Quark potential approach to baryons and mesons

Mukherjee, S. N.; Nag, R.; Sanyal, Sudip; Morii, Toshiyuki; Morishita, J.; Tsuge, Masayasu

doi:10.1016/0370-1573(93)90010-b

Cited by 60 publications

(45 citation statements)

References 283 publications

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“…They are used as the basic degrees of freedom in the 'constituent quark model'. This model yields a reasonable mass spectroscopy of hadrons (Lucha et al 1991;Mukherjee et al 1993), but its foundations are not very well established theoretically. First, a nonrelativistic treatment of light hadrons is not justified (see above).…”

Section: Introductionmentioning

confidence: 99%

Light-Cone Quantization: Foundations and Applications

Heinzl

2001

Methods of Quantization

111

139

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Abstract. These lecture notes review the foundations and some applications of lightcone quantization. First I explain how to choose a time in special relativity. Inclusion of Poincaré invariance naturally leads to Dirac's forms of relativistic dynamics. Among these, the front form, being the basis for light-cone quantization, is my main focus. I explain a few of its peculiar features such as boost and Galilei invariance or separation of relative and center-of-mass motion. Combining light-cone dynamics and field quantization results in light-cone quantum field theory. As the latter represents a first-order system, quantization is somewhat nonstandard. I address this issue using Schwinger's quantum action principle, the method of Faddeev and Jackiw, and the functional Schrödinger picture. A finite-volume formulation, discretized light-cone quantization, is analysed in detail. I point out some problems with causality, which are absent in infinite volume. Finally, the triviality of the light-cone vacuum is established. Coming to applications, I introduce the notion of light-cone wave functions as the solutions of the light-cone Schrödinger equation. I discuss some examples, among them nonrelativistic Coulomb systems and model field theories in two dimensions. Vacuum properties (like chiral condensates) are reconstructed from the particle spectrum obtained by solving the light-cone Schrödinger equation. In a last application, I make contact with phenomenology by calculating the pion wave function within the Nambu and Jona-Lasinio model. I am thus able to predict a number of observables like the pion charge and core radius, the r.m.s. transverse momentum, the pion structure function and the pion distribution amplitude. The latter turns out to be the asymptotic one.

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Section: Introductionmentioning

confidence: 99%

Light-Cone Quantization: Foundations and Applications

Heinzl

2001

Methods of Quantization

111

139

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“…Sendo assim, o sucesso dos modelos de potenciais para hádrons ordinários chega a parecer um milagre. Entretanto, com o aprimoramento dos métodos perturbativos, muitas ambigüidades e discussões que se apresentavam foram esclarecidas, resultando em um quadro consistente da QCD [30,39] sob a conotação dos modelos de potenciais. O ponto fraco de qualquer modelo sobre a interação entre quarks está justamente na falta de um critério em que se fundamente a validade do mesmo.…”

Section: A Interação Entre Quarks E Os Modelos De Potenciaisunclassified

“…Existem diversos trabalhos [28][29][30][31][32][33][34][35][36][37][38][39] que sugerem diferentes abordagens para o tratamento, relativístico ou semi-relativísitico, do termo cinético. Esse tratamento deve ser minuciosamente cuidadoso quando se deseja aplicar um modelo de potencial na obtenção de propriedades físicas de estados ligados, notoriamente, o espectro de massas e as taxas de decaimento.…”

Section: Introductionunclassified

Um modelo para interações entre quarks: a redução não-relativística em modelos de potenciais

Bernardini¹

2003

Rev. Bras. Ens. Fis.

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Modelos fenomenológicos de potenciais têm proporcionado resultados extremamente satisfatórios na descrição dos hádrons ordinários, mais especificamente no caso dos estados ligados quark-antiquark (mésons). Neste trabalho estudamos os principais aspectos na construção das interações em um estado ligado quark-antiquark proporcionando a obtenção das ferramentas genéricas para o estudo de modelos de potenciais. Analisamos os aspectos importantes na escolha do tratamento de maior concordância com a dinâmica de interação das partículas, considerando os aspectos relativísticos bem como as possibilidades de uma aproximação não-relativística. Inicialmente a cromodinâmica quântica (QCD) "macia"é empregada para determinar os termos do potencial efetivo estabelecendo o termo assintótico Coulombiano decorrente da aproximação pela troca de um glúon. Ao mesmo tempo, um termo linear de confinamentoé introduzido em concordância com a QCD e com a prescrição fenomenológica. Finalizando, discutimos as possibilidades gerais para o desenvolvimento de um modelo de potencial.Phenomenological potential models have provided extremely satisfactory results on description of ordinary hadrons, more specifically in the case of quark-antiquark bound states (mesons). In this work we study the main aspects in the construction of quark-antiquark interactions just providing the generic tools for potential model study. We analyze the important aspects in the choice of the treatment in good agreement with the dynamics of interacting particles, attempting to relativistic aspects as well as to the possibilities of nonrelativistic approximation. Initially the "soft QCD" is employed to determine the effective potential terms establishing the asymptotic Coulomb term from one gluon exchange approximation. At the same time, a linear confinement term is introduced in accordance with QCD and phenomenological prescription. At the end, we discuss the general developing possibilities of a potential model.

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“…This potential was originally derived from the t-channel one-gluon exchange S-matrix [7] or the t-channel one-gluon exchange kernel appearing in the Bethe-Salpeter (B-S) equation [4,5] . In the relativistic version, the potential may be represented in the form…”

Section: Introductionmentioning

confidence: 99%

Retardation Terms in the One-Gluon Exchange Potential

Chen

2001

Int. J. Mod. Phys. A

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It is pointed out that the retardation terms given in the original Fermi-Breit potential vanish in the center of mass frame. The retarded one-gluon exchange potential is rederived in this paper from the three-dimensional one-gluon exchange kernel which appears in the exact three-dimensional relativistic equation for quark-antiquark bound states. The retardation part of the potential given in the approximation of order p 2 /m 2 is shown to be different from those derived in the previous literature. This part is off-shell and does no longer vanish in the center of mass frame. PACS number(s): 12.40 Qq, 11.10.St, 14.40.Gx. Key words: One-gluon exchamge potential, Retardation effect.In the quark potential model [1−6] , the one-gluon exchange potential (OGEP), or say, the Fermi-Breit (F-B) potential, usually is chosen to describe the short-range interaction between two quarks (qq), two antiquarks (qq) or a quark and an antiquark (qq). This potential was originally derived from the t-channel one-gluon exchange S-matrix [7] or the t-channel one-gluon exchange kernel appearing in the Bethe-Salpeter (B-S) equation [4,5] . In the relativistic version, the potential may be represented in the form

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Quark potential approach to baryons and mesons

Cited by 60 publications

References 283 publications

Light-Cone Quantization: Foundations and Applications

Light-Cone Quantization: Foundations and Applications

Um modelo para interações entre quarks: a redução não-relativística em modelos de potenciais

Retardation Terms in the One-Gluon Exchange Potential

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