Precision predictions at ${\mathrm{N}}^3\mathrm{LO}$ for the Higgs boson rapidity distribution at the LHC

We present precise predictions for the Higgs boson rapidity distribution at the LHC in the gluon fusion production mode. Our approach relies on the fully analytic computation of six terms in a systematic expansion of the partonic differential cross section around the production threshold of the Higgs boson at next-to-next-to-next-to-leading order (${\mathrm{N}}^3\mathrm{LO}$) in QCD perturbation theory. We observe a mild correction compared to the previous perturbative order and a significant reduction of the dependence of the cross section on the perturbative scale throughout the entire rapidity range.

Figure 1

Approximate Higgs boson rapidity distribution with threshold expansion truncated at different orders. The left panel shows the ratio of the approximate NNLO to the exact result; the right panel shows the approximate ${\mathrm{N}}^3\mathrm{LO}$ result to the best prediction obtained in this work.

Figure 2

The Higgs boson rapidity distribution at different orders in perturbation theory. The lower panel shows the ${\mathrm{N}}^3\mathrm{LO}$ and NNLO predictions normalized to the ${\mathrm{N}}^3\mathrm{LO}$ prediction for $\mu =m_h/2$.