Factorization and N3LLp+NNLO predictions for the Higgs cross section with a jet veto

We have recently derived a factorization formula for the Higgs-boson production
cross section in the presence of a jet veto, which allows for a systematic resummation of large Sudakov logarithms of the form αn s lnm(pveto
T /mH), along with the large virtual corrections known to affect also the total cross section. Here we determine the ingredients entering this formula at two-loop accuracy. Specifically, we compute the dependence on the jet-radius parameter R, which is encoded in the two-loop coefficient of the collinear
anomaly, by means of a direct, fully analytic calculation in the framework of soft-collinear effective theory. We confirm the result obtained by Banfi et al. from a related calculation in QCD, and demonstrate that factorization-breaking, soft-collinear mixing effects do not arise at leading power in pveto
T /mH, even for R = O(1). In addition, we extract the two-loop collinear beam functions numerically. We present detailed numerical predictions
for the jet-veto cross section with partial next-to-next-to-next-to-leading logarithmic accuracy, matched to the next-to-next-to-leading order cross section in fixed-order perturbation theory. The only missing ingredients at this level of accuracy are the three-loop anomaly coefficient and the four-loop cusp anomalous dimension, whose numerical effects
we estimate to be small.