Resummation effects in the bottom-quark fragmentation function

We compute the perturbative component of the fragmentation function of the b quark to the best of the present theoretical knowledge. The fixed-order calculation to order alpha(2)(s) of the fragmentation function at the initial scale is matched with soft-emission logarithm resummation to next-to-next-to-leading logarithmic accuracy, so that order-alpha(2)(s) corrections are accounted for exactly, and logarithmically enhanced contributions from loops of b quarks are included. This requires the calculation of the Mellin transform of the order-alpha(2)(s) result in the whole complex plane for the Mellin variable, which we provide for the first time for all the fragmenting partons. Evolution is performed to next-to-next-to-leading log accuracy, and mixing with the gluon fragmentation function is taken into account. The perturbative fragmentation functions are made available via LHAPDF grids.

Automated summary

We compute the perturbative component of the fragmentation function of the b quark to the best of the present theoretical knowledge. The fixed-order calculation to order alpha(2)(s) of the fragmentation function at the initial scale is matched with soft-emission logarithm resummation to next-to-next-to-leading logarithmic accuracy, so that order-alpha(2)(s) corrections are accounted for exactly, and logarithmically enhanced contributions from loops of b quarks are included.