Possibility of charmoniumlike state X(3915) as χc0(2P)

Abstract

In this work, we seriously discuss whether X(3915) can be treated as a χ c0 (2P) state. Based on an unquenched quark model, we give the mass spectrum of the χ cJ (2P) states, where there are no free input parameters in our calculation. Our result shows that the mass gap between χ c0 (2P) and χ c2 (2P) can reach 13 MeV, which can reproduce the mass difference between Z(3930) and X(3915). Additionally, the calculated masses of χ c0 (2P) and χ c2 (2P) are consistent with experimental values of X(3915) and Z(3930), respectively. Besides, giving the mass spectrum analysis to support X(3915) as χ c0 (2P), we also calculate the width of χ c0 (2P) with the same framework, which is also consistent with the experimental data of X(3915). Thus, the possibility of charmoniumlike state X(3915) as χ c0 (2P) state is further enforced. ‡ Corresponding author * Electronic address: duanmx16@lzu.edu.cn † Electronic address: luosq15@lzu.edu.cn § Electronic address: xiangliu@lzu.edu.cn ¶ Electronic address: matsuki@tokyo-kasei.ac.jp η c (2S) 1986 h c (1P) 2003 X(3872) 2006 Z(3930) 2010 X(3915) 2013 X(3823) 2017 Y(4220) 2019 X(3842) Established charmonia XYZ states as the candidates of charmonium 17 years FIG. 1: The established charmonia and some XYZ states as possible candidates for charmonium.In 2009, focusing on 2P states, the Lanzhou group carried out the study of the mass spectrum and strong decay behav-arXiv:2002.03311v3 [hep-ph]

Role of the newly measured $B\to KD\bar{D}$ process to establish $χ_{c0}(2P)$ state

“…Moreover, in the D + D − channel, two charmonia χ c0 (3930) and χ c2 (3930) with J PC = 0 ++ and 2 ++ state, respectively, were found. Their masses and widths are determined to be [1,2] M χ c0 (3930) = 3.9238 ± 0.0015(stat) ± 0.0004(syst) GeV, Γ χ c0 (3930) = 17.4 ± 5.1(stat) ± 0.8(syst) MeV, M χ c2 (3930) = 3.927 ± 0.0024(stat) ± 0.0008(syst) GeV, Γ χ c2 (3930) = 34.2 ± 6.6(stat) ± 1.1(syst) MeV, which confirms the prediction from the Lanzhou group of small mass spliting and narrow width for the χ c0 (2P) and χ c2 (2P) states [3]. Especially, it is the first time to establish the χ c0 (2P) state in its open-charm decay channel, which also clarifies messy situation of the X(3915).…”

Analysis of the $$ \varvec{e^+ e^- \rightarrow J/\psi D{\bar{D}}}$$ reaction close to the threshold concerning claims of a $$\chi _{c0}(2P)$$ state

“…The χ c0 (2P) hypothesis for the X (3915) has been reinforced by new studies in Refs. [17,18]. In Ref.…”

“…In Ref. [18] it is shown that the use of the unquenched quark model, where, in addition to the quark components, the meson-meson components are taken into account via loops with these intermediate states [19][20][21][22][23], provides an answer to the problems posed to the χ c0 (2P) hypothesis in Refs. [11,12], in particular the puzzle of the charmonium masses and the decay widths discussed above.…”

“…[1], and a further discussion of these issues is given in Ref. [18], but it serves the purpose to show that the question of the assignment of the χ c0 (2P) state to some of the observed states or experimental peaks is the object of an intense debate at present.…”

A note for the effective $β$ value in a Simple Harmonic Oscillator wave function

“…For example, in the decay of highly partial wave in the QPC model, the amplitude has a strong dependence on the shape of the wave function, because of the nodal effect, i. e. the β value has a great impact on the numerical result of the width [22].…”