Pub Date : 2020-12-02DOI: 10.1103/PHYSREVD.103.L031501
Tian-Wei Wu, Ming-Zhu Liu, L. Geng
Motivated by the recent discovery of two new states in the $B^+rightarrow D^+D^-K^+$ decay by the LHCb Collaboration, we study the $Dbar{D}K$ three-body system by solving the Schr"odinger equation with the Gaussian Expansion Method. We show that the $Dbar{D}K$ system can bind with quantum numbers $I(J^P)=frac{1}{2}(0^-)$ and a binding energy of $B_3(Dbar{D}K)=48.9^{+1.4}_{-2.4}$ MeV. It can decay into $J/psi K$ and $D_sbar{D}^*$ via triangle diagrams, yielding a partial decay width of about 1 MeV. As a result, if discovered, it will serve as a highly nontrivial check on the nature of the many exotic hadrons discovered so far and on non-perturbative QCD as well. Assuming heavy quark spin symmetry, the same formalism is applied to study the $Dbar{D}^*K$ system, which is shown to also bind with quantum numbers $I(J^P)=frac{1}{2}(1^-)$ and a binding energy of $B_3(Dbar{D}^*K)simeq 77.3^{+3.1}_{-6.6}$ MeV, consistent with the results of previous works.
{"title":"Excited \u0000K\u0000 meson, \u0000Kc(4180)\u0000, with hidden charm as a \u0000DD¯K\u0000 bound state","authors":"Tian-Wei Wu, Ming-Zhu Liu, L. Geng","doi":"10.1103/PHYSREVD.103.L031501","DOIUrl":"https://doi.org/10.1103/PHYSREVD.103.L031501","url":null,"abstract":"Motivated by the recent discovery of two new states in the $B^+rightarrow D^+D^-K^+$ decay by the LHCb Collaboration, we study the $Dbar{D}K$ three-body system by solving the Schr\"odinger equation with the Gaussian Expansion Method. We show that the $Dbar{D}K$ system can bind with quantum numbers $I(J^P)=frac{1}{2}(0^-)$ and a binding energy of $B_3(Dbar{D}K)=48.9^{+1.4}_{-2.4}$ MeV. It can decay into $J/psi K$ and $D_sbar{D}^*$ via triangle diagrams, yielding a partial decay width of about 1 MeV. As a result, if discovered, it will serve as a highly nontrivial check on the nature of the many exotic hadrons discovered so far and on non-perturbative QCD as well. Assuming heavy quark spin symmetry, the same formalism is applied to study the $Dbar{D}^*K$ system, which is shown to also bind with quantum numbers $I(J^P)=frac{1}{2}(1^-)$ and a binding energy of $B_3(Dbar{D}^*K)simeq 77.3^{+3.1}_{-6.6}$ MeV, consistent with the results of previous works.","PeriodicalId":8457,"journal":{"name":"arXiv: High Energy Physics - Phenomenology","volume":"58 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79866059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}