Partial waves and largeN_Cresonance sum rules

Abstract

Using 1/N C expansion and dispersion theory techniques, without relying on any explicit resonance lagrangian, we generalize the KSRF relation beyond the leading chiral order. Two sum rules for the low energy constants L 2 , L 3 and a new relation between resonance couplings are derived. A rather detailed examination to the new relation is also given.

Some remarks on the Padé unitarization of low-energy amplitudes

“…In the next lines we will focus our attention on the IJ = 00 partial wave, but analogous results are found for the other channels. Former works pointed out that the PAs and other unitarizations fail to incorporate the crossed channel resonance exchanges [14,24]. Nonetheless, we will see that as N grows, the poles of the sequence [N/N ] actually tend to mimic not only the s-channel poles but also the left-hand cut contribution from diagrams with resonances in the t and u channels.…”

“…In order to broaden our analysis, we consider now a model with just vector mesons [14]. It could be derived either from the gauged chiral model [21] for the couplings 3g ρ F 2 = M 2 ρ , or from resonance chiral theory [22] with only vectors and the relation 3G 2 V = F 2 .…”

Pole Analysis on Unitarized SU(3) × SU(3) One Loop χPT Amplitudes

“…Using the PKU dispersive representation one obtains the same result as Eq. (18) under two additional assumptions: 1) neglect all crossed channel resonance exchanges (which contribute at leading order in 1/N c expansion); 2) assume in s channel there is only one pole involves [30].…”

The vector form factor at the next-to-leading order in 1/N C : chiral couplings L9(μ) and C88(μ) − C90(μ)

“…The second one was derived in ref. [27] from the LO ππ scattering amplitude. It is interesting to remark that the c d = 0 limit of this second relation, G V = F/ √ 3, has been obtained recently from a study of τ − → P − γ ν τ decays (P = π, K) [28].…”