Two-loop master integrals for the planar QCD massive corrections to di-photon and di-jet hadro-production

Matteo Becchetti,Roberto Bonciani

doi:10.1007/jhep01(2018)048

Matteo Becchetti, Roberto Bonciani

Open Access

https://doi.org/10.1007/jhep01(2018)048

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Abstract

We present the analytic calculation of the Master Integrals necessary to compute the planar massive QCD corrections to Di-photon (and Di-jet) production at hadron colliders. The master integrals are evaluated by means of the differential equations method and expressed in terms of multiple polylogarithms and one- or two-fold integrals of polylogarithms and irrational functions, up to transcendentality four.

Highlights

We present the analytic calculation of the Master Integrals necessary to compute the planar massive QCD corrections to Di-photon production at hadron colliders
In this article we presented the calculation of the master integrals needed for the evaluation of the NNLO QCD planar corrections to di-photon production in hadronic collisions
We represented these integrals in terms of Goncharov’s multiple polylogarithms (GPLs), whenever it was possible to linearize the set of square roots appearing in the corresponding alphabet

Summary

Notations

We consider the basic processes qq → γγ, (gg, qq) and the crossed q(q)g → q(q)g, in which the initial partons have momenta p1 and p2 and the final photons or partons have momenta p3 and p4. Since we consider 2 → 2 scattering processes with massless external particles, the physical region is defined through the following relations s s > 0 , t = − (1 − cos θ) < 0 , −s < t < 0 ,. The NNLO QCD planar corrections to the partonic processes listed above can be calculated reducing to the MIs two topologies, shown in figure 1 and defined by the integrals. There are three-point functions that are not included in the subtopologies of topologies A and B These are the three-point functions that occur for instance in the calculation of the NLO QCD corrections to the Higgs production in gluon fusion (or Higgs decay into a pair of photons) and the corresponding MIs were studied in [39, 40]

The system of differential equations

The master integrals

Conclusions

A Linearization of square roots

B Routing for the pre-canonical master integrals