder mode, with the up and down species coupling to conjugate ladder directions; a conjugation theorem forces Ad=AuA_d=A_u^* for every real transport, and the most general rung-generated rotor yields the exact one-parameter law ϕ12=2χ\phi_{12}=-2\chi: the (1,2)(1,2) transport phase is twice one Yukawa orientation angle. The programme's geometric rotor sits exactly at the quadrature-balanced point ϕ12=π/2|\phi_{12}|=\pi/2; the companion analysis reproduces the Cabibbo \emph{magnitude} Vus|V_{us}| with a single real tilt, leaving the rung near quadrature, but it does not extract a CKM CP phase, so the quark Dirac phase is fixed only once the underlying Yukawa orientation is computed. For leptons we prove a reality theorem: every charged-lepton and every neutrino transport amplitude is exactly real for every G2G_2 automorphism and every rotor that does not mix the identity line C1\mathbb C\cdot1 with the lepton--flavor plane span(e7,e5,e2)\mathrm{span}(e_7,e_5,e_2) a class that contains the entire quark-rung family--and identity--flavor mixing across that plane is the unique possible source of a leptonic phase. [Truncated]

Keywords

Cite

@article{arxiv.2606.27836,
  title  = {Leptonic CP Conservation and the Quark CP Phase from Octonionic Flavor Structure},
  author = {Bishnu Gupta Teli and Tejinder P. Singh},
  journal= {arXiv preprint arXiv:2606.27836},
  year   = {2026}
}

Comments

7 pages, 1 figure