The internal structure of all lowest-lying pseudoscalar mesons with heavy-light quark content is studied in detail using an algebraic model that has been applied recently, and successfully, to the same physical observables of pseudoscalar and vector mesons with hidden-flavor quark content, from light to heavy quark sectors. The algebraic model consists on constructing simple and evidence-based Ansätze of the meson’s Bethe-Salpeter amplitude (BSA) and quark’s propagator in such a way that the Bethe-Salpeter wave function (BSWF) can then be readily computed algebraically. Its subsequent projection onto the light front yields the light front wave function (LFWF) whose form allows us a simple access to the valence-quark parton distribution amplitude (PDA) by integrating over the transverse momentum squared. We exploit our current knowledge of the PDAs of lowest-lying pseudoscalar heavy-light mesons to compute their generalized parton distributions (GPDs) through the overlap representation of LFWFs. From these three dimensional knowledge, different limits/projections lead us to deduce the related parton distribution functions (PDFs), electromagnetic form factors (EFFs), and impact parameter space GPDs (IPS-GPDs). When possible, we make explicit comparisons with available experimental results and earlier theoretical predictions.

Inspired by the recent development of an algebraic model which provides an adequate and unified description of the internal structure of the lowest-lying pseudoscalar mesons, belonging both to the light quarks sector and to the one of heavy quarks, we perform its first extension to the vector-meson case. The algebraic model describes the meson’s structure in terms of the spectral density function that appears in a Nakanishi integral representation of the covariant quark-antiquark bound-state amplitude, i.e., the Bethe-Salpeter amplitude. We compute the leading-twist light-front wave functions of the $\rho (770)$, $\varphi (1020)$, $J/\psi$, and $\mathrm{\Upsilon }(1S)$ mesons through their connection with the parton distribution amplitudes. Among the results we present, the following are of particular interest: (i) transverse light-front wave functions can be obtained algebraically from the corresponding parton distribution amplitudes, whereas that is not the case for longitudinal light-front wave functions, which requires an intermediate step where a spectral density function must be derived from the particular parton distribution amplitude; (ii) the derived spectral density functions show marked differences between light and heavy vector mesons, the latter being narrower as compared to the former, and these are also nonpositive definite, although the integral over the entire curve is larger than zero as expected; and (iii) the longitudinal and transverse light-front wave functions of vector mesons with light quark content exhibit steep $x$ and $p_{\perp }^2$ dependence, while those of the $J/\psi$ and $\mathrm{\Upsilon }(1S)$ mesons are characterized by narrow distributions in the $x$ range but, comparatively, much more gradual falloffs with respect to the $p_{\perp }^2$ range depicted.

We construct a contact interaction model for the $\eta$ and ${\eta }^{\prime }$ mesons in the SDE-BSE approach to QCD and compute several static properties of these mesons and their transition form factors. We find that this model gives an excellent description of the $\eta$ and ${\eta }^{\prime }$ static properties, namely, their masses, decay width, and decay constants. However, a contact interaction disagrees with experimental data for $Q^2$ greater than $2{\mathrm{GeV}}^2$, and produces transition form factors in conflict with perturbative QCD prediction. This is not surprising and the reasons for this are explained.

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 η and η ′ mesons. This model facilitates the construction of the Bethe-Salpeter wave function, whose projection onto an appropriate flavor basis leads to the light-front wave function for convenient linear combinations of the s s ¯ and l l ¯ ∼ ( u u ¯ + d 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.

The internal structure of the lowest-lying pseudo-scalar mesons with heavy-light quark content is thoroughly studied using an algebraic model that has been successfully applied to similar physical observables of pseudoscalar and vector mesons with hidden-flavor quark content, ranging from light to heavy quark sectors. This model is based on constructing simple and evidence-based ansätze for the mesons' Bethe-Salpeter amplitude (BSA) and quark propagator, allowing the Bethe-Salpeter wave function (BSWF) to be computed algebraically. Its projection onto the light front yields the corresponding light-front wave function (LFWF), which provides easy access to the valence-quark Parton Distribution Amplitude (PDA) by integrating over the transverse momentum squared. We leverage our current knowledge of the PDAs of the lowest-lying pseudo-scalar heavy-light mesons to compute their Generalized Parton Distributions (GPDs) via the overlap representation of the LFWFs. From this three-dimensional information, various limits and projections allow us to deduce the related Parton Distribution Functions (PDFs), Electromagnetic Form Factors (EFFs), and Impact Parameter Space GPDs (IPS-GPDs). Whenever possible, we make explicit comparisons with available experimental results and previous theoretical predictions.