Dyonium Induced Fermion Number Violation

TL;DR

This paper investigates how dyonium configurations in a SU(2) x U(1) gauge theory can induce fermion number violation, providing insights into the dynamical conditions and zero modes involved in such processes.

Contribution

It introduces the concept of dyonium as a finite-sized dyon-anti-dyon pair and analyzes the fermionic zero modes in this background, extending previous monopolium studies.

Findings

Electric field excitation is necessary for anomaly fulfillment.

Fermionic zero modes are crucial for transition rate calculations.

The Dirac equation reduces to a single PDE similar to a renormalization group equation.

Abstract

Dyonium induced fermion number violation is studied in a SU(2) x U(1) gauge theory with a doublet Higgs field. Dyonium is a generalization of Nambu's monopolium, having finite sized pair of dyon and anti-dyon, connected with a thin string under the linear plus Coulomb force. This is a follow-up of the author's paper on monopolium induced neutrino mass (including the lepton and baryon number violations), studied with a SO(10) Grand Unified model in 1983. To fulfill the requirement from the chiral anomaly or its index theorem, an electric field should be excited in parallel to the dipole magnetic field. This crucial dynamical problem, not fully answered then, has been solved, by considering not monopolium but dyonium. The fermionic zero modes in the dyonium background fields are necessary in evaluating the transition rate of the fermion number violation processes. Their Dirac equation can be reduced to a single component partial differential equation, similar to the renormalization group equation, which may be useful to estimate the reaction rates.