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We compute one-loop correlation functions for the fluctuations of an interface using a field theory model. We obtain them from Feynman diagrams drawn with a propagator which is the inverse of the Hamiltonian of a Poschl-Teller problem. We…

High Energy Physics - Phenomenology · Physics 2009-11-10 A. Bessa , C. A. A. de Carvalho , E. S. Fraga

We explore the relation between resummation and explicit multi-loop calculations for QCD hard-scattering amplitudes. We describe how the factorization properties of amplitudes lead to the exponentiation of double and single poles at each…

High Energy Physics - Phenomenology · Physics 2014-11-17 George Sterman , Maria E. Tejeda-Yeomans

By identifying each standard flag with a trivalent Feynman diagram, the corresponding propagators can be read directly from the flag itself. Within the flag representation, the kinematic Jacobi identity (equivalently, the residue theorem on…

High Energy Physics - Theory · Physics 2025-12-04 Lili Yang

The perturbative approach to quantum field theories has made it possible to obtain incredibly accurate theoretical predictions in high-energy physics. Although various techniques have been developed to boost the efficiency of these…

High Energy Physics - Phenomenology · Physics 2021-05-05 Selomit Ramirez-Uribe , Roger J. Hernandez-Pinto , German Rodrigo , German F. R. Sborlini , William J. Torres Bobadilla

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 review several multi-loop techniques for analytical massless Feynman diagram calculations in relativistic quantum field theories: integration by parts, the method of uniqueness, functional equations and the Gegenbauer polynomial…

High Energy Physics - Theory · Physics 2019-05-21 A. V. Kotikov , S. Teber

Counting the independent sets of a graph is a classical #P-complete problem, even in the bipartite case. We give an exponential-time approximation scheme for this problem which is faster than the best known algorithm for the exact problem.…

Data Structures and Algorithms · Computer Science 2021-09-10 Leslie Ann Goldberg , John Lapinskas , David Richerby

This article displays a proof of concept of the mixed analytical/numerical method, presented in previous publications, to compute two-loop functions with up to five massive propagators in a scalar theory having three- and four-leg vertices…

High Energy Physics - Phenomenology · Physics 2021-09-15 J. Ph. Guillet , E. Pilon , Y. Shimizu , M. S. Zidi

We compute the six-dimensional hexagon integral with three non-adjacent external masses analytically. After a simple rescaling, it is given by a function of six dual conformally invariant cross-ratios. The result can be expressed as a sum…

High Energy Physics - Theory · Physics 2013-05-29 Vittorio Del Duca , Lance J. Dixon , James M. Drummond , Claude Duhr , Johannes M. Henn , Vladimir A. Smirnov

For any near-threshold asymptotic regime and for any Feynman diagram (involving loop and/or phase space integrals), a systematic prescription for explicitly constructing all-logs, all-powers (all-twists) expansions in perfectly factorized…

High Energy Physics - Phenomenology · Physics 2009-10-30 Fyodor V. Tkachov

A recently derived approach to the tensor reduction of 5-point one-loop Feynman integrals expresses the tensor coefficients by scalar 1-point to 4-point Feynman integrals completely algebraically. In this letter we derive extremely compact…

High Energy Physics - Phenomenology · Physics 2011-07-20 J. Fleischer , T. Riemann

Scalar field theories with quartic interactions are of central interest in the study of second-order phase transitions. For three-dimensional theories, numerous studies make use of the fixed-dimensional perturbative computation of [B.…

High Energy Physics - Theory · Physics 2024-05-14 Giacomo Sberveglieri , Gabriele Spada

The two point integrals contributing to the self energy of a particle in a three dimensional quantum field theory are calculated to two loop order in perturbation theory as well as the vacuum ones contributing to the effective potential to…

High Energy Physics - Phenomenology · Physics 2009-10-28 Arttu K. Rajantie

This thesis provides an extension of the work of Dirk Kreimer and Alain Connes on the Hopf algebra structure of Feynman graphs and renormalization to general graphs. Additionally, an algebraic structure of the asymptotics of formal power…

High Energy Physics - Theory · Physics 2018-07-06 Michael Borinsky

Correlators of Wilson-line operators are fundamental ingredients for the study of the infrared properties of non-abelian gauge theories. In perturbation theory, they are known to exponentiate, and their logarithm can be organised in terms…

High Energy Physics - Phenomenology · Physics 2021-06-22 Neelima Agarwal , Abhinava Danish , Lorenzo Magnea , Sourav Pal , Anurag Tripathi

We present analytic results for the finite diagrams contributing to the two-loop eight-point MHV scattering amplitude of planar N=4 SYM. We use a recently proposed representation for the integrand of the amplitude in terms of (momentum)…

High Energy Physics - Theory · Physics 2011-07-21 Luis F. Alday

N=4 supersymmetric Yang-Mills theory exhibits a rather surprising duality of Wilson-loop vacuum expectation values and scattering amplitudes. In this paper, we investigate this correspondence at the diagram level. We find that one-loop…

High Energy Physics - Theory · Physics 2015-03-17 Charalampos Anastasiou , Andrea Banfi

This paper presents a new method of numerical computation of the QED contributions to the electron anomalous magnetic moment which arises from Feynman graphs containing electron and photon lines and not containing electron loops. The method…

High Energy Physics - Phenomenology · Physics 2017-11-29 Sergey Volkov

We consider an interacting system of spin variables on a loopy interaction graph, identified by a tree graph and a set of loopy interactions. We start from a high-temperature expansion for loopy interactions represented by a sum of…

Disordered Systems and Neural Networks · Physics 2015-09-23 A. Ramezanpour , S. Moghimi-Araghi

The graph isomorphism problem looks deceptively simple, but although polynomial-time algorithms exist for certain types of graphs such as planar graphs and graphs with bounded degree or eigenvalue multiplicity, its complexity class is still…

Discrete Mathematics · Computer Science 2025-07-11 Stefan Klus , Patrick Gelß