Variational Worldline Approximation for the Relativistic Two-Body Bound State in a Scalar Model
arXiv:hep-ph/0601220 · doi:10.1007/s00601-006-0160-4
Abstract
We use the worldline representation of field theory together with a variational approximation to determine the lowest bound state in the scalar Wick-Cutkosky model where two equal-mass constituents interact via the exchange of mesons. Self-energy and vertex corrections are included approximately in a consistent way as well as crossed diagrams. Only vacuum-polarization effects of the heavy particles are neglected. In a path integral description of an appropriate current-current correlator an effective, retarded action is obtained by integrating out the meson field. As in the polaron problem we employ a quadratic trial action with variational functions to describe retardation and binding effects through multiple meson exchange.The variational equations for these functions are derived, discussed qualitatively and solved numerically. We compare our results with the ones from traditional approaches based on the Bethe-Salpeter equation and find an enhanced binding contrary to some claims in the literature. For weak coupling this is worked out analytically and compared with results from effective field theories. However, the well-known instability of the model, which usually is ignored, now appears at smaller coupling constants than in the one-body case and even when self-energy and vertex corrections are turned off. This induced instability is investigated analytically and the width of the bound state above the critical coupling is estimated.
arXiv comment62 pages, 7 figures, FBS style, published version
References in corpus (64)
- Quantum Chromodynamics and Other Field Theories on the Light Cone
- The Infrared Behavior of QCD Green's Functions - Confinement, Dynamical Symmetry Breaking, and Hadrons as Relativistic Bound States
- JaxoDraw: A graphical user interface for drawing Feynman diagrams
- Effective field theories for heavy quarkonium
- Dyson-Schwinger Equations: Density, Temperature and Continuum Strong QCD
- Dyson-Schwinger equations: a tool for hadron physics
- Theory of Light Hydrogenlike Atoms
- Perturbative Quantum Field Theory in the String-Inspired Formalism
- Field Theory Without Feynman Diagrams: One-Loop Effective Actions
- Explicitly Covariant Light-Front Dynamics and Relativistic Few-Body Systems
- The HQET/NRQCD Lagrangian to order alpha/m^3
- Electromagnetic structure of the deuteron
- Constant External Fields in Gauge Theory and the Spin 0, 1/2, 1 Path Integrals
- Calculation of the Electron Self Energy for Low Nuclear Charge
- Potential NRQED: The Positronium Case
- Nonperturbative study of generalized ladder graphs in a ϕ^2χtheory
- Solving Bethe-Salpeter equation in Minkowski space
- Light-Front Bethe-Salpeter Equation
- Worldline Path Integrals for Fermions with General Couplings
- The Feynman-Schwinger representation in QCD
- Threshold Expansion and Dimensionally Regularised NRQCD
- Electron-deuteron scattering in a current-conserving description of relativistic bound states: formalism and impulse approximation calculations
- Vacuum decay in quantum field theory
- Worldline path integral for the massive Dirac propagator : A four-dimensional approach
- Study of relativistic bound states for scalar theories in Bethe-Salpeter and Dyson-Schwinger formalism
- O(4) Expansion of the ladder Bethe-Salpeter equation
- Polaron Variational Methods In The Particle Representation Of Field Theory : I. General Formalism
- Two-fermion relativistic bound states in Light-Front Dynamics
- (In-)Consistencies in the relativistic description of excited states in the Bethe-Salpeter equation
- A variational calculation of particle-antiparticle bound states in the scalar Yukawa model
- Catalyzed decay of false vacuum in four dimensions
- Solving a Coupled Set of Truncated QCD Dyson-Schwinger Equations
- The stability of the scalar interaction
- Feynman-Schwinger representation approach to nonperturbative physics
- Lagrange mesh, relativistic flux tube, and rotating string
- Relativistic bound states in Yukawa model
- Nonperturbative renormalization in a scalar model within Light-Front Dynamics
- On The Ladder Bethe-Salpeter Equation
- Variational Two Fermion Wave Equations in QED: Muonium Like Systems
- Improved variational description of the Wick-Cutkosky model with the most general quadratic trial action
- Solving a Set of Truncated Dyson-Schwinger Equations with a Globally Converging Method
- Nonperturbative dynamics of scalar field theories through the Feynman-Schwinger representation
- Polaron Variational Methods In The Particle Representation Of Field Theory : II. Numerical Results For The Propagator
- Effective Lagrangians in bound state calculations
- Non-Perturbative Mass Renormalization in Quenched QED from the Worldline Variational Approach
- Some exact solutions of reduced scalar Yukawa theory
- Relativistic quantum mechanics: A Dirac's point-form inspired approach
- First Order Variational Calculation of Form Factor in a Scalar Nucleon--Meson Theory
- Particle decay in false vacuum
- Extrapolation of the Zalpha-Expansion and Two--Loop Bound--State Energy Shifts
- Search for Neutral Higgs Boson in CP-Conserving and CP-Violating MSSM Scenarios
- Variational Field Theoretic Approach to Relativistic Scattering
- Vacuum condensates, effective gluon mass and color confinement in a new reformulation of QCD
- Variational Calculation of Relativistic Meson-Nucleon Scattering In Zeroth Order
- Worldline Variational Approximation: A New Approach to the Relativistic Binding Problem
- Renormalized non-perturbative scalar and fermions models in Covariant Light Front Dynamics
- Nonperturbative treatment of the N-body system with dynamical mesons
- Nonperturbative evaluation of the few-body states for scalar interaction
- Matching in Nonrelativistic Effective Quantum Field Theories
- Bound states in quantum field theory, scalar fields
- Comment on the paper: ``Feynman-Schwinger representation approach to nonperturbative physics'' by C. Savkli et al. [Phys. Rev. C 60, 055210 (1999), hep-ph/9906211]
- Validity of the one-body current for the calculation of form factors in the point form of relativistic quantum mechanics
- On bound states in quantum field theory
- Vacuum Polarization Effects in the Worldline Variational Approach to Quantum Field Theory
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- Studying the scalar bound states of the system in the Bethe-Salpeter formalism
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- Integral representations combining ladders and crossed-ladders
- Asymptotic behavior and critical coupling in the scalar Yukawa model from Schwinger-Dyson equations
- Variational Approximations in a Path-Integral Description of Potential Scattering
- Exact Path-Integral Representations for the -Matrix in Nonrelativistic Potential Scattering