Studying the {bar{D}}_1K molecule in the Bethe\u2013Salpeter equation approach

Jing-Juan Qi,Zhen-Yang Wang,Xin-Heng Guo,Zhu-Feng Zhang

doi:10.1140/epjc/s10052-021-09422-z

Jing-Juan Qi, Zhen-Yang Wang + Show 2 more

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https://doi.org/10.1140/epjc/s10052-021-09422-z

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Abstract

We interpret the X_1(2900) as an S-wave {bar{D}}_1K molecular state in the Bethe–Salpeter equation approach with the ladder and instantaneous approximations for the kernel. By solving the Bethe–Salpeter equation numerically with the kernel containing one-particle-exchange diagrams and introducing three different form factors (monopole, dipole, and exponential form factors) in the verties, we find the bound state exists. We also study the decay width of the decay X_1(2900) to D^-K^+.

Highlights

Two new open flavor states were observed by LHCb collaboration in the D− K + invariant mass distribution of B+ → D+ D− K +, and the parameters are determined to be [1]
Since the resonances X0(2900) and X1(2900) are observed in the D− K + channel, they should be manifestly exotic and have minimal quark content cdus. These two states are new fully open flavor states after the discovery of X (5568), which was reported by D0 collaboration in the Bsπ invariant mass distribution in 2016
We can solve the BS equation numerically and study whether the S-wave D 1 K bound state exists or not. It can be seen from Eq (14) that there is only one free parameter in our model, the cutoff, which enters through various phenomenological form factors in Eq (10)

Summary

Introduction

Two new open flavor states were observed by LHCb collaboration in the D− K + invariant mass distribution of B+ → D+ D− K +, and the parameters are determined to be [1]. Since the resonances X0(2900) and X1(2900) are observed in the D− K + channel, they should be manifestly exotic and have minimal quark content cdus These two states are new fully open flavor states after the discovery of X (5568) (subd), which was reported by D0 collaboration in the Bsπ invariant mass distribution in 2016. From the QCD Sum Rules, the X0(2900) and X1(2900) were studied in molecular and diquark-antidiquark tetraquark pictures, respectively, and the results for masses are in good agreement with the observed masses in the experiment [14].

The BS formalism for D 1 K system

The normalization condition of the BS wave function

Summary and discussion