Solution of the Bethe-Salpeter equation for pion-nucleon scattering

Lahiff, A. D.; Afnan, I. R.

doi:10.1103/physrevc.60.024608

Cited by 48 publications

(64 citation statements)

References 66 publications

(95 reference statements)

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“…At the same time, an analysis of the data on πN scattering yields a much more modest value, κ ρ ≈ 1 − 3 for this parameter (see, e.g. [1]). Thus the short-ranged central and tensor nucleon-nucleon forces in boson-exchange models are enhanced "by hand" to reproduce the experimental NN phase shifts.…”

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confidence: 99%

Description of intermediate- and short-range NN nuclear force within a covariant effective field theory

2005

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confidence: 99%

Description of intermediate- and short-range NN nuclear force within a covariant effective field theory

2005

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“…In principle, crossing symmetry is violated and the well-defined power counting scheme in ChPT is lost by rescatterings. On the other hand, MEM's [ 11,12] have also been shown to give a good description of low energy πN data, in addition to an excellent agreement with the data at higher energies. It is therefore assuring that similar success can also be achieved for the pion EM production.…”

mentioning

confidence: 58%

“…The solutions of the scattering equation include rescattering effects to all orders and hence unitarity is ensured, while crossing symmetry is violated. Such models [ 6,7,8,9,10,11,12] have been able to provide a good description of πN scattering lengths and phase shifts in S-, P -, and D-waves up to 600 MeV pion laboratory kinetic energy.MEM's have been constructed for pion EM production as well [ 10,13] and good …”

mentioning

confidence: 99%

Threshold π0 photo- and electro-production in a meson-exchange model

YANG¹,

CHEN²,

KAMALOV³

et al. 2004

Nuclear Physics A

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We show that, within a meson-exchange dynamical model describing well most of the existing pion electromagnetic production data up to the second resonance region, one is also able to obtain a good agreement with the π 0 photo-and electroproduction data near threshold. In the case of π 0 production, the effects of final state interaction in the threshold region are nearly saturated by single charge exchange rescattering. This indicates that in ChPT, it might be sufficient to carry out the calculation just up to one-loop diagrams for threshold neutral pion production.Photo-and electroproduction of π 0 near threshold have been a subject of many experimental and theoretical studies in the last decade. It was prompted by the discrepancy between the "old" low-energy-theorem (LET) prediction of E 0 + = −2.4 × 10 −3 /m π and the "new" experimental measurements [ 1,2], which yielded E 0 + ∼ −1.3 × 10 −3 /m π . The discrepancy between LET and the experimental data was eventually resolved by the chiral perturbation theory (ChPT) calculation [ 3] which showed that the loop corrections gave rise to nonanalytical terms in m π . Since then precise measurements on the π 0 electromagnetic (EM) production near threshold have been performed [ 4] and the ChPT calculations to one loop O(p 3 ) (O(p 4 ) in the case of photoproduction) have been carried out in the heavy baryon formulation [ 5]. Nice agreement between theory and experiment was reached not only for the S-wave multipoles but also for the P -wave amplitudes.Meson-exchange models (MEM's), as in ChPT, also start from an effective chiral Lagrangian. However, they differ from ChPT in the approach to calculate the scattering amplitudes. In ChPT, crossing symmetry is maintained in the perturbative field-theoretic calculation, and the agreement between its predictions and the data is expected as long as the series converges. In MEM's, the effective Lagrangian is used in the construction of potential for use in the scattering equation. The solutions of the scattering equation include rescattering effects to all orders and hence unitarity is ensured, while crossing symmetry is violated. Such models [ 6,7,8,9,10,11,12] have been able to provide a good description of πN scattering lengths and phase shifts in S-, P -, and D-waves up to 600 MeV pion laboratory kinetic energy.MEM's have been constructed for pion EM production as well [ 10,13] and good

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“…With the advent of solutions to the Bethe-Salpeter (BS) equation for the off-mass-shell πN amplitude, [2] it is now possible to compare the results of the traditional approach based on two-body scattering, with the LET. Here we will present solutions to the BS equation based on a potential derived from the chirally invariant Lagrangian.…”

Section: The Bethe-salpeter Amplitudementioning

confidence: 99%