Dimension 7 operators in the b to s transition

TL;DR

This paper extends the effective field theory for b to s transitions to include dimension 7 operators, computes their anomalous dimensions, and explores implications for rare B meson decays within an extended Standard Model framework.

Contribution

It introduces the calculation of anomalous dimensions for dimension 7 operators and provides a solution to their renormalization group equations, extending previous dimension 6 analyses.

Findings

Derived anomalous-dimension matrix for dimension 7 operators

Solved RG equations involving dimension 7 operators

Placed limits on electroweak-magnetic operator from B decay data

Abstract

We extend the low-energy effective field theory relevant for b to s transitions up to operators of mass-dimension 7 and compute the associated anomalous-dimension matrix. We then compare our findings to the known results for dimension 6 operators and derive a solution for the renormalization group equations involving operators of dimension 7. We finally apply our analysis to a particularly simple case where the Standard Model is extended by an electroweak-magnetic operator and consider limits on this scenario from the decays Bs to mu+ mu- and B to K nu nubar.