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Structure function evolution at next-to-leading order and beyond

Andreas Vogt

TL;DR

This work analyzes DIS scaling violations to extract the QCD coupling with reduced theoretical uncertainties by employing a factorization-scheme independent, observable-based evolution framework. It presents a NLO flavour-singlet analysis (BV99) yielding $\alpha_s(M_Z) = 0.114$ with controlled experimental and scale uncertainties and identifies a safe kinematic region for fits. It also investigates NNLO non-singlet evolution (NV99), constraining the 3-loop splitting function $P_{\text{NS}}^{(2+)}$ using available moments, and finds meaningful constraints for $x \gtrsim 0.15$ with reduced impact from small-$x$ uncertainty due to convolutions. The results indicate NNLO corrections will sharpen $\alpha_s$ determinations and enable targeted NNLO analyses, with extensions to the singlet sector planned.

Abstract

Results are presented of two studies addressing the scaling violations of deep-inelastic structure functions. Factorization-scheme independent fits to all ep and mu p data on F_2 are performed at next-to-leading order (NLO), yielding alpha_s(M_Z) = 0.114 +- 0.002_exp (+0.006-0.004)_th . In order to reduce the theoretical error dominated by the renormalization-scale dependence, the next-higher order (NNLO) needs to be included. For the flavour non-singlet sector, it is shown that available calculations provide sufficient information for this purpose at x > 10^-2.

Structure function evolution at next-to-leading order and beyond

TL;DR

This work analyzes DIS scaling violations to extract the QCD coupling with reduced theoretical uncertainties by employing a factorization-scheme independent, observable-based evolution framework. It presents a NLO flavour-singlet analysis (BV99) yielding with controlled experimental and scale uncertainties and identifies a safe kinematic region for fits. It also investigates NNLO non-singlet evolution (NV99), constraining the 3-loop splitting function using available moments, and finds meaningful constraints for with reduced impact from small- uncertainty due to convolutions. The results indicate NNLO corrections will sharpen determinations and enable targeted NNLO analyses, with extensions to the singlet sector planned.

Abstract

Results are presented of two studies addressing the scaling violations of deep-inelastic structure functions. Factorization-scheme independent fits to all ep and mu p data on F_2 are performed at next-to-leading order (NLO), yielding alpha_s(M_Z) = 0.114 +- 0.002_exp (+0.006-0.004)_th . In order to reduce the theoretical error dominated by the renormalization-scale dependence, the next-higher order (NNLO) needs to be included. For the flavour non-singlet sector, it is shown that available calculations provide sufficient information for this purpose at x > 10^-2.

Paper Structure

This paper contains 4 sections, 4 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Flavour-singlet evolution in NLO BV99
  3. Non-singlet evolution in NNLO NV99
  4. Summary and outlook

Figures (4)

  • Figure 1: The dependence of the fit results for the energy-momentum sum and for $\alpha_s(M_Z)$ on the $Q^2$-cut imposed in addition to $W^2 \! >\! 10 \hbox{GeV}^2$.
  • Figure 2: The dependence of the optimal values for $\alpha_s(M_Z)$ on the renormalization scale $\mu_r$.
  • Figure 3: Representative approximate results for the flavour-number independent part of the 3-loop non-singlet$^+$$\overline {\hbox{MS}}$ splitting function.
  • Figure 4: The first three steps in the expansion of the scaling violations of the non-singlet component of $F_2$ for typical input parameters.