Solving the Bethe-Salpeter Equation in Minkowski Space for a Fermion-Scalar system

Abstract

The ladder Bethe-Salpeter Equation of a bound (1/2)+ system, composed by a fermion and a scalar boson, is solved in Minkowski space, for the first time. The formal tools are the same already successfully adopted for two-scalar and two-fermion systems, namely the Nakanishi integral representation of the Bethe-Salpeter amplitude and the light-front projection of the fulfilled equation. Numerical results are presented and discussed for two interaction kernels: i) a massive scalar exchange and ii) a massive vector exchange, illustrating both the correlation between binding energies and the interaction coupling constants, as well as the valence content of the interacting state, through the valence probabilities and the light-front momentum distributions. In the case of the scalar exchange, an interesting side effect, to be ascribed to the repulsion generated by the small components of the Dirac spinor, is pointed out, while for the vector exchange the manifestation of the helicity conservation opens new interesting questions to be addressed within a fully non-perturbative framework, as well as the onset of a scale-invariant regime.

arXiv comment38 pages, 6 figures. To appear in Phys. Rev. D

References in corpus (30)

• Quantum Chromodynamics and Other Field Theories on the Light Cone
• Dyson-Schwinger Equations and the Application to Hadronic Physics
• The Infrared Behavior of QCD Green's Functions - Confinement, Dynamical Symmetry Breaking, and Hadrons as Relativistic Bound States
• Dyson-Schwinger equations: a tool for hadron physics
• Infrared Properties of QCD from Dyson-Schwinger equations
• Baryons as relativistic three-quark bound states
• Collective perspective on advances in Dyson-Schwinger Equation QCD
• Imaging dynamical chiral symmetry breaking: pion wave function on the light front
• Symmetry preserving truncations of the gap and Bethe-Salpeter equations
• Solving Bethe-Salpeter equation in Minkowski space
• Solving the Bethe-Salpeter equation for bound states of scalar theories in Minkowski space
• Quantitative studies of the homogeneous Bethe-Salpeter Equation in Minkowski space
• Solving Bethe-Salpeter equation for two fermions in Minkowski space
• Two-body scattering states in Minkowski space and the Nakanishi integral representation onto the null plane
• Cross-ladder effects in Bethe-Salpeter and Light-Front equations
• Recent developments in bound-state calculations using the Dyson-Schwinger and Bethe-Salpeter equations
• Advances in solving the two-fermion homogeneous Bethe-Salpeter equation in Minkowski space
• Bethe-Salpeter bound-state structure in Minkowski space
• Solving the inhomogeneous Bethe-Salpeter Equation in Minkowski space: the zero-energy limit
• Features of ghost-gluon and ghost-quark bound states related to BRST quartets
• Minkowski solution of Dyson-Schwinger equations in momentum subtraction scheme
• Fermionic bound states in Minkowski-space: Light-cone singularities and structure
• Two-Fermion Bound States within the Bethe-Salpeter Approach
• A Novel Algorithm for Extracting the Parton Distribution Amplitude from the Euclidean Bethe-Salpeter Wave Function
• Feynman-Schwinger representation approach to nonperturbative physics
• Bound state equation for the Nakanishi weight function
• Angular Momentum Conservation Law in Light-Front Quantum Field Theory
• Bound state structure and electromagnetic form factor beyond the ladder approximation
• Covariant QCD Modeling of Light Meson Physics
• Bethe-Salpeter equation in Minkowski space with cross-ladder kernel

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• Basis Light-Front Quantization for a Chiral Nucleon-Pion Lagrangian
• The analytic structure of three-point functions from contour deformations
• Proton quark distributions from a light-front Faddeev-Bethe-Salpeter approach
• Extracting a model quark propagator's spectral density
• The chiral limit of a fermion-scalar $(1/2{)}^{+}$ system in covariant gauges