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 $\mathcal{O}\left({\Lambda }_{\mathrm{QCD}}^2\right)$ instead of $\mathcal{O}\left({\Lambda }_{\mathrm{QCD}}^4\right)$.