Ir-improved Dglap Theory †

We show that it is possible to improve the infrared aspects of the standard treatment of the DGLAP evolution theory to take into account a large class of higher order corrections that significantly improve the precision of the theory for any given level of fixed-order calculation of its respective kernels. We illustrate the size of the effects we resum using the moments of the parton distributions. In the preparation of the physics for the precision QCD×EW(electroweak) [1,2] LHC physics studies, all aspects of the calculation of the cross sections and distributions for the would-be physical observables must be reexamined if precision tags such as that envisioned for the luminosity theoretical precision are to be realized, i.e., 1% cross section predictions for single heavy gauge boson production in 14 TeV pp collisions when that heavy gauge boson decays into a light lepton pair. The QCD DGLAP [3] evolution of the structure functions from the typical reference scale of data input, µ 0 ∼ 1 − 2GeV , to the respective hard scale is one step that warrants further study, as it is well-known to many. Many authors [4–7] have provided excellent realizations of this evolution in the recent literature. Here, we will reexamine the infrared aspects of the basic DGLAP theory itself to try to improve the treatment to a level consistent with the new era of precision QCD×EW physics needed for the LHC physics objectives. Specifically, the motivation for the improvement which we develop can be seen already in the basic results in Refs. [3] for the kernels that determine the evolution of the structure functions by the attendant DGLAP evolution of the corresponding parton densities by the standard methodology. Consider the evolution of the non-singlet(NS) parton density function q N S (x), where x can be identified as Bjorken's variable as usual. The basic starting point of our analysis is the infrared divergence in the kernel that determines this evolution: dq N S (x, t) dt = α s (t) 2π 1 x dy y q N S (y, t)P qq (x/y) (1) where the well-known result for the kernel P qq (z) is, for z < 1, P qq (z) = C F 1 + z 2 1 − z (2) when we set t = ln µ 2 /µ 2 0 for some reference scale µ 0 with which we study evolution to the scale of interest …