Possible $K{\bar{K}}^{\ast }$ and $D{\bar{D}}^{\ast }$ resonances by solving Schrödinger equation

Abstract

The one-pion exchange interaction between the kaon and the vector antikaon is investigated by solving the Schrödinger equation in the S-wave approximation. In addition to the particle $f_1(1285)$, another bound state of $K{\bar{K}}^{\ast }$ is obtained, which is approximately 9 MeV below the threshold of $K{\bar{K}}^{\ast }$ and labeled $f_1(1378)$ for convenience in this manuscript. Under the outgoing wave condition, two resonance states of $K{\bar{K}}^{\ast }$ are produced with different coupling constants fixed with the binding energies of $f_1(1285)$ and $f_1(1378)$, respectively. Both of the resonance states are located in the vicinity of 1400 MeV, and thus it is reasonable to assume that these two resonance states correspond to the $f_1(1420)$ particle in the review of the Particle Data Group simultaneously. This method is extended to study the $D{\bar{D}}^{\ast }$ system analogously. When the particle ${\chi }_{c1}(3872)$ is treated as a bound state of $D{\bar{D}}^{\ast }$, the particles $T_{c\bar{c}1}(3900)$, $T_{c\bar{c}}(4020)$ and $X(3940)$ can be obtained as solutions of the Schrödinger equation under the outgoing wave condition, which implies the spin and parity of these particles are all $J^P=1^{+}$.

Comments: 6 pages,3 figures, to be published in Proceedings of The 21st International Conference on Hadron Spectroscopy and Structure(HADRON2025), Osaka University, Japan, 27-31 March, 2025