Resummed next-to-soft corrections to rapidity distribution of Higgs boson to NNLO plus NNLL

We present the resummed 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 up to next-to-next-to-leading order plus next-to-next-to-leading-logarithmic (NNLO + NNLL) accuracy at LHC. Using our recent formalism, 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 transformation 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 NNLO + NNLL order. Further, we observe that the inclusion of resummed NSV contribution improves the renormalization scale uncertainty at every order in perturbation theory. However, the uncertainty due to factorization scale increases by the addition of resummed SV + NSV predictions to the fixed-order rapidity distribution.

Automated summary

In this study, we present accurate predictions for the rapidity distribution of Higgs boson using perturbative QCD, including both soft-virtual and next-to-soft-virtual threshold logarithms. The resummation is carried out using the double Mellin space method and only diagonal gg channel NSV contributions are considered. The results show that the prediction for the rapidity distribution becomes more reliable at NNLO + NNLL order, and the inclusion of resummed NSV contributions improves the renormalization scale uncertainty.