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We present the differential predictions for the rapidity distribution ofpseudo-scalar Higgs boson through gluon fusion at the LHC. These results areobtained taking into account the soft-virtual (SV) as well as the next-to-softvirtual (NSV) resummation effects to next-to-next-to-leading-logarithmic($\rm{\overline{NNLL}}$) accuracy and matching them to the approximate fixedorder next-to-next-to-leading-order ($\rm{NNLO_A}$) computation. We perform theresummation in two dimensional Mellin space using our recent formalism\cite{Ajjath:2020lwb} by limiting ourselves to the contributions only fromgluon-gluon ($gg$) initiated channels. The $\rm{NNLO_A}$ rapidity distributionof pseudo-scalar Higgs is obtained by applying a ratio method on the NNLOrapidity distribution of the scalar Higgs boson. We also present the firstanalytical results of $\rm{N^3LO}$ rapidity distribution of pseudo-scalar Higgsat SV+NSV accuracy. The phenomenological impacts of$\rm{{NNLO}_A+\overline{{NNLL}}}$ predictions for 13 TeV LHC are studied. Weobserve 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 improvedsubstantially by the inclusion of NSV resummed predictions at $\rm\overline{NNLL}$ accuracy.

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