# Non-minimal flavour violation in $A_4\times SU(5)$ SUSY GUTs with smuon assisted dark matter

## TL;DR

This paper investigates how non-minimal flavour violation in $A_4 imes SU(5)$ SUSY GUTs affects dark matter relic density, highlighting the importance of parameter correlations and cancellations in constraining flavour-violating parameters.

## Contribution

It provides a detailed analysis of flavour violation constraints in SUSY GUTs with dark matter, emphasizing the impact of multiple parameter variations and correlations on these constraints.

## Key findings

- Dark matter relic density constrains flavour-violating parameters.
- Simultaneous variation of parameters relaxes constraints due to cancellations.
- Correlations between GUT scale and low-scale flavour violation are significant.

## Abstract

We study CP-conserving non-minimal flavour violation in $A_4 \times SU(5)$ inspired Supersymmetric Grand Unified Theories (GUTs), focussing on the regions of parameter space where dark matter is successfully accommodated due to a light right-handed smuon a few GeV heavier than the lightest neutralino. In this region of parameter space we find that some of the flavour-violating parameters are constrained by the requirement of the dark matter relic density, due to the delicate interplay between the smuon and neutralino masses. By scanning over GUT scale flavour violating parameters, constrained by low-energy quark and lepton flavour violating observables, we find a striking difference in the results in which individual parameters are varied to those where multiple parameters are varied simultaneously, where the latter relaxes the constraints on flavour violating parameters due to cancellations and/or correlations. Since charged lepton-flavour violation provides the strongest constraints within a GUT framework, due to relations between quark and lepton flavour violation, we examine in detail a prominent correlation between some of the flavour violating parameters at the GUT scale consistent with the stringent lepton flavour violating process $\mu \rightarrow e \gamma$. We also examine the relation between GUT scale and low scale flavour violating parameters, for both quarks and leptons, and show how the usual expectations may be violated due to the correlations when multiple parameters are varied simultaneously.