Theoretical Study Of The Three-body Light Meson System

Quantum Chromodynamics（QCD）is the theoretical bases in studying strong interaction.We know that the β function of QCD is minus from solving the renormalization group.Thus the effective coupling constant increases as the transfer momentum decreases.In the hadronic scale,the perturbation QCD can’t be used.We need employ the effective theory to study hadron-hadron interaction.Now,a lot of exotic hadrons have been observed in experiment.There are somewhat discrepancies on hadron mass and width between experimental measurement and the prediction of traditional quark model.Experimental and theoretical studies on those exotic states are helpful to understand the internal structure and interaction of hadrons.Now,there exist some interpretations on those states,such as tight multi-quark state,molecular state and hybrid state.In light meson sector,the observed exotic mesons include f₀（500）、f₀（980）、a₀（980）、π₁（1600）and K（1460）.In this work,we focus on π₁（1600）and K（1460）.And we interpret π₁（1600）as π（?）K^* three-body molecular state,K（1460）as KK（?） molecular state.We use fixed center approximation（FCA）to Faddeev equation to study π（?）K^* three-body interaction.Under FCA,KK^* is assumed forming a stable cluster f₁（1285）.The π（?）K^* three-body interaction is reduced to the interaction of π and the cluster KK^*.For π-KK^* scattering,we get a resonant structure around 1650 MeV in the three-body T amplitude.This state can be identified with the observed π₁（1600） in experiment.Meanwhile,we have also studied the η（?）K^* three-body system in order to look for possible isospin scalar JPC=1-+ state.And we find that there exists a resonance from the interaction of η（?）K^* with quantum number IG（JPC）=0+（1-+）.Within Isobar model,we have studied the KK（?） three-body system.Under Isobar model,the K（?） interaction is parameterized via the f₀（980） and a₀（980）poles.Then,the KK（?） three-body is reduced to coupled channel Kf₀（980）-Ka₀（980）interaction.The interactions of coupled channel Kf₀（980）-Ka₀（980） are through one-kaon exchange.After solving the Lippmann-Schwinger equation,one finds that there exist a bound state.And this state can be identified with the observed K（1460）.Within this approach,the t-channel amplitude is not covariance.To recover covariance,we need to consider the contribution from the loop diagrams,the numerical results indicate that the violation of the covariance is small.We have also studied the al（1260） in the process of γp→π⁺π⁺π^-n and the decays of a₁（1260）→3π.In this study,we assumed a₁（1260）is dynamical generated from ρπinteraction.The numerical results show that a₁（1260）can be observed in the process of γp→π⁺π⁺π^-n.And in the decay of a₁（1260）→3π,the contribution from the tree diagram is dominant.