Extending the LCSR method to the electromagnetic pion form factor at low momenta using QCD renormalization-group summation

TL;DR

This paper extends the light cone sum rules method with QCD renormalization-group summation to accurately compute the electromagnetic pion form factor at low momentum transfers, aligning well with experimental data.

Contribution

It introduces a novel RG summation approach within LCSRs that improves predictions of the pion form factor at low Q^2, avoiding Landau singularities.

Findings

Accurately reproduces experimental data below 1 GeV^2

Eliminates Landau singularities in the strong coupling

Provides improved predictions over fixed-order expansions

Abstract

We obtain the electromagnetic pion form factor (emFF) $F_\pi$ for spacelike mid-range of momentum transfer in QCD. We use renormalization group (RG) summation within the light cone sum rules (LCSRs) to obtain the QCD radiative corrections to the $F_\pi$ and involve contributions of the leading twist 2 and, twists 4, 6. The additional conditions to apply here this RG summation are discussed in details. The strong coupling constants in this approach are free of Landau singularities, which allows one to go down to the lower transferred momentum $Q^2$. The prediction of the calculations performed reproduces the experimental data below/around $Q^2= 1$~GeV$^2$ significantly better than analogous predictions based on a fixed-order power-series expansion in the standard QCD.