Abstract
We calculate the three-loop soft function for the production of an electroweak boson (Higgs, γ, W±, Z) with large transverse momentum at a hadron collider. It is the first time a soft function for a three-parton process is computed at next-to-next-to-next-to-leading order (N3LO). As a technical novelty, we perform the calculation in terms of forward-scattering-type loop diagrams rather than evaluating phase space integrals. Our three-loop result contains color-tripole contributions and explicitly confirms predictions on the universal infrared structure of QCD scattering amplitudes with three massless parton legs. The soft function is a central ingredient in the factorized cross section for electroweak boson production near the kinematic endpoint (threshold), where the invariant mass of the recoiling hadronic radiation is small compared to its transverse momentum. Our result is required for predictions of the near-threshold cross sections at N3LO and for the resummation of threshold logarithms at primed next-to-next-to-next-to-leading logarithmic (N3LL′) accuracy.
Highlights
Reached NNLO precision [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]
The soft function is a central ingredient in the factorized cross section for electroweak boson production near the kinematic endpoint, where the invariant mass of the recoiling hadronic radiation is small compared to its transverse momentum
In order to improve the predictions for EW boson production near threshold to N3LO and N3LL accuracy2 the factorization functions are required at three-loop order
Summary
Reached NNLO precision [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. Depending on the kinematic region and the type of process the NNLO corrections can be substantial. In the limit, where the transverse momentum of the EW boson becomes maximal (at fixed rapidity), the invariant mass of the recoiling hadronic radiation vanishes and vice versa Close to this threshold all final state QCD radiation is either soft or anti-collinear to the direction of the EW boson and the production cross section can be factorized into a convolution of hard, jet, and soft functions [17, 18]. Solving these and evolving the functions from the respective physical hard, jet, and soft scales to a common renormalization scale systematically resums large threshold logarithms (of the ratio between the transverse momentum and the hadronic invariant mass) In this way near-threshold predictions for cross sections with NNLL and partial N3LL resummation along with the corresponding NNLO threshold corrections were obtained [18, 25,26,27,28,29,30].
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