A confining potential for quarks

Ripelle, M. Fabre de la

doi:10.1016/0370-2693(88)90406-6

Cited by 51 publications

(23 citation statements)

References 14 publications

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“…This is a well-known result: a linear potential does not lead to linear Regge trajectories in a nonrelativistic description; correct Regge trajectories can only be obtained with confining potentials rising as r 2/3 [11]. For large radial quantum numbers (n ≫ ℓ), the orbits have a large eccentricity, and thus r 1 ≈ r − ≈ 0 and η ≈ 1.…”

Section: A Nonrelativistic Calculationsmentioning

confidence: 81%

Bohr-Sommerfeld quantization and meson spectroscopy

Brau

2000

Phys. Rev. D

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

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Section: A Nonrelativistic Calculationsmentioning

confidence: 81%

Bohr-Sommerfeld quantization and meson spectroscopy

Brau

2000

Phys. Rev. D

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“…[43][44][45], the square-root trajectory is obtained by combining both Regge poles and cuts. The Schrödinger equation with the Cornell potential produces the Regge trajectories M 2 ∼βl 4/3 , and the linear Regge trajectories demands the confining potential rising as r 2/3 [46]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

Regge trajectories for heavy quarkonia from the quadratic form of the spinless Salpeter-type equation

Chen

2018

Eur. Phys. J. C

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In this paper, we present one new form of the Regge trajectories for heavy quarkonia which is obtained from the quadratic form of the spinless Salpeter-type equation (QSSE) by employing the Bohr-Sommerfeld quantization approach. The obtained Regge trajectories take the parameterized form M 2 = β(c l l + π n r + c 0 ) 2/3 + c 1 , which are different from the present Regge trajectories. Then we apply the obtained Regge trajectories to fit the spectra of charmonia and bottomonia. The fitted Regge trajectories are in good agreement with the experimental data and the theoretical predictions.

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“…It is well known that this behavior can be obtained in potential models by using a confinement potential well adjusted for the kinematics. In non-relativistic descriptions of meson spectra, a r 2/3 confining potential must be used [1], while in relativistic kinematics the linear Regge trajectories are obtained with a linear confinement [2] and results also naturally from the relativistic flux tube model of mesons [3,4]. It is worth noting that this mass behavior is also expected for heavy-light mesons.…”

Section: Introductionmentioning

confidence: 99%

Universality of Regge and vibrational trajectories in a semiclassical model

1998

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The orbital and radial excitations of light-light mesons are studied in the framework of the dominantly orbital state description. The equation of motion is characterized by a relativistic kinematics supplemented by the usual funnel potential with a mixed scalar and vector confinement. The influence of finite quark masses and potential parameters on Regge and vibrational trajectories is discussed. The case of heavy-light mesons is also presented.

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A confining potential for quarks

Cited by 51 publications

References 14 publications

Bohr-Sommerfeld quantization and meson spectroscopy

Bohr-Sommerfeld quantization and meson spectroscopy

Regge trajectories for heavy quarkonia from the quadratic form of the spinless Salpeter-type equation

Universality of Regge and vibrational trajectories in a semiclassical model

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