Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2007-10-30
Physics
High Energy Physics
High Energy Physics - Phenomenology
25 pages; version 2: modified presentation in section 2 and Appendix A, added comments; version 3: incorrect treatment of the
Scientific paper
A simple ansatz is suggested for the structure of threshold resummation of the momentum space physical evolution kernels (`physical anomalous dimensions') at all orders in (1-x), taking as examples Deep Inelastic Scattering (F_2(x, Q^2) and F_L(x, Q^2)) and the Drell-Yan process. Each term in the expansion is associated to a distinct renormalization group and scheme invariant perturbative object (`physical Sudakov anomalous dimension') depending on a single momentum scale variable. Both logarithmically enhanced terms and constant terms are captured by the ansatz at any order in the expansion. The ansatz is motivated by a large--beta_0 dispersive calculation. A dispersive representation at finite beta_0 of the physical Sudakov anomalous dimensions is also obtained, associated to a set of `Sudakov effective charges' which encapsulate the non-Abelian nature of the interaction. It is found that the dispersive representation requires a non-trivial, and process-dependent, choice of variables in the (x,Q^2) plane. Some interesting properties of the physical Sudakov anomalous dimensions are pointed out. The ensuing 1/N expansion in moment space is straightforwardly derived from the momentum space expansion.
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