Higgs boson rapidity distribution in bottom annihilation at NNLL and beyond

Abstract

We present precise resummed predictions for Higgs boson rapidity distribution through bottom quark annihilation at next-to-next-to-leading logarithmic (NNLL) accuracy matched to next-to-next-to-leading order (NNLO) and at next-to-next-to-next-to-leading logarithmic (N3LL) accuracy matched to next-to-next-to-next-to-leading order soft-virtual (N3LOsv) in the strong coupling. Exploiting the universal behavior of soft radiation near the threshold, we determine the analytic expressions for the process-dependent and universal perturbative ingredients for threshold resummation in double singular limits of partonic threshold variables $z_1,z_2$. Subsequently, the threshold resummation is performed in the double Mellin space within the standard QCD framework. The new third-order process-dependent non-logarithmic coefficients are determined using three-loop bottom quark form factor and third-order quark soft distribution function in rapidity distribution. The effect of these new resummed coefficients are studied at the $13$ TeV LHC. We observe a better perturbative convergence in the resummed predictions on the Higgs rapidity spectrum in bottom quark annihilation. We also find that the NNLL and N3LL corrections are sizeable which typically are of the order of $-2.5\%$ and $-1.5\%$ over the respective available fixed orders with the scale uncertainty remaining at the same level as the fixed order.