Baryon and lepton number violating effective operators in a non-universal extension of the Standard Model

TL;DR

This paper explores how instanton-induced baryon and lepton number violations are affected by flavor structures in a non-universal extension of the Standard Model, providing new insights into flavor effects in such processes.

Contribution

It introduces a method to incorporate flavor interactions into instanton solutions within a non-universal gauge model, highlighting their potential significance.

Findings

Set bounds on the $SU(2)_h$ gauge coupling from instanton transitions.

Demonstrated the importance of flavor structure in baryon and lepton number violations.

Extended instanton analysis to a non-universal gauge framework.

Abstract

It is well known that non-abelian Yang-Mills theories present non-trivial minima of the action, the so-called instantons. In the context of electroweak theories these instanton solutions may induce violations of baryon and lepton number of the form $\Delta B = \Delta L = n_f$, with $n_f$ being the number of families coupled to the gauge group. An interesting feature of these violations is that the flavor structure of the gauge couplings is inherited by the instanton transitions. This effect is generally neglected in the literature. We will show that the inclusion of flavor interactions in the instanton solutions may be interesting in certain theoretical frameworks and will provide an approach to include these effects. In particular we will perform this implementation in the non-universal $SU(2)_l \otimes SU(2)_h \otimes U(1)_Y$ model that singularizes the third family. Within this framework, we will use the instanton transitions to set a bound on the $SU(2)_h$ gauge coupling.