Dπ Scattering Study In The K-matrix Method

The strong interactions between hadrons and the properties and internal structure of hadrons are the most important tasks in the field of hadronic physics. Quantum Chromodynamics (QCD)is the most successful theory to depict the strong interaction. Since the non-perturbative QCD can still not be solved rigorously, hadronic physics research have to in virtue of different models and low-energy effective theories. Chiral perturbation theory (ChPT) is one of the most successful low-energy effective theories. It succeeded in explaining the near threshold physics of pseudoscalar meson scattering. In this thesis, our work is based on the chiral Lagrangian which was constructed in chiral perturbation theory.Since the heavy meson contains charm quark or bottom quark with large masses, the heavy meson study would provide more clear information about strong interactions and the internal structure of hadrons. In the past few years,some new heavy meson were discovered in the experiment, such as D_s0^*(2317), D_s1(2460), D₀^*(2400),X(3872) and so on. These new heavy meson have the same quantum numbers with the S-wave interactions between chiral Goldstone bosons and the pseudo-scalar meson ground states, and they are very close to the threshold of corresponding channels. So, it is signification to understand these heavy meson properties to study S-wave interactions between light pseudo-scalar mesons and heavy mesons. In this paper, we will use K-matrix method to study S-wave interactions between light pseudo-scalar mesons and heavy mesons, the concrete research instance is the S-wave interaction between D meson andÏ€meson.First, we will construct the chiral Lagrangian which contain pseudo-scalar meson, pseudo-scalar meson and vector meson coupling interaction. Consider separately the instance of theρmeson exchange and D^* meson exchange, and we will obtain the I = 12 and I = 32 DÏ€scattering Born amplitudes. And we obtain the full DÏ€scattering amplitudes by using the K-matrix method. We will obtain the partial wave amplitudes from the full amplitude by the standard projection formula. In the interest of the effect to consider the description hadron internal structure, we use a parameterization form factor to drop the large momentum being living to transfer meson contribution. The liberal parameter of theory is the form factor parameter blocking. Utilize derivation DÏ€S-Wave scattering amplitude, we calculated S-Wave scattering phase shift. Since still not found the experimental data of scattering phase shift at the moment. We can not to be distinguish our computational solution is good or not.To study the charmed meson resonances with J^P= 0⁺ and C =±1which generated dynamically in the DÏ€scattering, we investigate the singularity of DÏ€S-Wave scattering amplitude. For I = 1/2 S-Wave DÏ€scattering, we find a pole (2.00743-0.346222i) in the scatter amplitudes without consider form factor. This pole is under and very close to the channel threshold. The imaginary part of this pole is considerably large. This pole should reflect the threshold enhancement effect, and it is not a resonance. Considering the form factor, we can find a pole at 2.03628-0.3126i which is lying above and very closed to the channel threshold. If the pole correspond to a resonance, it is a broad resonance with mass 2.03628GeV and width 0.625GeV. Such a broad resonance can not be fond in the PDG. The new scalar charmed meson D₀^* with mass and width can not be generated dynamically in our calculation. One possible reason is that we only considered the single DÏ€channel and omitted the couple channel effects of Dηand DS K channel.