Analytic QCD: Recent Results

TL;DR

This article surveys analytic QCD with emphasis on the MA (analytic) coupling and its variants, particularly a form that remains well-behaved near the Landau scale $Q^2 oughly oldsymbol{\Lambda}^2$. It develops a $1/L$ expansion for derivatives of the coupling with respect to $L$ using fractional derivatives, enabling derivative series to replace powers of $a_s$ and providing LO and NLO representations for the MA coupling. The key finding is that analytic-coupling corrections are negligible at extreme $Q^2$ but become significant around $Q^2 o oldsymbol{\Lambda}^2$, with explicit expressions in terms of Lerch and zeta-type functions that are practical near the threshold region; these results have been used to analyze sum rules such as the polarized Bjorken and GLS sum rules, demonstrating the utility of the $Q^2 oughly oldsymbol{\Lambda}^2$-friendly MA form in low-$Q^2$ phenomenology.

Abstract

We present a brief overview of analytical QCD, focusing primarily on a less common form of the analytical coupling A_{\rm MA}(Q^2), which is particularly convenient for Q^2\simΛ^2. This form has been extensively used in recent studies of the (polarized) Bjorken sum rule and the Gross-Llewellyn Smith sum rule.

Figures (1)

• Figure 1: Results for $A^{(1)}_{\rm MA,\nu=1,0}(Q^2)$, $A^{(2)}_{\rm MA,\nu=1,1}(Q^2)$, and $\delta^{(2)}_{\rm MA,\nu=1,1}(Q^2)$.