Analytic Form of the Full Two-Loop Five-Gluon All-Plus Helicity Amplitude

Two-Loop Helicity Amplitudes for Diphoton Plus Jet Production in Full Color

We present the two-loop QCD amplitudes for the production of two photons and a jet at hadron colliders with full-color dependence. This is the first time that radiative corrections for a five-particle scattering process have been computed beyond the leading-color approximation at this perturbative order in QCD. The results presented in this Letter will be crucial to guaranteeing reliable predictions with unprecedented precision for diphoton production at hadron colliders. The methodologies that we describe lead to a significant simplification of the calculation and their applicability extends to a wider range of five-point scattering processes.

Bootstrapping a Two-Loop Four-Point Form Factor

We compute the two-loop four-point form factor of a length-3 half-BPS operator in planar N=4 SYM theory, which belongs to the class of two-loop five-point scattering observables with one off-shell color-singlet leg. A new bootstrapping strategy is developed to obtain this result by starting with an ansatz expanded in terms of master integrals and then solving the master coefficients via various physical constraints. We find that consistency conditions of infrared divergences and collinear limits, together with the cancellation of spurious poles, can fix a significant part of the ansatz. The remaining degrees of freedom can be fixed by one simple type of two-double unitarity cut. Full analytic results in terms of both symbol and Goncharov polylogarithms are provided.

Two-Loop QCD Corrections to Wbb[over ¯] Production at Hadron Colliders

We present an analytic computation of the two-loop QCD corrections to ud[over ¯]→W^{+}bb[over ¯] 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.

A Stroll through the Loop-Tree Duality

The Loop-Tree Duality (LTD) theorem is an innovative technique to deal with multi-loop scattering amplitudes, leading to integrand-level representations over a Euclidean space. In this article, we review the last developments concerning this framework, focusing on the manifestly causal representation of multi-loop Feynman integrals and scattering amplitudes, and the definition of dual local counter-terms to cancel infrared singularities.

Diphoton Amplitudes in Three-Loop Quantum Chromodynamics

We consider the three-loop scattering amplitudes for the production of a pair of photons in quark-antiquark annihilation in QCD. We use suitably defined projectors to efficiently calculate all helicity amplitudes. We obtain relatively compact analytic results that we write in terms of harmonic polylogarithms or, alternatively, multiple polylogarithms of up to depth three. This is the first calculation of a three-loop four-point scattering amplitude in full QCD.

Two-Loop Four-Graviton Scattering Amplitudes

We present the analytic form of the two-loop four-graviton scattering amplitudes in Einstein gravity. To remove ultraviolet divergences we include counterterms quadratic and cubic in the Riemann curvature tensor. The two-loop numerical unitarity approach is used to deal with the challenging momentum dependence of the interactions. We exploit the algebraic properties of the integrand of the amplitude in order to reduce it to a minimal basis of Feynman integrals. Analytic expressions are obtained from numerical evaluations of the amplitude. Finally, we show that four-graviton scattering observables depend on fewer couplings than naïvely expected.