Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2010-07-26
Physics
High Energy Physics
High Energy Physics - Phenomenology
v2; 14 pages, 3 tables; references, a new table and several footnotes added, text refined; a minus sign added for the definiti
Scientific paper
The very recent analysis by BaBar Collaboration indicates that the $X(3872)$ may favor the quantum number $J^{PC}=2^{-+}$ rather than the previously assumed $1^{++}$. By pretending the $\eta_{c2}(1D)$ charmonium to be the $X(3872)$, we study the parity-even radiative transition processes $\eta_{c2}(1D)\to J/\psi(\psi')+\gamma$ within several phenomenological potential models. We take the ${}^3D_1$ admixture in $\psi'$ into account, and consider the contributions from the magnetic dipole ($M1$), electric quadrupole ($E2$), and magnetic octupole ($M3$) amplitudes. It is found that the ratio of the branching fractions of these two channels, as well as the absolute branching fraction of $\eta_{c2}\to \psi'\gamma$, are in stark contradiction with the existing \textsc{BaBar} measurements. This may indicate that the $2^{-+}$ assignment for the $X(3872)$ is highly problematic.
Jia Yu
Sang Wen-Long
Xu Jia
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