Heavy-light scalar-quark system in the leading-log effective-action model: Exact solution

Journal Article · Fri Dec 01 04:00:00 EST 1989 · Physical Review (Section) D: Particles and Fields; (USA)

DOI:https://doi.org/10.1103/PhysRevD.40.3708· OSTI ID:7265551

Mendel, R R ^[1]; Trottier, H D ^[2]

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1. Department of Applied Mathematics, The University of Western Ontario, London, Ontario, Canada N6A 5B9 (Canada)
2. Center for Theoretical Physics Laboratory for Nuclear Science Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (USA)

An exact solution is obtained in a renormalization-group-improved effective-action model of QCD, for a system containing an infinitely heavy antiquark and a scalar quark of arbitrary mass. The solution corresponds to a solitonlike {ital S}-wave state of finite radius {ital R}. The only input parameters are the QCD scale {Lambda}{sub M{bar S}} (where M{bar S} denotes the modified minimal subtraction scheme), the number of light quark flavors {ital N}{sub {ital f}}, and the scalar-quark mass {ital m}. Color confinement arises from the nonlinear properties of the effective action. An analysis of the radial excitations ({ital m}=0) of the {ital S}-wave soliton state clearly shows that this confinement is linear. We find for high radial excitations that the leading behavior of the total energy of the system ({ital m}=0) is {ital U}{sub {ital N}}={ital Q}{kappa}{ital R}{sub {ital N}}+{ital const}, where {ital Q}={radical}4/3, {kappa}{sup 1/2}=1.043{Lambda}{sub M{bar S}} ({ital N}{sub {ital f}}=3), and {ital R}{sub {ital N}} is the radius of the soliton corresponding to the {ital N}th radial excitation. A detailed description is given of the properties of the ground-state soliton as a function of {ital N}{sub {ital f}} and {ital m}. An analytical expression is obtained for the short-distance behavior of the scalar-quark wave function.

• OSTI ID: 7265551
• Journal Information: Physical Review (Section) D: Particles and Fields; (USA), Journal Name: Physical Review (Section) D: Particles and Fields; (USA) Vol. 40:11; ISSN 0556-2821; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645204 -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- Strong Interactions & Properties
645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BAG MODEL
BOUNDARY CONDITIONS
COLOR MODEL
COMPOSITE MODELS
COULOMB FIELD
DIFFERENTIAL EQUATIONS
ELECTRIC FIELDS
ELEMENTARY PARTICLES
EQUATIONS
EQUATIONS OF MOTION
EXTENDED PARTICLE MODEL
FERMIONS
FIELD THEORIES
FLAVOR MODEL
FUNCTIONS
LAGRANGIAN FUNCTION
MASS
MATHEMATICAL MODELS
PARTIAL DIFFERENTIAL EQUATIONS
PARTIAL WAVES
PARTICLE MODELS
POSTULATED PARTICLES
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
QUARK MODEL
QUARKS
QUASI PARTICLES
RENORMALIZATION
S WAVES
SOLITONS
WAVE FUNCTIONS