We present the analytical results for the two-loop form factors needed for χQ,J production and decay. We consider the two-loop corrections to the process \( \gamma \gamma \leftrightarrow {}^3{P}_J^{\left[1\right]} \) , that has been known only numerically before, and the processes \( gg\leftrightarrow {}^3{P}_J^{\left[1\right]} \) , \( \gamma g\leftrightarrow {}^3{P}_J^{\left[8\right]} \) and \( gg\leftrightarrow {}^3{P}_J^{\left[8\right]} \) , which have not been computed before. We observe that the NRQCD pole structure of the two-loop amplitude in the gg channel is more involved for the spin-triplet P-wave case than for the pseudo-scalar S-wave case. It involves in addition to the standard Coulomb singularity also a new singularity whose cancellation requires the inclusion of the \( gg\leftrightarrow {}^3{S}_1^{\left[8\right]} \) form factor. We give the high precision numerical results for the hard functions that can be used to compute χQ,J production and decay up to NNLO accuracy.
