$\eta_{c}$ Elastic and Transition Form Factors: Contact Interaction and Algebraic Model

TL;DR

This paper calculates the elastic and transition form factors of the $ ext{η}_c$ meson using contact interaction and algebraic models within a symmetry-preserving framework, comparing results with lattice QCD, perturbative QCD, and experimental data.

Contribution

It introduces a combined approach using contact interaction and algebraic models within SDE-BSE formalism to study $ ext{η}_c$ form factors, extending previous light-quark models to heavy quark systems.

Findings

CI results match lattice data at low $Q^2$

Deviations from lattice data grow beyond $Q_0^2$

Results agree with perturbative QCD and experiments

Abstract

For the flavor-singlet heavy quark system of charmonia in the pseudoscalar ($\eta_c(1S)$) channel, we calculate the elastic (EFF) and transition form factors (TFF) ($\eta_c(1S) \rightarrow \gamma \gamma^*$) for a wide range of photon momentum transfer squared ($Q^2$). The framework for this analysis is provided by a symmetry-preserving Schwinger-Dyson equation (SDE) and Bethe-Salpeter equation (BSE) treatment of a vector$\times$vector contact interaction (CI). We also employ an algebraic model (AM), developed earlier to describe the light quark systems. It correctly correlates infrared and ultraviolet dynamics of quantum chromodynamics (QCD). The CI results agree with the lattice data for low $Q^2$. For $Q^2 \geqslant Q_0^2$, the results start deviating from the lattice results by more than $20 \%$. $Q_0^2 \thickapprox 2.5 {\rm GeV}^2$ for the EFF and $\thickapprox 25 {\rm GeV}^2$ for the TFF. We also present the results for the EFF, TFF as well as $\eta_c(1S)$ parton distribution amplitude for the AM. Wherever the comparison is possible, these results are in excellent agreement with the lattice, perturbative QCD, the results obtained through an SDE-BSE study, employing refined truncations, as well as the experimental findings of the BABAR experiment.