N$^{3}$LO predictions for the decay of the Higgs boson to bottom quarks

Abstract

We present a fully-differential calculation of the $H\rightarrow b\overline{b}$ decay at next-to-next- to-next-to-leading order (N$^3$LO) accuracy. Our calculation considers diagrams in which the Higgs boson couples directly to the bottom quarks, i.e. the perturbative order we consider is $\mathcal{O}(\alpha_s^3y_b^2)$. In order to regulate the infrared divergences present at this order we use the Projection-to-Born technique coupled with N-jettiness slicing. After validating our methodology at next-to-next-to-leading order (NNLO) we present exclusive jet rates and differential distributions for jet observables at N3LO accuracy using the Durham jet algorithm in the Higgs rest frame.