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 Hank...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.展开更多
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(sys...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.展开更多
文摘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.
文摘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.
