# NLO corrections to $h\to b\bar b$ decay in SMEFT

## TL;DR

This paper provides a comprehensive calculation of NLO corrections to the Higgs decay into bottom quarks within the SMEFT framework, enabling more precise theoretical predictions for this process.

## Contribution

It presents the first complete NLO SMEFT calculation for $h o bar{b}$ decay, including 45 operators and addressing technical challenges like Higgs-$Z$ mixing and tadpole treatment.

## Key findings

- Analytic and numerical results for 45 dimension-6 operators at NLO.
- Identification of subtleties in Higgs-$Z$ mixing and tadpole renormalization.
- Demonstration of decoupling relations to control tadpole corrections.

## Abstract

We calculate the full set of next-to-leading order (NLO) corrections to $h\to b\bar{b}$ decay in the dimension-6 Standard Model Effective Field Theory (SMEFT). Our calculation forms the basis for precision studies of this decay mode in effective field theory, providing analytic and numerical results for contributions of the 45 dimension-6 operators appearing at NLO. On the technical side, we discuss several complications in NLO SMEFT computations which have not yet been addressed in the literature. These include subtleties in Higgs-$Z$ mixing, electric charge renormalization, and especially the treatment of tadpoles in SMEFT. In particular, we highlight the role of decoupling relations in eliminating potentially large tadpole corrections to the decay rate in hybrid renormalization schemes which employ the $\overline{\hbox{MS}}$~scheme for some Standard Model parameters (such as the $b$-quark mass and electric charge) and the on-shell scheme for others.