arXiv subjects

Andreas Rapakoulias

Publications and source records attributed to Andreas Rapakoulias.

6 recordsLinked to original sources

arXiv2026

Phase-space integrals through Mellin-Barnes representation

We compute angular phase-space integrals with three and four denominators analytically, working within dimensional regularisation via the Mellin-Barnes (MB) representation. The approach converts multifold MB integrals into real parametric integrals and expresses all results in terms of Goncharov polylogarithms (GPLs). For three denominators, all-massless results are obtained to $\mathcal{O}(ε^2)$ and the single-massive case to $\mathcal{O}(ε)$; for four denominators, both the massless and single-massive cases are solved to $\mathcal{O}(ε^0)$. Integrals with multiple massive momenta follow from a partial fraction decomposition reducing them to the single-massive case. Recursion relations relating integrals with higher denominator powers to master integrals are derived. These are essential ingredients to solving full phase-space integrals.

hep-ph↗

arXiv2025

Angular phase-space integrals with four denominators through Mellin--Barnes

We compute four-denominator angular phase-space integrals using the Mellin--Barnes (MB) technique in dimensional regularisation. Independent of the scattering process, an angular integral can be categorised based on the nature of the momenta appearing in the denominators. We address all scenarios involving fully massless and massive momenta. We present a partial fraction decomposition that relates angular integrals with multiple massive momenta to those with a single massive momentum. By solving six- and seven-fold MB integrals, we express the final results up to the finite order in the dimensional regulator in terms of Goncharov polylogarithms.

hep-ph↗

arXiv2025

NNLO phase-space integrals for semi-inclusive deep-inelastic scattering

We evaluate the phase-space integrals that arise in double real emission diagrams for semi-inclusive deep-inelastic scattering at next-to-next-to-leading order (NNLO) in QCD. Utilizing the reverse unitarity technique, we convert these integrals into loop integrals, allowing us to employ integration-by-parts identities and reduce them to a set of master integrals. The master integrals are then solved using the method of differential equations and expressed in terms of Goncharov polylogarithms. By examining the series expansion in the dimensional regulator, we discover additional relations among some of the master integrals. As an alternative approach, we solve the master integrals by decomposing them into angular and radial components. The angular parts are evaluated using Mellin-Barnes representation, while special attention is given to the singular structures of the radial integrals to handle them accurately. Here the results are provided in terms of one-fold integrals over classical polylogarithms. This approach provides a clearer understanding of the origin of soft and collinear singularities.

hep-ph↗

arXiv2024

Phase-space integrals through Mellin-Barnes representation

This letter introduces a novel analytical approach to calculating phase-space integrals, crucial for precision in particle physics. We develop a method to compute angular components using multifold Mellin-Barnes integrals, yielding results in terms of Goncharov polylogarithms for integrals involving three denominators. Our results include expressions for massless momenta up to $\cal{O}(ε^2)$ and for one massive momentum up to $\cal{O}(ε)$. Additionally, we derive recursion relations that reduce integrals with higher powers of denominators to simpler ones. We detail how to combine the angular part with the radial one which requires a careful handling of singularities.

hep-ph↗

arXiv2023

Lattice Correlation Functions from Differential Equations

We discuss how methods developed in the context of perturbation theory can be applied to the computation of lattice correlation functions, in particular in the non perturbative regime. The techniques we consider are integration-by-parts identities (supplemented with symmetry relations) and the method of differential equations, cast in the framework of twisted co-homology. We report on calculations of correlation functions for a scalar $λϕ^4$ theory and lattices of small size, both in Euclidean and Minkowskian signature.

hep-th↗

arXiv2022

Non-perturbative computation of lattice correlation functions by differential equations

We show that methods developed in the context of perturbative calculations can be transferred to non-perturbative calculations. We demonstrate that correlation functions on the lattice can be computed with the method of differential equations, supplemented with techniques from twisted cohomology. We derive differential equations for the variation with the coupling or -- more generally -- with the parameters of the action. Already simple examples show that the differential equation with respect to the coupling has an essential singularity at zero coupling and a regular singularity at infinite coupling. The properties of the differential equation at zero coupling can be used to prove that the perturbative series is only an asymptotic series.

hep-th↗