Crossing heavy-flavour thresholds in fragmentation functions

In analogy with parton distribution functions, also parton fragmentation functions obey matching conditions when crossing heavy-flavour thresholds. We compute these matching conditions at next-to-leading order in the strong coupling constant αs in the M-bar S-bar scheme. Our results can be used for the dynamical generation of the heavy-flavour component in next-to-leading order fits to light-hadrons fragmentation functions. Furthermore, when computing perturbatively the charm fragmentation function from first principles and evolving it to higher scales, our matching conditions should be used for consistency when crossing the bottom threshold