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Related papers: Mellin$-$Barnes Transformation for Two-Loop Master…

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During the last several years remarkable progress has been made in numerical calculations of dimensionally regulated multi-loop Feynman diagrams using Mellin-Barnes (MB) representations. The bottlenecks were non-planar diagrams and…

High Energy Physics - Phenomenology · Physics 2017-08-02 Ievgen Dubovyk , Janusz Gluza , Tomasz Jelinski , Tord Riemann , Johann Usovitsch

We compute the master integrals relevant for the two-loop corrections to pseudo-scalar quarkonium and leptonium production and decay. We present both analytic and high-precision numerical results. The analytic expressions are given in terms…

High Energy Physics - Phenomenology · Physics 2022-11-18 Samuel Abreu , Matteo Becchetti , Claude Duhr , Melih A. Ozcelik

3-loop diagrams of the ladder-type, which emerge for local quarkonic twist-2 operator matrix elements, are computed directly for general values of the Mellin variable $N$ using Appell-function representations and applying modern summation…

High Energy Physics - Phenomenology · Physics 2015-06-05 Jakob Ablinger , Johannes Blümlein , Alexander Hasselhuhn , Sebastian Klein , Carsten Schneider , Fabian Wißbrock

We present the two-loop master integrals relevant to the ${\mathcal O}(\alpha \alpha_s)$-corrections to the decay $H \rightarrow b \bar{b}$ through a $H t \bar{t}$-coupling. We keep the full dependence on the heavy particle masses, but…

High Energy Physics - Phenomenology · Physics 2019-06-26 Ekta Chaubey , Stefan Weinzierl

In this article, we construct two-dimensional integrable and superintegrable sys- tems in terms of the master function formalism and relate them to Mielnik;s and Marquette;s construction in supersymmetric quantum mechanics. For two diferent…

Mathematical Physics · Physics 2017-10-13 Z. Alizadeh , H. Panahi

We propose a framework for calculating two-loop Feynman diagrams which appear within a renormalizable theory in the general mass case and at finite external momenta. Our approach is a combination of analytical results and of high accuracy…

High Energy Physics - Phenomenology · Physics 2009-10-30 A. Ghinculov , Y. -P. Yao

We discuss computational details of our recent result, namely, the first derivation of the two-loop gluon Regge trajectory within the framework of Lipatov's high energy effective action. In particular, we elaborate on the direct evaluation…

High Energy Physics - Phenomenology · Physics 2013-07-31 G. Chachamis , M. Hentschinski , J. D. Madrigal , A. Sabio Vera

We show how to evaluate one-dimensional Minkowski-region Mellin-Barnes representations arising from massive loop integrals, by modifying the contours of integration. We implement an exact solution to the differential equation determining…

High Energy Physics - Phenomenology · Physics 2017-05-03 Janusz Gluza , Tomasz Jelinski , David A. Kosower

We consider Mellin-Barnes transform of triangle ladder-like scalar diagram in d=4 dimensions. It is shown how the multi-fold MB transform of the momentum integral corresponding to an arbitrary number of rungs is reduced to the two-fold MB…

High Energy Physics - Theory · Physics 2015-06-05 Pedro Allendes , Bernd Kniehl , Igor Kondrashuk , Eduardo A. Notte Cuello , Marko Rojas Medar

We investigate a relation between the Mordell-Tornheim type of multiple Dirichlet series and a confluent hypergeometric function. We prove it by applying the Mellin-Barnes integral formula. Also, main results in this paper contain two kinds…

Number Theory · Mathematics 2023-02-01 Yuichiro Toma

The general lines of the derivation and the main properties of the master equations for the master amplitudes associated to a given Feynman graph are recalled. Some results for the 2-loop self-mass graph with 4 propagators are then…

High Energy Physics - Theory · Physics 2007-05-23 M. Caffo , H. Czyz , S. Laporta , E. Remiddi

We provide analytic results for two-loop four-point master integrals with one massive propagator and one massive leg relevant to single top production. Canonical bases of master integrals are constructed and the Simplified Differential…

High Energy Physics - Phenomenology · Physics 2023-05-31 Nikolaos Syrrakos

A master formula of transformation formulas for bilinear sums of basic hypergeometric series is proposed. It is obtained from the author's previous results on a transformation formula for Milne's multivariate generalization of basic…

Classical Analysis and ODEs · Mathematics 2019-08-15 Yasushi Kajihara

We derive a compact expression for the three-point MHV form factors of half-BPS operators in N=4 super Yang-Mills at two loops. The main tools of our calculation are generalised unitarity applied at the form factor level, and the compact…

High Energy Physics - Theory · Physics 2015-06-03 Andreas Brandhuber , Gabriele Travaglini , Gang Yang

Using Mellin-Barnes integrals we give a method to compute a relevant subgroup of the monodromy group of an A-hypergeometric system of differential equations. Presumably this group is the full monodromy group of the system. This article is a…

Algebraic Geometry · Mathematics 2018-05-08 Frits Beukers

We compute the master integrals for two-loop QCD corrections to quasi parton distribution functions (PDFs) in large momentum effective theory. Analytical results of the master integrals are derived using the method of differential…

High Energy Physics - Phenomenology · Physics 2020-10-28 Long-Bin Chen , Wei Wang , Ruilin Zhu

We present the analytic calculation of the Master Integrals necessary to compute the planar massive QCD corrections to Di-photon (and Di-jet) production at hadron colliders. The masters are evaluated by means of the differential equations…

High Energy Physics - Phenomenology · Physics 2018-02-14 Matteo Becchetti , Roberto Bonciani

We compute the master integrals that arise in the calculation of the leading penguin amplitudes in non-leptonic B-decays at two-loop order. The application of differential equations in a canonical basis enables us to give analytic results…

High Energy Physics - Phenomenology · Physics 2015-06-23 Guido Bell , Tobias Huber

We calculate analytically the three-loop planar master integrals relevant for heavy-to-light form factors using the method of differential equations. After choosing a proper canonical basis, the boundary conditions are easy to be…

High Energy Physics - Phenomenology · Physics 2018-10-24 Long-Bin Chen , Jian Wang

This manuscript introduces a generalization of the Mellin integral transform within the framework of weighted fractional calculus with respect to an increasing function. The proposed transform is much more suitable for working with…

Functional Analysis · Mathematics 2025-12-09 Gustavo Dorrego , Luciano Luque y Rubén Cerutti