New Determination of the Pion-Nucleon Coupling Constant ands-Wave Scattering Lengths

Abstract

The most accurate determination of the pionnucleon coupling constant published to date is that of Woolcock 1 using the dispersion relation for the invariant amplitude B+ in the forward direction. (The subscript + refers to ir + p elastic scattering.) This method gave / 2 = 0.081 ±0.003.Although we were satisfied that the method was reliable and that the quoted error was realistic, we thought that a more accurate result could now be obtained by a more direct method. This is simply to re-evaluate the familiar dispersion relations for the n^p elastic-scattering amplitudes in the forward direction, taking account of the large amount of experimental data now available. This calculation also yields the s-wave scattering lengths. Since the results are interesting (and surprising), we give here a brief account of the method used, and of the values obtained for the constants.Instead of writing the dispersion relations in the usual form, first written down by Goldbe rger, Miyazawa, and Oehme, 2 we take advantage of the sum rule discussed in the same paper to eliminate one of the scattering-length combinations. The most convenient form for evaluation is to write D ± , the real parts of the TT*/) forward-scattering amplitudes in the laboratory system, in the form 2/ 2

π+Photoproduction Between 1.2 and 3 GeV at Very Small Angles

“…The errors in/ 2 are estimated to be of the order of 15-20% and are due to counting statistics, systematic errors, and uncertainties in choosing the correct order of fit. Therefore, the disagreement with the value of/ 2 E s = 1.5 GeV = 0.0822 ±0.0018 obtained in pion-nucleon scattering 5 does not seem to be significant.…”

Pion-Nucleon Interactions

“…There is a disagreement with the results 1.34 of Samaranayake & Woolcock (12), which Hamilton (16) has criticized as being dependent on uncertainties in the high-energy total cross-section behaviour owing to the relatively slowly convergent integrals 1.31 and 1.32. Hamilton (16) argues powerfully that al -a3 = 0.271 ± 0.007, al + 2aa = -0.002 ± 0.008 1.37…”

“…Samaranayake & Woolcock (12) have used 1. 24 with the assumption, consistent with the high-energy data, that above 10 GeV (13)3…”

The K− Meson‐Proton Interaction at Low Energies

“…The inequalities (3.5) are valid for Y*, (1405) if we assume that this part of the scattering length for C x + E x in isospin 0, which is not coupled to the EN system. has about the same order of magnitnde as Nx -+ Nx scattering length [24]. I n (2.6) this means: -Kf, M 0.2f.…”