# Resummed prediction for Higgs boson production through $b\bar{b}$ annihilation at N$^3$LL

## TL;DR

This paper provides a highly precise theoretical prediction for Higgs boson production via bottom quark annihilation at the LHC, incorporating advanced N$^3$LO and N$^3$LL QCD corrections to improve accuracy.

## Contribution

It introduces the third order perturbative QCD correction to the process-dependent constant in the resummed expression, enabling consistent N$^3$LO+N$^3$LL predictions for Higgs production cross-sections.

## Key findings

- Enhanced accuracy of Higgs production cross-section predictions.
- Detailed analysis of threshold resummation effects at various energies.
- Assessment of scale dependence at high perturbative orders.

## Abstract

We present an accurate theoretical prediction for the production of Higgs boson through bottom quark annihilation at the LHC up to next-to-next-to-next-to leading order (N$^3$LO) plus next-to-next-to-next-to-leading logarithmic (N$^3$LL) accuracy. We determine the third order perturbative Quantum Chromodynamics (QCD) correction to the process dependent constant in the resummed expression using the three loop bottom quark form factor and third order quark soft distribution function. Thanks to the recent computation of N$^3$LO corrections to this production cross-section from all the partonic channels, an accurate matching can be obtained for a consistent predictions at N$^3$LO+N$^3$LL accuracy in QCD. We have studied in detail the impact of resummed threshold contributions to inclusive cross-sections at various centre-of-mass energies and also discussed their sensitivity to renormalization and factorization scales at next-to-next-to leading order (NNLO) matched with next-to-next-to leading logarithm (NNLL). At N$^3$LO+N$^3$LL, we predict the cross-section for different centre-of-mass energies using the recently available results in \cite{Duhr:2019kwi} as well as study the renormalization scale dependence at the same order.