Resummation effects in the bottom-quark fragmentation function
Fabio Maltoni, Giovanni Ridolfi, Maria Ubiali, Marco Zaro
Abstract
A bstract 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 $$ {\alpha}_s^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> 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- $$ {\alpha}_s^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> 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- $$ {\alpha}_s^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>α</mml:mi> <mml:mi>s</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> 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.