Decay properties of the X(3872) through the Fierz rearrangement

We systematically construct all the tetraquark currents of J^PC = 1⁺⁺ with the quark configurations $[{cq}][\bar{c}\bar{q}]$, $[\bar{c}q][\bar{q}c]$, and $[\bar{c}c][\bar{q}q]$ (q = u/d). Their relations are derived using the Fierz rearrangement of the Dirac and color indices, through which we study decay properties of the X(3872) under both the compact tetraquark and hadronic molecule interpretations. We conduct a search for the X(3872) → χ_c0π, η_cππ, and χ_c1ππ decay processes in particle experiments.     

The quintessential exotic X(3872)

The experimental evidence for the exotic meson, X(3872), is summarized and the various proposed theoretical models for it are reviewed. It is pointed out that several important experimental measurements have marginal statistical significance and disagreements between different sources. Until these problems are resolved, the understanding of the structure of X(3872) is likely to remain controversial.     

The Charmonium-Molecule Hybrid Structure of the X(3872)

In order to understand the structure of the X(3872) the effects of the ${{\rm c\overline{c}}}$ charmonium core state coupling to the ${D^0\overline{D}^{*0}}$ and D ⁺ D ^*? molecule states are studied. The obtained structure of the X(3872) is about 9 % of ${{\rm c}\overline{{\rm c}}}$ charmonium, 75 % of the isoscalar ${D\overline{D}}$ molecule and 16 % of the isovector ${D\overline{D}}$ molecule which explains observed properties of the X(3872) well.     

Detecting the long-distance structure of the X(3872)

Several investigations show that in a very small length scale there exist corrections to the entropy of black hole horizon. Due to fluctuations of the background metric and the external fields the action incorporates corrections. In the low energy regime, the one-loop effective action in four dimensions leads to trace anomaly. We start from the Noether current corresponding to the Einstein–Hilbert plus the one-loop effective action to calculate the charge for the diffeomorphisms which preserve the Killing horizon structure. Then a bracket for the charges is calculated. We show that the Fourier modes of the bracket are exactly similar to the Virasoro algebra. Then using the Cardy formula the entropy is evaluated. Finally, the explicit terms of the entropy expression is calculated for a classical background. It turns out that the usual expression for the entropy; i.e. the Bekenstein–Hawking form, is not modified.     

Simple explanation for the X(3872) mass shift observed in the decay X(3872)-->D*0 D0

We propose a simple explanation for the increase of approximately 3 MeV/c;{2} in the mass value of the X(3872) obtained from D(*0)D(0) decay relative to that obtained from decay to J/psipi(+)pi(-). If the total width of the X(3872) is 2-3 MeV, the peak position in the D(*0)D(0) invariant mass distribution is sensitive to the final state orbital angular momentum because of the proximity of the X(3872) to D(*0)D(0) threshold. We show that for total width 3 MeV and one unit of orbital angular momentum, a mass shift approximately 3 MeV/c(2) is obtained; experimental mass resolution should slightly increase this value. A consequence is that spin-parity 2(-) is favored for the X(3872).     

Radiative X(3872) Decays in Charmonium-Molecule Hybrid Model

We study the radiative decays of the X(3872) in the charmonium-molecule model combined with the quark potential model. We obtain \({\Gamma(X(3872) \to J/\psi \, \gamma) = 29.2\,{\rm keV}}\) and \({\Gamma(X(3872) \to \psi' \, \gamma) = 6.3\,{\rm keV}}\) . The ratio of these two is 0.22, which is much smaller than the BABAR observation. We find that the result is very sensitive to the amount of the \({\chi_{c1}(1P)}\) component in the X(3872).     

BESIII 实验对奇特态 X(3872) 的研究

量子色动力学允许超出夸克模型中重子和介子的奇特态的存在。对奇特态的研究是当前高能物理实验的热门话题之一。X(3872)是第一个被实验上观测到的奇特态候选者。实验和理论上对X(3872)的研究从未间断,这使得X(3872)成为了解最好的奇特态。运行在北京正负电子对撞机(BEPCII)上的北京谱仪(BESIII)实验积累了大量的质心能量从3.87 到 4.70 GeV的正负电子对撞数据样本。利用这些数据样本,得到了很多关于X(3872)的实验结果。本文将回顾BESIII上关于X(3872)所取得一系列成果及最新实验进展。对X(3872)等奇特态的研究,将有利于我们对自然界的基本相互作用的理解,也将促进标准模型理论的完善。     

Is X(3872) really a molecular state?

After taking into account both the pion and sigma meson exchange potential, we have performed a dynamical calculation of the D⁰D̄^*0 system. The σ meson exchange potential is repulsive from heavy quark symmetry and numerically important for a loosely bound system. Our analysis disfavors the interpretation of X(3872) as a loosely bound molecular state if we use the experimental D^*Dπ coupling constant g=0.59 and a reasonable cutoff around 1 GeV, which is the typical hadronic scale. Bound state solutions with negative eigenvalues for the DD̄^* system exist only with either a very large coupling constant (twice the experimental value) or a large cutoff (Λ ∼ 6 GeV or β ∼ 6 GeV²). In contrast, there probably exists a loosely bound S-wave BB̄^* molecular state. Once produced, such a molecular state would be rather stable, since its dominant decay mode is the radiative decay through B^*→Bγ. Experimental search of these states will be very interesting. PACS  12.39.Pn; 12.40.Yx; 13.75.Lb     

Analysis of the quantum numbers J(PC) of the X(3872) particle

We present an analysis of angular distributions and correlations of the X(3872) particle in the exclusive decay mode X(3872)-->J/psipi+ pi- with J/psi-->mu+ mu-. We use 780 pb-1 of data from pp[over ] collisions at sqrt[s]=1.96 TeV collected with the CDF II detector at the Fermilab Tevatron. We derive constraints on spin, parity, and charge conjugation parity of the X(3872) particle by comparing measured angular distributions of the decay products with predictions for different J(PC) hypotheses. The assignments J(PC)=1++ and 2-+ are the only ones consistent with the data.     

Mass of X(3872) in Bethe–Salpeter Equation for Quarks

From Bethe–Salpeter equation, we deduce the equation which describes the two-body system consisting of a scalar meson and a vector meson. This equation is applied to investigate the exotic narrow state X(3872) assumed as a molecule state composed of D⁰D^*0. The contribution of the resonance D^-0 is the attractive interaction between two heavy mesons in this molecule state. The calculated mass of X is consistent with the experimental data.     

Search for X(3872) in gammagamma fusion and radiative production at CLEO

We report on a search for the recently reported X(3872) state using 15.1 fb(-1) of e(+)e(-) data taken in the sqrt[s] = 9.46-11.30 GeV region. Separate searches for the production of the X(3872) in untagged gammagamma fusion and e(+)e(-) annihilation following initial state radiation are made by taking advantage of the unique angular correlation between the leptons from the decay J/psi --> l(+)l(-) in X(3872) decay to pi(+)pi(-)J/psi. No signals are observed in either case, and 90% confidence upper limits are established as (2J+1)Gamma(gammagamma)(X(3872))B(X --> pi(+)pi(-)J/psi) < 12.9 eV and Gamma(ee)(X(3872))B(X- -> pi(+)pi(-)J/psi) < 8.3 eV.     

Production of the X( 3872) in B-meson decay by the coalescence of charm mesons

If the recently discovered charmonium state X( 3872) is a loosely bound S-wave molecule of the charm mesons D0 D(*0) or D(*0) D0, it can be produced in B-meson decay by the coalescence of charm mesons. If this coalescence mechanism dominates, the ratio of the differential rate for B+ -->D(0) D(* 0)K+ near the D0 D(*0) threshold and the rate for B+ -->XK+ is a function of the D0 D(*0) invariant mass and hadron masses only. The identification of the X( 3872) as a D0 D(*0)/D(*0)D0 molecule can be confirmed by observing an enhancement in the D0 D(*0) invariant mass distribution near the threshold. An estimate of the branching fraction for B+ -->XK+ is consistent with observations if X has quantum numbers J(PC)=1(++ ) and if J/psi pi(+) pi(-) is one of its major decay modes.     

Production of the X(4014) as the Spin-2 Partner of X(3872) in e+e- Collisions

<正>In 2021, the Belle collaboration reported the first observation of a new structure in the ψ(2S)γ final state produced in the two-photon fusion process. In the hadronic molecule picture, this new structure can be associatedwith the shallow isoscalar ■ bound state and as such is an excellent candidate for the spin-2 partner of the X(3872) with the quantum numbers J^PC=2⁺⁺ conventionally named X₂.     

Indications of a four-quark structure for the X(3872) and X(3876) particles from recent Belle and BABAR data

Recent results by Belle and BABAR point to the existence of a second X particle decaying in D(0)D(0)pi(0), a few MeV above the X(3872). We identify the two X states with the neutral particles predicted by the four-quark model and show that production and decays are consistent with this assignment. We consider the yet-to-be-observed charged partners and give new hints on how to look for them.     

Note on X(3872) production at hadron colliders and its molecular structure

The production of the X(3872) as a hadronic molecule in hadron colliders is clarified. We show that the conclusion of Bignamini et al., Phys. Rev. Lett. 103(2009) 162001, that the production of the X(3872) at high pT implies a non-molecular structure, does not hold. In particular, using the well understood properties of the deuteron wave function as an example, we identify the relevant scales in the production process.     

Calculation of the Mass of X（3872） by the Mandelstam Generalization of the Gell-Mann-Low Method

On the basis of assuming that the narrow state X（3872） is a molecule state consisting of D0 and D＊0, we apply the Mandelstam generalization of the Ge11-Mann-Low method to calculate the matrix element of quark current between the heavy meson states described by Bether-Salpeter wave function. In calculation of the matrix element of quark current the operator product expansion is used in order to include the nonperturbative contribution of the vacuum condensates. In this scheme we calculate the mass of X（3872）. We believe that this scheme is closer to QCD than the previous work.     

Analysis of the charmonium-like states X~*(3860), X(3872), X(3915),X(3930) and X(3940) according to their strong decay behaviors

Inspired by the newly observed state X~*(3860), we analyze the strong decay behaviors of some charmoniumlike states, X~*(3860), X(3872), X(3915), X(3930) and X(3940), with the ~3P_0 model. We carry out our work based on the hypothesis that all of these states are charmonium systems. Our analysis indicates that, as a 0~(++) charmonium state, X~*(3860) can reproduce the experimental data. As for X(3872), it can tentatively be interpreted as the mixture0 of a cc system and a D~*D~0 molecular state. If we consider X(3940) as a 3~1 S_0 state, its total width in the present work is much lower than the experimental result. Thus, the 3~1 S_0 charmonium state seems not to be a good candidate for X(3940). Furthermore, our analysis implies that it is reasonable to assign X(3915) and X(3930) to be the same state, 2~(++). However, combining our analysis with that in Refs.[14, 71], we speculate that X(3915)/X(3930) might also be the mixture of a cc system and a molecular state.     

Isospin breaking of the narrow charmonium state of Belle at 3872 MeV as a deuson

We investigate the continuum limit of a compact formulation of the lattice U(1) gauge theory in 4 dimensions using a nonperturbative gauge-fixed regularization. We find clear evidence of a continuous phase transition in the pure gauge theory for all values of the gauge coupling (with gauge symmetry restored). When probed with quenched staggered fermions with U(1) charge, the theory clearly has a chiral transition for large gauge couplings. We identify the only possible region in the parameter space where a continuum limit with nonperturbative physics may appear.