Finite temperature corrections and embedded strings in noncommutative geometry and the standard model with neutrino mixing

TL;DR

This paper investigates finite temperature effects and embedded string stability within a noncommutative geometry extension of the Standard Model, revealing a first-order electroweak phase transition and enhanced cosmic string stability.

Contribution

It introduces finite temperature corrections in a noncommutative geometry framework, showing their impact on phase transition order and cosmic string stability, with novel insights into torsion effects and neutrino mass generation.

Findings

Electroweak phase transition is first order at finite temperature.

New scalar interactions improve Z string stability.

Non-zero Majorana mass field in the physical vacuum.

Abstract

The recent extension of the standard model to include massive neutrinos in the framework of noncommutative geometry and the spectral action principle involves new scalar fields and their interactions with the usual complex scalar doublet. After ensuring that they bring no unphysical consequences, we address the question of how these fields affect the physics predicted in Weinberg-Salam theory, particularly in the context of the Electroweak phase transition. Applying the Dolan-Jackiw procedure, we calculate the finite temperature corrections, and find that the phase transition is first order. The new scalar interactions significantly improve the stability of the Electroweak Z string, through the ``bag'' phenomenon described by Watkins and Vachaspati. (Recently cosmic strings have climbed back into interest due to new evidence). Sourced by static embedded strings, an internal space analogy of Cartan's torsion is drawn, and a possible Higgs-force-like `gravitational' effect of this non-propagating torsion on the fermion masses is described. We also check that the field generating the Majorana mass for the $\nu_R$ is non-zero in the physical vacuum.