# NNLO QCD$\oplus$QED corrections to Higgs production in bottom quark annihilation

## TL;DR

This paper calculates the NNLO QED and mixed QCD-QED corrections to Higgs production via bottom quark annihilation at the LHC, improving precision in theoretical predictions for collider experiments.

## Contribution

It provides the first systematic inclusion of NNLO QED and mixed QCD-QED corrections to this process, analyzing infrared structure and deriving relevant contributions.

## Key findings

- QED and QCD-QED corrections significantly affect Higgs production rates.
- Infrared poles are governed by universal anomalous dimensions.
- Numerical impact of NNLO corrections is quantified at LHC energies.

## Abstract

We present next-to-next-to leading order (NNLO) quantum electrodynamics (QED) corrections to the production of the Higgs boson in bottom quark annihilation at the Large Hadron Collider (LHC) in the five flavor scheme. We have systematically included the NNLO corrections resulting from the interference of quantum chromodynamics (QCD) and QED interactions. We have investigated the infrared (IR) structure of the bottom quark form factor up to two loop level in QED and in QCD$\times$QED using K+G equation. We find that the IR poles in the form factor are controlled by the universal cusp, collinear and soft anomalous dimensions. In addition, we derive the QED as well as QCD$\times$QED contributions to soft distribution function as well as to the ultraviolet renormalization constant of the bottom Yukawa coupling up to second order in strong coupling and fine structure constant. Finally, we report our findings on the numerical impact of the NNLO results from QED and QCD$\times$QED at the LHC energies taking into account the dominant NNLO QCD corrections.