Erratum: η-nucleon scattering length and effective range uncertainties [Phys. Rev. C 71, 014001 (2005)]

Abstract

The coupled ηN , πN , γN , ππN system is described by a K-matrix method. The parameters in this model are adjusted to get an optimal fit to πN → πN , πN → ηN , γN → πN and γN → ηN data in an energy range of about 100 MeV or so each side of the η-threshold. Compared with our earlier analysis, we now utilize recent Crystal Ball data. However, the outcome confirms our previous result that the η-nucleon scattering length (a) is large with a value of 0.91(6)+i0.27(2) fm.PACS numbers: 13.75.-n, 25.80.-e, 25.40.V

Search for quasi boundηmesons

“…For this curve the ηN scattering length is (0.250 + 0.123i) fm, corresponding to an imaginaryto-real ratio R of 0.49. This is in agreement with the values given in Table 4 except for the Green Wycech (GW) model [35]. If the interference is neglected a scattering length a = (0.292 ± 0.077i) fm is necessary to get the experimental peak parameters.…”

“…For the K-matrix analysis, which is close to the one from Ref. [35] they determined a(ηN) = 1.14 + i0.31 fm. However, the global fit yields a(ηN) = 0.41+i0.56 fm.…”

“…In the following we will discuss the methods leading to very small and very large values of the scattering length. Green and Wycech [35] applied the K-matrix formalism treating all available data at the time of their publication (i. e. their parameter set A). They considered two nucleon resonances which couple to the ηN channel: the previously mentioned N * (1535) and the N * (1650).…”

“…In The energy dependence of the real and imaginary part of the elastic η-nucleon T -matrix. The curves with the 1σ error band are from Mai et al [21], the curves without error bands are from Green and Wycech [35]. The vertical lines indicated thresholds for free ηN → ηN scattering, ηN → KΛ and ηN → KΣ reactions.…”

ηN scattering lengths favour ηd and ηα states

“…In this model, the πN, ηN and π∆ (ππN) channels were treated in a coupled channel formalism (so that an additional self-energy term appears in the propagator in Eq. (16) There also exists a recent model of the ηN interaction [40], which predicts a scattering length of a ηN = (0.91, 0.27) fm, from a fit to the πN → πN, πN → ηN, γN → πN and γN → ηN data. However, we have not used it for our present FRA calculations since the T -matrix which fits the data very well is an on-shell T -matrix.…”