Abstract
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 KK*and DD*are investigated.In the KK*sector,the f1(1285)particle is treated as a K(K)*bound state,therefore,the coupling constant in the K(K)*Yukawa potential can be fixed according to the binding energy of the f1(1285)particle.Consequently,a K(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 KK*resonance state at 1417-i18 MeV might correspond to the f1(1420)particle in the review of the Particle Data Group.In the D(D)*sector,since the X(3872)particle is almost located at the D(D)*threshold,its binding energy is approximately equal to zero.Therefore,the coupling constant in the D(D)*Yukawa potential is determined,which is related to the first zero point of the zero-order Bessel function.Similarly to the K(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),the xc1(4274)and Xc1(4685)particles,respectively.It is noted that all solutions are isospin degenerate.
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