Electroweak parameters from mixed SU(2) Yang-Mills Thermodynamics

TL;DR

This paper models the electron as an extended monopole droplet derived from SU(2) Yang-Mills thermodynamics, calculating electroweak parameters and phase stability conditions.

Contribution

It introduces a novel model of the electron as a monopole droplet from pure SU(2) thermodynamics, linking it to electroweak parameters and phase stability.

Findings

Electromagnetic fine-structure constant estimated as ~1/134.

Mixing angle θ_W approximated at ~30° from phase stability.

Core radius of monopole about 1% of droplet radius.

Abstract

Based on the thermal phase structure of pure SU(2) quantum Yang-Mills theory, we describe the electron at rest as an extended particle, a droplet of radius $r_0\sim a_0$, where $a_0$ is the Bohr radius. This droplet is of vanishing pressure and traps a monopole within its bulk at a temperature of $T_c=7.95$ keV. The monopole is the Bogomolny-Prasad-Sommerfield (BPS) limit. It is interpreted in an electric-magnetically dual way. Utilizing a spherical mirror-charge construction, we approximate the droplet's charge at a value of the electromagnetic fine-structure constant $\alpha$ of $\alpha^{-1}\sim 134$ for soft external probes. It is shown that the droplet does not exhibit an electric dipole or quadrupole moment due to averages of its far-field electric potential over monopole positions. We also calculate the mixing angle $\theta_{\rm W}\sim 30^{\circ}$ which belongs to deconfining phases of two SU(2) gauge theories of very distinct Yang-Mills scales ($\Lambda_{\rm e}=3.6\,$keV and $\Lambda_{\rm CMB}\sim 10^{-4}\,$eV). Here, the condition that the droplet's bulk thermodynamics is stable determines the value of $\theta_W$. The core radius of the monopole, whose inverse equals the droplet's mass in natural units, is about 1% of $r_0$.