New insights on low energy $$\pi N$$ π N scattering amplitudes

Abstract

The S-and P-wave phase shifts of low-energy pion-nucleon scatterings are analysed using Peking University representation, in which they are decomposed into various terms contributing either from poles or branch cuts. We estimate the left-hand cut contributions with the help of treelevel perturbative amplitudes derived in relativistic baryon chiral perturbation theory up to O( p 2 ). It is found that in S 11 and P 11 channels, contributions from known resonances and cuts are far from enough to saturate experimental phase shift data -strongly indicating contributions from low lying poles undiscovered before, and we fully explore possible physics behind. On the other side, no serious disagreements are observed in the other channels.

On the existence of N*(890) resonance in S11 channel of πN scatterings

“…The second term (circular cut) is a new contribution compared with the study of Ref. [23]. This term and the third term are found to be numerically small: the former appears purely at O(p 3 ) level, while the latter stems from u-channel nucleon exchange diagrams, which can be approximated as contact interaction in the low energy region.…”

“…However, the conclusions are drawn in Ref. [23] with the left-hand cuts estimated by tree-level BChPT amplitudes. That is, only the kinematical cut (−∞, (M N −m π ) 2 ] and the segment cut…”

“…The application of PKU representation is not confined to meson-meson [24,25] or meson-baryon interactions [23] only. In the classical field of nucleon-nucleon scatterings, an illuminating example can clearly re-depict the major physical picture therein.…”

“…Returning to the study of πN scatterings, in Ref. [23] the application of the PKU representation has led to very interesting findings: a resonance below πN threshold in the S 11 channel is called for to saturate the huge discrepancy between the phase shift data and the known contributions, and a companionate virtual state of the nucleon in the P 11 channel is found.…”

“…The indices b, v and r denote bound states, virtual states and resonances, respectively (see Ref. [23] for detailed expressions). The exponential term is a background that carries the information of left-hand cuts (l.h.c.s) and right-hand inelastic cut (r.h.i.c.)…”