This paper reports the first prediction for the Higgs production rate when events with hard jets are vetoed, computed at third logarithmic order in quantum chromodynamics (QCD). Jet vetoes are widely used at the Large Hadron Collider to remove backgrounds with energetic radiation. But the veto introduces large “Sudakov” logarithms—terms that grow at each order in the usual expansion—so a fixed-order calculation alone can be unreliable. The authors sum those large terms to all orders (a procedure called resummation) and combine that result with the best fixed-order calculation to give a more stable prediction.

The team matches the next-to-next-to-next-to-leading order (N3LO) fixed-order calculation with next-to-next-to-next-to-leading logarithmic (N3LL) resummation. They work within the soft‑collinear effective theory (SCET) framework, which separates radiation into pieces that can be treated independently and then evolved back to a common scale. The calculation uses a number of recent high-order ingredients: three-loop results for certain anomalous dimensions that control the resummed logarithms, two-loop beam- and soft-function inputs, and a four-loop cusp anomalous dimension where needed. A key new ingredient was the three-loop rapidity anomalous dimension, which for the first time includes a dependence on the choice of jet algorithm.

When evaluated at a phenomenologically relevant jet veto scale of about 30 GeV and a common jet radius of R = 0.4, the resummation raises the pure fixed-order prediction by roughly 3%. After combining resummation and fixed order, the residual uncertainty from missing higher-order terms is also about 3%. The authors note that the N3LL corrections are sizable, consistent with the observation that the three-loop rapidity anomalous dimension is numerically large.

This result matters because it brings the theoretical precision for the zero-jet Higgs cross section closer to the level expected to be useful at the high-luminosity LHC. The zero-jet bin is important for precise determinations of Higgs couplings and for analyses that suppress backgrounds from top-quark decays. Beyond Higgs production, the methods and ingredients developed here can be applied to other color-singlet processes, heavy-quark production, jet observables, and to improve the matching of fixed-order calculations to parton-shower simulations.