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Specifically, we include the ${}^3\\!S_1^{[1]}$ and ${}^3\\!P_{J}^{[1]}$ color-singlet and the ${}^3\\!S_1^{[8]}$, ${}^1\\!S_{0}^{[8]}$, and ${}^3\\!P_{J}^{[8]}$ color-octet channels as well as the effects due to the mixing between the ${}^3\\!S_1^{[8]}$ and ${}^3\\!D_1^{[8]}$ channels. We provide all the squared hard-scattering amplitudes in analytic form. 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