Abstract
We study the possible bound states of the $D_1D$ system in the Bethe-Salpeter (BS) formalism in the ladder and instantaneous approximations. By solving the BS equation numerically with the kernel containing one-particle exchange diagrams and introducing three different form factors (monopole, dipole, and exponential form factors) at the vertices, we investigate whether the isoscalar and isovector $D_1D$ bound states may exist, respectively. We find that $Y(4260)$ could be accommodated as a $D_1D$ molecule, whereas the interpretation of $Z_2^+(4250)$ as a $D_1D$ molecule is disfavored. The bottom analog of $Y(4260)$ may exist but that of $Z_2^+(4250)$ does not.
Highlights
The charmoniumlike state Yð4260Þ [or named as ψð4260Þ] was first observed by BABAR Collaboration in the initial-state radiation process eþe− → γISRJ=ψπþπ− in2005 [1] and immediately confirmed by CLEO [2]and Belle [3] Collaborations in the same process
We studied whether Yð4260Þ and Zþ2 ð4250Þ could be a D1D molecular state in the Bethe-Salpeter equation approach
The cutoff Λ introduced in the form factors reflects the effects of the structures of interacting particles
Summary
The charmoniumlike state Yð4260Þ [or named as ψð4260Þ] was first observed by BABAR Collaboration in the initial-state radiation process eþe− → γISRJ=ψπþπ− in. Years ago Belle Collaboration observed two charged resonancelike structures, Zþ1 ð4051Þ and Zþ2 ð4250Þ, with the significance of more than 5σ in the χc1πþ mass distribution in B → K−πþχc decays [33] Their BreitWigner masses and widths are M1 1⁄4 4051 Æ 14þ−4210 MeV, Γ1 1⁄4 82−þ3291−þ6417 MeV, and M2 1⁄4 4248−þ2494−þ31580 MeV, Γ2 1⁄4 177−þ3594−þ63116 MeV, respectively. We will vary the binding energy Eb 1⁄4 M − MD1 − MD (where M is the mass of the bound state) in a wide range and search for all the possible solutions with the cutoff parameter Λ in the form factor in a reasonable interval Through this process, we will naturally check whether Yð4260Þ and Zþ2 ð4250Þ may exist as an S-wave D1D molecular state.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call