Structure function for large x and renormalization of Wilson loop ∗

We discuss the relation between hard distributions near the phase space boundary, such as structure function for large x, and Wilson loop expectation values calculated along paths partially lying on the light-cone. Due to additional light cone singularities, multiplicative renormalizability for these expectation values is lost. Nevertheless we establish the renormalization group equation for the light like Wilson loops and show that it is equivalent to the evolution equation for the physical distributions. By performing a two loop calculation we verify these properties and show that the universal form of the splitting function near the phase space boundary originates from the cusp anomalous dimension of Wilson loops. Research supported in part by Ministero dell’Universtà e della Ricerca Scientifica e Tecnologica. On leave from the Laboratory of Theoretical Physics, JINR, Dubna, Russia INFN Fellow