# Effective Sextic Superpotential and $B-L$ violation in NMSGUT

## TL;DR

This paper analyzes the effective superpotential in the NMSGUT, focusing on operators up to sextic degree, their coefficients, and the impact of GUT scale threshold corrections on $B$ and $B-L$ violation, with implications for baryogenesis.

## Contribution

It provides explicit expressions for effective operators in the NMSGUT and explores how threshold corrections influence $B$ and $B-L$ violation, including the discovery of a novel $B, B-L$ violating operator.

## Key findings

- Identification of sextic superpotential operators and their coefficients.
- Threshold corrections can suppress $B$ violation to acceptable levels.
- Discovery of a new $B, B-L$ violating operator leading to $n o e^- K^+$.

## Abstract

We list operators of the superpotential of the effective MSSM that emerges from the NMSGUT up to sextic degree. We give illustrative expressions for the coefficients in terms of NMSGUT parameters. We also estimate the impact of GUT scale threshold corrections on these effective operators in view of the demonstration that $B$ violation via quartic superpotential terms can be suppressed to acceptable levels after including such corrections in the NMSGUT. We find a novel $B, B-L$ violating quintic operator that leads to the decay mode $n\to e^- K^+$. We also remark that the threshold corrections to the Type I seesaw mechanism make the deviation of right handed neutrino masses from the GUT scale more natural while Type II seesaw neutrino masses, which earlier tended to utterly negligible receive threshold enhancement. Our results are of relevance for analyzing $B-L$ violating operator based, sphaleron safe, Baryogenesis.