Pseudo-scalar Higgs boson production at N${}^3$LO${}_{\text{A}}$+N${}^3$LL${}^{\prime }$

Abstract

We consider the production of a pseudo-scalar particle $A$ at the LHC, and present accurate theoretical predictions for its inclusive cross section in gluon fusion. The prediction is based on combining fixed-order perturbation theory and all-order threshold resummation. At fixed order we include the exact next-to-next-to-leading order (NNLO) plus an approximate next-to-next-to-next-to-leading order (N${}^3$LO${}_{\mathrm{A}}$) which is based on the recent computation at this order for the scalar case. We then add threshold resummation at next-to-next-to-next-to leading logarithmic accuracy (N${}^3$LL${}^{\prime }$). Various forms of threshold resummation are considered, differing by the treatment of subleading terms, allowing a robust estimate of the theoretical uncertainties due to missing higher orders. With particular attention to pseudo-scalar masses of $200$ GeV and $750$ GeV, we also observe that perturbative convergence is much improved when resummation is included. Additionally, results obtained with threshold resummation in direct QCD are compared with analogous results as computed in soft-collinear effective theory, which turn out to be in good agreement. We provide precise predictions for pseudo-scalar inclusive cross section at $13$ TeV LHC for a wide range of masses. The results are available through updated versions of the public codes ggHiggs and TROLL.

14 pages, 7 figures, 1 table. Now includes a more precise assessment of the uncertainty on the approximate N3LO. Final version accepted by EPJC

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