A multidimensional landscape of the $\eta$ and $\eta'$ mesons

Abstract

We employ a recently proposed form-invariant algebraic model for the quark propagator and the Bethe-Salpeter amplitude of pseudoscalar mesons to study the internal structure of $\eta$ and $\eta'$ mesons. This model facilitates the construction of the Bethe-Salpeter wavefunction, whose projection onto an appropriate flavor-basis leads to the light-front wavefunction for convenient linear combinations of the $s \bar{s}$ and $l\bar{l}\sim(u \bar{u} + d \bar{d})$ states. Using an overlap representation, we compute the valence-quark generalized parton distributions (GPDs). The construction of the model ensures that this multidimensional quantity is determined entirely by the corresponding valence-quark distribution amplitudes. Once the GPDs are constructed, we carry out a straightforward derivation of other desired physical observables such as the distribution functions and the electromagnetic form factors. We also provide explicit comparisons with available results, demonstrating that the present model offers a consistent physical picture for all ground-state pseudoscalar mesons.