Factorization analysis for the fragmentation functions of hadrons containing a heavy quark

Using methods of effective field theory, a systematic analysis of the fragmentation functions Da/H(x,mQ, μ) of a hadron H containing a heavy quark Q is performed (with a = Q, Q̄, q, q̄, g). By integrating out pair production of virtual and real heavy quarks, the fragmentation functions are matched onto a single nonperturbative function describing the fragmentation of the heavy quark Q into the hadron H in “partially quenched” QCD. All calculable, short-distance dependence on x is extracted in this step. For x → 1, the remaining fragmentation function can be matched further onto a universal function defined in heavy-quark effective theory in order to factor off its residual dependence on the heavy-quark mass. By solving the evolution equation in the effective theory analytically, large logarithms of the ratio μ/mQ are resummed to all orders in perturbation theory. Connections with existing approaches to heavy-quark fragmentation are discussed. In particular, it is shown that previous attempts to extract ln(1−x) terms from the fragmentation function DQ/H(x,mQ, μ) are incompatible with a proper separation of shortand long-distance effects. On leave from Laboratory for Elementary-Particle Physics, Cornell University, Ithaca, NY 14853, U.S.A.