Resummed next-to-soft corrections to rapidity distribution of Higgs Boson to $ \textbf{NNLO} + \overline{\textbf{NNLL} } $

TL;DR

This paper provides resummed predictions for the Higgs boson rapidity distribution at the LHC, incorporating next-to-soft corrections up to NNLO + NNLL accuracy, improving theoretical precision and scale uncertainty estimates.

Contribution

It introduces a formalism for resumming both soft-virtual and next-to-soft threshold logarithms for Higgs rapidity distribution at NNLO + NNLL, including the impact of NSV contributions from the gg channel.

Findings

Resummation improves the convergence of the rapidity distribution predictions.

Including NSV contributions reduces renormalisation scale uncertainty.

Factorisation scale uncertainty increases with resummation.

Abstract

We present the resumed predictions consisting of both soft-virtual(SV) as well as next-to-SV(NSV) threshold logarithms to all orders in perturbative QCD for the rapidity distribution of Higgs Boson till $\rm NNLO + \overline{NNLL}$ accuracy at LHC. Using our recent formalism\cite{Ajjath:2020lwb}, the resummation is carried out in the double Mellin space by restricting the NSV contributions only from diagonal $gg$ channel. We perform the inverse Mellin ransformation using the minimal prescription procedure and match it with the corresponding fixed order results. We do a detailed analysis of the numerical impact of the resummed result. The K-factor values at different logarithmic accuracy suggest that the prediction for the rapidity distribution converges and becomes more reliable at $\rm NNLO + \overline{NNLL}$ order. We further observed that the inclusion of resumed NSV contribution improves the renormalisation scale uncertainty at every order in perturbation theory. However, the uncertainty due to factorisation scale increases by the addition of resummed SV+NSV predictions to the fixed order rapidity distribution.