Flavor Patterns of Fundamental Particles from Quantum Entanglement?

TL;DR

This paper explores a novel connection between quantum entanglement and flavor mixing matrices in particle physics, suggesting that entanglement minimization could be a fundamental principle influencing particle parameters.

Contribution

It introduces a new perspective linking quantum entanglement to the structure of CKM and PMNS matrices, proposing entanglement minimization as a potential fundamental principle.

Findings

Entanglement is minimized when the CKM matrix is nearly diagonal.

Entanglement minimization occurs with large mixing angles in the PMNS matrix.

Hints at suppressed CP violation related to entanglement considerations.

Abstract

The Cabibbo-Kobayashi-Maskawa (CKM) matrix, which controls flavor mixing between the three generations of quark fermions, is a key input to the Standard Model of particle physics. In this paper, we identify a surprising connection between quantum entanglement and the degree of quark mixing. Focusing on a specific limit of $2 \to 2$ quark scattering mediated by electroweak bosons, we find that the quantum entanglement generated by scattering is minimized when the CKM matrix is almost (but not exactly) diagonal, in qualitative agreement with observation. With the discovery of neutrino masses and mixings, additional angles are needed to parametrize the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix in the lepton sector. Applying the same logic, we find that quantum entanglement is minimized when the PMNS matrix features two large angles and a smaller one, again in qualitative agreement with observation, plus a hint for suppressed CP violation. We speculate on the (unlikely but tantalizing) possibility that minimization of quantum entanglement might be a fundamental principle that determines particle physics input parameters.