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Higher-order multipole amplitudes in charmonium radiative transitions

Using 24 million $ψ' \equiv ψ(2S)$ 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 $ψ' \to γχ_{c1,2}$ and $χ_{c1,2} \to γJ/ψ$, 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 $χ_{cJ}$. 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 $a_2^{J=1}/a_2^{J=2} = 0.676 \pm 0.071$ and $a_2^{J=1}/b_2^{J=1} = -2.27 \pm 0.16$.