Spacelike and timelike form factors for the $(\pi^0,\eta,\eta')\to\gamma^*\gamma$ transitions in the light-front quark model

TL;DR

This paper uses a light-front quark model to analyze the transition form factors of neutral mesons to photons in both spacelike and timelike regions, introducing a new direct method for timelike calculations and comparing results with experimental data.

Contribution

The paper presents a novel direct method for calculating meson-photon transition form factors in the timelike region within the light-front quark model, avoiding analytic continuation.

Findings

The direct timelike calculation agrees with analytic continuation and dispersion relation results.

LFQM results match experimental data for low-energy transition form factors and slope parameters.

Incorporating QCD factorization, the model reproduces the asymptotic behavior of form factors.

Abstract

We investigate the $(\pi^0,\eta,\eta')\to\gamma^*\gamma$ transitions both for the spacelike region and the timelike region using the light-front quark model (LFQM). In particular, we present the new direct method to explore the timelike region without resorting to mere analytic continuation from the spacelike region to the timelike region. Our direct calculation in timelike region shows the complete agreement not only with the analytic continuation result from the spacelike region but also with the result from the dispersion relation between the real and imaginary parts of the form factor. For the low energy regime, we compare our LFQM results of the transition form factors (TFFs) for the low timelike momentum transfer region and the slope parameters at $q^2=0$ with the recent experimental data from the Dalitz decays of $(\pi^0,\eta,\eta')$. For the high energy regime, we incorporate the QCD factorization in our LFQM to examine the asymptotic behavior of TFFs both for the spacelike region and the timelike region. We compare our results with the available experimental data.