Is the $J^P=2^-$ assignment for the $X(3872)$ compatible with the radiative transition data?

Abstract

The very recent analysis by BaBar Collaboration indicates that the X(3872) may favor the quantum number J P C = 2 −+ rather than the previously assumed 1 ++ . By pretending the η c2 (1D) charmonium to be the X(3872), we study the parity-even radiative transition processes η c2 (1D) → J/ψ(ψ ′ ) + γ within several phenomenological potential models. We take the 3 D 1 admixture in ψ ′ into account, and consider the contributions from the magnetic dipole (M 1), electric quadrupole (E2), and magnetic octupole (M 3) amplitudes. It is found that the ratio of the branching fractions of these two channels, as well as the absolute branching fraction of η c2 → ψ ′ γ, are in stark contradiction with the existing BaBar measurements. This may indicate that the 2 −+ assignment for the X(3872) is highly problematic.

X(3872) as the 1 D 2 charmonium

“…However further reasons for the 1 D 2 interpretation to be problematic have started to show up. First, radiative decay transitions 1 D 2 → γJ/ψ(ψ ′ ) rates are shown to be incompatible with the data [21]. Second, the production cross section of the 1 D 2 level at CDF is predicted to be much smaller than the one actually observed for the X [18].…”

“…In Ref. [21] both widths were calculated in a quite elaborated (though rather model-dependent) NRQCD approach, with the result:…”

“…Notice that formula (3) does not take into account recoil corrections, while the formalism of Ref. [21] accounts for the recoil only via the multipole expansion. Because of a small photon energy this seems reasonable for the ψ ′ (3686) final state while, for the J/ψ final state, the photon energy is much larger, so that the value ( 6) is probably an overestimation.…”

Spectroscopy results from BELLE

“…• Y. Jia et al [12] estimated the partial widths to be Γ(η c2 → γψ ′ ) ∼ 0.4 keV and Γ(η c2 → γJ/ψ) ∼ 9 keV. This favors the Belle measurement where the ratio Γ(η c2 →γψ ′ ) Γ(η c2 →γJ/ψ) is smaller.…”

Lattice study on eta_c2 and X(3872)

“…In this work, we will focus on the study of the properties of η c2 , such as its mass and radiative transition width to J/ψ. There are actually several phenomenological studies on this topic [26][27][28], but they are rather model dependent. In contrast, the lattice QCD approach, as a method from first principles, can provide information that is more model independent.…”