Modified Reconstruction of Standard Model in Non-Commutative Differential Geometry

TL;DR

This paper presents a modified approach to reconstruct the Standard Model within non-commutative geometry, allowing for more flexible mass relations and Higgs potential without restrictive assumptions.

Contribution

It introduces a new scheme that incorporates generation mixing into non-commutative geometry, extending previous models to avoid specific mass and potential restrictions.

Findings

Reconstructed Standard Model without mass relation constraints

Allowed flexible Higgs potential in the non-commutative framework

Incorporated generation mixing into the geometric formulation

Abstract

Sogami recently proposed the new idea to express Higgs particle as a kind of gauge particle by prescribing the generalized covariant derivative with gauge and Higgs fields operating on quark and lepton fields. The field strengths for both the gauge and Higgs fields are defined by the commutators of the covariant derivative by which he could obtain the Yang-Mills Higgs Lagrangian in the standard model. Inspired by Sogami's work, we present a modification of our previous scheme to formulate the spontaneously broken gauge theory in non-commutative geometry on the discrete space; Minkowski space multiplied by two points space by introducing the generation mixing matrix in operation of the generalized derivative on the more fundamental fields a_i(x,y) which compose the gauge and Higgs fields. The standard model is reconstructed according to the modified scheme, which does not yields not only any special relations between the particle masses but also the special restriction on the Higgs potential.