Resummed Higgs boson cross section at next-to SV to NNLO plus NNLL

We present the resummed predictions for inclusive cross section for the production of Higgs boson at nextto-next-to leading logarithmic (NNLL) accuracy taking into account both soft-virtual (SV) and next-to SV (NSV) threshold logarithms. We derive the N-dependent coefficients and the N-independent constants in Mellin-N space for our study. Using theminimal prescriptionwe perform the inverse Mellin transformation and match it with the corresponding fixed order results. We report in detail the numerical impact of N-independent part of resummed result and explore the ambiguity involved in exponentiating them. By studying the K factors at different logarithmic accuracy, we find that the perturbative expansion shows better convergence improving the reliability of the prediction at NNLO+ NNLL accuracy. For instance, the cross-section at NNLO + NNLL accuracy reduces by 3.15% as compared to the NNLO result for the central scale mu R = mu F = mH/2 at 13 TeV LHC. We also observe that the resummed SV + NSV result improves the renormalisation scale uncertainty at every order in perturbation theory. The uncertainty from the renormalisation scale mu R ranges between (+8.85%,-10.12%) at NNLO whereas it goes down to (+6.54%,-8.32%) at NNLO+ NNLL accuracy. However, the factorisation scale uncertainty isworsened by the inclusion of these NSV logarithms hinting the importance of resummation beyond NSV terms. We also present our predictions for SV + NSV resummed result at different collider energies.

Automated summary

This study presents the resummed predictions for the production of Higgs boson at NNLL accuracy, considering soft-virtual and next-to soft-virtual threshold logarithms. The perturbative expansion shows better convergence at NNLO+NNLL accuracy, reducing the uncertainty from the renormalisation scale. However, the inclusion of NSV logarithms worsens the uncertainty from the factorisation scale, indicating the importance of resummation beyond NSV terms.