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

A bstract We present the calculation of the decay H → b b ¯ 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 α s 3 y b 2 . 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 → b b ¯ j and present jet rates and differential distributions in the Higgs rest frame using the Durham jet algorithm.