\(Z_c(4200)^+\) decay width as a charmonium-like tetraquark state
Eur. Phys. J. C
Zc(4200)+ decay width as a charmonium-like tetraquark state
Wei Chen 2
T. G. Steele 2
Hua-Xing Chen 1
Shi-Lin Zhu 0 3 4
0 School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University , Beijing 100871 , China
1 School of Physics and Nuclear Energy Engineering and International Research Center for Nuclei and Particles in the Cosmos, Beihang University , Beijing 100191 , China
2 Department of Physics and Engineering Physics, University of Saskatchewan , Saskatoon, SK S7N 5E2 , Canada
3 Center of High Energy Physics, Peking University , Beijing 100871 , China
4 Collaborative Innovation Center of Quantum Matter , Beijing 100871 , China
To identify the nature of the newly observed charged resonance Zc(4200)+, we study its hadronic decays Zc(4200)+ → J /ψ π +, Zc(4200)+ → ηcρ+ and Zc(4200)+ → D+ D¯ ∗0 as a charmonium-like tetraquark state. In the framework of the QCD sum rules, we calculate the three-point functions and extract the coupling constants and decay widths for these interaction vertices. Including all these channels, the full decay width of the Zc(4200)+ state is consistent with the experimental value reported by the Belle Collaboration, supporting the tetraquark interpretation of this state.
1 Introduction
Recently, a new charged charmonium-like resonance
Zc(4200)+ was observed by the Belle Collaboration [1]. It
was observed in the Zc(4200)+ → J /ψ π + process with
the mass and decay width M = 4196−+2391−+1137 MeV and
Γ = 370−+7700−+17302 MeV, with a significance of 6.2σ . Its
preferred assignment of the quantum numbers is J P = 1+. The
G-parity of Zc(4200)+ is positive. Thus, the quantum
numbers of its neutral partner is I G J PC = 1+1+−.
The family of the charged charmonium-like states have
become more abundant after the discovery of Zc(4200)+ [1]
and Zc(4050) [2]. Before this, the first member Z (4430)+
was observed in the ψ (2S)π + invariant mass spectrum in the
process B¯ 0 → ψ (2S)π + K − by the Belle Collaboration [3]
and confirmed recently by the LHCb Collaboration [4]. Later,
Belle also reported a broad doubly peaked structure in the
π +χc1 invariant mass distribution, of which the peaks are
called Z (4050)+ and Z (4250)+ [5]. Several other similar
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b e-mail:
charged states were observed in last two years. In 2013, the
BESIII Collaboration reported Zc(3900)+ in J /ψ π + final
states in the process Y (4260) → J /ψ π +π − [6]. Zc(3900)+
was also observed by Belle [7] and confirmed in CLEO
data [8]. The BESIII Collaboration also observed Zc(4025)±
in the π ∓ recoil mass spectrum in the e+e− → (D∗ D¯ ∗)±π ∓
process [9] and Zc(4020)± in the hcπ ± mass spectrum in the
process e+e− → hcπ +π − [10]. Moreover, the Belle
Collaboration also observed two charged bottomonium-like states
Zb(10610) and Zb(10650) in the π ±Υ (n S) and hbπ ± mass
spectra in the Υ (5S) decay [11].
These newly observed charged states have the exotic
flavor contents cc¯ud¯ for Zc states and bb¯ud¯ for Zb states.
It is natural to understand them as different manifestations
of four-quark states: hadron molecules [12–18], tetraquark
states [19–21], or many other configurations [22–24]. For
example, Z (4430)+ was described as a D∗ D¯ 1 molecular
state in Refs. [25–28] and a tetraquark state in Refs. [29–
31]; the Zc(3900)+ was speculated to be a molecular state
in Refs. [32–34]; the Zc(4025)+ was interpreted as a D∗ D¯ ∗
molecular state in Ref. [35]; the Zb(10610) and Zb(10650)
were studied as B¯ B∗ and B¯ ∗ B∗ molecular states in Ref. [36].
One can consult Refs. [37–42] and references therein for
recent reviews of these charged resonances.
Being composed of a diquark and antidiquark pair, a
hidden-charm tetraquark state can decay very easily into a
pair of open-charm D mesons or one charmonium state plus
a light meson through quark rearrangement, implying that
tetraquark states should be very broad resonances, while the
experimental X Y Z states are usually quite narrow, such as
Zc(3900)+ [6–8] and Zc(4025)+ [9,10]. However, the
experimental width value of the Zc(4200)+ [1] is broad enough
to be a good tetraquark candidate. In Ref. [43], Zc(4200)+
was studied as a tetraquark state by considering the
colormagnetic interaction. In Ref. [44], the authors tried to search
for Zc+ exotic states in lattice QCD. However, they found no
convincing signal for Zc+ state below 4.2 GeV.
The hidden-charm tetraquark states with J PC = 1+−
has been studied using the method of QCD sum rule in
Refs. [24,45–50]. We have also done similar QCD sum-rule
studies in Refs. [51,52], in which the extracted mass was
found to be consistent with the experimental value of the
Zc(4200)+ mass. In this work, we will study the hadronic
decays of the Zc(4200)+ as a tetraquark state in QCD sum
rules. The three-point functions for the Zc J /ψ π, Zcηcρ, and
Zc D D∗ vertices will be studied to calculate the
corresponding coupling constants needed to extract the decay widths.
This paper is organized as f (...truncated)