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28 pages, 2099 KiB

Open AccessArticle

Electroweak Parameters from Mixed SU(2) Yang–Mills Thermodynamics

by Janning Meinert and Ralf Hofmann

Symmetry 2024, 16(12), 1587; https://doi.org/10.3390/sym16121587 - 27 Nov 2024

Cited by 2 | Viewed by 1323

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 [...] Read more.

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 in 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

α

α^{- 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

θ_{W} \sim 30 °

, which belongs to deconfining phases of two SU(2) gauge theories of very distinct Yang–Mills scales (

Λ_{e} = 3.6

keV and

Λ_{CMB} \sim 10^{- 4}

eV). Here, the condition that the droplet’s bulk thermodynamics is stable determines the value of

θ_{W}

. The core radius of the monopole, whose inverse equals the droplet’s mass in natural units, is about 1% of

r_{0}

. Full article

(This article belongs to the Special Issue Fundamental Aspects of Theoretical Physics - Memorial Issue for Prof. Dr. Weinberg)

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12 pages, 400 KiB

Open AccessArticle

Toward Three-Loop Feynman Massive Diagram Calculations

by Ievgen Dubovyk, Johann Usovitsch and Krzysztof Grzanka

Symmetry 2021, 13(6), 975; https://doi.org/10.3390/sym13060975 - 31 May 2021

Cited by 4 | Viewed by 2782

Abstract

There are many methods of searching for traces of the so-called new physics in particle physics. One of them, and the main focus of this paper, is athe study of the Z-boson decay in

e^{+} e^{-}

collisions. An improvement in [...] Read more.

There are many methods of searching for traces of the so-called new physics in particle physics. One of them, and the main focus of this paper, is athe study of the Z-boson decay in

e^{+} e^{-}

collisions. An improvement in the precision of calculations of the Standard Model (SM) electroweak pseudo-observables, such as scattering asymmetries, effective weak mixing angles, and decay widths, related to the Z-boson will meet severe experimental requirements at the planned

e^{+} e^{-}

colliders and will increase the chance to detect non-standard effects in experimental analysis. To reach this goal, one has to calculate the next order of perturbative SM theory, namely three-loop Feynman integrals. We discuss the complexity of the problem, as well as the methods crucial for completing three-loop calculations. We show several numerical solutions for some three-loop Feynman integrals using sector decomposition, Mellin–Barnes (MB), and differential equation methods. Full article

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15 pages, 416 KiB

Open AccessArticle

Asymmetries in Processes of Electron–Positron Annihilation

by Andrej Arbuzov, Serge Bondarenko and Lidia Kalinovskaya

Symmetry 2020, 12(7), 1132; https://doi.org/10.3390/sym12071132 - 7 Jul 2020

Cited by 5 | Viewed by 3988

Abstract

Processes of electron–positron annihilation into a pair of fermions were considered. Forward–backward and left–right asymmetries were studied, taking into account polarization of initial and final particles. Complete 1-loop electroweak radiative corrections were included. A wide energy range including the Z boson peak and [...] Read more.

e^{+} e^{-}

colliders was covered. Sensitivity of observable asymmetries to the electroweak mixing angle and fermion weak coupling was discussed. Full article

(This article belongs to the Special Issue Symmetry in Particle Physics)

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10 pages, 1913 KiB

Open AccessConference Report

Spontaneous μ-τ Reflection Symmetry Breaking in Neutrino Phenomenology

by Guo-Yuan Huang, Zhi-Zhong Xing and Jing-Yu Zhu

Universe 2018, 4(12), 141; https://doi.org/10.3390/universe4120141 - 4 Dec 2018

Cited by 3 | Viewed by 2614

Abstract

The latest global analysis of neutrino oscillation data indicates that the normal neutrino mass ordering is favored over the inverted one at the

3 σ

level. The best-fit values of the largest neutrino mixing angle

θ_{23}^{}

and the Dirac CP-violating phase [...] Read more.

The latest global analysis of neutrino oscillation data indicates that the normal neutrino mass ordering is favored over the inverted one at the

3 σ

level. The best-fit values of the largest neutrino mixing angle

θ_{23}^{}

and the Dirac CP-violating phase

δ

are located in the higher octant and the third quadrant, respectively. We show that these experimental trends can be naturally explained by the

μ

τ

reflection symmetry breaking, triggered by the one-loop renormalization-group equations (RGEs) running from a superhigh energy scale down to the electroweak scale in the framework of the minimal supersymmetric standard model (MSSM). The complete parameter space is numerically explored for both the Majorana and Dirac cases, by allowing the smallest neutrino mass

m_{1}^{}

and the MSSM parameter

tan β

to vary within their reasonable ranges. Full article

(This article belongs to the Special Issue Selected Papers from the 7th International Conference on New Frontiers in Physics (ICNFP 2018))

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