An algebraic model to study the internal structure of pseudo-scalar mesons with heavy-light quark content

TL;DR

This paper introduces an algebraic model to analyze the internal structure of pseudo-scalar mesons with heavy-light quark content, enabling calculation of their wave functions, GPDs, PDFs, and form factors with comparisons to experimental data.

Contribution

The paper develops a novel algebraic approach to compute the internal structure of heavy-light pseudo-scalar mesons, extending previous models to new meson types and observables.

Findings

Computed GPDs, PDFs, and form factors for heavy-light mesons.

Achieved good agreement with experimental data where available.

Provided a unified algebraic framework for meson internal structure analysis.

Abstract

The internal structure of all lowest-lying pseudo-scalar 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 pseudo-scalar and vector mesons with hidden-flavor quark content, from light to heavy quark sectors. The algebraic model consists on constructing simple and evidence-based \emph{ans\"atze} 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 pseudo-scalar 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.