Singularity Structures in Coulomb-Type Potentials in Two Body Dirac Equations of Constraint Dynamics

Abstract

Two Body Dirac Equations (TBDE) of Dirac's relativistic constraint dynamics have been successfully applied to obtain a covariant nonperturbative description of QED and QCD bound states. Coulomb-type potentials in these applications lead naively in other approaches to singular relativistic corrections at short distances that require the introduction of either perturbative treatments or smoothing parameters. We examine the corresponding singular structures in the effective potentials of the relativistic Schroedinger equation obtained from the Pauli reduction of the TBDE. We find that the relativistic Schroedinger equation lead in fact to well-behaved wave function solutions when the full potential and couplings of the system are taken into account. The most unusual case is the coupled triplet system with S=1 and L={(J-1),(J+1)}. Without the inclusion of the tensor coupling, the effective S-state potential would become attractively singular. We show how including the tensor coupling is essential in order that the wave functions be well-behaved at short distances. For example, the S-state wave function becomes simply proportional to the D-state wave function and dips sharply to zero at the origin, unlike the usual S-state wave functions. Furthermore, this behavior is similar in both QED and QCD, independent of the asymptotic freedom behavior of the assumed QCD vector potential. Light- and heavy-quark meson states can be described well by using a simplified linear-plus-Coulomb-type QCD potential apportioned appropriately between world scalar and vector potentials. We use this potential to exhibit explicitly the origin of the large pi-rho splitting and effective chiral symmetry breaking. The TBDE formalism developed here may be used to study quarkonia in quark-gluon plasma environments.

23 pages, 4 figures

References in corpus (18)

• Experimental and Theoretical Challenges in the Search for the Quark Gluon Plasma: The STAR Collaboration's Critical Assessment of the Evidence from RHIC Collisions
• Formation of dense partonic matter in relativistic nucleus-nucleus collisions at RHIC: Experimental evaluation by the PHENIX collaboration
• Quark Gluon Plasma an Color Glass Condensate at RHIC? The perspective from the BRAHMS experiment
• The PHOBOS Perspective on Discoveries at RHIC
• Observation of the bottomonium ground state in the decay Upsilon(3S) -> gamma eta_b
• Heavy Quarkonium Dissociation Cross Sections in Relativistic Heavy-Ion Collisions
• NN Core Interactions and Differential Cross Sections from One Gluon Exchange
• BB Intermeson Potentials in the Quark Model
• Relativistic Calculation of the Meson Spectrum: a Fully Covariant Treatment Versus Standard Treatments
• I=3/2 $K\pi$ Scattering in the Nonrelativisitic Quark Potential Model
• Tests of Two-Body Dirac Equation Wave Functions in the Decays of Quarkonium and Positronium into Two Photons
• The relativistic two-body potentials of constraint theory from summation of Feynman diagrams
• Potential Models and Lattice Gauge Current-Current Correlators
• Two-Body Dirac Equations for Nucleon-Nucleon Scattering
• How to obtain a covariant Breit type equation from relativistic Constraint Theory
• Quarkonia and Quark Drip Lines in Quark-Gluon Plasma
• Singularity-Free Breit Equation from Constraint Two-Body Dirac Equations
• Gauge transformations in relativistic two-particle constraint theory

Cited by in corpus (26)

• Heavy quark potential in quark-gluon Plasma: Deep neural network meets lattice quantum chromodynamics
• Applications of Two-Body Dirac Equations to the Meson Spectrum with Three versus Two Covariant Interactions, SU(3) Mixing, and Comparison to a Quasipotential Approach
• Relativistic Correction to Charmonium Dissociation Temperature
• Flavor Dependence of Meson Melting Temperature in Relativistic Potential Model
• Heavy flavor dissociation in the framework of multi-body Dirac equations
• Two body relativistic wave equations
• Magnetic States at Short Distances
• Quantum effects on an atom with a magnetic quadrupole moment in a region with a time-dependent magnetic field
• On the stability of the open-string QED neutron and dark matter
• Signature of the Fragmentation of a Color Flux Tube
• Baryon Spectrum Analysis using Dirac's Covariant Constraint Dynamics
• The relativistic correction of the quarkonium melting temperature with a holographic potential
• On the question of quark confinement in the Abelian U(1) QED gauge interaction
• Symmetry of Dirac Equation and Corresponding Phenomenology
• Relativistic two-body calculation of $b\bar{b}$-mesons radiative decays
• QED meson description of the anomalous particles at ~17 and ~38 MeV
• Sequential hadronization in heavy ion collisions
• The Spectrum of Low-$p_T$ $J/\psi$ in Heavy-Ion Collisions in a Statistical Two-Body Fractal Model
• On a neutral particle with a magnetic quadrupole moment in a uniform effective magnetic field
• On the Mass Difference between pion and rho meson using a Relativistic Two-Body Model
• Confinement of Fermions in Tachyon Matter at Finite Temperature
• Dirac Equation Solution with Generalized tanh-Shaped Hyperbolic Potential: Application to Charmonium and Bottomonium Mass Spectra
• Relativistic correction to the dissociation temperature of B_c mesons in the hot medium
• Investigation of spin-$0$ massive charged particle subject to a homogeneous magnetic field with potentials in a topologically trivial flat class of Gödel-type space-time
• Re-study on the contribution of scalar potential and spectra of $c\bar{c}$, $b\bar{b}$ and $b\bar{c}(\bar{b}c)$ families
• Phenomenological study on the significance of the scalar potential and Lamb shift