Light Stop Decay in the MSSM with Minimal Flavour Violation

TL;DR

This paper calculates the exact one-loop decay width of a light stop in the MSSM with Minimal Flavour Violation, highlighting the importance of resummation of large logarithms for accurate predictions relevant to LHC measurements.

Contribution

It provides the first exact one-loop calculation of the decay width in MFV, including resummation of large logarithms, improving upon previous approximate formulas.

Findings

Exact one-loop decay width differs by ~10% from approximate formula at large MFV scales.

Resummation of large logarithms significantly affects decay width predictions.

Negligible difference in branching ratios between exact and approximate calculations.

Abstract

In supersymmetric scenarios with a light stop particle $\tilde{t}_1$ and a small mass difference to the lightest supersymmetric particle (LSP) assumed to be the lightest neutralino, the flavour changing neutral current decay $\tilde{t}_1 \to c \tilde{\chi}_1^0$ can be the dominant decay channel and can exceed the four-body stop decay for certain parameter values. In the framework of Minimal Flavour Violation (MFV) this decay is CKM-suppressed, thus inducing long stop lifetimes. Stop decay length measurements at the LHC can then be exploited to test models with minimal flavour breaking through Standard Model Yukawa couplings. The decay width has been given some time ago by an approximate formula, which takes into account the leading logarithms of the MFV scale. In this paper we calculate the exact one-loop decay width in the framework of MFV. The comparison with the approximate result exhibits deviations of the order of 10% for large MFV scales due to the neglected non-logarithmic terms in the approximate decay formula. The difference in the branching ratios is negligible. The large logarithms have to be resummed. The resummation is performed by the solution of the renormalization group equations. The comparison of the exact one-loop result and the tree level flavour changing neutral current decay, which incorporates the resummed logarithms, demonstrates that the resummation effects are important and should be taken into account.