Higher-order multipole amplitudes in charmonium radiative transitions

Abstract

Using 24 million ${\psi }^{\prime }\equiv \psi (2S)$ decays in CLEO-c, we have searched for higher multipole admixtures in electric-dipole-dominated radiative transitions in charmonia. We find good agreement between our data and theoretical predictions for magnetic quadrupole (M2) amplitudes in the transitions ${\psi }^{\prime }\to \gamma {\chi }_{c1,2}$ and ${\chi }_{c1,2}\to \gamma J/\psi$, in striking contrast to some previous measurements. Let $b_2^J$ and $a_2^J$ denote the normalized M2 amplitudes in the respective aforementioned decays, where the superscript $J$ refers to the angular momentum of the ${\chi }_{cJ}$. By performing unbinned maximum likelihood fits to full five-parameter angular distributions, we determine the ratios $a_2^{J=1}/a_2^{J=2}=0.67_{-0.13}^{+0.19}$ and $a_2^{J=1}/b_2^{J=1}=-2.27_{-0.99}^{+0.57}$, where the theoretical predictions are independent of the charmed quark magnetic moment and are $a_2^{J=1}/a_2^{J=2}=0.676\pm 0.071$ and $a_2^{J=1}/b_2^{J=1}=-2.27\pm 0.16$.

32 pages, 7 figures, acceptance update