Model Independent Evolution of Transverse Momentum Dependent Distribution Functions (TMDs) at NNLL

TL;DR

This paper develops a universal, spin-independent evolution framework for TMDs at NNLL accuracy, reducing model dependence and enabling more precise predictions for transverse momentum distributions in high-energy physics.

Contribution

It introduces a model-independent evolution kernel for TMDs at NNLL, applicable across different distributions and compatible with the CSS approach, with implications for phenomenology.

Findings

Derived a universal evolution kernel for TMDs at NNLL

Reduced model dependence in TMD evolution calculations

Applied the kernel to unpolarized and Sivers TMDs, demonstrating negligible non-perturbative effects under certain conditions

Abstract

We discuss the evolution of the eight leading twist transverse momentum dependent parton distribution functions, which turns out to be universal and spin independent. By using the highest order perturbatively calculable ingredients at our disposal, we perform the resummation of the large logarithms that appear in the evolution kernel of transverse momentum distributions up to next-to-next-to-leading logarithms (NNLL), thus obtaining an expression for the kernel with highly reduced model dependence. Our results can also be obtained using the standard CSS approach when a particular choice of the $b^*$ prescription is used. In this sense, and while restricted to the perturbative domain of applicability, we consider our results as a "prediction" of the correct value of $b_{\rm max}$ which is very close to $1.5 {\rm GeV}^{-1}$. We explore under which kinematical conditions the effects of the non-perturbative region are negligible, and hence the evolution of transverse momentum distributions can be applied in a model independent way. The application of the kernel is illustrated by considering the unpolarized transverse momentum dependent parton distribution function and the Sivers function.