Alphabet of one-loop Feynman integrals

Abstract

In this paper, we present the universal structure of the alphabet of one-loop Feynman integrals. The letters in the alphabet are calculated using the Baikov representation with cuts. We consider both convergent and divergent cut integrals and observe that letters in the divergent cases can be easily obtained from convergent cases by applying certain limits. The letters are written as simple expressions in terms of various Gram determinants. The knowledge of the alphabet enables us to easily construct the canonical differential equations of the $d\log$ form and aids in bootstrapping the symbols of the solutions.

arXiv comment13 pages, 2 figures; v3: published version in Chinese physics C

References in corpus (38)

• Multiloop integrals in dimensional regularization made simple
• The Singular Behaviour of QCD Amplitudes at Two-loop Order
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Dimensionally Regulated Pentagon Integrals
• Connection between Feynman integrals having different values of the space-time dimension
• Numerical evaluation of multiple polylogarithms
• On the Structure of Infrared Singularities of Gauge-Theory Amplitudes
• Infrared singularities of scattering amplitudes in perturbative QCD
• Local Integrals for Planar Scattering Amplitudes
• Multi-loop Amplitudes and Resummation
• Dimensionally Regulated One-Loop Integrals
• From polygons and symbols to polylogarithmic functions
• The Two-loop Soft Anomalous Dimension Matrix and Resummation at Next-to-next-to Leading Pole
• Infrared singularities of QCD amplitudes with massive partons
• Space-time dimensionality D as complex variable: calculating loop integrals using dimensional recurrence relation and analytical properties with respect to D
• The Two-loop Anomalous Dimension Matrix for Soft Gluon Exchange
• Explicit solutions of the multi-loop integral recurrence relations and its application
• Two-loop divergences of massive scattering amplitudes in non-abelian gauge theories
• Two-loop divergences of scattering amplitudes with massive partons
• Leading singularities and off-shell conformal integrals
• Cuts of Feynman Integrals in Baikov representation
• On the Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
• Generalised power series expansions for the elliptic planar families of Higgs + jet production at two loops
• The three-loop form factor in N=4 super Yang-Mills
• Multiple polylogarithms with algebraic arguments and the two-loop EW-QCD Drell-Yan master integrals
• Diagrammatic Hopf algebra of cut Feynman integrals: the one-loop case
• HandyG -- rapid numerical evaluation of generalised polylogarithms in Fortran
• Cuts from residues: the one-loop case
• The algebraic structure of cut Feynman integrals and the diagrammatic coaction
• Constructing Canonical Feynman Integrals with Intersection Theory
• Evaluating two-loop non-planar master integrals for Higgs + jet production with full heavy-quark mass dependence
• Logarithmic forms and differential equations for Feynman integrals
• Leading singularities in Baikov representation and Feynman integrals with uniform transcendental weight
• All-Mass $n$-gon Integrals in $n$ Dimensions
• One-Loop Integrals from Spherical Projections of Planes and Quadrics
• SymBuild: a package for the computation of integrable symbols in scattering amplitudes
• FastGPL: a C++ library for fast evaluation of generalized polylogarithms
• Two-loop infrared singularities in the production of a Higgs boson associated with a top-quark pair

Cited by in corpus (5)

• Symbol Alphabets from the Landau Singular Locus
• A study of Feynman integrals with uniform transcendental weights and the symbology from dual conformal symmetry
• Intersection theory rules symbology
• One-loop hexagon integral to higher orders in the dimensional regulator
• The recursive structure of Baikov representations I: generics and application to symbology