Abstract
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 \( {\alpha}_s^2 \) 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-\( {\alpha}_s^2 \) 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-\( {\alpha}_s^2 \) 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.
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Maltoni, F., Ridolfi, G., Ubiali, M. et al. Resummation effects in the bottom-quark fragmentation function. J. High Energ. Phys. 2022, 27 (2022). https://doi.org/10.1007/JHEP10(2022)027
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DOI: https://doi.org/10.1007/JHEP10(2022)027