Infrared renormalon effects in color dipole TMD PDF at small-$x$

Abstract

The uncertainties from the infrared renormalons in the (color dipole) gluon distribution is estimated. It is shown that non-linear saturation effects at small-$x$ shift the first IR pole at the Borel plane from $2/\beta_2$ to $1/\beta_2$. As a consequence the estimated uncertainty is found to be ${\cal O}\left(\Lambda_{\rm QCD}^2\right)$ instead of ${\cal O}\left(\Lambda_{\rm QCD}^4\right)$.