Form factor π0γ*γ in lightcone sum rules combined with renormalization-group summation vs experimental data.

C Ayala,A V Pimikov,N G Stefanis,S V Mikhailov

doi:10.1051/epjconf/201922203017

Abstract

We consider the lightcone sum-rule (LCSR) description of the pionphoton transition form factor in combination with the renormalization group of QCD. The emerging scheme represents a certain version of Fractional Analytic Perturbation Theory and significantly extends the applicability domain of perturbation theory towards lower momenta Q2 ≲ 1 GeV2. We show that the predictions calculated herewith agree very well with the released preliminary data of the BESIII experiment, which have very small errors just in this region, while the agreement with other data at higher Q2 is compatible with the LCSR predictions obtained recently by one of us using fixed-order perturbation theory.

Highlights

In this work we consider the calculation of the π0γ∗γ transition form factor (TFF) within the lightcone sum-rule (LCSR) approach, see, e.g., [1, 2], going beyond fixed-order perturbation theory (FOPT)
We considered the lightcone sum-rule description of the pion-photon transition form factor in combination with the renormalization group of QCD and compared the obtained TFF predictions with the corresponding fixed-order results
We showed that the LCSR method, augmented with the RG summation of radiative corrections, naturally leads to a version of fractional analytic perturbation theory that is free of Landau singularities and provides the possibility to include QCD radiative corrections in a resummed way [3]

Summary

Introduction

In this work we consider the calculation of the π0γ∗γ transition form factor (TFF) within the LCSR approach, see, e.g., [1, 2], going beyond fixed-order perturbation theory (FOPT). From the calculational point of view, this FAPT-related approach helps avoid the appearance of large radiative corrections to the pion-photon TFF at low/moderate momenta. This is because such terms become small by virtue of the FAPT summation in contrast to the currently known [2] FOPT results (up to the order of O(α2sβ0)). For the Born contribution the corresponding Im part is generated by the singularity of T0(Q2, −σ; y) (multiplied by a power of(logarithms), while) for the RG summed radiative corrections, one term originates from the Im aνs(−σy + Q2y)/π contribution

Key element of the radiative corrections

Pion-photon TFF in FAPT

Numerical results for the TFF and comparison with the experimental data

Conclusion