Related papers: Two-Loop Diagrams in Causal Perturbation Theory
The loop-tree duality (LTD) has become a novelty alternative to bootstrap the numerical evaluation of multi-loop scattering amplitudes. It has indeed been found that Feynman integrands, after the application of LTD, display a representation…
For massless quenched QED in three dimensions, we evaluate a non-perturbative expression for the fermion propagator which agrees with its two loop perturbative expansion in the weak coupling regime. This calculation is carried out by making…
We describe the calculation of the two--loop massive operator matrix elements with massive external fermions in QED. We investigate the factorization of the $O(\alpha^2)$ initial state corrections to $e^+e^-$ annihilation into a virtual…
We relate a $l$-loop Feynman integral to a sum of phase space integrals, where the integrands are determined by the spanning trees of the original $l$-loop graph. Causality requires that the propagators of the trees have a modified…
We present an evaluation of the two master integrals for the crossed vertex diagram with a closed loop of top quarks that allows for an easy numerical implementation. The differential equations obeyed by the master integrals are used to…
In this paper, we present analytical results for the two-loop QCD corrections to the production of two partons or a photon and a parton in hadronic collisions, mediated by loops of massive quarks. These amplitudes involve Feynman integrals…
We describe an efficient position space technique to calculate lattice Feynman integrals in infinite volume. The method applies to diagrams with massless propagators. For illustration a set of two-loop integrals is worked out explicitly. An…
We present the analytic calculation of two-loop master integrals that are relevant for $tW$ production at hadron colliders. We focus on the integral families with only one massive propagator. After choosing a canonical basis, the…
In the models defined on the inhomogeneous background the propagators depend on the two space - time momenta rather than on one momentum as in the homogeneous systems. Therefore, the conventional Feynman diagrams contain extra integrations…
One of the main difficulties in studying Quantum Field Theory, in the perturbative regime, is the calculation of D-dimensional Feynman integrals. In general, one introduces the so-called Feynman parameters and associated with them the…
The conventional second-order Path Integral Monte Carlo method is plagued with the sign problem in solving many-fermion systems. This is due to the large number of anti-symmetric free fermion propagators that are needed to extract the…
We discuss new ideas for consideration of loop diagrams and angular integrals in $D$-dimensions in QCD. In case of loop diagrams, we propose the covariant formalism of expansion of tensorial loop integrals into the orthogonal basis of…
In the context of high-energy particle physics, a reliable theory-experiment confrontation requires precise theoretical predictions. This translates into accessing higher-perturbative orders, and when we pursue this objective, we inevitably…
The composite operator effective potential is compared with the conventional Dyson-Schwinger method as a calculational tool for (2+1)-dimensional quantum electrodynamics. It is found that when the fermion propagator ansatz is put directly…
Negative dimensional integration method (NDIM) is a technique which can be applied, with success, in usual covariant gauge calculations. We consider three two-loop diagrams: the scalar massless non-planar double-box with six propagators and…
We derive a duality relation between one-loop integrals and phase-space integrals emerging from them through single cuts. The duality relation is realized by a modification of the customary +i0 prescription of the Feynman propagators. The…
We demonstrate that summation of connected diagrams to high order starting from a BCS hamiltonian is a viable generic unbiased approach for strongly correlated fermions in superconducting or superfluid phases. For the 3D attractive Hubbard…
We propose a multiloop generalization of the Bern-Kosower formalism, based on Strassler's approach of evaluating worldline path integrals by worldline Green functions. Those Green functions are explicitly constructed for the basic two-loop…
We consider chiral perturbation theory in the meson sector at order $E^6$. In the terminology of the external field technique, the two--loop graphs so generated are of the sunset type. We discuss the evaluation of several of these in the…
The calculation of higher-order corrections in Quantum Field Theories is a challenging task. In particular, dealing with multiloop and multileg Feynman amplitudes leads to severe bottlenecks and a very fast scaling of the computational…