The analytic structure of three-point functions from contour deformations
arXiv:2212.02515 · doi:10.1103/PhysRevD.107.074026
Abstract
We explore the analytic structure of three-point functions using contour deformations. This method allows continuing calculations analytically from the spacelike to the timelike regime. We first elucidate the case of two-point functions with explicit explanations how to deform the integration contour and the cuts in the integrand to obtain the known cut structure of the integral. This is then applied to one-loop three-point integrals. We explicate individual conditions of the corresponding Landau analysis in terms of contour deformations. In particular, the emergence and position of singular points in the complex integration plane are relevant to determine the physical thresholds. As an exploratory demonstration of this method's numerical implementation we apply it to a coupled system of functional equations for the propagator and the three-point vertex of theory. We demonstrate that under generic circumstances the three-point vertex function displays cuts which can be determined from modified Landau conditions.
arXiv comment26 pages, 21 figures, 1 table; v2: typos fixed, references added
References in corpus (97)
- Baryons as relativistic three-quark bound states
- Explanation and Prediction of Observables using Continuum Strong QCD
- Analytic properties of the Landau gauge gluon and quark propagators
- Landau gauge Yang-Mills correlation functions
- Non-perturbative quark, gluon and meson correlators of unquenched QCD
- Gauge bosons at zero and finite temperature
- Light mesons in QCD and unquenching effects from the 3PI effective action
- Confinement and complex singularities in QED3
- Modeling the Gluon Propagator in Landau Gauge: Lattice Estimates of Pole Masses and Dimension-Two Condensates
- Analytic structure of the Landau gauge gluon propagator
- n-Particle irreducible effective action techniques for gauge theories
- The three-gluon vertex in Landau gauge
- Gluonic three-point correlations in pure Landau gauge QCD
- Spectral functions of confined particles
- Two- and three-point Green's functions in two-dimensional Landau-gauge Yang-Mills theory
- Reconstructing the gluon
- Källén-Lehmann spectroscopy for (un)physical degrees of freedom
- Probing Unquenching Effects in the Gluon Polarisation in Light Mesons
- Fully coupled functional equations for the quark sector of QCD
- Solving Bethe-Salpeter equation in Minkowski space
- Numerical analytic continuation of Euclidean data
- Five loop renormalization of theory with applications to the Lee-Yang edge singularity and percolation theory
- Correlation functions of Landau gauge Yang-Mills theory
- The Landau gauge gluon and ghost propagator in the refined Gribov-Zwanziger framework in 3 dimensions
- Solving the Bethe-Salpeter equation for bound states of scalar theories in Minkowski space
- Reconstructing QCD Spectral Functions with Gaussian Processes
- The infrared behavior of Landau gauge Yang-Mills theory in d=2, 3 and 4 dimensions
- Quantitative studies of the homogeneous Bethe-Salpeter Equation in Minkowski space
- Solving Bethe-Salpeter equation for two fermions in Minkowski space
- Gribov horizon and i-particles: about a toy model and the construction of physical operators
- On Gribov's supercriticality picture of quark confinement
- Algorithmic derivation of functional renormalization group equations and Dyson-Schwinger equations
- Analytic structure of QCD propagators in Minkowski space
- Landau gauge Yang-Mills propagators in the complex momentum plane
- Correlation functions of three-dimensional Yang-Mills theory from the FRG
- Two- and three-point functions in two-dimensional Landau-gauge Yang-Mills theory: Continuum results
- Ghost spectral function from the spectral Dyson-Schwinger equation
- Algorithmic derivation of Dyson-Schwinger Equations
- Spectral functions in the -theory from the spectral DSE
- Electromagnetic decays of the neutral pion
- On mass generation in Landau-gauge Yang-Mills theory
- Spectral representation of lattice gluon and ghost propagators at zero temperature
- Correlation functions of three-dimensional Yang-Mills theory from Dyson-Schwinger equations
- A covariant view on the nucleons' quark core
- Advances in solving the two-fermion homogeneous Bethe-Salpeter equation in Minkowski space
- Spectrum of scalar and pseudoscalar glueballs from functional methods
- Infrared Behavior of Three-Point Functions in Landau Gauge Yang-Mills Theory
- The generalised infrared structure of the gluon propagator
- On the analytic structure of scalar glueball operators at Born level
- Techniques for n-Particle Irreducible Effective Theories
- The analytic structure of the lattice Landau gauge gluon and ghost propagators
- Scattering amplitudes and contour deformations
- CrasyDSE: A framework for solving Dyson-Schwinger equations
- Four-quark states from functional methods
- Vector mesons as dynamical resonances in the Bethe-Salpeter framework
- Elucidating the effect of intermediate resonances in the quark interaction kernel on the time-like electromagnetic pion form factor
- Study of relativistic bound states for scalar theories in Bethe-Salpeter and Dyson-Schwinger formalism
- Complex poles and spectral function of Yang-Mills theory
- DoFun 3.0: Functional equations in Mathematica
- The effects of Gribov copies in 2D gauge theories
- The non-perturbative structure of the photon and gluon propagators
- Bethe-Salpeter bound-state structure in Minkowski space
- Higher spin glueballs from functional methods
- Examining the Analytic Structure of Green's Functions: Massive Parallel Complex Integration using GPUs
- Lattice three-gluon vertex in extended kinematics: planar degeneracy
- Reconstructing confined particles with complex singularities
- Minkowski solution of Dyson-Schwinger equations in momentum subtraction scheme
- Solving the inhomogeneous Bethe-Salpeter Equation in Minkowski space: the zero-energy limit
- Fermionic bound states in Minkowski-space: Light-cone singularities and structure
- On the computation of the spectral density of two-point functions: complex masses, cut rules and beyond
- Modeling the Landau-Gauge Ghost Propagator in 2, 3 and 4 Space-Time Dimensions
- Going to the light front with contour deformations
- Complex poles and spectral functions of Landau gauge QCD and QCD-like theories
- Comparison of two Minkowski-space approaches to heavy quarkonia
- On the effect of resonances in the quark-photon vertex
- Covariant spectator theory of quark-antiquark bound states: Mass spectra and vertex functions of heavy and heavy-light mesons
- Quark propagator in Minkowski space
- Reflection positivity and complex analysis of the Yang-Mills theory from a viewpoint of gluon confinement
- Dynamical chiral symmetry breaking with Minkowski space integral representations
- Fermion and Photon gap-equations in Minkowski space within the Nakanishi Integral Representation method
- Dynamical mass generation in Minkowski space at QCD scale
- Exact Solutions to the Fermion Propagator Schwinger-Dyson Equation in Minkowski space with on-shell Renormalization for Quenched QED
- More on the properties of the first Gribov region in Landau gauge
- Dyson-Schwinger equation constraints on the gluon propagator in BRST quantised QCD
- Solving the three-body bound-state Bethe-Salpeter equation in Minkowski space
- Neural network approach to reconstructing spectral functions and complex poles of confined particles
- Quark mass function from a one-gluon-exchange-type interaction in Minkowski space
- Solving the Schwinger-Dyson equation for a scalar propagator in Minkowski space
- Solving the Bethe-Salpeter Equation in Minkowski Space for a Fermion-Scalar system
- Probing the singularities of the Landau-gauge gluon and ghost propagators with rational approximants
- Bethe-Salpeter equation in Minkowski space with cross-ladder kernel
- The analytic structure of the Landau gauge quark propagator from Padé analysis
- Deep reinforcement learning for complex evaluation of one-loop diagrams in quantum field theory
- From Euclidean to Minkowski space with the Cauchy-Riemann equations
- Pion inspired by QCD: Nakanishi and Light-Front Integral Representations
- Elucidating the rho-meson's role as intermediate resonance in the time-like electromagnetic pion form factor
- A machine learning pipeline for autonomous numerical analytic continuation of Dyson-Schwinger equations