Discrete Transformation of Baryon- and Lepton-Nonconserving Processes

TL;DR

This paper challenges the traditional set of fermionic phases ($\u2212 1, , , $) used in discrete symmetry transformations for baryon- and lepton-number violating processes, showing they are not universally valid.

Contribution

It introduces the $F$ number to accurately count fermions and demonstrates that for operators breaking $B-L$ symmetry, the standard phases are insufficient.

Findings

Standard fermionic phases are not always correct for $B-L$ violating processes.

Discrete transformations can alter fermionic phases from  to .

The $F$ number helps determine the proper phases for such operators.

Abstract

We consider discrete transformations ($C, P, T$ and $CP$) of baryon- and lepton-nonconserving processes. It has long been thought that values ($\pm 1, \pm i$) form the correct set of fermionic arbitrary phases for discrete transformations. In this paper we show that this idea is not generally true. In order to count the number of fundamental fermions in a process, $F$ number has been introduced. According to our evaluation for any operator which breaks $B-L$ symmetry and violate $F$ number the set of values ($\pm 1, \pm i$) is not the correct set of fermionic arbitrary phases, due to the fact that discrete transformations of such operators will change by altering the fermionic phases from $\pm 1$ to $\pm i$.