Abstract
We present one-loop contributions to the fully differential Higgs boson gluon-fusion cross-section for Higgs production via gluon fusion. Our results constitute a necessary ingredient of a complete N3LO determination of the cross-section. We perform our computation using a subtraction method for the treatment of soft and collinear singularities. We identify the infrared divergent parts in terms of universal splitting and eikonal functions, and demonstrate how phase-space integrations yield poles (up to 1/ε6) in the dimensional regulator ε = (4 − d)/2. We compute the coefficients of the ε expansion, including the finite part numerically. As a demonstration of our numerical implementation, we present the corrections at N3LO due to one-loop amplitudes in the rapidity and transverse momentum of the Higgs boson.
Highlights
Has been obtained [3] by combining the fully differential cross-section for pp → H + 1 jet at NNLO [4,5,6,7,8] with the N3LO inclusive cross-section [1, 2]
We present one-loop contributions to the fully differential Higgs boson gluonfusion cross-section for Higgs production via gluon fusion
As a demonstration of our numerical implementation, we present the corrections at N3LO due to one-loop amplitudes in the rapidity and transverse momentum of the Higgs boson
Summary
We present the tree and one-loop amplitudes which are required for the gluon-fusion Higgs production cross-section at N3LO in perturbative QCD. The coefficient Ah admits a perturbative expansion in the bare strong coupling constant αs, Ah = C1. We can further relate the form factors A1, A2a, A2b, A2c to helicity amplitudes [22]:. Notice that all of the above relations are valid at any order in the perturbative expansion in the strong coupling constant. At one-loop, the amplitude coefficients A(11), A(21a), A(21b), A(21c) are linear combinations of the bubble and box integrals, which are defined as. The expressions for the amplitudes Ai written in terms of these Master Integrals are given in the appendix A. Each of the amplitude coefficients in eq (3.28) can be expanded as a power series in the strong coupling constant (3.30). The one-loop A(21), A(31) amplitude coefficients are presented in the appendix A
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