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

Abstract

We study the ππN system by solving the Faddeev equations, for which the input twobody t-matrices are obtained by solving the Bethe-Salpeter equation in the coupled channel formalism. The potentials for the ππ, πN sub-systems and their coupled channels are obtained from chiral Lagrangians, which have been earlier used to study resonances in these systems successfully. In this work, we find a resonance in the ππN system with a mass of 1704−i375/2 MeV and with quantum numbers I = 1/2, J π = 1/2 + . We identify this state with the N * (1710). This peak is found where the energies of the ππ sub-system fall in the region of the σ resonance. We do not find evidence for the Roper resonance in our study indicating a more complex structure for this resonance, nor for any state with total isospin I = 3/2 or 5/2. IntroductionThe excited states of the nucleon have been studied extensively theoretically as well as experimentally. This is evident from the fact that many of these states, especially those in the energy region below 1750 MeV, have been assessed either three or four stars by the particle data group (PDG) [1]. Even then, there are some resonances in this low energy region which still need unanimous agreement on their characteristics or existence, e.g., the J π = 1/2 + resonances in the isospin 1/2 domain. The N * (1440) or Roper resonance is a subject of continuous debate and the existence of the N * (1710) is even questioned. The quark models face difficulties in reproducing both these states [2,3,4]. 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. However, the width of this resonance is not known precisely, with the widths listed in [1] ranging from ∼ 90 -480 MeV. The authors of [15] re-analyzed the πN → KΛ reaction and found that a narrow width of the N * (1710) [1] was incompatible with the data and proposed the existence of another narrow resonance in this energy region. The partial wave analyses group who do not find a pole for the N * (1710) suggested to look for other resonance in this energy region as a possible narrow, non-strange partner of the θ + [16,17]. The debate on this issue has continued with new analyses which do not find a signal for the θ + , as a consequence of which, the ca...

Study of theKN−K*Ncoupled system ins-wave

“…In this sense, such strangeness −1 or 0 resonances can also be considered as pentaquark states. Actually similar investigations have even been extended to systems of two-mesons and a baryon where resonances arising purely from the three-body dynamics have been deduced [41][42][43][44], thus indicating the importance of a heptaquark content in some cases. Proceeding in a similar way we investigate if mesonbaryon configurations with a positive strangeness also form a resonance or a bound state.…”

Bayesian Inference of the Resonance Content ofp(γ,K+)Λ

“…In the latest SAID analyses [11,39], this resonance was not needed for the description of πN scattering either. The P 11 (1710)'s negligible coupling to πN and its absence in reactions where the ππN channels are not relevant can be attributed to it being a resonance in the ππN system [40].…”

Plausible explanation for theΔ5/2+(2000)puzzle

“…For instance π∆ 3/2 − (1700) may contribute to N 3/2 + (1720) and π∆ 1/2 − (1620) as well as σN to N 1/2 + (1710). Indeed in this latter case the resonance has been dynamically generated as a σN state [31]. …”