Connection between Feynman integrals having different values of the space-time dimension

From MaRDI portal
Publication:4256553

DOI10.1103/PhysRevD.54.6479zbMath0925.81121arXivhep-th/9606018WikidataQ74444793 ScholiaQ74444793MaRDI QIDQ4256553

Oleg V. Tarasov

Publication date: 18 November 1999

Published in: Physical Review D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9606018



Related Items

TWO-LOOP VACUUM DIAGRAMS IN BACKGROUND FIELD AND THE HEISENBERG–EULER EFFECTIVE ACTION, Four-loop HQET propagators from the DRA method, Module intersection and uniform formula for iterative reduction of one-loop integrals, The ice cone family and iterated integrals for Calabi-Yau varieties, An algorithmic approach to finding canonical differential equations for elliptic Feynman integrals, The on-shell expansion: from Landau equations to the Newton polytope, On a procedure to derive \(\epsilon\)-factorised differential equations beyond polylogarithms, Two-loop corrections to Lamb shift and hyperfine splitting in hydrogen via multi-loop methods, Bootstrapping the relativistic two-body problem, Feynman integrals from positivity constraints, Non-factorizable virtual corrections to Higgs Boson production in weak Boson fusion beyond the eikonal approximation, AdS super gluon scattering up to two loops: a position space approach, Symbol alphabets from the Landau singular locus, Loop-by-loop differential equations for dual (elliptic) Feynman integrals, Revisiting the double-soft asymptotics of one-loop amplitudes in massless QCD, Factorization of covariant Feynman graphs for the effective action, Inelastic exponentiation and classical gravitational scattering at one loop, Anomalous Ward identities for on-shell amplitudes at the conformal fixed point, \(\mathcal{O}(m \alpha^2(Z\alpha)^6)\) contribution to Lamb shift from radiative corrections to the Wichmann-Kroll potential, Tensor reduction of loop integrals, ALGEBRAIC-NUMERICAL METHODS FOR EVALUATING MULTI-LEG AND MULTI-LOOP FEYNMAN DIAGRAMS, The two-loop sunrise graph with arbitrary masses, New results for the \(\varepsilon{}\)-expansion of certain one-, two- and three-loop Feynman diagrams, An approach toward the numerical evaluation of multi-loop Feynman diagrams, Massless on-shell box integral with arbitrary powers of propagators, Two-loop electroweak threshold corrections in the Standard Model, A geometrical angle on Feynman integrals, Feynman Graphs, The two-loop sunrise integral around four space-time dimensions and generalisations of the Clausen and Glaisher functions towards the elliptic case, SECTOR DECOMPOSITION, Hypergeometric Functions and Feynman Diagrams, A probabilistic angle on one-loop scalar integrals, All loop structures in supergravity amplitudes on AdS5 × S5 from CFT, The SAGEX review on scattering amplitudes Chapter 3: Mathematical structures in Feynman integrals, The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations, Electroweak radiative corrections for collider physics, Differential equations and dispersion relations for Feynman amplitudes. The two-loop massive sunrise and the kite integral, NumExp: numerical epsilon expansion of hypergeometric functions, The \(a\)-function in six dimensions, One-loop pentagon integral in \(d\) dimensions from differential equations in \(\epsilon\)-form, A planar four-loop form factor and cusp anomalous dimension in QCD, Adaptive integrand decomposition in parallel and orthogonal space, Debye screening mass of hot Yang-Mills theory to three-loop order, A minimal approach to the scattering of physical massless bosons, INTEGRATION BY PARTS: AN INTRODUCTION, Hypergeometric functions differential reduction (HYPERDIRE): MATHEMATICA based packages for differential reduction of generalized hypergeometric functions: \(F_D\) and \(F_S\) Horn-type hypergeometric functions of three variables, The two-loop sunrise graph in two space-time dimensions with arbitrary masses in terms of elliptic dilogarithms, Maximal cuts and differential equations for Feynman integrals. An application to the three-loop massive banana graph, Analytic results for massless three-loop form factors, Massive Feynman diagrams and inverse binomial sums, Two-loop tensor integrals in quantum field theory, Analytic treatment of the two loop equal mass sunrise graph, Five-particle phase-space integrals in QCD, Two-loop renormalization of the magnetic coupling and non-perturbative sector in hot QCD, Reduction of one-loop tensor form factors to scalar integrals: a general scheme, Beta functions and anomalous dimensions up to three loops, The three-loop splitting functions \(P_{q g}^{(2)}\) and \(P_{g g}^{(2, \operatorname{N}_{\operatorname{F}})}\), Introducing SummerTime: a package for high-precision computation of sums appearing in DRA method, New developments in FeynCalc 9.0, Three-loop contributions to the \(\rho\) parameter and iterated integrals of modular forms, Logarithmic forms and differential equations for Feynman integrals, Algorithms and tools for iterated Eisenstein integrals, Space-time dimensionality \(\mathcal D\) as complex variable: calculating loop integrals using dimensional recurrence relation and analytical properties with respect to \(\mathcal D\), The two-loop five-point amplitude in $ \mathcal{N}=8$ supergravity, The quark and gluon form factors to three loops in QCD through to \(\mathcal{O}\left( \epsilon^2 \right)\), Analytic epsilon expansion of three-loop on-shell master integrals up to four-loop transcendentality weight, FEYNMAN DIAGRAMS AND DIFFERENTIAL EQUATIONS, Analytic result for the one-loop scalar pentagon integral with massless propagators, Macaulay matrix for Feynman integrals: linear relations and intersection numbers, Differential reduction of generalized hypergeometric functions from Feynman diagrams: one-variable case, Three-loop master integrals for the Higgs boson self-energy with internal top-quarks and \(W\)-bosons, SecDec: A general program for sector decomposition, A new hypergeometric representation of one-loop scalar integrals in \(d\) dimensions, Recursion-free solution for two-loop vacuum integrals with ``collinear masses, One-loop hexagon integral to higher orders in the dimensional regulator, Effective field theory islands from perturbative and nonperturbative four-graviton amplitudes, Derivation of functional equations for Feynman integrals from algebraic relations, Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case, Algorithms for minimal Picard-Fuchs operators of Feynman integrals, On the all-order \(\epsilon \)-expansion of generalized hypergeometric functions with integer values of parameters, Master integrals for four-loop massless propagators up to weight twelve, Schouten identities for Feynman graph amplitudes: The Master Integrals for the two-loop massive sunrise graph, Numerical evaluation of multi-loop integrals by sector decomposition, Finding new relationships between hypergeometric functions by evaluating Feynman integrals, All-mass \(n\)-gon integrals in \(n\) dimensions, The unequal mass sunrise integral expressed through iterated integrals on \(\overline{\mathcal{M}}_{1,3}\), Feynman integrals and intersection theory, Towards \(pp \to VVjj\) at NLO QCD: bosonic contributions to triple vector boson production plus jet, Massive kite diagrams with elliptics, Collider physics at the precision frontier, Feynman integral relations from parametric annihilators, Some Open Problems on Feynman Periods, \textit{Package}-X 2.0: a \textit{Mathematica} package for the analytic calculation of one-loop integrals, The Sudakov form factor at four loops in maximal super Yang-Mills theory, Transforming differential equations of multi-loop Feynman integrals into canonical form, Cuts from residues: the one-loop case, A quasi-finite basis for multi-loop Feynman integrals, SecDec-3.0: numerical evaluation of multi-scale integrals beyond one loop, Application of the DRA method to the calculation of the four-loop QED-type tadpoles, Golem95: A numerical program to calculate one-loop tensor integrals with up to six external legs, Hypergeometric representation of the two-loop equal mass sunrise diagram, On triple-cut of scattering amplitudes, Four loop \(\overline{\mathbf {MS}}\) mass anomalous dimension in the Gross-Neveu model, (Z\(\alpha )^{4}\) order of the polarization operator in Coulomb field at low energy, Towards all-order Laurent expansion of generalised hypergeometric functions about rational values of parameters, Symmetric reduction of high-multiplicity one-loop integrals and maximal cuts, Functional equations for one-loop master integrals for heavy-quark production and Bhabha scattering, The iterated structure of the all-order result for the two-loop sunrise integral, Using functional equations to calculate Feynman integrals, A fresh look on three-loop sum-integrals, The dimensional recurrence and analyticity method for multicomponent master integrals: using unitarity cuts to construct homogeneous solutions, Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections, The \(\varepsilon\)-form of the differential equations for Feynman integrals in the elliptic case, New ideas for handling of loop and angular integrals in D-dimensions in QCD, Planar master integrals for four-loop form factors, Decomposition of Feynman integrals on the maximal cut by intersection numbers, Automatic reduction of four-loop bubbles, Evaluating double and triple (?) boxes, Periods and Feynman integrals, Application of the negative-dimension approach to massless scalar box integrals, Analytical results for dimensionally regularized massless on-shell double boxes with arbitrary indices and numerators, Algebraic reduction of one-loop Feynman graph amplitudes, Angular integrals in d dimensions, TARCER -- a Mathematica program for the reduction of two-loop propagator integrals, Scattering amplitudes in the Regge limit and the soft anomalous dimension through four loops, Non-planar elliptic vertex, Duals of Feynman integrals. II: Generalized unitarity, Yangian Ward identities for fishnet four-point integrals, Functional reduction of one-loop Feynman integrals with arbitrary masses, Complete collection of one-loop triple-collinear splitting operators for dimensionally-regulated QCD, A numerical evaluation of the scalar hexagon integral in the physical region, Integration by parts identities in integer numbers of dimensions. A criterion for decoupling systems of differential equations, Master integrals for the four-loop Sudakov form factor, \(\overline{MS}\) vs. pole masses of gauge bosons. II: Two-loop electroweak fermion corrections



Cites Work