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In this presentation, we review the general features of integrand-reduction techniques, with a particular focus on their generalization beyond one loop. We start with a brief discussion of the one-loop scenario, a case in which…
We present the analytic expressions of the three-loop virtual corrections to the helicity amplitudes of 2 -> 2 four-fermion scattering processes in massless QED. The contributing Feynman diagrams are grouped into integrand families…
Splitting amplitudes govern the behavior of scattering amplitudes at the momenta of external legs become collinear. In this talk we outline the calculation of two-loop splitting amplitudes via the unitarity sewing method. This method…
We present a construction of the integrand of the correlation function of four stress-tensor multiplets in N=4 SYM at weak coupling. It does not rely on Feynman diagrams and makes use of the recently discovered symmetry of the integrand…
We present analytic results for the finite diagrams contributing to the two-loop eight-point MHV scattering amplitude of planar N=4 SYM. We use a recently proposed representation for the integrand of the amplitude in terms of (momentum)…
We use the method of differential equations to analytically evaluate all planar three-loop Feynman integrals relevant for form factor calculations involving massive particles. Our results for ninety master integrals at general $q^2$ are…
The use of complex analysis for computing one-loop scattering amplitudes is naturally induced by generalised unitarity-cut conditions, fulfilled by complex values of the loop variable. We report on two techniques: the cut-integration with…
It is by now well established that, by means of the integration by part identities, all the integrals occurring in the evaluation of a Feynman graph of given topology can be expressed in terms of a few independent master integrals. It is…
We study partial fraction decompositions (PFDs) in several variables using tools from commutative algebra. We give criteria for when a rational function with poles on a hyperplane arrangement has a desirable PFD. Our criteria are obtained…
We compute for the first time the two-loop five-particle amplitude in $\mathcal{N}=8$ supergravity. Starting from the known integrand, we perform an integration-by-parts reduction and express the answer in terms of uniform weight master…
We investigate the production of spin-3/2 hadrons in semi-inclusive deep inelastic lepton-nucleon scatterings. The complete differential cross section is derived through the kinematic analysis and expressed in terms of 288 structure…
We present analytic results for one of two types of planar QED two-loop integrals for $\mu e$ scattering including finite lepton masses. No approximations are made, such that the results are valid not only in the limit of a small electron…
We compute, at two-loop order, one-particle-irreducible Green functions and effective action in noncommutative $\lambda[\Phi^3]_\star$-theory for both planar (g=0, h=3) and nonplanar (g=1, h=1) contributions. We adopt worldline formulation…
We implement the worldline formalism in phase space to compute scattering amplitudes. First, the Feynman rules exhibit several useful universal features, reflecting elements of the symplectic geometry of the phase space target. Next,…
We apply the recently proposed amplitude reduction at the integrand level method, to the computation of the scattering process 2 photons -> 4 photons, including the case of a massive fermion loop. We also present several improvements of the…
We extend the applications of prescriptive unitarity beyond the planar limit to provide local, polylogarithmic, integrand-level representations of six-particle MHV scattering amplitudes in both maximally supersymmetric Yang-Mills theory and…
We compute the complete potential-graviton contributions to the conservative radial action and scattering angle for two non-spinning bodies in general relativity, accurate through fifth order in Newton's constant and including second-order…
We characterize the optical response of a three-level atom subjected to an incoherent pump and continuously illuminated with a weak, quasi-resonant probe field. To this end, we apply a wavefunction approach based on QED Hamiltonian…
Two-loop massive Feynman integrals for $\phi^4$ field-theoretical model with long-range correlated disorder are considered. Massive integrals for the vertex function $\Gamma^{(4)}$ including two or three massless propagators for generic…
I discuss the recent advances in the computation of two-loop scattering amplitudes for five-particle processes. The latter are fundamental ingredients to obtain predictions at the next-to-next-to-leading order (NNLO) in QCD for many…