Collider physics at the precision frontier

We present the complete set of leading-color two-loop contributions required to obtain next-to-next-to-leading-order (NNLO) QCD corrections to three-jet production at hadron colliders. We obtain analytic expressions for a generating set of finite remainders, valid in the physical region for three-jet production. The analytic continuation of the known Euclidean-region results is determined from a small set of numerical evaluations of the amplitudes. We obtain analytic expressions that are suitable for phenomenological applications and we present a C++ library for their efficient and stable numerical evaluation.

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Leading-color two-loop QCD corrections for three-photon production at hadron colliders

We calculate the complete set of two-loop leading-colour QCD helicity amplitudes for γγj-production at hadron colliders. Our results are presented in a compact, fully-analytical form.

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Two-loop leading-colour QCD helicity amplitudes for two-photon plus jet production at the LHC

We present an analytic computation of the gluon-initiated contribution to diphoton plus jet production at hadron colliders up to two loops in QCD. We reconstruct the analytic form of the finite remainders from numerical evaluations over finite fields including all colour contributions. Compact expressions are found using the pentagon function basis. We provide a fast and stable implementation for the colour- and helicity-summed interference between the one-loop and two-loop finite remainders in C++ as part of the NJet library.

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Virtual QCD corrections to gluon-initiated diphoton plus jet production at hadron colliders

We compute the two-loop QCD helicity amplitudes for the production of a Higgs boson in association with a bottom-quark pair at a hadron collider. We take the approximations of leading colour and work in the five flavour scheme, where the bottom quarks are massless while the Yukawa coupling is non-zero. We extract analytic expressions from multiple numerical evaluations over finite fields and present the results in terms of an independent set of special functions that can be reliably evaluated over the full phase space.

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Two-loop leading-colour QCD helicity amplitudes for Higgs boson production in association with a bottom-quark pair at the LHC

We present an analytic computation of the two-loop QCD corrections to $u\overline{d}\ensuremath{\rightarrow}{W}^{+}b\overline{b}$ for an on-shell $W$ boson using the leading color and massless bottom quark approximations. We perform an integration-by-parts reduction of the unpolarized squared matrix element using finite field reconstruction techniques and identify an independent basis of special functions that allows an analytic subtraction of the infrared and ultraviolet poles. This basis is valid for all planar topologies for five-particle scattering with an off-shell leg.

Two-Loop QCD Corrections to W b b ¯ Production at Hadron Colliders

We present analytic results for all planar two-loop Feynman integrals contributing to five-particle scattering amplitudes with one external massive leg. We express the integrals in terms of a basis of algebraically-independent transcendental functions, which we call one-mass pentagon functions. We construct them by using the properties of iterated integrals with logarithmic kernels. The pentagon functions are manifestly free of unphysical branch cuts, do not require analytic continuation, and can be readily evaluated over the whole physical phase space of the massive particle production channel. We develop an efficient algorithm for their numerical evaluation and present a public implementation suitable for direct phenomenological applications.

Simone Zoia

Papers

Two-Loop QCD Corrections to W b b ¯ Production at Hadron Colliders

Pentagon Functions for One-Mass Planar Scattering Amplitudes