H→ bb¯ j at next-to-next-to-leading order accuracy

We present the calculation of the decay H→ bb¯ j at next-to-next-to-leading order (NNLO) accuracy in QCD. We treat the bottom quarks as massless with a non-zero Higgs Yukawa coupling y_b. We consider contributions in which the Higgs boson couples directly to bottom quarks, i.e. our predictions are accurate to order O(αs3yb2). We calculate the various components needed to construct the NNLO contribution, including an independent calculation of the two-loop amplitudes. We compare our results for the two-loop amplitudes to an existing calculation finding agreement. We present additional checks on our two-loop expression using the known infrared factorization properties as the emitted gluon becomes soft or collinear. We use our results to construct a Monte Carlo implementation of H→ bb¯ j and present jet rates and differential distributions in the Higgs rest frame using the Durham jet algorithm.