πN→ηNData Require the Existence of theN(1710)P

Abstract

In spite of prolonged polemics, the agreement on the existence of N(1710) P11 resonance has not until now been reached, and the Particle Data Group declares it as a 3-star resonance only. We show that the proper inclusion of inelastic channels in the coupled-channel formalism indisputably demands the existence of N(1710) P11 state, and that it presumably stays "hidden" within the continuum ambiguity of any typical single channel partial wave analyses. Consequently, its Particle Data Group confidence rating should be raised to a 4-star resonance.

The N*(1710) as a resonance in the ππN system

“…In case of the N * (1710), some partial wave analyses [5,6] do not find any pole corresponding to it, while others claim a * kanchan@ific.uv.es † amartine@ific.uv.es ‡ oset@ific.uv.es 1 clear manifestation of this resonance [7,8,9,10]. On the other hand, the authors of [11] claim an indisputable existence of the N * (1710) from their study of the πN → ηN reaction in the coupled channel formalism and suggest that the status of this resonance should be improved from three-star to four-star.Another controversy about the N * (1710) started after the finding of a narrow peak in the γA → (K + n)X reaction at LEPS [12], suggesting the existence of a pentaquark state which some groups associated to a SU(3) antidecuplet to which the N * (1710) would also belong (see, for example, [13,14]). In order to be compatible with the Θ + , the N * (1710) is required to be narrow.…”

Poles as the only true resonant-state signals extracted from a worldwide collection of partial-wave amplitudes using only one, well controlled pole-extraction method

“…[40] we have shown that including inelastic channels into the analysis is a natural way for eliminating continuum ambiguities. We have concluded that, by fitting only elastic channel, some of the resonant states which dominantly couple to inelastic channels might remain unrevealed, and we had to fit as many channels as possible.…”

“…[40]. The problem with stability of minimization solutions lies in the fact that the ηN channel data are old, scarce, and unreliable (for instance Brown data at higher energies -see discussion in ref.…”

“…[40] we have discussed the continuum ambiguity problem in coupled-channel formalisms. Namely, once the inelastic channels are opened, it turns out that the differential cross sections themselves are not sufficient to determine the scattering amplitude.…”

“…However, as we know that inelastic channels are extremely important in CMB formalism to ensure the stability of solutions (see following chapter and ref. [40]), we have decided to constrain elastic KH80 amplitudes with πN → ηN WI08 amplitudes which fairly correctly depict the world agreement of the ηN channel amplitudes at lower energies -see Fig. 3.…”