Regge trajectories in an ultra-relativistic treatment of fermion-antifermion bound states

Lucha, Wolfgang; Rupprecht, Heinz; Schöberl, Franz F.

doi:10.1016/0370-2693(91)90464-2

Cited by 11 publications

(7 citation statements)

References 8 publications

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“…A similar observation has already been made in Ref [14]. within a slightly different context[15,16].…”

supporting

confidence: 87%

“…the very pleasing result E 2 eff (λ min ) = 9 a ℓ. Accordingly, the effectively semi-relativistic energy eigenvalues of the linear potential are perfectly able to reproduce the observed linearity of the Regge trajectories with, however, a slope which is slightly larger than the one obtained within different analyses based on the true semi-relativistic Hamiltonian (1), all of which end up with one and the same finding: E 2 SR = 8 a ℓ [13,14]. Moreover, from the point of view of a correct description of the linear Regge trajectories, both of the semi-relativistic treatments are clearly superior to the corresponding nonrelativistic approach, which gives for the energy eigenvalues of the linear potential [3,4]…”

Section: Linear Potentialmentioning

confidence: 51%

“…. Accordingly, the effectively semirelativistic energy eigenvalues of the linear potential are perfectly able to reproduce the observed linearity of the Regge trajectories with, however, a slope which is slightly larger than the one obtained within difFerent investigations [14,15] This funnel potential is, beyond any doubt, not of the power-law type. Consequently, it cannot be subjected to the general effective formalism developed so far but deserves a special treatment, which might consist of some purely numerical approach.…”

Section: Variational Methodsmentioning

confidence: 74%

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Semirelativistic Hamiltonians of apparently nonrelativistic form

Lucha

Schöberl

1995

Phys. Rev. A

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We construct effective Hamiltonians which, despite their apparently nonrelativistic form, incorporate relativistic effects by involving parameters which depend on the relevant momentum. For some potentials the corresponding energy eigenvalues may be determined analytically. Applied to two-particle bound states, it turns out that in this way a nonrelativistic treatment may indeed be able to simulate relativistic effects. Within the framework of hadron spectroscopy, this lucky circumstance may be an explanation for the sometimes extremely good predictions of nonrelativistic potential models even in relativistic regions.PACS number(s): 03.65.Ge

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“…A similar observation has already been made in Ref [14]. within a slightly different context[15,16].…”

supporting

confidence: 87%

Section: Linear Potentialmentioning

confidence: 51%

Section: Variational Methodsmentioning

confidence: 74%

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Semirelativistic Hamiltonians of apparently nonrelativistic form

Lucha

Schöberl

1995

Phys. Rev. A

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“…[1,2]. The obvious advantage of our approach is its physical transparency.The basic idea of the proposed effective-Hamiltonian method [5,6] is to approximate by a potential the (perturbatively accessible part of the) interaction between particles which in fact are described by some quantum field theory. T o this end consider the elastic scattering of the involved fermion f and antifermion 7 (with masses m , and m,, respectively).…”

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confidence: 99%

Comment on "Relativistic description of quark-antiquark bound states"

1992

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COMMENTS Comments are short papers which criticize or correct papers of other authors previously published in the Physical Review. EachComment should state clearly to which paper it refers and must be accompanied by a brief abstract. The same publication schedule as for regular articles is followed, and page proofs are sent to authors.By means of an effective-Hamiltonian method we reconsider the derivation of the effective interaction in a fermion-antifermion system. Furthermore, we point out some errors of Gara and co-workers in their treatment of fermion-antifermion bound states by solving the reduced Salpeter equation in configuration space.PACS number(s): 12.40. Qq, ll.lO.St, In two recent papers [1,2] Gara and co-workers investigated the relativistic description of bound states of quark-antiquark pairs. Their analysis was based on the reduced Salpeter equation. The Salpeter equation [3] is derived from the Bethe-Salpeter equation [4] upon eliminating any dependence on timelike variables in a suitable manner. Some standard and plausible approximations, such as the restriction to positive-energy solutions, then lead to the reduced Salpeter equation.In this Comment we would like to present an alternative way of treating fermion-antifermion bound states relativistically, namely, by construction of an effective Hamiltonian for the two-particle system under consideration. The procedure advocated for consists of two main steps [5,6].(1) Compute the effective interaction potential between the bound-state constituents (at least to the extent you trust in perturbation theory) from the elastic scattering of the involved particles, more precisely, from the Fourier transform o f the corresponding transition amplitude [7,81. -(2) Use this potential in a multiparticle Schrijdinger equation with relativistically correct kinetic Hamiltonian in order to determine the energy eigenvalues and corresponding eigenstate vectors of the bound state under consideration.Obviously, this effective-Hamiltonian method might be regarded as the relativistic generalization of the description of fermion-antifermion bound states in terms of nonrelativistic potential models. As far as the incorporation of relativistic kinematics is concerned, it provides a description of bound states which is of equal quality as the reduced Salpeter equation adopted in Refs. [1,2]. The obvious advantage of our approach is its physical transparency.The basic idea of the proposed effective-Hamiltonian method [5,6] is to approximate by a potential the (perturbatively accessible part of the) interaction between particles which in fact are described by some quantum field theory. T o this end consider the elastic scattering of the involved fermion f and antifermion 7 (with masses m , and m,, respectively). Expressed in terms of Dirac spinors u ( p ,~) and u ( p ,~) , the general form of the corresponding transition amplitude T is where r i , i = 1,2, represent some Dirac matrices. The (unspecified) interaction kernel, which depends on the dynamics of the theory respon...

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“…The Regge trajectory is one of the effective approaches for studying hadron spectra [2][3][4][5][6][7][8][9][10][11]. The orbital and radial Regge trajectories [12] for pion are often taken as being approximately linear in the (M 2 , l) plane and in the (M 2 , n r ) plane, respectively, M 2 = α 1 l+α 2 n r +c [13][14][15][16][17][18][19][20], where M is the mass, α 1 and α 2 are the Regge slopes, l is the orbital angular momentum, n r is the radial quantum number, and c is a constant. The pion Regge trajectories are in fact nonlinear when they are examined more precisely, see Fig.…”

Section: Introductionmentioning

confidence: 99%

Revisiting the pion Regge trajectories

Chen¹

2022

Preprint

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We propose a model-independent ansatz M = βx (x + c0) ν + c1 (x = l, nr) and then use it to fit the orbital and radial pion Regge trajectories without the preset values. It is shown that nonzero c1 is reasonable and acceptable. Nonzero c1 gives an explanation for the nonlinearity of the pion Regge trajectories in the usually employed (M 2 , x) plane. As mR or c1 is chosen appropriately, both the orbital and radial pion Regge trajectories are linear in the ((M − mR) 2 , x) plane whether the π 0 is included or not on the Regge trajectories. The fitted pion Regge trajectories suggest 0.45 ≤ ν ≤ 0.5, which indicates the confining potential r a with 9/11≤a ≤ 1. Moreover, it is illustrated in appendix B that mR can be nonzero for the light mesons and the fitted Regge trajectories are also linear when they are plotted in the ((M − mR) 2 , x) plane. We present discussions in the appendix A on the structure of the Regge trajectories plotted in the (M, x) plane and on the structure of the Regge trajectories in the ((M − mR) 2 , x) plane based on the potential models and the string models.

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Regge trajectories in an ultra-relativistic treatment of fermion-antifermion bound states

Cited by 11 publications

References 8 publications

Semirelativistic Hamiltonians of apparently nonrelativistic form

Semirelativistic Hamiltonians of apparently nonrelativistic form

Comment on "Relativistic description of quark-antiquark bound states"

Revisiting the pion Regge trajectories

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