πN→multi-πNscattering in the1/Ncexpansion

Abstract

We extend the 1/Nc meson-baryon scattering formalism to πN → multi-πN case. We first show that the leading-order large Nc processes proceed through resonant intermediate states (e.g., ρN or π∆). We find that the pole structure of baryon resonances can be uniquely identified by their (non)appearance in ηN or mixed partial-wave π∆ final states.

1/Nc Corrections in Meson-Baryon scattering

“…( 19) plus Eqs. (17) and (18) for the 3-flavor case [or just Eq. ( 15) for the 2-flavor case] to give the corresponding s-channel suppressed amplitudes.…”

“…A recent and extensive body of literature [6,10,11,12,13,14,15,16,17,18] builds upon not only this connection to large N c , but also upon the observation that having an underlying conserved quantum number contributing to multiple partial waves means that a resonant pole of a given mass and width appearing in one partial wave of given I, J P quantum numbers also appears in numerous others, giving rise to multiplets of baryon resonances degenerate in mass and width. Here, however, we are more interested in the structure of the amplitudes themselves in terms of the 1/N c expansion, rather than poles that lie within them.…”

Pion electroproduction amplitude relations in the1/Ncexpansion

“…The large N c scattering method [12] explains the existence of baryon resonance multiplets that share similarities (but are not identical to) those appearing in large N c quark models; in particular, one can study resonances with arbitrarily large widths [13], exotics [14], and three-flavor resonances [15]. In addition, the means by which the spurious N c > 3 states may be removed [16] has been explored, as well as the nature of the competing chiral and large N c limits [17], and results for multipion processes [18].…”

“…In addition, the means by which the spurious N c > 3 states may be removed [16] has been explored, as well as the nature of the competing chiral and large N c limits [17], and results for multipion processes [18].…”

πN → MULTI-πN SCATTERING IN THE 1/Nc EXPANSION

“…This talk mainly focuses on πN → multi-πN processes in the 1/N c scattering formalism. 1 Recent development of the original scattering formalism [2][3][4][5][6][7][8] can be reviewed in Refs. 9 The central idea rests upon symmetries that emerge for QCD in the large N c limit.…”