Related papers: The diamond rule for multi-loop Feynman diagrams
Calculation of amplitudes in perturbative quantum field theory involve large loop integrals. The complexity of those integrals, in combination with the large number of Feynman diagrams, make the calculations very difficult. Reduction…
Recently a reformulation of the MHV diagram method in N=4 supersymmetric Yang-Mills theory in momentum twistor space was presented and was shown to be equivalent to the perturbative expansion of the expectation value of a supersymmetric…
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…
We develop a generating-function formulation for the symbolic reduction of multi-loop Feynman integrals. In this framework, integration-by-parts identities are rewritten as differential equations for sector-wise generating functions, so the…
We present some techniques which have been developed recently or in the recent past to compute Feynman graphs beyond one-loop order. These techniques are useful to compute the three-loop splitting functions in QCD and to obtain the complete…
In this work, we systematically analyse Feynman integrals in the `t Hooft-Veltman scheme. We write an explicit reduction resulting from partial fractioning the high-multiplicity integrands to a finite basis of topologies at any given loop…
We present a technique that enables the evaluation of perturbative expansions based on one-loop-renormalized vertices up to large expansion orders. Specifically, we show how to compute large-order corrections to the random phase…
The standard procedure for computing scalar multi-loop Feynman integrals consists in reducing them to a basis of so-called master integrals, derive differential equations in the external invariants satisfied by the latter and, finally, try…
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…
The Symmetries of Feynman Integrals method (SFI) associates a natural Lie group with any diagram, depending only on its topology. The group acts on parameter space and the method determines the integral's dependence within group orbits.…
The massless sunrise diagram with an arbitrary number of loops is calculated in a simple but formal manner. The result is then verified by rigorous mathematical treatment. Pitfalls in the calculation with distributions are highlighted and…
We study perturbative aspects of recently proposed integrated four-point correlators in $\mathcal{N}=4$ supersymmetric Yang-Mills with all classical gauge groups using standard Feynman diagram computations. We argue that perturbative…
We study a two-loop contribution to the dark-matter trispectrum and evaluate it numerically using an infrared-safe integrand. The calculation is organized as an expansion around a fixed reference cosmology: the linear matter power spectrum…
Feynman diagrams in the instanton background are used for the calculation of the tunneling amplitude, up to the two-loops order. Some mistakes made in the previous works are corrected. The same method is applied to the next-order…
We present an improved form of the integration technique known as NDIM (Negative Dimensional Integration Method), which is a powerful tool in the analytical evaluation of Feynman diagrams. Using this technique we study a $% \phi ^{3}\oplus…
In this paper I discuss how to consistently incorporate higher-order corrections to the bubble-nucleation rate at finite temperature. Doing so I examine the merits of different approaches, with the goal of reducing uncertainties for…
A comprehensive study is performed of two-loop Feynman diagrams with three external legs which, due to the exchange of massless gauge-bosons, give raise to infrared and collinear divergencies. Their relevance in assembling realistic…
Different mathematical methods have been applied to obtain the analytic result for the massless triangle Feynman diagram yielding a sum of four linearly independent hypergeometric functions of two variables $F_4$. These are defined for…
Numerical evaluations of Feynman integrals often proceed via a deformation of the integration contour into the complex plane. While valid contours are easy to construct, the numerical precision for a multi-loop integral can depend…
This paper deals with quantum fluctuations near the classical instanton configuration. Feynman diagrams in the instanton background are used for the calculation of the tunneling amplitude (the instanton density) in the three-loop order for…