ρρinteraction in the hidden gauge formalism and thef0(1370)andf

Abstract

The ρρ interaction in the hidden gauge formalism and the f 0 (1370) and f 2 (1270) resonances. AbstractWe have studied the interaction of vectors mesons within the hidden gauge formalism and applied it to the particular case of the ρρ interaction. We find a strong attraction in the isospin, spin channels I,S=0,0 and 0,2, which is enough to bind the ρρ system. We also find that the attraction in the I,S=0,2 channel is much stronger than in the 0,0 case. The states develop a width when the ρ mass distribution is considered, and particularly when the ππ decay channel is turned on. Using a regularization scheme with cut offs of natural size, we obtain results in fair agreement with the mass and the width of the f 0 (1370) and f 2 (1270) meson states, providing a natural explanation of why the tensor state is more bound than the scalar and offering a new picture for these states, which would be dynamically generated from the ρρ interaction or, in simpler words, ρρ molecular states.

Y(3940),Z(3930), and theXMolina1, Oset2 2009Phys. Rev. DSelf Cite

“…After that, the radiative decay of these states into γγ was studied in [35], obtaining results in good agreement with the PDG [36]. The work of [34] was later extended to SU(3) [37], where several states were found that could also be identified with some of the PDG. Recently, the ρD * , ωD * interaction was studied within the same formalism [38], generalizing to SU(4) the basic hidden gauge Lagrangians, but breaking the SU(4) symmetry in the vector exchange diagrams.…”

“…In the present work we shall present results for the case of all the channels which couple to D * D * or D * sD * s . The formalism is the same used in [34] and [38]. Some approximations were made there which make the formalism handy and reliable, by neglecting the three-momentum of the vector mesons with respect to their masses.…”

“…Our work is based on the hidden gauge symmetry (HGS) formalism for the interaction of vector mesons, which was introduced by Bando-Kugo-Yamawaki [31,32,33]. This hidden gauge formalism has been applied in [34] for the ρρ interaction, giving rise to two bound ρρ states that could be identified with the f 0 (1370) and f 2 (1270). After that, the radiative decay of these states into γγ was studied in [35], obtaining results in good agreement with the PDG [36].…”

The hidden-charm pentaquark and tetraquark states

“…Wu et al also took into account some decay mechanisms by considering the decay of the states to a light baryon plus either a light meson or a charmonium through heavy charmed meson exchanges, as done in Refs. [291,292]. Table 12: Mass (M), total width (Γ), and the partial decay width (Γ i ) for the states from PB → PB, with units in MeV, taken from Refs.…”

Nuclear medium effects on the meson

“…The self-energy Π ρ,(b) K * has to be determined self-consistently since it is obtained from the in-medium amplitude T ρ K * N which contains theK * N loop function G ρK * N , and this last quantity itself is a function of the complete self-energy Π ρK * = Π a2), taking all the cuts into account properly, and adding the resultinḡ K * N →K * N terms to the V B → V ′ B ′ potential coming from vectormeson exchange, in a similar way as done for the study of the vector-vector interaction in Refs. [21,22]. Preliminar results of this procedure in free space indicate that the generated resonances barely change their position for spin 3/2 and only by a moderate amount in some cases for spin 1/2.…”