Quasiclassical theory of the Dirac equation with a scalar-vector interaction and its applications in the physics of heavy-light mesons

Journal Article · Fri Apr 01 04:00:00 EDT 2011 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.83.076003· OSTI ID:21537758

Lazur, V Yu; Reity, O K; Rubish, V V ^[1]

---

1. Department of Theoretical Physics, Uzhgorod National University, Voloshyna Street 54, Uzhgorod 88000 (Ukraine)

We construct a relativistic potential quark model of D, D{sub s}, B, and B{sub s} mesons in which the light quark motion is described by the Dirac equation with a scalar-vector interaction and the heavy quark is considered a local source of the gluon field. The effective interquark interaction is described by a combination of the perturbative one-gluon exchange potential V{sub Coul}(r)=-{xi}/r and the long-range Lorentz-scalar and Lorentz-vector linear potentials S{sub l.r.}(r)=(1-{lambda})({sigma}r+V{sub 0}) and V{sub l.r.}(r)={lambda}({sigma}r+V{sub 0}), where 0{<=}{lambda}<1/2. Within the quasiclassical approximation, we obtain simple asymptotic formulas for the energy and mass spectra and for the mean radii of D, D{sub s}, B, and B{sub s} mesons, which ensure a high accuracy of calculations even for states with the radial quantum number n{sub r{approx}}1. We show that the fine structure of P-wave states in heavy-light mesons is primarily sensitive to the choice of two parameters: the strong-coupling constant {alpha}{sub s} and the coefficient {lambda} of mixing of the long-range scalar and vector potentials S{sub l.r.}(r) and V{sub l.r.}(r). The quasiclassical formulas for asymptotic coefficients of wave functions at zero and infinity are obtained.

• OSTI ID: 21537758
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 7 Vol. 83; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ACCURACY
APPROXIMATIONS
ASYMPTOTIC SOLUTIONS
B S MESONS
BEAUTY MESONS
BEAUTY PARTICLES
BOSONS
CALCULATION METHODS
CHARM PARTICLES
CHARMED MESONS
COMPOSITE MODELS
COMPUTERIZED SIMULATION
D S MESONS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
ELEMENTARY PARTICLES
ENERGY RANGE
EQUATIONS
FERMIONS
FIELD EQUATIONS
FINE STRUCTURE
FUNCTIONS
GLUONS
HADRONS
INTERACTIONS
MASS SPECTRA
MATHEMATICAL MODELS
MATHEMATICAL SOLUTIONS
MESONS
P WAVES
PARTIAL DIFFERENTIAL EQUATIONS
PARTIAL WAVES
PARTICLE MODELS
PSEUDOSCALAR MESONS
QUARK MODEL
QUARKS
RELATIVISTIC RANGE
SIMULATION
SPECTRA
STRANGE MESONS
STRANGE PARTICLES
STRONG-COUPLING MODEL
WAVE EQUATIONS
WAVE FUNCTIONS