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

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 ${\theta }_{\mathrm{W}}\sim 30^{\circ }$ which belongs to deconfining phases of two SU(2) gauge theories of very distinct Yang-Mills scales (${\Lambda }_{\mathrm{e}}=3.6$keV and ${\Lambda }_{\mathrm{CMB}}\sim 10^{-4}$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 $r_0$.

15 pages, 6 figures

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Cited by in corpus (1)

• Jacobson's thermodynamic approach to classical gravity applied to non-Riemannian geometries: remarks on the simplicity of Nature