γ*γ*→ηc(1S,2S) transition form factors for spacelike photons

Izabela Babiarz,Victor P Goncalves,Antoni Szczurek,Wolfgang Schäfer,Roman Pasechnik

doi:10.1103/physrevd.100.054018

Abstract

We derive the light-front wave function (LFWF) representation of the $\gamma^* \gamma^* \to \eta_c(1S)\,,\eta_c(2S)$ transition form factor $F(Q_1^2, Q_2^2)$ for two virtual photons in the initial state. For the LFWF, we use different models obtained from the solution of the Schr\"odinger equation for a variety of $c \bar c$ potentials. We compare our results to the BaBar experimental data for the $\eta_c(1S)$ transition form factor, for one real and one virtual photon. We observe that the onset of the asymptotic behaviour is strongly delayed and discuss applicability of the collinear and/or massless limit. We present some examples of two-dimensional distributions for $F (Q_1^2,Q_2^2)$. A factorization breaking measure is proposed and factorization breaking effects are quantified and shown to be almost model independent. Factorization is shown to be strongly broken, and a scaling of the form factor as a function of $\bar Q^2 = (Q_1^2 + Q_2^2)/2$ is obtained.

Highlights

The description of the hadronic structure in terms of the quark and gluon degrees of freedom is one of the main goals of quantum chromodynamics (QCD)
For the light-front wave function (LFWF), we use different models obtained from the solution of the Schrödinger equation for a variety of ccpotentials
We compare our results to the BABAR experimental data for the ηcð1SÞ transition form factor, for one real and one virtual photon

Summary

INTRODUCTION

The description of the hadronic structure in terms of the quark and gluon degrees of freedom is one of the main goals of quantum chromodynamics (QCD). A lot of attention has been paid to the case of pseudoscalar light meson-photon transition form factors [6,7], mainly motivated by the experimental data from the CLEO, BABAR, Belle, and L3 collaborations for the π0, η, and η0 production in eþe− collisions. These collaborations have extracted the transition form factor from single-tag events where only one of the leptons in the final state is measured.

Light-front wave function of ηc

Schrödinger equation and ccinteraction potentials

Light-front representation of the amplitude and transition form factor

NUMERICAL RESULTS

CONCLUSIONS