Main Image
Volume 297 - XXV International Workshop on Deep-Inelastic Scattering and Related Subjects (DIS2017) - WG2 Low x and Diffraction
TMD splitting functions and the corresponding evolution equation
A. Kusina
Full text: pdf
Pre-published on: 2017 September 21
Published on: 2018 January 16
Abstract
We generalize the Catani Hautmann formalism to calculate the $P_{gq}$ and $P_{qq}$ transverse momentum dependent splitting functions. Then we use the obtained $P_{gq}$ kernel to construct a low-$x$ evolution equation for gluons that takes into account the effect of non-diagonal quark-to-gluon splittings. In order to write down a consistent equation we resum virtual corrections coming from the gluon channel and demonstrate that this implies a suitable regularization of the $P_{gq}$ singularity, corresponding to a soft emitted quark. We also note that the obtained equation is in a straightforward manner generalized to a nonlinear evolution equation which takes into account effects due to the presence of high gluon densities.
DOI: https://doi.org/10.22323/1.297.0049
Open Access
Creative Commons LicenseCopyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.