Pion-Nucleon Scattering in theP11State

Abstract

The Pn pion-nucleon scattering amplitude is studied in order to determine the dynamical status of the nucleon. A simple one-channel static model is constructed in which a good fit to the low-energy data is obtained with a Castillejo-Dalitz-Dyson (CDD) pole. If there is, in fact, such a pole, with the strength indicated by our model, then one must conclude that other channels play a significant, although not overwhelming, part in forming the nucleon. It is also possible to reconcile all the available information with a model containing no CDD poles in which the nucleon is formed to a good approximation in the pion-nucleon channel alone. A few ways by which one may hope to choose between the two models are discussed. It is shown how the success of certain "reciprocal bootstrap" calculations can be understood, whether or not a CDD pole is required. The large inelasticity and phase shift in the Pn pion-nucleon channel at energies of 400 to 600 MeV are probably due to coupling with the 7nriV channel, with all three particles in relative 5 waves. This latter channel seems to be significant for the properties of the 1400-MeV (Roper) resonance, but probably plays a small role in the formation of the nucleon.

EmpiricalNDPotential and Castillejo-Dalitz-Dyson Poles in the Pion-NucleonP11State

“…Rev. Letters 17, 1303(1966. 14 The electromagnetic self-mass will diverge in this case because of the slow q 2 variation of the Pomeranchukon contribution.…”

P11π−NScattering and BrokenSU(3)Brehm1, Cook2 1968Phys. Rev.8000View full textAdd to dashboardCite

“…Since 8® 10 does not_contain 10, iV^>io scattering would play no role for a 10 resonance. This argument, of course, begs the question somewhat, but other calculations 19 have already indicated that the role of the TN* channel is not a large one.…”

“…Typically, N* and N exchange in a single-channel model do not bind the nucleon if physical couplings are em-ployed. 19 However, such calculations have not included the additional channels arising in Ps-B 8 scattering. By ignoring the inelastic contributions in the calculation given here, we find the same result.…”

“…17 This is not surprising since the reciprocal bootstrap does not include inelastic effects, and it is known that such effects must play an important role for the iV'. [18][19][20] Dynamical models always involve a truncation of the unitarity relation and thus a specific selection of inelastic channels. This choice is based on a variety of physical arguments as well as practical considerations.…”

Dynamical Implication of the πNP11Data

“…Taking account of the width of 0, we adopt the following definition for P2: I8 It is very difficult to know the details of the left-hand discontinuities, especially when the channel coupling plays an important role. We are interested in the gross features of them and adopt the pole approximation as (10) We put…”