ρρ scattering revisited with coupled channels of pseudoscalar mesons

Abstract

The ρρ scattering has been studied by two groups which both claimed a dynamical generated scalar meson, most likely to be f 0 (1370). Here we investigate the influence of coupled-channels of pseudoscalar mesons, i.e., ππ andKK, on this dynamical generated scalar state. With the coupled channel effect included, the pole and partial decay widths are found to be more close to PDG values for f 0 (1500). * relativistic ρ propagators in solving the B-S equation for ρρ scattering. Both scalar state and tensor state associated with f 0 (1370) and f 2 (1270), respectively, were found in consistence with the conclusion of Ref. [4].From the studies of above two groups, obviously, for the energies around f 2 (1270) well below ρρ threshold, there is strong model dependence for the interaction of two far off-massshell ρ mesons. For the scalar state closer to the ρρ threshold, the two groups got similar result rather model independently. In this paper we shall study the influence of coupledchannels of pseudoscalar mesons, i.e., ππ andKK, on this dynamical generated scalar state. In the ρρ − KK coupling we consider the case of K and K * exchange, while in the ρρ − ππ coupling we consider the case of π and ω exchange. Formalism ρρ → ππ with π-exchangeWe investigate the coupled channel effect based on a chiral covariant framework [5]. We follow the formalism of the hidden gauge interaction which provides the ρππ coupling by means of the Lagrangian [12,13] (1)where the symbol . . . stands for the trace in the SU (3) space with the coupling constant g = M V /2f π with M V the mass of vector meson and f π = 93M eV the pion decay constant. The matrices V µ and P are given by

Further study of $f_0(1710)$ with coupled-channel approach and hadron molecular picture

“…And we also find the lower resonance at 1.46 − 0.012iGeV for q max = 1.0GeV and 1.48 − 0.008iGeV for q max = 0.875GeV . Compared to our previous work [29], the resonance move down a little alone the real axis, which is 1.52 − 0.009iGeV for q max = 1.0GeV and 1.53 − 0.005iGeV for q max = 0.875GeV in [29].…”

Two dynamical generated $a_0$ resonances by interactions between vector mesons

“…Up to now, for the I = 0 sector, there are three hadronic molecules calimed to be dynamically generated from the K K, ρρ, K * K * interaction through vector meson exchange potentials, which are assigned to f 0 (980), f 0 (1500), f 0 (1710), respectively [9,34,35]. For the I = 1 sector, the attractive potentials for the K K and K * K * channels are much weaker than the corresponding isoscalar cases.…”

“…Previously, both f 0 (1500) and f 0 (1710) have been considered as glueball candidates and extensively studied within the quarkonia-guleball mixing picture [36][37][38][39][40][41][42]. With the success of the new possible configuration as hadron molecule to explain their properties [34,35], to pin down their nature, it is crucial to study also their relevant iso-vector a 0 mesons. While scalar glueballs are not ecpected to have iso-vector partners, the f 0 (1500) and f 0 (1710) as scalar hadronic molecules should have nearly degenerate iso-vector partners, a 0 (1450) and a 0 (1710), respectively, just as nearly degenerate f 0 (980) and a 0 (980) as KK molecules.…”

Two dynamical generated $$a_0$$ resonances by interactions between vector mesons

“…Up to now, for the I = 0 sector, there are three hadronic molecules claimed to be dynamically generated from the K K , ρρ, K * K * interaction through vector meson exchange potentials, which are assigned to f 0 (980), f 0 (1500), f 0 (1710), respectively [9,29,30]. For the I = 1 sector, the attractive potentials for the K K and K * K * channels are much weaker than the corresponding isoscalar cases.…”

“…Previously, both f 0 (1500) and f 0 (1710) have been considered as glueball candidates and extensively studied within the quarkonia-guleball mixing picture [31][32][33][34][35][36][37][38]. With the success of the new possible configuration as hadron molecule to explain their properties [29,30], to pin down their nature, it is crucial to study also their relevant iso-vector a 0 mesons. While scalar glueballs are not expected to have iso-vector partners, the f 0 (1500) and f 0 (1710) as scalar hadronic molecules should have nearly degenerate iso-vector partners, a 0 (1450) and a 0 (1710), respectively, just as nearly degenerate f 0 (980) and a 0 (980) as K K molecules.…”