The possible KK^(*)and D^(*)bound and resonance states by solving the Schrodinger equation

The Schrodinger equation with a Yukawa type of potential is solved analytically.When different boundary conditions are taken into account,a series of solutions are indicated as a Bessel function,the first kind of Hankel function and the second kind of Hankel function,respectively.Subsequently,the scattering processes of K^(*)and D^(*)are investigated.In the K^(*)sector,the f_(1)(1285)particle is treated as a K^(*)bound state,therefore,the coupling constant in the K^(*)Yukawa potential can be fixed according to the binding energy of the f_(1)(1285)particle.Consequently,a K^(*)resonance state is generated by solving the Schrodinger equation with the outgoing wave condition,which lies at 1417-i18 MeV on the complex energy plane.It is reasonable to assume that the K^(*)resonance state at 1417-i18 MeV might correspond to the f_(1)(1420)particle in the review of the Particle Data Group.In the D^(*)sector,since the X(3872)particle is almost located at the D^(*)threshold,its binding energy is approximately equal to zero.Therefore,the coupling constant in the D^(*)Yukawa potential is determined,which is related to the first zero point of the zero-order Bessel function.Similarly to the K^(*)case,four resonance states are produced as solutions of the Schrodinger equation with the outgoing wave condition.It is assumed that the resonance states at 3885~i1 MeV,4029-i108 MeV,4328-i191 MeV and 4772-i267 MeV might be associated with the Zc(3900),the X(3940),theχ_(c1)(4274)andχ_(c1)(4685)particles,respectively.It is noted that all solutions are isospin degenerate.

The Φp bound state in the unitary coupled-channel approximation

The strong attractive interaction of the φ meson and the proton has recently been reported by the ALICE Collaboration.The corresponding scattering length f_(0) is given as Re(f_(0))=0.85±0.34(stat)±0.14(syst)and Im(f_(0))=0.16±0.10(stat)±0.09(syst)fm.The fact that the real part is significant in contrast to the imaginary part indicates a dominant role of elastic scattering,whereas the inelastic process is less important.In this work,such scattering processes are inspected based on a unitary coupled-channel approach inspired by the Bethe-Salpeter equation.The φp scattering length is calculated based on this approach,and it is found that the experimental value of the φp scattering length can be obtained only if the attractive interaction of the φ meson and the proton is taken into account.A significant outcome of such attractive interaction is a two-pole structure in the φp scattering amplitude.One of the poles,located at(1969−i283)MeV might correspond to N(1895)1/2^(−)or N(1875)3/2^(−)as listed in the review of the Particle Data Group(PDG).The other one,located at 1949−i3 MeV should be a φN bound state,which has no counterpart in the PDG data.

Pseudoscalar meson and baryon octet interaction with strangeness zero in the unitary coupled-channel approximation

The interaction of the pseudoscalar meson and the baryon octet is investigated by solving the Bethe-Salpeter equation in the unitary coupled-channel approximation. In addition to the Weinberg-Tomozawa term, the contribution of the s-and u-channel potentials in the-wave approximation are taken into account. In the sector of isospin I=1/2 and strangeness S =0, a pole is detected in a reasonable region of the complex energy plane of ■ in the center-of-mass frame by analyzing the behavior of the scattering amplitude, which is higher than the ηN threshold and lies on the third Riemann sheet. Thus, it can be regarded as a resonance state and might correspond to the N(1535) particle of the Particle Data Group(PDG) review. The coupling constants of this resonance state to the πN,ηN,KΛ and KΣ channels are calculated, and it is found that this resonance state couples strongly to the hidden strange channels. Apparently, the hidden strange channels play an important role in the generation of resonance states with strangeness zero. The interaction of the pseudoscalar meson and the baryon octet is repulsive in the sector of isospin I = 3/2 and strangeness S = 0, so that no resonance state can be generated dynamically.

The pseudoscalar meson and baryon octet interaction with strangeness S=-2 in the unitary coupled-channel approximation

The interaction of the pseudo scalar meson and the b ary on octet with strangeness S=-2 and isospin I=1/2 is investigated by solving the Bethe-Salpeter equation in the infinite and finite volume respectively.It is found that there is a resonance state generated dynamically,which owns a mass of about 1550 MeV and a large decay width of 120-200 MeV.This resonance state couples strongly to theπΞchannel.Therefore,it might not correspond to theΞ(1620)particle announced by Belle collaboration.At the same time,this problem is studied in the finite volume,and an energy level at 1570 MeV is obtained,which is between theπΞand KΛthresholds and independent of the cubic box size.