Relativistic Spin–Flavor States in Light Front Dynamics

Beyer, Michael; Kuhrts, C.; Weber, H. J.

doi:10.1006/aphy.1998.5837

Cited by 23 publications

(35 citation statements)

References 19 publications

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“…It is worthwhile to note that for large invariant cut-off masses the resulting function M 3B (M 2B ) coincides with the result that utilizes (4) and solves (14) without cut-off restrictions. In this sense we reproduce the result of Ref.…”

Section: Discussionsupporting

confidence: 74%

“…To solve (14) we use the cut-off parameters Λ = 4m, 6m, 8m, where m is the constituent mass, and Λ/m = 10 15 → ∞. In Fig.…”

Section: Discussionmentioning

confidence: 99%

“…For a more detailed description the spin has to be included on the light front, e.g., along the lines of Ref. [14]. The scale restricts the parameter space (m, λ, Λ) resulting in a two-dimensional surface of allowed parameters.…”

Section: Introducing a Scalementioning

confidence: 99%

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Stability of Three-Body Bound States on the Light Front

Beyer

Mattiello²,

Frederico³

et al. 2003

Few-Body Systems

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Section: Discussionsupporting

confidence: 74%

“…To solve (14) we use the cut-off parameters Λ = 4m, 6m, 8m, where m is the constituent mass, and Λ/m = 10 15 → ∞. In Fig.…”

Section: Discussionmentioning

confidence: 99%

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Stability of Three-Body Bound States on the Light Front

Beyer

Mattiello²,

Frederico³

et al. 2003

Few-Body Systems

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“…This is consistent with the spinor invariants for N * (1535) constructed in reference [8], where the total momentum wave function was written as s µ u λ and contracted with γ µ instead of…”

Section: Conversion Of Dirac To Bargmann-wigner Basissupporting

confidence: 85%

“…For example, there are three nucleon states compared to the single S-state of the NQM in the static limit and five N * (1535) states. The alternative Bargmann-Wigner basis [10] (BW), which is in one-to-one correspon-dence with the Dirac basis [8], sheds light on this problem from another point of view. It is based on the equivalence of the infinite momentum frame (IMF) and light front dynamics which implies that quarks bound in a hadron in the IMF are all collinear, that is, have equal velocities p i /m = P/M, where M is the baryon mass and m a constituent quark mass.…”

Section: Introductionmentioning

confidence: 99%

Melosh Construction of Relativistic Three-Quark Baryon Wave Functions

Sun

Weber

2002

Int. J. Mod. Phys. A

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A method for constructing a complete set of relativistic three-quark states in light front dynamics is implemented for the nucleon, N * (1520) and N * (1535). This approach facilitates constructing states containing virtual antiquarks and a physical interpretation is provided in terms of transition amplitudes from quark to quark-gluon or quark-Goldstone boson Fock states of chiral dynamics generated by flux tube breaking expected in QCD at intermediate distances.

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The Nucleon Wave Function in Light-Front Dynamics

Karmanov¹

1999

N* Physics and Nonperturbative Quantum Chromodynamics

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The general spin structure of the relativistic nucleon wave function in the 3qmodel is found. It contains 16 spin components, in contrast to 8 ones known previously, since in a many-body system the parity conservation does not reduce the number of the components. The explicitly covariant form of the wave function automatically takes into account the relativistic spin rotations, without introducing any Melosh rotation matrices. It also reduces the calculations to the standard routine of the Dirac matrices and of the trace techniques. In examples of the proton magnetic moment and of the axial nucleon form factor, with a particular wave function, we reproduce the results of the standard approach. Calculations beyond the standard assumptions give different results. * e-mail: karmanov@sci.lebedev.ru known long ago [16] that in a many-body system the parity conservation does not reduce the number of the spin components. Hence, for the nucleon we get 2×2×2×2 = 16. This opportunity is absent in any two-body system and in the nonrelativistic three-body one. Technically, the extra components can be constructed since the particle four-momenta in any off-energy-shell relativistic amplitude, in particular, in the wave function, are not related by the conservation law: for the minus-projections k − = k 0 − k z the sum of the quark momenta k 1,2,3 and the nucleon momentum p are not equal to each other: (k 1 + k 2 + k 3 ) − = p − . Hence, we have in our disposal 4 four-vectors and can construct the pseudoscalar C ps = e µνργ k 1µ k 2ν k 3ρ p γ . Due to that, in addition to "old" eight components given in [8], we construct another eight spin structures with "wrong" P-parity (the pseudoscalar structures) and then "correct" them by multiplying by C ps . However, this way to find the spin components is not obligatory. One can construct an equivalent set of sixteen components such that only a few of them (less than eight) contain the factor C ps . These extra components (relative to the paper [8]) are necessary in order to represent even symmetric S-wave spin structure (initially given in c.m.-system) in arbitrary system of reference in terms of the Dirac matrices sandwiched with the spinors. In other language this corresponds to multiplying the center-of-mass wave function by the Melosh rotation matrices. If we will omit these extra components and come back to the c.m.-system, we would not reproduce our initial S-wave but again will find some extra components. In general case one should start with the wave function containing all sixteen components in any system of reference. They are forming the full basis. Their total number does not depends, of course, on the representation. Their relative magnitude is determined by dynamics.Secondly, we will represent the nucleon wave function in the 3q model in the explicitly covariant form. This will allow one to use in calculations the standard Dirac-matrices algebra and the trace techniques. In particular, we will see that there is no any need to introduce explicitly any Melosh rotation matr...

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Relativistic Spin–Flavor States in Light Front Dynamics

Cited by 23 publications

References 19 publications

Stability of Three-Body Bound States on the Light Front

Stability of Three-Body Bound States on the Light Front

Melosh Construction of Relativistic Three-Quark Baryon Wave Functions

The Nucleon Wave Function in Light-Front Dynamics

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