The Transverse Momentum Dependent Fragmentation Function at NNLO

TL;DR

This paper computes the unpolarized TMD fragmentation function at NNLO, demonstrating the cancellation of rapidity divergences and providing a key matching coefficient for high-precision transverse momentum resummation.

Contribution

It presents the first calculation of the TMDFF at NNLO, including the soft factor and collinear correlator, and extracts the matching coefficient for advanced resummation accuracy.

Findings

Successful cancellation of rapidity divergences at NNLO

Extraction of the NNLO matching coefficient for TMD resummation

Facilitates future calculations of all TMDs at NNLO

Abstract

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. The universal character of the soft function, which enters the definition of all (un)polarized TMD distribution/fragmentation functions, facilitates the future calculation of all the other TMDs and their coefficients at NNLO, pushing forward the accuracy of theoretical predictions for the current and next generation of high energy colliders.