Higgs Rapidity Distribution in $b {\bar b}$ Annihilation at Threshold in N$^{3}$LO QCD

We present the rapidity distribution of the Higgs boson produced through bottom quark annihilation at third order in QCD using the threshold approximation. We provide a framework, based on the factorization properties of the QCD amplitudes along with Sudakov resummation and the renormalization group invariance, that allows one to perform the computation of the threshold corrections in a consistent, systematic and accurate way. The recent results on threshold N$^3$LO correction in QCD for the Drell-Yan production and on three loop QCD correction to Higgs form factor with bottom anti-bottom quark are used to achieve this task. We also demonstrate the numerical impact of these corrections at the LHC.

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