Two-loop form factors for P-wave quarkonium production and decay

Le résumé fourni par la source

A bstract 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 $$ \gamma \gamma \leftrightarrow {}^3{P}_J^{\left[1\right]} $$ γγ ↔ P J 1 3 , that has been known only numerically before, and the processes $$ gg\leftrightarrow {}^3{P}_J^{\left[1\right]} $$ gg ↔ P J 1 3 , $$ \gamma g\leftrightarrow {}^3{P}_J^{\left[8\right]} $$ γg ↔ P J 8 3 and $$ gg\leftrightarrow {}^3{P}_J^{\left[8\right]} $$ gg ↔ P J 8 3 , 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 $$ gg\leftrightarrow {}^3{S}_1^{\left[8\right]} $$ gg ↔ S 1 8 3 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.

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