Threshold resummation of rapidity distributions at fixed partonic rapidity

We derive a general expression for the resummation of rapidity distributions for processes with a colorless final state, such as Drell-Yan or Higgs production, in the limit in which the center-of-mass energy goes on threshold, but with fixed rapidity of the Higgs or gauge boson in the partonic center-of-mass frame. The result is obtained by suitably generalizing the renormalization-group based approach to threshold resummation previously pursued by us. The ensuing expression is valid to all logarithmic orders but the resummation coefficients must be determined by comparing to fixed order results. We perform this comparison for the Drell-Yan process using the fixed-order next-to-next-to-leading (NNLO) result, thereby determining resummation coefficients up to next-to-next-to-leading logarithmic (NNLL) accuracy, for the quark-antiquark coefficient function in the quark nonsinglet channel. We provide a translation to direct QCD of a result for this resummation previously obtained using SCET methods, and we show that it agrees with our own.