Pion Form Factor in QCD: How to Calculate?

TL;DR

This paper reviews methods for calculating the pion form factor in QCD, comparing nonlocal condensate sum rules, perturbative, lattice QCD, and local duality approaches, highlighting the Q^2 dependence of key parameters.

Contribution

It introduces an analysis of the local duality approach for the pion form factor, emphasizing the Q^2 dependence of the main parameter, s_0^{LD}(Q^2), for Q^2 > 2 GeV^2.

Findings

Nonlocal condensate sum rule results agree with lattice and perturbative QCD.

The parameter s_0^{LD}(Q^2) increases with Q^2 for Q^2 > 2 GeV^2.

Q^2 dependence of s_0^{LD} improves the local duality approach's accuracy.

Abstract

We discuss the pion form factor calculation in QCD.We shortly consider the main points of the nonlocal condensate QCD sum rule approach and show its results for the pion form factor, $F_\pi(Q^2)$. These results are compared with predictions of the perturbative and lattice QCD. Then we consider the Local Duality (LD) approach for the pion FF in QCD and show that for $Q^2\gtrsim 2$ GeV$^2$ the main parameter of the approach, namely, $s_0^{\text{LD}}(Q^2)$ should grow with $Q^2$ rather than be a constant.