Bohr-Sommerfeld quantization and meson spectroscopy

Abstract

We use the Bohr-Sommerfeld quantization approach in the context of constituent quark models. This method provides, for the Cornell potential, analytical formulae for the energy spectra which closely approximate numerical exact calculations performed with the Schrodinger or the spinless Salpeter equations. The Bohr-Sommerfeld quantization procedure can also be used to calculate other observables such as r.m.s. radius or wave function at the origin. Asymptotic dependence of these observables on quantum numbers are also obtained in the case of potentials which behave asymptotically as a power-law. We discuss the constraints imposed by these formulae on the dynamics of the quark-antiquark interaction.

13 pages

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Cited by in corpus (28)

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• Concavity of the meson Regge trajectories
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• Analytic Representation of The Square-Root Operator
• Note on universal description of heavy and light mesons
• Structure of the meson Regge trajectories
• Regge-like spectra of excited singly heavy mesons
• Improvement of the envelope theory with the dominantly orbital state method
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• Duality relations in the auxiliary field method
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• Regge trajectories for the heavy-light diquarks
• Regge trajectories for the triply heavy bottom-charm baryons in the diquark picture
• Regge trajectory relations for the universal description of the heavy-light systems: diquarks, mesons, baryons and tetraquarks
• Regge trajectories for the light diquarks
• A mass formula for light mesons from a potential model
• Two- and three-body calculations within the dominantly orbital state method
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• Regge trajectories for the triply heavy triquarks
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• $\lambda$ and $\rho$ Regge trajectories for bottom-charm tetraquarks $(bq)(\bar{c}{\bar{q}}^{\prime })$ and $(cq)(\bar{b}{\bar{q}}^{\prime })$
• Analytical approximations to the spectra of quark-antiquark potentials