Extending the application of the LCSR method to low momenta using QCD renormalization-group summation. Theory and phenomenology

TL;DR

This paper improves the lightcone sum rules method for calculating the $\pi-\gamma$ transition form factor at low momenta by using renormalization-group summation, enabling more accurate phenomenological analysis below 1 GeV$^2$.

Contribution

It introduces a renormalization-group summation approach to extend LCSR applicability to low momenta, providing a more reliable and accurate determination of the pion distribution amplitude and form factor.

Findings

Enhanced LCSR method with RG summation removes Landau singularities.

Accurate fit to BESIII data below 1.5 GeV$^2$ for the form factor.

Determination of pion distribution amplitude parameters consistent with lattice and sum rule constraints.

Abstract

We show that using renormalization-group summation to generate the QCD radiative corrections to the $\pi-\gamma$ transition form factor, calculated with lightcone sum rules (LCSR), renders the strong coupling free of Landau singularities while preserving the QCD form-factor asymptotics. This enables a reliable applicability of the LCSR method to momenta well below 1 GeV$^2$. This way, one can use the new preliminary BESIII data with unprecedented accuracy below 1.5 GeV$^2$ to fine tune the prefactor of the twist-six contribution. Using a combined fit to all available data below 3.1 GeV$^2$, we are able to determine all nonperturbative scale parameters and a few Gegenbauer coefficients entering the calculation of the form factor. Employing these ingredients, we determine a pion distribution amplitude with conformal coefficients $(b_2,b_4)$ that agree at the $1\sigma$ level with the data for $Q^2 \leqslant 3.1$ GeV$^2$ and fulfill at the same time the lattice constraints on $b_2$ at N$^3$LO together with the constraints from QCD sum rules with nonlocal condensates.The form-factor prediction calculated herewith reproduces the data below 1 GeV$^2$ significantly better than analogous predictions based on a fixed-order power-series expansion in the strong coupling constant.