$Λ_{\rm QCD}$ and $α_s(M_Z^2)$ from DIS Structure Functions

Abstract

A brief summary is given on recent determinations of ΛQCD and αs(M 2 Z ) from deeply inelastic structure functions.

Two-loop massive operator matrix elements for unpolarized heavy flavor production to

“…Qg with the corresponding contribution in the 2-loop on-shell photon propagator. The terms a (2) (N) can be expressed in terms of polynomials of the basic nested harmonic sums up to weight w = 4 and derivatives thereof. They belong to the complexity-class of the general two-loop Wilson coefficients or hard scattering cross sections in massless QED and QCD found for spaceand time-like unpolarized and polarized anomalous dimensions, massless Wilson coefficients for deeply inelastic scattering, parton fragmentation, the Drell-Yan process, hadronic Higgs-and pseudoscalar Higgs production in the heavy mass limit as well as the soft-and virtual contribution to Bhabha-scattering, cf.…”

“…Here we discuss the case of conserved currents, which have vanishing anomalous dimensions. 2 The RGE for the Wilson coefficients and the parton distributions read [23,28]…”

“…The current world data for the nucleon structure functions F p,d 2 (x, Q 2 ) reached the precision of a few per cent over a wide kinematic region. Therefore both for the determination of the QCD scale Λ QCD and the detailed shapes of the partonic distribution functions the analysis at the level of the O(α 3 s ) corrections is required to control the theory-errors on the level of the experimental accuracy and below [2]. In a recent non-singlet analysis [3] errors for α s (M 2 Z ) of O(1.5 %) were obtained extending the analysis effectively to N 3 LO.…”

Implications of HERA measurements for LHC

“…Apart from extracting parton densities, such analyses also permit an extraction of the strong coupling constant α s , whose precision has become very competitive with other determinations, see [13,14]. In this field, HERA contributes both with DIS structure functions in a wide range of Q 2 and with dedicated analyses of jet production [15].…”

Two-Loop Massive Operator Matrix Elements for Polarized and Unpolarized Deep-Inelastic Scattering

“…The heavy-flavor corrections to deeply inelastic structure functions are very important for the range of small values of x and do contribute there on the level of 20-40%. They have to be known at the same level of accuracy as the light-flavor contributions for precision measurements of Λ QCD [1] and the parton distributions. The next-to-leading order corrections were given semi-analytically in [2] for the general kinematic range.…”