Rapidity distribution of pseudo-scalar Higgs boson to $\rm{\textbf{NNLO}_A+\overline{\textbf {NNLL}}}$

We present the differential predictions for the rapidity distribution of pseudo-scalar Higgs boson through gluon fusion at the LHC. These results are obtained taking into account the soft-virtual (SV) as well as the next-to-soft virtual (NSV) resummation effects to next-to-next-to-leading-logarithmic ($\rm{\overline{NNLL}}$) accuracy and matching them to the approximate fixed order next-to-next-to-leading-order ($\rm{NNLO_A}$) computation. We perform the resummation in two dimensional Mellin space using our recent formalism \cite{Ajjath:2020lwb} by limiting ourselves to the contributions only from gluon-gluon ($gg$) initiated channels. The $\rm{NNLO_A}$ rapidity distribution of pseudo-scalar Higgs is obtained by applying a ratio method on the NNLO rapidity distribution of the scalar Higgs boson. We also present the first analytical results of $\rm{N^3LO}$ rapidity distribution of pseudo-scalar Higgs at SV+NSV accuracy. The phenomenological impacts of $\rm{{NNLO}_A+\overline{{NNLL}}}$ predictions for 13 TeV LHC are studied. We observe that, for $m_A$ =125(700) GeV, the SV+NSV resummation at $\rm{ \overline{NNLL}}$ level brings about 14.76\% (11.48\%) corrections to the $\rm{NNLO}_A$ results at the central scale value of $\mu_R=\mu_F=m_A$. Further, we find that the sensitivity to the renormalisation scale gets improved substantially by the inclusion of NSV resummed predictions at $\rm \overline{NNLL}$ accuracy.