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Register a new userInvestigating different structures for the $X(3872)$
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Using the QCD spectral sum rule approach we investigate different currents with $J^{PC}=1^{++}$, which could be associated with the $X(3872)$ meson. Our results indicate that, with a four-quark or molecular structure, it is very difficult to explain the narrow width of the state unless the quarks have a special color configuration.
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We introduce a near-threshold parameterization that is more general than the effective-range expansion up to and including the effective-range because it can also handle with a near-threshold zero in the $D^0bar{D}^{*0}$ $S$-wave. In terms of it we analyze the CDF data on inclusive $pbar{p}$ scattering to $J/psi pi^+pi^-$, and the Belle and BaBar data on $B$ decays to $K, J/psi pi^+pi^-$ and $K Dbar{D}^{*0}$ around the $D^0bar{D}^{*0}$ threshold. It is shown that data can be reproduced with similar quality for the $X(3872)$ being a bound {it and/or} a virtual state. We also find that the $X(3872)$ might be a higher-order virtual-state pole (double or triplet pole), in the limit in which the small $D^{*0}$ width vanishes. Once the latter is restored the corrections to the pole position are non-analytic and much bigger than the $D^{*0}$ width itself. The $X(3872)$ compositeness coefficient in $D^0bar{D}^{*0}$ ranges from nearly 0 up to 1 in the different scenarios.
In this paper we consider all possible 1D and 2P ccbar assignments for the recently discovered X(3872). Taking the experimental mass as input, we give numerical results for the E1 radiative widths as well as the three principal types of strong decays; open-charm, ccbar annihilation and closed-charm hadronic transitions. We find that many assignments may be immediately eliminated due to the small observed total width. The remaining viable ccbar assignments are 3D3, 3D2, 1D2, 2 3P1 and 2 1P1. A search for the mode J/psi pi0 pi0 can establish the C-parity of the X(3872), which will eliminate many of these possibilities. Radiative transitions can then be used to test the remaining assignments, as they populate characteristic final states. The 3D2 and 1D2 states are predicted to have large (ca.50%) radiative branching fractions to chi_1 gamma and h_c gamma respectively. We predict that the 3D3 will also be relatively narrow and will have a significant (ca.10%) branching fraction to chi_2 gamma, and should also be observable in B decay. Tests for non-ccbar X(3872) assignments are also discussed.
It was recently proposed that the $X(3872)$ binding energy, the difference between the $D^0bar D^{*0}$ threshold and the $X(3872)$ mass, can be precisely determined by measuring the $gamma X(3872)$ line shape from a short-distance $D^{*0}bar D^{*0}$ source produced at high-energy experiments. Here, we investigate the feasibility of such a proposal by estimating the cross sections for the $e^+e^-topi^0gamma X(3872)$ and $pbar ptogamma X(3872)$ processes considering the $D^{*0}bar D^{*0}D^0/bar D^{*0}D^{*0}bar D^0$ triangle loops. These loops can produce a triangle singularity slightly above the $D^{*0}bar D^{*0}$ threshold. It is found that the peak structures originating from the $D^{*0}bar D^{*0}$ threshold cusp and the triangle singularity are not altered much by the energy dependence introduced by the $e^+e^-topi^0D^{*0}bar D^{*0}$ and $pbar ptobar D^{*0}D^{*0}$ production parts or by considering a finite width for the $X(3872)$. We find that $sigma(e^+e^-topi^0gamma X(3872)) times {rm Br}(X(3872)topi^+pi^-J/psi)$ is $mathcal{O}(0.1~{rm fb})$ with the $gamma X(3872)$ invariant mass integrated from 4.01 to 4.02 GeV and the c.m. energy of the $e^+e^-$ pair fixed at 4.23 GeV. The cross section $sigma(pbar ptogamma X(3872))times {rm Br}(X(3872)topi^+pi^-J/psi)$ is estimated to be of $mathcal{O}(10~{rm pb})$. Our results suggest that a precise measurement of the $X(3872)$ binding energy can be done at PANDA.
We investigate heavy quark symmetries for heavy meson hadronic molecules, and explore the consequences of assuming the X(3872) and $Z_b(10610)$ as an isoscalar $Dbar D^*$ and an isovector $Bbar B^*$ hadronic molecules, respectively. The symmetry allows to predict new hadronic molecules, in particular we find an isoscalar $1^{++}$ $Bbar B^*$ bound state with a mass about 10580 MeV and the isovector charmonium partners of the $Z_b(10610)$ and the $Z_b(10650)$ states. Next, we study the $X(3872) to D^0 bar D^0pi^0$ three body decay. This decay mode is more sensitive to the long-distance structure of the X(3872) resonance than its $J/psipipi$ and $J/psi3pi$ decays, which are mainly controlled by the short distance part of the X(3872) molecular wave function. We discuss the $D^0 bar D^0$ final state interactions, which in some situations become quite important. Indeed in these cases, a precise measurement of this partial decay width could provide precise information on the interaction strength between the $D^{(*)}bar D^{(*)}$ charm mesons.
It has been proposed recently (Phys. Rev. Lett. 115 (2015), 022001) that the charmoniumlike state named X(3915) and suggested to be a $0^{++}$ scalar, is just the helicity-0 realisation of the $2^{++}$ tensor state $chi_{c2}(3930)$. This scenario would call for a helicity-0 dominance, which were at odds with the properties of a conventional tensor charmonium, but might be compatible with some exotic structure of the $chi_{c2}(3930)$. In this paper, we investigate, if such a scenario is compatible with the assumption that the $chi_{c2}(3930)$ is a $D^*bar D^*$ molecular state - a spin partner of the $X(3872)$ treated as a shallow bound state. We demonstrate that for a tensor molecule the helicity-0 component vanishes for vanishing binding energy and accordingly for a shallow bound state a helicity-2 dominance would be natural. However, for the $chi_{c2}(3930)$, residing about 100 MeV below the $D^*bar D^*$ threshold, there is no a priori reason for a helicity-2 dominance and thus the proposal formulated in the above mentioned reference might indeed point at a molecular structure of the tensor state. Nevertheless, we find that the experimental data currently available favour a dominant contribution of the helicity-2 amplitude also in this scenario, if spin symmetry arguments are employed to relate properties of the molecular state to those of the X(3872). We also discuss what research is necessary to further constrain the analysis.
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