Chiral Unitary Approach To The Meson-baryon Scattering In The S=0,C=+1 Sector

The interaction between hadrons,the internal structure and the properties of hadrons are the newest topics in the field of hadron physics.The chiral perturbative approach(CHPA)is an effective approach that deals with non-perturbative QCD in the research of hadron spectrum and exploration of new hadronic states.The chiral per-turbative approach is the low-energy effective theory and its basic degrees of freedom are Goldstone bosons which are produced by the spontaneous chiral symmetry break-ing from SU(3)L(?) SU(3)R to SU(3)v.Goldstone bosons are the lightest pseudoscalar meson octet.However,CHPA can't describe resonances.In order to break through the limitations of chiral perturbation theory, Chiral unitary approach(CHUA) was de-veloped base on CHPA.It can successfully describe the resonances.As an effective theory in low energy,CHUA succeeds in explanation of meson-meson and meson-baryon scatterings.By using the corresponding chiral Lagrangian, the resonances, such asσ,f0(980),ao(980),A(1405)and so on,are dynamically generated,which fit well with the experimental data. In this paper,the coupled-channel Bethe-Salpeter(BS) equation is used to study the pseudoscalar meson-baryon scatterings(including the P-wave scattering and the D-wave scattering) in I=0,1,S=0,C=+1 sectors.Under the strong interaction the total angular momentum J,the isospin I and its third com-ponent I3,the strangeness S,the charm C,the bottom B and the parity P of scattering system are conserved.There are eight coupled channels in I=0,1,S=0,C=+1 sec-tor:πΣc,DN,ηΛc,KΞC,KΞc,DsΛ,η'Λc,ηcΛc;There are also eight coupled channels in I=1,S=0,C=+1 sector:XΛc,πΣc,DN,KΞc,ηΣc,KΞ'c, DsΣ,η'Σc.The scat-tering amplitudes of all channels,which are drawn from the lowest order meson-baryon chiral Lagrangian, are employed as the kernel potentials of a set of coupled-channel BS equations to sum an infinite number of scattering loops,and the obtained total amplitude satisfies the unitary relation exactly.We will deal with the divergence of one loop integral in three-momentum cut-off regularization method.The cut-off qmax is the only free parameter in our calculation. Corresponding to the different qmax,the results differ little.So,the results are not sensitive to the value of qmax.In the pseudoscalar meson-baryon P-wave scattering in I=0,S=0,C= +1 sector,fourΛc resonances with JP=1／2+ or 3／2+ are generated dynamically in the scattering. They are:Λc(1)(M=2748.09MeV,Γ=126.6MeV),Λc(2)(M 2936.04MeV,Γ=20.6MeV),Λc(3)(M=3024.01MeV,Γ:93.8MeV),Λc(4)(M 3134.28MeV,Γ=136.3MeV).The mass,width and decay property ofΛc(2)(2936) are consistent with those ofΛc(2940)+.Thus we identifyΛc(2)(2936)asΛc.(2940)+.Un-der the framework of CHUA,a baryon state,which is generated dynamically in the two body scattering, has the molecular structure of meson-baryon.SoΛc(2940)+is a molecule of meson-baryon with JP=1／2+ or 3／2+.In D-wave scattering,there are twoΛc resonances generated dynamically with JP=3／2- or 5／2-:Λ以(1)(M 2748.56MeV,Γ=151.34MeV)andΛc(2)(M=3000.44MeV,Γ=98.12MeV).The coupling constants of the predicted states are also calculated,For the pseudoscalar meson-baryon P-wave scattering in I=0,S=0,C=+1 sector,we find fourΣc resonances with JP=1／2+or 3／2+:Σc(1)(M=2770.87MeV,r 67.56MeV),Σc(2)(M:2846.08MeV,Γ=89.24MeV),Σc(3)(M=2929.25MeV,Γ96.44MeV)andΣc(4)(M=3206.98MeV,Γ=108.66MeV).The mass and width ofΣc(1)(2770)are consistent with those ofΛc(2765)+(orΣc(2765)).SoΣc(1)(2770)is likelyΣc(1)(2765).In D-wave scattering,there are fourΣc resonances with JP=3／2-or 5／2-Σc(1)(M=2742.24MeV,Γ=41.54MeV),Σc(2)(M=2778.21MeV,Γ=171.22MeV),Σc(3)(M=2839.78MeV,Γ=487.56MeV)andΣc(4)(M=3107.98MeV,r=52.66MeV). The mass ofΣc(1)(2742)is similar to that ofΣc(2800),and its width is in the range ofΣc(2800)'s width.We tend to identiflyΣc(1)(2742)to beΣc(2800).