Abstract
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.
Highlights
Electroweak boson production in association with photons and jets plays a key role in the physics program of hadron colliders such as the Large Hadron Collider (LHC)
We present analytic results for all planar two-loop Feynman integrals contributing to five-particle scattering amplitudes with one external massive leg
The modern approach to computing scattering amplitudes analytically relies on the fact that they can be expressed in terms of linear combinations of scalar Feynman integrals
Summary
Electroweak boson production in association with photons and jets plays a key role in the physics program of hadron colliders such as the Large Hadron Collider (LHC). [36], their numerical evaluation was performed through series expansion of their DEs These developments have led to the first analytic calculations of two-loop five-particle amplitudes with an external massive leg, for the production of a W and a Higgs bosons associated with a pair of bottom quarks [44, 45], as well as of the two-loop four-point form factor of a length-3 half-BPS operator in planar N = 4 sYM [46]. The numerical evaluation of the weight three and four pentagon functions on the other hand is significantly more challenging compared to their massless counterpart This is due to the non-trivial geometry of the phase space, which we study in detail, and to the presence of non-linear spurious singularities in the one-dimensional integral representations. We include a number of appendices, where we discuss in detail the physical phase-space geometry and the positivity properties of the symbol alphabet
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