相关论文: Reduction of two-loop Feynman integrals in paramet…

In this work, we calculate two-loop six-point planar massless Feynman integrals at higher orders in the dimensional regulator $\epsilon$, corresponding to higher transcendental weights. In previous works, these integrals were calculated up…

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…

Recently the Cachazo-He-Yuan (CHY) approach has been extended to loop level, but the resulting loop integrand has propagators that are linear in the loop momentum unlike Feynman's. In this note we present a new technique that directly…

A method is developed whereby spinor helicity techniques can be used to simplify the calculation of loop amplitudes. This is achieved by using the Feynman-parameter representation where the offending off-shell loop momenta do not appear.…

We describe the application of a novel approach for the reduction of scattering amplitudes, based on multivariate polynomial division, which we have recently presented. This technique yields the complete integrand decomposition for…

We describe the application of differential reduction algorithms for Feynman Diagram calculation. We illustrate the procedure in the context of generalized hypergeometric functions, and give an example for a type of q-loop bubble diagram.

We present a new approach to the reduction of one-loop amplitudes obtained by reconstructing the tensorial expression of the scattering amplitudes. The reconstruction is performed at the integrand level by means of a sampling in the…

We present a formalism for the calculation of multi-particle one-loop amplitudes, valid for an arbitrary number N of external legs, and for massive as well as massless particles. A new method for the tensor reduction is suggested which…

The integrand-level methods for the reduction of scattering amplitudes are well-established techniques, which have already proven their effectiveness in several applications at one-loop. In addition to the automation and refinement of tools…

Evaluation of a wide variety of Feynman diagrams with multi-loop integrals and physical parameters and its comparison with high energy experiments are expected to investigate new physics beyond the Standard Model. We have been developing a…

Finite Feynman integrals have been advocated as the optimal components for constructing a basis of master integrals in multiloop calculations, due to their improved analytic and numerical properties. In this paper, we show how the Loop-Tree…

We present OPITeR, a FORM program for the reduction of multi-loop tensor Feynman integrals. The program can handle tensors, including spinor indices, with rank of up to 20 and can deal with up to 8 independent external momenta. The…

We calculate the three-loop master integrals contributing to the three-loop five-point amplitude on the special Coulomb branch of $\mathcal{N}=4$ SYM theory. For the genuine pentagon integrals, we follow the approach of Ref. [JHEP 12 (2025)…

The Moller experiment and the P2 experiment aim at measuring the weak mixing angle at low scales. The Moller experiment uses $e^- e^- \rightarrow e^- e^-$-scattering, the P2 experiment uses $e^- N \rightarrow e^- N$-scattering. In both…

In this thesis, we study the three-loop QCD form factors. After an introduction and a discussion of the physics motivation, we generate the quark form factor using Qgraf. We then show how to bring the Feynman integrals into a unique form by…

We introduce a machine-learning framework based on symbolic regression to extract the full symbol alphabet of multi-loop Feynman integrals. By targeting the analytic structure rather than reduction, the method is broadly applicable and…

It is known that one-loop Feynman integrals possess an algebraic structure encoding some of their analytic properties called the coaction, which can be written in terms of Feynman integrals and their cuts. This diagrammatic coaction, and…

We present a new FORM program for analytically evaluating four-loop massless propagator-type Feynman integrals in an efficient way. Our program Forcer implements parametric reductions of the aforementioned class of Feynman integrals into a…

In this article we present an analytic solution of the famous problem of diffraction and interference of electrons through one and two slits (for simplicity, only the one-dimensional case is considered). In addition to exact formulas, we…

We show that the problem of solving recurrence relations for L-loop (R+1)-point Feynman integrals within the method of integration by parts is equivalent to the corresponding problem for (L+R)-loop vacuum or (L+R-1)-loop propagator-type…