Relating Quarkonium Wave Functions at the Origin

Abstract

Within the context of nonrelativistic potential models, we obtain several formulas (with varying degrees of rigor) relating the wave functions at the origin of the $c\bar{c}$, $b\bar{c}$ and $b\bar{b}$ S-wave quarkonium systems. One of our main results is a model-independent relation which seems to hold to within 3% for any reasonable choice of interquark potential and any choice of radial quantum number -- namely, $|{\Psi }_{b\bar{c}}(0){|}^2\simeq |{\Psi }_{c\bar{c}}(0){|}^{1.3}|{\Psi }_{b\bar{b}}(0){|}^{0.7}$ (the exponents are motivated in the text). One of the physical consequences of this result is the following relationship between heavy meson masses which we expect to hold at about the 10% level: $M_{B_c^{\ast }}-M_{B_c}\simeq (0.7)(M_{J/\psi }-M_{{\eta }_c}{)}^{0.65}(M_{{\rm Y}}-M_{{\eta }_b}{)}^{0.35}$.

TEX, 9 pages, requires harvmac

References in corpus (3)

• Rigorous QCD Analysis of Inclusive Annihilation and Production of Heavy Quarkonium
• Quarkonium Wave Functions at the Origin
• Quarkonium Decay Matrix Elements from Quenched Lattice QCD

Cited by in corpus (9)

• Properties of $Q\bar{Q}$ mesons in non-relativistic QCD formalism
• Phenomenological prediction of the properties of the B_{C} system
• Spectroscopy of $B_c$ meson in a semi-relativistic quark model using the shifted large-N expansion method
• Properties of $Q\bar{Q}$ $(Q\epsilon b,c)$ mesons in Coulomb plus Power potential
• Mass Spectra of Heavy Quarkonia and B_{c} Decay Constant for Static Scalar-Vector Interactions with Relativistic Kinematics
• B_{c} and heavy meson spectroscopy in the local approximation of the Schrodinger equation with relativistic kinematics
• Variational Estimation of the Wave Function at Origin for Heavy Quarkonium
• Three-loop matching coefficients for heavy flavor-changing currents and the phenomenological applications
• Simple Baryon-Meson Mass Relations For A Logarithmic Interquark Potential