Higher-order multipole amplitudes in charmonium radiative transitions

Using 24 million ${\psi }^{\mathrm{\prime }}\equiv \psi (2S)$ 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 ${\psi }^{\mathrm{\prime }}\to \gamma {\chi }_{c1,2}$ and ${\chi }_{c1,2}\to \gamma J\mathrm{/}\psi$, 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 $a_2^{J=1}/a_2^{J=2} = 0.67^{+0.19}{-0.13}$and$a_2^{J=1}/b_2^{J=1} = -2.27^{+0.57}{-0.99}$, where the theoretical predictions are independent of the charmed quark magnetic moment and are $a_2^{J=1}\mathrm{/}{a}_2^{J=2}=0.676\pm 0.071$ and $a_2^{J=1}/b_2^{J=1} = -2.27 \pm 0.16$.