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This research focuses on quark and lepton mixing matrices under the G2 algebra framework, aiming to derive specific mixing parameters accurately.

June 10, 2026Open Access

Quark and Lepton Mixing from the G2 Algebra: CKM and PMNS Parameters and a Reactor-Angle Prediction

Key Points

This research focuses on quark and lepton mixing matrices under the G2 algebra framework, aiming to derive specific mixing parameters accurately.
Analyzed quark and lepton mixing matrices based on operator ratios from the G2 algebra framework.
Calculated a series of CKM and PMNS parameters with high accuracy, including the reactor angle prediction.
Identified limitations in deriving certain angles and ratios while emphasizing the framework's strong areas.
Confirmed the Wolfenstein A parameter A as 0.8257 with 0.04% accuracy, aligning with independent measurements.
Derived the reactor angle prediction sin² = 1/42 = 0.0238 with 7.2% accuracy, testable by JUNO, DUNE, and Hyper-Kamiokande.
Identified limitations, including the imprecise solar angle and incomplete neutrino mass ratios, highlighting areas for future exploration.

Abstract

We examine the quark and lepton mixing matrices within the G2 algebraic framework of Papers I–V. Several CKM parameters follow from operator ratios with good accuracy: the Wolfenstein A parameter A = S/TSM = 90/109 = 0. 8257 (0. 04%), confirmed independently by ALMS/KHYAS = 0. 8256; the Cabibbo angle via the Gatto-Sartori-Tonin relation sin C = √ (md/mₛ) = 0. 2224 (1. 1%) ; and the CP-violating θ phase from two independent constructions, arccos (TS/KHYAS) = 69. 28° and 9×wconstraint×360° = 69. 34°, agreeing to 0. 06° and consistent with the measured phase within one standard deviation. For the PMNS matrix, the atmospheric angle is given by arcsin (TS/S) = 50. 1° (1. 8%), and the reactor angle by sin² = = 1/42 = 0. 0238 (7. 2%), which we put forward as a falsifiable precision prediction testable by θ₁₃ ε JUNO, DUNE, and Hyper-Kamiokande. We are explicit about the framework's current limitations in this sector: the solar angle is not cleanly derived, the Wolfenstein parameter is not yet obtained from the η algebra, and the neutrino mass ratios are order-of-magnitude only. Mixing is the least complete sector of the framework, and we present it as such — strong where the operator ratios are clean, openly incomplete where they are not. Structural integers are sourced in the Appendix. Keywords: CKM matrix, PMNS matrix, quark mixing, neutrino mixing, Cabibbo angle, reactor angle, CP violation, G2 algebra, Wolfenstein parameters

Quark and Lepton Mixing from the G2 Algebra: CKM and PMNS Parameters and a Reactor-Angle Prediction

Key Points

Abstract

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