Abstract
We present the computation of a full set of planar five-point two-loop master integrals with one external mass. These integrals are an important ingredient for two-loop scattering amplitudes for two-jet-associated W-boson production at leading color in QCD. We provide a set of pure integrals together with differential equations in canonical form. We obtain analytic differential equations efficiently from numerical samples over finite fields, fitting an ansatz built from symbol letters. The symbol alphabet itself is constructed from cut differential equations and we find that it can be written in a remarkably compact form. We comment on the analytic properties of the integrals and confirm the extended Steinmann relations, which govern the double discontinuities of Feynman integrals, to all orders in ϵ. We solve the differential equations in terms of generalized power series on single-parameter contours in the space of Mandelstam invariants. This form of the solution trivializes the analytic continuation and the integrals can be evaluated in all kinematic regions with arbitrary numerical precision.
Highlights
Which are not manifest in the action
We present the computation of a full set of planar five-point two-loop master integrals with one external mass
We demonstrate the readiness of the method for Large Hadron Collider (LHC) physics in a number of ways, such as computing high-precision boundary conditions for the integrals at hand in both Euclidean and physical regions and showing the efficiency with various studies over physical phase space
Summary
The main result of this paper is a calculation of a basis of two-loop integrals relevant for planar five-point scattering processes with a single massive external leg. In this paper we use the metric g = diag(+, −, −, −), which we extend with further minus signs when working in D dimensions These variables are not sufficient to characterize the kinematics of the scattering process: there is an additional parity label which can be captured by the parity-odd Levi-Civita contraction tr5 = 4iεαβγδ pα pβ2 pγ pδ4. We finish this section with a brief comment on the analytic structure of Feynman integrals, to which we will return later in the paper They evaluate to functions of the Mandelstam variables s with a complicated branch cut structure. This physical process is a natural application of the one-mass five-point two-loop integrals.
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