  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.
