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Anomalous Dimension of Non-Singlet Wilson Operators at O(1/N_f) in Deep Inelastic Scattering
J. A. Gracey
TL;DR
The paper addresses the need for independent information about perturbative anomalous dimensions of non-singlet Wilson operators in deep inelastic scattering. It uses large-N_f self-consistency and critical-point methods, reproduces known two-loop structure, and derives higher-order expressions for all moments at O(1/N_f).
Problem
Independent methods are needed to obtain perturbative information on anomalous dimensions of physical operators beyond computationally demanding multiloop calculations.
Source: pp. 2–3Method
The paper applies a large-N_f self-consistency formalism with critical propagators to compute non-singlet Wilson-operator anomalous dimensions.
Source: pp. 3, 5, 6Results
The method agrees with known low-order results and provides higher-order perturbative structure for the non-singlet anomalous dimensions.
Source: pp. 7–9Takeaways & Limitations
The formalism offers an alternative way to calculate anomalous dimensions and deduce higher-order perturbative information at leading order in 1/N_f.
Source: pp. 3, 9The calculation is restricted to the non-singlet case, while O(1/N_f^2) corrections require the yet-uncomputed quark anomalous dimension η2.
Source: pp. 3, 9
Abstract
from arXiv · showhide
We use the large N_f self consistency formalism to compute the $O(1/N_f)$ critical exponent corresponding to the renormalization of the flavour non-singlet twist two Wilson operators which arise in the operator product expansion of currents in deep inelastic processes. Expanding the $d$-dimensional expression in powers of $\epsilon$ $=$ $(4-d)/2$ the coefficients of $\epsilon$ agree with the known two loop structure of the corresponding renormalization group function and we deduce analytic expressions for all moments, $n$, at three and higher orders in perturbation theory in the $\overline{\mbox{MS}}$ scheme at $O(1/N_f)$.
Figure Captions.
Figure 1 presents the leading-order graphs associated with η(n).
- Figure 1 is labeled as showing leading-order graphs.Source: Figure 1
- The displayed graphs concern η(n).Source: Figure 1
- The figure is supplied as a PNG image.Source: Figure Captions · p. 14