Rapidity distribution of pseudoscalar Higgs boson to ${\mathrm{NNLO}}_A+\overline{\mathrm{NNLL}}$

We present the differential predictions for the rapidity distribution of pseudoscalar 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 ($\overline{\mathrm{NNLL}}$) accuracy and matching them to the approximate fixed order next-to-next-to-leading-order (${\mathrm{NNLO}}_A$) computation. We perform the resummation in two-dimensional Mellin space by limiting ourselves to the contributions only from gluon-gluon ($gg$) initiated channels. The ${\mathrm{NNLO}}_A$ rapidity distribution of pseudoscalar 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 $N^3\mathrm{LO}$ rapidity distribution of pseudoscalar Higgs at $\mathrm{SV}+\mathrm{NSV}$ accuracy. The phenomenological impacts of ${\mathrm{NNLO}}_A+\overline{\mathrm{NNLL}}$ predictions for 13 TeV LHC are studied. We observe that for $m_A=125\left(700\right)\mathrm{GeV}$ the $\mathrm{SV}+\mathrm{NSV}$ resummation at the $\overline{\mathrm{NNLL}}$ level brings about 14.76% (11.48%) corrections to the ${\mathrm{NNLO}}_A$ results at the central scale value of ${\mu }_R={\mu }_F=m_A$. Further, we find that the sensitivity to the renormalization scale gets improved substantially by the inclusion of NSV resummed predictions at $\overline{\mathrm{NNLL}}$ accuracy.