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Low Energy Pion – Nucleon Scattering in the Heavy Baryon and Infrared Schemes
| Content Provider | Semantic Scholar |
|---|---|
| Author | Torikoshi, Kenichi |
| Abstract | Pion-nucleon scattering is a fundamental process which one would like to describe using the low-energy realization of quantum chromodynamics, namely chiral perturbation theory [1,2]. This is an attractive approach because it not only embodies chiral symmetry, which is fundamental to low-energy physics, but also offers a systematic expansion in powers of the momentum. Further it ensures unitarity order by order. Gasser and Leutwyler [2] have shown that ChPT works nicely for mesons and high accuracy can now be achieved for the ππ scattering lengths [3]. However, the power counting fails when baryons are introduced [4]. The power counting can be restored in heavy baryon chiral perturbation theory (henceforth referred to as HB) [5] where the heavy components of the baryon fields are integrated out. An alternative – the infrared regularization scheme (henceforth referred to as IR) – has been proposed [6], based on the ideas in Ref. [7]. This preserves the chiral power counting and has the advantage that it is manifestly Lorentz invariant and avoids the voluminous effective Lagrangian of the HB approach. Generally favorable results have been obtained with the IR scheme in a number of applications [8]. By suitable approximation of the IR expressions the HB formulae can be regained. A recent review of the HB and IR formalisms has been given by Meißner [9]. The first fit to the pion-nucleon scattering phase shift data using chiral perturbation theory was carried out in Ref. [7], henceforth referred to as I, using the HB scheme. In addition to the nucleon and pion fields, the ∆ resonance field was included explicitly since the intent was to fit out to energies in the ∆ resonance region. The calculation was carried to O(Q3), where Q is a generic small momentum scale, and it was found possible to obtain a reasonable fit up to energies slightly below the ∆ resonance. Subsequently Fettes and Meißner carried out several HB studies both with [10] and without [11,12] explicit inclusion of the ∆ field. The calculation with the ∆ field to O(Q3) appeared to be a little better than the O(Q4) calculation without it; for further discussion see Ref. [13]. Fettes and Meißner [14] have also studied isospin violation in the π −N system, although here we shall focus on the isospin symmetric case. All of these calculations were carried out with the HB approach and it is natural to examine the IR method in this context. Becher and Leutwyler [15] have used the IR approach in the sub-threshold region, where the HB scheme is inappropriate, and found that the IR representation of the scattering amplitude was not sufficiently accurate to allow the extrapolation of the experimental data to this region. The purpose of the present work is to study the IR scheme in the physical region at O(Q3) and compare it with the HB approach in order to see whether an improved fit to the phase shift data can be obtained. The organization of this paper is as follows. In Sec. II we review our notation for the effective Lagrangian and discuss the O(Q3) calculation of the scattering amplitudes in the IR scheme and their reduction to HB form. Formulae for the σ term and effective vertex couplings are also given. In Sec. III our fit to the phase shift data is described, first for the HB scheme and then for the IR approach. Our conclusions are presented in Sec. IV. Expressions for the IR integrals mentioned in the text are given in the Appendix, together with their HB reductions. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://cds.cern.ch/record/577832/files/0208049.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Appendix Approximation Chirality (chemistry) Energy, Physics Extrapolation GSAP gene Lagrangian (field theory) Mesons Nucleons Order by Perturbation theory Power (Psychology) Resonance Unitarity (physics) Vertex notation pi-Mesons |
| Content Type | Text |
| Resource Type | Article |
