On the quark distribution in an on-shell heavy quark and its all-order relations with the perturbative fragmentation function

I present new results on the quark distribution in an on-shell heavy quark inperturbative QCD and explore its all-order relations with heavy-quarkfragmentation. I first compute the momentum distribution function to all ordersin the large-beta_0 limit and show that it is identical to the perturbativeheavy-quark fragmentation function in the same approximation. I then analyzethe Sudakov limit of the distribution and the fragmentation functions usingWilson lines and prove that the corresponding Sudakov exponents in thenon-Abelian theory are the same to any logarithmic accuracy. The anomalousdimension is then determined to two-loop order, corresponding tonext-to-next-to-leading logarithmic accuracy in the exponent, in two ways: thefirst by extracting the singular terms from a recent calculation of thefragmentation function and the second by performing the two-loop Wilson-linecalculation in configuration space. I find perfect agreement between the two.Comment: 27 pages, 3 figure