Renormalization-group equations of the LEFT at two loops: dimension-five effects

TL;DR

This paper calculates the two-loop anomalous dimensions at dimension five in the low-energy effective field theory, providing essential corrections and methods for precise BSM physics predictions.

Contribution

It presents the first systematic two-loop calculation of anomalous dimensions in LEFT at dimension five, including finite counterterms and scheme comparisons.

Findings

Results for the CP-even sector in naive dimensional regularization scheme.

Two consistent methods to avoid explicit gauge-variant operator construction.

Advances towards a complete EFT framework for BSM physics at NLL accuracy.

Abstract

We present the first part of a systematic calculation of the two-loop anomalous dimensions in the low-energy effective field theory (LEFT): the effects at dimension five in the power counting. Our calculation is performed in a basis with generic mass matrices, we employ the algebraically consistent 't Hooft-Veltman scheme for $\gamma_5$, and we correct for evanescent as well as chiral-symmetry-breaking effects by including the appropriate finite counterterms. We also provide results for the $CP$-even sector in a scheme that coincides with naive dimensional regularization. We discuss two methods to avoid the explicit construction of gauge-variant operators, which in principle are needed for the cancellation of sub-divergences, even in the background-field method. The two methods are consistent with each other and with existing partial results. Our work is a further step towards a complete EFT framework for physics beyond the Standard Model at next-to-leading-logarithmic accuracy.