The Transverse Momentum Dependent Fragmentation Function at NNLO

Understand

We calculate the unpolarized transverse momentum dependent fragmentation function (TMDFF) at next-to-next-to-leading order (NNLO), evaluating separately TMD soft factor and TMD collinear correlator.

• For the first time the cancellation of spurious rapidity divergences in a properly defined individual TMD beyond the first non-trivial order is shown.
• This represents a strong check of the given TMD definition.
• We extract the matching coefficient necessary to perform the transverse momentum resummation at next-to-next-to-next-to-leading-logarithmic accuracy.