Resummation effects in the bottom-quark fragmentation function
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jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pWe compute the perturbative component of the fragmentation function of the jats:italicb</jats:italic> quark to the best of the present theoretical knowledge. The fixed-order calculation to order jats:inline-formulajats:alternativesjats:tex-math$$ {\alpha}_s^2 $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msubsup mml:miα</mml:mi> mml:mis</mml:mi> mml:mn2</mml:mn> </mml:msubsup> </mml:math></jats:alternatives></jats:inline-formula> 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-jats:inline-formulajats:alternativesjats:tex-math$$ {\alpha}_s^2 $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msubsup mml:miα</mml:mi> mml:mis</mml:mi> mml:mn2</mml:mn> </mml:msubsup> </mml:math></jats:alternatives></jats:inline-formula> corrections are accounted for exactly, and logarithmically enhanced contributions from loops of jats:italicb</jats:italic> quarks are included. This requires the calculation of the Mellin transform of the order-jats:inline-formulajats:alternativesjats:tex-math$$ {\alpha}_s^2 $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msubsup mml:miα</mml:mi> mml:mis</mml:mi> mml:mn2</mml:mn> </mml:msubsup> </mml:math></jats:alternatives></jats:inline-formula> 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.</jats:p>
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1029-8479