Abstract
We compute the contribution to the total cross section for the inclusive production of a Standard Model Higgs boson induced by two quarks with different flavour in the initial state. Our calculation is exact in the Higgs boson mass and the partonic center-of-mass energy. We describe the reduction to master integrals, the construction of a canonical basis, and the solution of the corresponding differential equations. Our analytic result contains both Harmonic Polylogarithms and iterated integrals with additional letters in the alphabet.
Highlights
Reduction and canonical master integralsWe generate all two- and three-loop forward-scattering amplitudes for the process q(p1)q (p2) → q(p1)q (p2) involving a virtual Higgs boson with the help of qgraf [57] and process the output file to select the contributions which contain cuts through the Higgs
JHEP07(2015)140 calculation, are provided in refs. [27,28,29]
Our calculation is exact in the Higgs boson mass and the partonic center-of-mass energy
Summary
We generate all two- and three-loop forward-scattering amplitudes for the process q(p1)q (p2) → q(p1)q (p2) involving a virtual Higgs boson with the help of qgraf [57] and process the output file to select the contributions which contain cuts through the Higgs. Note that we have performed the calculation for general gauge parameter ξ which drops out after relating master integrals from the different families. This constitutes a strong check on the correctness of our result. [61] and construct a canonical basis which allows for a simple and straightforward solution of the corresponding differential equations Besides the simple solution of the differential equations the canonical basis has the advantage that for the initial conditions only the leading terms of order y0 are needed in the soft limit. No explicit calculation is needed in case the first non-zero contribution of a canonical master integral is of O(y) or higher.
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