Discrete Transformation of Baryon- and Lepton-Nonconserving Processes

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 $\pm i$.