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

Abstract

Pole analysis on unitarized SU (3) × SU (3) one loop χPT amplitudes (3) chiral perturbation theory. By fitting phase shift and inelasticity data, we determine pole positions in different channels (f 0 (980), a 0 (980),f 0 (600), K * 0 (800), K * (892), ρ(770)) and trace their N c trajectories. We stress that a couple channel Breit-Wigner resonance should exhibit two poles on different Riemann sheets that reach the same position on the real axis when N c = ∞. Poles are hence classified using this criteria and we conclude that K * (892) and ρ(770) are unambiguous Breit-Wigner resonances. For scalars the situation is much less clear. We find that f 0 (980) is a molecular state rather than a Breit-Wigner resonance, while a 0 (980), though behaves oddly when varying N c , does maintain a twin pole structure.

Study ofηKK¯andη′KK¯with the fixed center approximation to Faddeev equations

“…[31,32]). Along the same lines, the unitarity approach with the coupled channels explains successfully both the experimental data for the light scalar mesons [25,33,34] (such as a 0 (980), f 0 (980), σ, and κ [or K * (800)]) and the light baryons [21,24,[35][36][37][38][39], two Λ(1405), Λ(1670), N * (1535), ∆(1620), etc. Extrapolation of this dynamics to the charm sector has also produced many meson states, as the D * s0 (2317), D * 0 (2400), X(3700), X(3872), etc [40][41][42][43][44], as well as baryon states like the Λ c (2595) [45][46][47].…”

Resonance effects in pion and kaon decay constants

“…On the other hand, the nature of the light scalar resonances, such as f 0 (500),f 0 (980), K * 0 (800), etc., is still unclear and various descriptions are proposed by different groups: meson-meson molecular, tetraquark, standardqq with a strong pion cloud, etc. As a result of this, their N C behavior is also under debate [28,29,[31][32][33][34]. Though the N C trajectories of the scalar resonances reported by different groups diverge from each other, surprisingly there is one common feature from Refs.…”

“…Though the N C trajectories of the scalar resonances reported by different groups diverge from each other, surprisingly there is one common feature from Refs. [28,29,[31][32][33]: a scalar resonance with mass around 1 GeV appears at large N C . Based on these results and the success of this hypothesis in previous analyses [10,11,27], we will assume in the present article the existence of a large-N C scalar nonet with a bare mass around 1 GeV.…”

New insights into theDs0*(2317)and other charm scalar mesons

“…(26,27), on the determinations of the pole trajectories with varying N C . The corresponding results together with the ones by only considering the leading N C scalings, are shown in Figs.…”

“…[22,23]. Another kind of pole trajectories with varying N C , with N C the number of colors in QCD, has been demonstrated to be useful to discriminate different explanations for light-flavor resonances [24][25][26][27][28], such as for f 0 (500), ρ(770), etc. However, the study of the N C trajectories of the D * s0 (2317) state is still lacking.…”