Linear confinement in momentum space: Singularity-free bound-state equations

Leitão, Sofia; Stadler, Alfred; Peña, M. T.; Biernat, Elmar P.

doi:10.1103/physrevd.90.096003

Cited by 29 publications

(28 citation statements)

References 32 publications

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“…The numerical methods, and in particular the way how a linear confining interaction and its covariant generalization can be treated in momentum space, have been described in some detail in Refs. [42,59,60].…”

Section: Formalismmentioning

confidence: 99%

Covariant spectator theory of quark-antiquark bound states: Mass spectra and vertex functions of heavy and heavy-light mesons

Leitão¹,

Stadler

Peña

et al. 2017

Phys. Rev. D

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We use the covariant spectator theory with an effective quark-antiquark interaction, containing Lorentz scalar, pseudoscalar, and vector contributions, to calculate the masses and vertex functions of, simultaneously, heavy and heavy-light mesons. We perform least-square fits of the model parameters, including the quark masses, to the meson spectrum and systematically study the sensitivity of the parameters with respect to different sets of fitted data. We investigate the influence of the vector confining interaction by using a continuous parameter controlling its weight. We find that vector contributions to the confining interaction between 0 % and about 30 % lead to essentially the same agreement with the data. Similarly, the light quark masses are not very tightly constrained. In all cases, the meson mass spectra calculated with our fitted models agree very well with the experimental data. We also calculate the mesons wave functions in a partial wave representation and show how they are related to the meson vertex functions in covariant form.

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Section: Formalismmentioning

confidence: 99%

Covariant spectator theory of quark-antiquark bound states: Mass spectra and vertex functions of heavy and heavy-light mesons

Leitão¹,

Stadler

Peña

et al. 2017

Phys. Rev. D

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“…The kernel employed in our calculations with the 1CSE consists of a covariant generalization of the linear (L) confining potential used in [12], a color Coulomb (Coul), and a constant (C) interaction:…”

Section: Formalismmentioning

confidence: 99%

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Leitão¹,

Stadler²,

Peña³

et al. 2018

Light Cone 2016

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As an application of the Covariant Spectator Theory (CST) we calculate the spectrum of heavy-light and heavy-heavy mesons using covariant versions of a linear confining potential, a onegluon exchange, and a constant interaction. The CST equations possess the correct one-body limit and are therefore well-suited to describe mesons in which one quark is much heavier than the other. We find a good fit to the mass spectrum of heavy-light and heavy-heavy mesons with just three parameters (apart from the quark masses). Remarkably, the fit parameters are nearly unchanged when we fit to experimental pseudoscalar states only or to the whole spectrum. Because pseudoscalar states are insensitive to spin-orbit interactions and do not determine spin-spin interactions separately from central interactions, this result suggests that it is the covariance of the kernel that correctly predicts the spin-dependent quark-antiquark interactions.

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“…To find an appropriate way to treat a linear confining interaction in momentum space, and to test the required numerical methods, in [8] we used the SE to calculate the two-body bound states of a linear potential. Since in S waves these solutions are known exactly, this is an ideal test case.…”

Section: Pseudoscalar Meson Spectra With the One-channel Cst Equationmentioning

confidence: 99%

“…The kernel employed in our calculations with the 1CSE consists of a covariant generalization of the linear (L) confining potential used in [8], a one-gluon exchange (OGE), and a constant (C) interaction,…”

Section: Pseudoscalar Meson Spectra With the One-channel Cst Equationmentioning

confidence: 99%

Quarkonia and heavy-light mesons in a covariant quark model

Leitão

Stadler

Peña

et al. 2016

EPJ Web of Conferences

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Abstract. Preliminary calculations using the Covariant Spectator Theory (CST) employed a scalar linear confining interaction and an additional constant vector potential to compute the mesonic mass spectra. In this work we generalize the confining interaction to include more general structures, in particular a vector and also a pseudoscalar part, as suggested by a recent study [1]. A one-gluon-exchange kernel is also implemented to describe the short-range part of the interaction. We solve the simplest CST approximation to the complete Bethe-Salpeter equation, the one-channel spectator equation, using a numerical technique that eliminates all singularities from the kernel. The parameters of the model are determined through a fit to the experimental pseudoscalar meson spectra, with a good agreement for both quarkonia and heavy-light states.

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Linear confinement in momentum space: Singularity-free bound-state equations

Cited by 29 publications

References 32 publications

Covariant spectator theory of quark-antiquark bound states: Mass spectra and vertex functions of heavy and heavy-light mesons

Covariant spectator theory of quark-antiquark bound states: Mass spectra and vertex functions of heavy and heavy-light mesons

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Quarkonia and heavy-light mesons in a covariant quark model

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