Two-loop form factors for P-wave quarkonium production and decay - Melih A. Ozcelik (Journal of High Energy Physics)
Abstract We present the analytical results for the two-loop form factors needed for χ Q,J production and decay. We consider the two-loop corrections to the process γγ ↔ P J 1 3 $$ \gamma \gamma \leftrightarrow {}^3{P}_J^{\left[1\right]} $$ , that has been known only numerically before, and the processes gg ↔ P J 1 3 $$ gg\leftrightarrow {}^3{P}_J^{\left[1\right]} $$ , γg ↔ P J 8 3 $$ \gamma g\leftrightarrow {}^3{P}_J^{\left[8\right]} $$ and gg ↔ P J 8 3 $$ gg\leftrightarrow {}^3{P}_J^{\left[8\right]} $$ , 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 ↔ S 1 8 3 $$ gg\leftrightarrow {}^3{S}_1^{\left[8\right]} $$ form factor. We give the high precision numerical results for the hard functions that can be used to compute χ Q,J production and decay up to NNLO accuracy.