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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 K (K) over bar* and D (D) over bar* are investigated. In the K (K) over bar* sector, the f1(1285) particle is treated as a K (K) over bar* bound state, therefore, the coupling constant in the K (K) over bar* Yukawa potential can be fixed according to the binding energy of the f1(1285) particle. Consequently, a K (K) over bar* 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 (K) over bar* 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) over bar* sector, since the X(3872) particle is almost located at the D (D) over bar* threshold, its binding energy is approximately equal to zero. Therefore, the coupling constant in the D (D) over bar* Yukawa potential is determined, which is related to the first zero point of the zero-order Bessel function. Similarly to the K (K) over bar* 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 chi(c1)(4274) and chi(c1)(4685) particles, respectively. It is noted that all solutions are isospin degenerate.
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Source :
COMMUNICATIONS IN THEORETICAL PHYSICS
ISSN: 0253-6102
Year: 2024
Issue: 10
Volume: 76
3 . 1 0 0
JCR@2022
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SCOPUS Cited Count:
ESI Highly Cited Papers on the List: 0 Unfold All
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Chinese Cited Count:
30 Days PV: 11
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