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We consider the production of a pseudo-scalar particle $A$ at the LHC, andpresent accurate theoretical predictions for its inclusive cross section ingluon fusion. The prediction is based on combining fixed-order perturbationtheory and all-order threshold resummation. At fixed order we include the exactnext-to-next-to-leading order (NNLO) plus an approximatenext-to-next-to-next-to-leading order (N$^3$LO$_{\rm A}$) which is based on therecent computation at this order for the scalar case. We then add thresholdresummation 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 ofthe theoretical uncertainties due to missing higher orders. With particularattention to pseudo-scalar masses of $200$ GeV and $750$ GeV, we also observethat perturbative convergence is much improved when resummation is included.Additionally, results obtained with threshold resummation in direct QCD arecompared with analogous results as computed in soft-collinear effective theory,which turn out to be in good agreement. We provide precise predictions forpseudo-scalar inclusive cross section at $13$ TeV LHC for a wide range ofmasses. The results are available through updated versions of the public codesggHiggs and TROLL.

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