Potential model calculations and predictions for heavy quarkonium

We study the charmonium spectrum using a complete one gluon exchange approach based on a phenomenological relativistic qq potential model with Dirac spinors in momentum space. We use phenomenological screening factors to include vacuum quantum effects. Our formulation does not rely on nonrelativistic approximations. We fit the lowest-lying charmonia (below the DD threshold) and predict the higher-lying resonances of the spectrum. In general, we reproduce the overall structure of the charmonium spectrum and, in particular, we can reasonably describe the X(3872) resonance mass as (mostly) a cc state. The numerical values of the free parameters of the model are determined taking into account also the experimental uncertainties of the resonance energies. In this way, we are able to obtain the uncertainties of the theoretical resonance masses and the correlation among the free parameters of the model.

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“…There exist a wide range of models for the scalar and vector potentials [29,30,74]. In this work we use the following effective potentials:…”

Section: Scalar Interactionmentioning

confidence: 99%

Charmonium spectrum with a Dirac potential model in the momentum space

2017

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“…Given the set of parameters, we predict the masses of the forty two bb states shown in Table 1, where we compare the present theoretical predictions with those from the relativized extension of the nonrelativistic model [25] and a semirelativistic Hamiltonian under nonperturbative framework [22]. Fig.…”

Section: Mass Spectrummentioning

confidence: 99%

“…Therefore, both perturbation and nonperturbative treatments have been taken into account recently in Ref. [22], which indicates the most significant effect of different treatments on the wave functions. The nonperturbative treatment brings each state with its own wave function, while the perturbative treatment leads to the same angular momentum multiplets sharing the identical wave function.…”

Section: Introductionmentioning

confidence: 99%

Bottomonium states versus recent experimental observations in the QCD-inspired potential model

Tian¹,

Cao²,

Yang³

et al. 2013

Chinese Phys. C

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In the QCD-inspired potential model where the quark-antiquark interaction consists of the usual onegluon-exchange and the mixture of long-range scalar and vector linear confining potentials with the lowest order relativistic correction, we investigate the mass spectra and electromagnetic processes of a bottomonium system by using the Gaussian expansion method. It reveals that the vector component of the mixing confinement is anticonfining and takes around 18.51% of the confining potential. Combining the new experimental data released by Belle, BaBar and LHC, we systematically discuss the energy levels of the bottomonium states and make the predictions of the electromagnetic decays for further experiments.

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“…By using, for the interaction, only central potentials, we shall not take into account the effects related to the spin-spin, spin-orbit and tensor interaction. These corrective contributions, that are extremely relevant for a detailed study of charmonium spectroscopy [5][6][7][8], can be introduced perturbatively carefully considering the Lorentz transformation properties of the interaction operators. The aim of the following analysis is only to demonstrate that our relativistic equation, with a local kinetic operator, can adequately reproduce the main structure of the charmonium spectrum for the low-lying resonances.…”

Section: A Numerical Application To the Charmonium Spectrummentioning

confidence: 99%

“…(1), is exactly consistent only for the zero component of a vector field. If a scalar (effective) field is considered, as it is usually done, in particular, for the study ¯ and ¯ spectra [5][6][7][8], one should add the corresponding scalar interaction operators to the constituent masses by means of the substitution that will be discussed in Section 3. However, these scalar interaction operators would appear in the square roots of the relativistic energies, giving rise to very serious difficulties for the calculations, unless an approximate Taylor expansion of the square roots is performed.…”

Section: Introductionmentioning

confidence: 99%

A relativistic wave equation with a local kinetic operator and an energy-dependent effective interaction for the study of hadronic systems

Sanctis

2014

Open Physics

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Abstract:We study a fully relativistic, two-body, quadratic wave equation for equal mass interacting particles. With this equation the difficulties related to the use of the square roots in the kinetic energy operators are avoided. An energy-dependent effective interaction, also containing quadratic potential operators, is introduced. For pedagogical reasons, it is previously shown that a similar procedure can be also applied to the well-known case of a one-particle Dirac equation. The relationships of our model with other relativistic approaches are briefly discussed. We show that it is possible to write our equation in a covariant form in any reference frame.A generalization is performed to the case of two particles with different mass. We consider some cases of potentials for which analytic solutions can be obtained. We also study a general numerical procedure for solving our equation taking into account the energy-dependent character of the effective interaction. Hadronic physics represents the most relevant field of application of the present model. For this reason we perform, as an example, specific calculations to study the charmonium spectrum. The results show that the adopted equation is able to reproduce with good accuracy the experimental data. PACS

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Potential model calculations and predictions for heavy quarkonium

Cited by 157 publications

References 49 publications

Charmonium spectrum with a Dirac potential model in the momentum space

Charmonium spectrum with a Dirac potential model in the momentum space

Bottomonium states versus recent experimental observations in the QCD-inspired potential model

A relativistic wave equation with a local kinetic operator and an energy-dependent effective interaction for the study of hadronic systems

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