Study Of The ?K*(?)* Three-body System With The Fixed Center Approximation To Faddeev Equations

The interactions between hadrons. the structure of hadron and its properties, and the hadronic spectroscopy are the major challenges of high energy physics. The Chiral Unitary Approach has been used to study of the hadronic interactions projection on S-wave in meson-meson, meson-baryon and the baryon-baryon system. It is an effective method to study the hadronic resonant nature, and the results are agreed well with the mass and width of some particles found in experiments.In this work, the three-body system of ?K*(?)* is studied under the theoretical framework of the Chiral Unitary Approach, adopting the fixed center approximation to Faddcev equations. In the case that two particles of the three-body system can form a relative stable cluster, the cluster can be approximately seen as a fixed center. The Faddeev equation under Fixed Center Approximation is an effective method to deal with the three-body system.This paper is based on the work dealed with the theoretical framework of the Chiral Unitary Approach to study the light vector-light vector (V-V)interacting by L. S. Geng et al., whose result showed that the tensor meson f2'(1525) with IG(JPC)= 0+(2++) can be dynamically generated in the VV?VV scattering. The tensor state was found to be the K*(?)* resonance. Based on this result, in the study of the ?K*(?)* three-body interacting system, K*(?)* can be treated as the relatively stable cluster being the fixed center. In this work, the fixed center approximation to Faddeev equations is used to describe the ?K*(?)* three-body scattering. After getting the total amplitudes of VV?VV two-body scattering, one can solve the Faddeev equation under the fixed center approximation to get the total three-body scattering amplitude.In the paper of L. S. Geng et al., the lowest amplitudes of the VV?VV scattering were calculated, starting from the lowest Chiral Lagrangian for light vector meson-light vector meson interactions. The contributions from the contact terms and the tree level diagram of u(t)-channel vector exchange and the box of pseudoscalar mesons exchange were included in the calculation. By solving the Bethe-Salpeter equation with coupling channels. one can get the total amplitude of VV?VV two-body scattering. The result shows that the box terms of exchanging pseudoscalar mesons don't affect the mass of the dynamically generated state obviously, but there is extremely effect on the generated state's width.During the calculating, we adopt the dimension regularization method to deal with the divergence of the loop integral. In this way, the renormalization constant ?(?) is introduced which is the free parameter in our calculation. Here we use the same parameters as the ones'in L. S. Geng's paper in studying the corresponding sector, taking the renormalization parameters as ?=1000MeV and ?(?)=-1.85. Since the width of the ? meson is rather broad (???150MeV). we need to consider the effect of the ??. By solving the Faddeev equation under fixed center approximation, we can get the total amplitude of the ?K*(?)* three-body scattering. In the figure of the modulus squared of amplitude, there is a apparent resonance structure with mass and width being (M, ?)?(1960,105)MeV.The quantum numbers IG(JPC) of the dynamically generated resonance should be 1+(3--), which are consistent with the IG(JPC) quantum numbers of p3(1990) meson found in experiment. Meanwhile the mass and the width of the dynamically generated resonance is also in agreement with those of ?3(1990). Thus, the resonance dynamically generated from the the ?K*(?)* three-body scattering can be considered as ?3(1990). Under our theoretical framework, the p3(1990) is a ?K*(?)* three-body molecular state.