Fermionic bound states in Minkowski-space: Light-cone singularities and structure

Abstract

The Bethe-Salpeter equation for two-body bound system with spin $1/2$ constituent is addressed directly in the Minkowski space. In order to accomplish this aim we use the Nakanishi integral representation of the Bethe-Salpeter amplitude and exploit the formal tool represented by the exact projection onto the null-plane. This formal step allows one i) to deal with end-point singularities one meets and ii) to find stable results, up to strongly relativistic regimes, that settles in strongly bound systems. We apply this technique to obtain the numerical dependence of the binding energies upon the coupling constants and the light-front amplitudes for a fermion-fermion $0^{+}$ state with interaction kernels, in ladder approximation, corresponding to scalar-, pseudoscalar- and vector boson exchanges, respectively. After completing the numerical survey of the previous cases, we extend our approach to a quark-antiquark system in $0^{-}$ state, taking both constituent-fermion and exchanged boson masses, from lattice calculations. Interestingly, the calculated light-front amplitudes for such a mock pion show peculiar signatures of the spin degrees of freedom.

22 pages, 7 figures, bst file included

References in corpus (28)

• Quantum Chromodynamics and Other Field Theories on the Light Cone
• Parton Physics on Euclidean Lattice
• Transverse Polarisation of Quarks in Hadrons
• Explicitly Covariant Light-Front Dynamics and Relativistic Few-Body Systems
• The QCD Running Coupling
• A Lattice Calculation of Parton Distributions
• Scaling behavior of quark propagator in full QCD
• Running Gluon Mass from Landau Gauge Lattice QCD Propagator
• Solving Bethe-Salpeter equation in Minkowski space
• Light-Front Bethe-Salpeter Equation
• 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
• Hadron Transverse Momentum Distributions in Muon Deep Inelastic Scattering at 160 GeV/$c$
• 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
• Note on lattice regularization and equal-time correlators for parton distribution functions
• Advances in solving the two-fermion homogeneous Bethe-Salpeter equation in Minkowski space
• Transverse-momentum dependent parton distribution functions beyond leading twist in quark models
• Effects of TMD evolution and partonic flavor on $e^{+}{e}^{-}$ annihilation into hadrons
• Bethe-Salpeter bound-state structure in Minkowski space
• Solving the inhomogeneous Bethe-Salpeter Equation in Minkowski space: the zero-energy limit
• Projecting the Bethe-Salpeter Equation onto the Light-Front and back: A Short Review
• Two-Fermion Bound States within the Bethe-Salpeter Approach
• Bound state equation for the Nakanishi weight function
• Light-front Ward-Takahashi Identity for Two-Fermion Systems
• End-point singularities of Feynman graphs on the light cone
• Excited states of the Wick-Cutkosky model with the Nakanishi representation in the Light-Front framework

Cited by in corpus (17)

• Parton distribution amplitudes: revealing diquarks in the proton and Roper resonance
• Scattering amplitudes and contour deformations
• Observing the Minkowskian dynamics of the pion on the null-plane
• Going to the light front with contour deformations
• Frame dependence of form factors in light-front dynamics
• Fermion and Photon gap-equations in Minkowski space within the Nakanishi Integral Representation method
• Dynamical mass generation in Minkowski space at QCD scale
• Solving the Bethe-Salpeter Equation in Minkowski Space for a Fermion-Scalar system
• Thermodynamical phases in a PNJL model at zero temperature
• Three-boson bound states in Minkowski space with contact interactions
• The analytic structure of three-point functions from contour deformations
• Kaon Structure in the Nuclear Medium within the Light Front Approach
• Pion inspired by QCD: Nakanishi and Light-Front Integral Representations
• Extracting a model quark propagator's spectral density
• The chiral limit of a fermion-scalar $(1/2{)}^{+}$ system in covariant gauges
• The Bethe-Salpeter approach to bound states: from Euclidean to Minkowski space
• Pion electromagnetic form factor with Minkowskian dynamics