Recent developments in bound-state calculations using the Dyson-Schwinger and Bethe-Salpeter equations

Abstract

We review in detail modern numerical methods used in the determination and solution of Bethe-Salpeter and Dyson--Schwinger equations. The algorithms and techniques described are applicable to both the rainbow-ladder truncation and its non-trivial extensions. We discuss pedagogically the steps involved in constructing conventional mesons and baryons as systems of two- and three-quarks respectively. As further application we describe the self-consistent calculation of form-factors and highlight the challenges that remain therein.

37 pages, 9 figures. Version accepted for publication in Computer Physics Communications

References in corpus (20)

• Infrared Properties of QCD from Dyson-Schwinger equations
• Baryons as relativistic three-quark bound states
• Pinch Technique: Theory and Applications
• Nucleon electromagnetic form factors from the covariant Faddeev equation
• Masses of ground and excited-state hadrons
• Beyond the rainbow: effects from pion back-coupling
• Spectra of heavy mesons in the Bethe-Salpeter approach
• FormTracer - A Mathematica Tracing Package Using FORM
• Dynamical chiral symmetry breaking and a critical mass
• $\bar{q}q$ condensate for light quarks beyond the chiral limit
• Mass spectra and Regge trajectories of light mesons in the Bethe-Salpeter approach
• Delta and Omega electromagnetic form factors in a Dyson-Schwinger/Bethe-Salpeter approach
• The analytic properties of the quark propagator from an effective infrared interaction model
• A covariant study of tensor mesons
• Matrix algorithms for solving (in)homogeneous bound state equations
• Aspects of open-flavour mesons in a comprehensive DSBSE study
• Numerical Investigation of Fermion Mass Generation in QED
• Solving a Set of Truncated Dyson-Schwinger Equations with a Globally Converging Method
• Excited mesons in a Bethe-Salpeter approach
• Properties of quarks and mesons in the Dyson-Schwinger/Bethe-Salpeter approach

Cited by in corpus (43)

• QCD at finite temperature and chemical potential from Dyson-Schwinger equations
• Diquark Correlations in Hadron Physics: Origin, Impact and Evidence
• Fully coupled functional equations for the quark sector of QCD
• Reconstructing QCD Spectral Functions with Gaussian Processes
• Light Baryon Spectroscopy
• Ghost spectral function from the spectral Dyson-Schwinger equation
• Scattering amplitudes and contour deformations
• Four-quark states from functional methods
• Elucidating the effect of intermediate resonances in the quark interaction kernel on the time-like electromagnetic pion form factor
• Vector mesons as dynamical resonances in the Bethe-Salpeter framework
• Four-quark states with charm quarks in a two-body Bethe-Salpeter approach
• DoFun 3.0: Functional equations in Mathematica
• Pion and Kaon box contribution to $a_{\mu }^{\text{HLbL}}$
• $X(3872)$ as a four-quark state in a Dyson-Schwinger/Bethe-Salpeter approach
• The $\sigma$-meson: four-quark vs. two-quark components and decay width in a Bethe-Salpeter approach
• Dense two-color QCD from Dyson-Schwinger equations
• Practical scheme from QCD to phenomena via Dyson-Schwinger equations
• On the effect of resonances in the quark-photon vertex
• Quarks and light (pseudo-)scalar mesons at finite chemical potential
• Fermion and Photon gap-equations in Minkowski space within the Nakanishi Integral Representation method
• The impact of transverse Slavnov-Taylor identities on dynamical chiral symmetry breaking
• The light scalars: four- vs. two-quark states in the complex energy plane from Bethe-Salpeter equations
• Solving the Bethe-Salpeter Equation in Minkowski Space for a Fermion-Scalar system
• The time-like electromagnetic kaon form factor
• On the complex structure of Yang-Mills theory
• The Podolsky propagator in gap and bound-state equations
• Dynamical Chiral Symmetry Breaking in Quantum Chromo Dynamics: Delicate and Intricate
• Timelike form factor for the anomalous process ${\gamma }^{\ast }\pi \to \pi \pi$
• The quark spectral functions and the Hadron Vacuum Polarization from application of DSEs in Minkowski space
• Space-like Electromagnetic Form Factors of Lambda- and Sigma-Baryons from Quark-Diquark Faddeev Equations
• Deep reinforcement learning for complex evaluation of one-loop diagrams in quantum field theory
• Radially excited pion: electromagnetic form factor and the box contribution to the muon's $g-2$
• On the low-energy spectrum of an SU(2) gauge theory with dynamical fermions
• The rainbow modified-ladder approximation and degenerate pion
• Distribution amplitudes of heavy-light pseudo-scalar and vector mesons from Dyson-Schwinger equations framework
• Renormalized Schwinger-Dyson functional
• Influence of light quark loops on the Wigner phase with Dyson-Schwinger equations approach
• Pole-fitting for complex functions: enhancing standard techniques by artificial-neural-network classifiers and regressors
• Baryonic form factors of light pseudoscalar mesons
• $D^{\ast }D\pi$ and $B^{\ast }B\pi$ couplings from Dyson-Schwinger equations framework
• Curve fitting on a quantum annealer for an advanced navigation method
• Electromagnetic and strong isospin breaking in light meson masses
• Quark-photon vertex from lattice QCD in Landau gauge