Scheme-invariant NNLO evolution for unpolarized DIS structure functions

Abstract

We discuss the combination of NNLO standard QCD evolution and scheme-invariant analysis for unpolarized DIS structure functions data as a method to reduce the theoretical errors on the determination of αs(M 2 Z ) to ∼ 1% in order to match the accuracy forseen for experimental errors from future high statistics measurements.

Analytic Integration Methods in Quantum Field Theory: An Introduction

“…Representations in Mellin N -space allow the exact analytic solution of evolution equations [206] and scheme-invariant evolution equations can be derived in this way [207,208]. The x-space representation is then obtained by a single numerical integral around the singularities of the respective quantity for N ∈ C, cf.…”

“…The final goal is here the precision measurement of the strong coupling constant α s (M 2 Z ) in a widely unique manner. This can also be achieved using the method of scheme-invariant evolution equations [240] for which the initial conditions are measured directly. Furthermore, one would like to determine at least the charm quark mass, m c [241], in a correlated way with the parton densities and α s (M 2 Z ).…”

Large Scale Analytic Calculations in Quantum Field Theories

“…Physical observables based on single scale quantities can either be represented in Mellin N -space or x-space. Representations in Mellin N -space allow the exact analytic solution of evolution equations [208] and schemeinvariant evolution equations can be derived in this way [209,210]. The xspace representation is then obtained by a single numerical integral around the singularities of the respective quantity for N ∈ C, cf.…”

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

“…[8], showing that the remaining uncertainties there do not affect the value of Λ QCD . Alternatively to the standard MS-analysis one may perform factorization scheme-invariant analyzes [13], based on observables only. This method is free of shape-assumptions, in particular for the gluon density.…”