Zc(3900)峰的非三角形奇点来源分析
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"这篇研究论文探讨了Zc(3900)峰的来源，指出这一峰值并非由“三角形奇点”引起。作者通过对比分析三角形图和$D\bar{D}^*$气泡链的贡献，以及$e^+e^-\rightarrow J/\psi\pi^+\pi^-$和$e^+e^-\rightarrow(D\bar{D}^*)^{\mp}\pi^{\pm}$这两个过程，发现三角形图无法解释BESIII合作组在4.23和4.26 GeV质心能量下的实验观测数据。相反，将Zc(3900)解释为分子态的假设能更好地描述这些数据。"
这篇开放访问的文章发表于Eur. Phys. J. C，作者们主要关注了Zc(3900)这一奇异的带电 charmmonium-like（类似charm夸克对的态）粒子。Zc(3900)最初由BESIII合作组在$e^+e^-\rightarrow J/\psi\pi^+\pi^-$过程中观察到，并得到了Belle和CDF的确认。传统的理论认为，这种峰值可能源自三角形奇异点，即在某些特定条件下，三个不同的介子可以相互交换，形成一个临时的奇异点。
然而，研究团队通过细致的分析发现，当他们尝试匹配$J/\psi\pi$的最大谱和$D\bar{D}^*$的谱时，三角形图的贡献并不足以解释在4.23和4.26 GeV的实验观测结果。这意味着Zc(3900)的出现不能简单地归因于这种基本的量子色动力学效应。相反，他们提出Zc(3900)可能是一种分子态，由D和$\bar{D}^*$介子对构成，这样的解释更符合实验数据。
1. 引言部分强调了Zc(3900)的发现及其在 charm meson 谱中的重要性，同时也指出了现有理论模型面临的挑战。
2. 研究方法包括对不同过程的计算和比较，特别是三角形图和气泡链的贡献，以及这两个与Zc(3900)相关的衰变过程。
3. 结果显示，传统的三角形奇异点解释与实验数据不符，而分子态的假设提供了一种更合理的解释框架。
4. 这一发现对于理解强相互作用下重味粒子的性质，尤其是非传统夸克对结合形式，有着重要的理论和实验意义。
该研究论文对Zc(3900)的物理特性提出了新的见解，挑战了现有的理论模型，并提供了分子态解释作为未来研究的一个方向。这一工作对深入探索强相互作用和夸克-胶子动力学提供了宝贵的数据和理论依据。
Eur. Phys. J. C (2018) 78:276
https://doi.org/10.1140/epjc/s10052-018-5690-7
Regular Article - Theoretical Physics
The Z
c
(3900) peak does not come from the “triangle singularity”
Qin-Rong Gong
1
, Jing-Long Pang
1
, Yu-Fei Wang
1
, Han-Qing Zheng
1,2,a
1
Department of Physics, State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China
2
Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
Received: 2 October 2017 / Accepted: 5 March 2018
© The Author(s) 2018
Abstract We compare contributions from the triangle dia-
gram and the D
¯
D
∗
bubble chain with the processes of
e
+
e
−
→ J/ψ π
+
π
−
and e
+
e
−
→ (D
¯
D
∗
)
∓
π
±
.Byfit-
ting the J/ψπ maximum spectrum and the D
¯
D
∗
spectrum,
we find that the triangle diagram cannot explain the new
experimental results from BESIII Collaboration at center of
mass at 4.23 and 4.26 GeV, simultaneously. On the contrary,
the molecular assignment of Z
c
(3900) gives a much better
description.
1 Introduction
The charged charmonium-like state Z
c
(3900) was observed
in J/ψ π
±
mass spectrum by BES III Collaboration in
e
+
e
−
→ J /ψπ π process [1], and confirmed by Belle [2]
and CLEO [3] Collaborations in the same processes. After-
wards, it was also observed in the (D
¯
D
∗
)
±
invariant mass
spectrum in the process of e
+
e
−
→ D
¯
D
∗
π
∓
, and the quan-
tum number of Z
c
(3900) was determined to be I(J
P
) =
1(1
+
) by angular distribution analysis of the π Z
c
(3900) sys-
tem [4]. The experimental discovery has stimulated a lot of
discussion because of the unique nature of Z
c
(3900),asit
could be (together with Z
b
) an unambiguous candidate of the
long wished-for tetra-quark state.
In a recent paper [5], we have made a detailed comparison
between the D
¯
D
∗
molecule picture and the “elementary” pic-
ture, and we concluded that Z
c
(3900) is of D
¯
D
∗
molecular
nature, using the pole counting method [6,7].
However, there is also found in the literature another pos-
sible mechanism, called the anomalous triangle singularity
(ATS), to explain the singularity structure at Z
c
(3900).ATS
refers to a branch cut in a three-point loop function other than
the normal threshold. The study of ATS can be traced back to
about 60 years ago. In Ref. [8] Mandelstam worked out the
ATS branch point and discussed its effects on the deuteron
a
e-mail: zhenghq@pku.edu.cn
electromagnetism form factor, and in Ref. [9] the Landau
equations were used to analyze ATS in triangle diagrams.
Extensive studies on the triangle singularity using dispersion
techniques can also be found in Refs. [10–15]. Especially in
the paper by Lucha, Melikhov and Simula of Refs. [10–15],
a detailed dispersive analysis is given on different variables.
Some similar analyses of triangle singularity based on the
non-relativistic expression can be found in Ref. [16].
ATS has attracted renewed interests, recently, because it
may contribute to peaks in some certain invariant-mass spec-
tra. In other words, some so-called “exotic hadron states”
could be just the ATS peak rather than real particles; or even
if real exotic hadron states exist, there may be some non-
negligible contributions from ATS. For example, it is sug-
gested in Refs. [17–19] that the singularity structure of the
triangle diagram (see Fig. 1), which contains both the nor-
mal threshold effect and the anomalous threshold effect, may
lead to the peak at 3900 MeV. In Refs. [20,21] it is empha-
sized that the anomalous triangle singularity may have signif-
icant impact in understanding the nature of the near-threshold
state. The possible impact of triangle singularity on Z
c
(3900)
has also been discussed in Refs. [22].
This paper is devoted to the study of the triangle diagram
contribution to the Z
c
(3900) peak. In Sect. 2 we give a ped-
agogical analysis of general three-point loop functions using
the Feynman parameter representation that can be found in
most textbooks, and we discuss the properties of the ATS. In
Sect. 3 we calculate the triangle diagram corresponding to
e
+
e
−
→ J/ψπ
+
π
−
and e
+
e
−
→ (D
¯
D
∗
)
∓
π
±
processes
and fit the experimental data to test whether the Z
c
(3900)
peak comes from the triangle diagram. In Sect. 4 the major
conclusion of the present paper is reached: basically, it is
found that the new experimental results from Refs. [23,24]
play a crucial role in clarifying the issue of the triangle dia-
gram contribution: the experimental data indicate that the
peak at 4.23 GeV is higher than that at 4.26 GeV, whereas
the triangle diagram predicts an opposite behavior. Our anal-
ysis reveals that the Z
c
(3900) peak cannot be explained from
123
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