An explicit calculation of pseudo-goldstino mass at the leading three-loop level

TL;DR

This paper explicitly calculates the pseudo-goldstino mass at the three-loop level in a two-sector SUSY breaking scenario with gauge mediation, revealing sensitivity to messenger mass ratios and providing analytical results.

Contribution

It provides the first explicit three-loop calculation of pseudo-goldstino mass considering general messenger masses and higher order SUSY breaking effects.

Findings

Pseudo-goldstino mass can be as low as 0.1 GeV.

Results are sensitive to messenger mass ratios.

Higher order SUSY breaking terms are relatively small.

Abstract

Pseudo-goldstinos appear in the scenario of multi-sector SUSY breaking. Unlike the true goldstino which is massless and absorbed by the gravitino, pseudo-goldstinos could obtain mass from radiative effects. In this note, working in the scenario of two-sector SUSY breaking with gauge mediation, we explicitly calculate the pseudo-goldstino mass at the leading three-loop level and provide the analytical results. In our calculation we consider the general case of messenger masses (not necessarily equal) and include the higher order terms of SUSY breaking scales. Our results can reproduce the numerical value estimated previously at the leading order of SUSY breaking scales with the assumption of equal messenger masses. It turns out that the results are very sensitive to the ratio of messenger masses, while the higher order terms of SUSY breaking scales are rather small in magnitude. Depending on the ratio of messenger masses, the pseudo-goldstino mass can be as low as ${{\cal O} (0.1)}$ GeV.