Heavy-light mesons from a flavour-dependent interaction

TL;DR

The paper addresses the challenge of describing heavy-light mesons in QCD by developing a symmetry-preserving framework that incorporates flavour-dependent contributions into the bound-state and gap equations via fully-dressed quark-gluon vertices. A central idea is to construct a flavour-dependent one-gluon exchange kernel whose universal part is governed by the STI-enhanced Taylor charge while the flavour dependence enters through the quark wave-function dressings, yielding the interaction \\mathcal{I}_{ff'}(q^2) = \\tilde{α}_T(q^2) A_f(q^2) A_{f'}(q^2) with \\tilde{α}_T(q^2) = α_T(q^2) \\tilde{X}_0^2(q^2). Using lattice inputs for the Green functions, the authors solve the gap equation and the Bethe-Salpeter equation to predict masses and decay constants for D, B, η, and related states, achieving good agreement with experiment and lattice results without free parameters. The approach preserves the axial Ward-Takahashi identity and enables a continuous light-to-heavy transition by varying current-quark masses, with potential broader applications to form factors and parton distributions. This framework offers a first-principles, parameter-free route to heavy-light phenomenology grounded in QCD correlators and lattice data, and sets the stage for systematic improvements beyond the one-gluon exchange truncation.

Abstract

We introduce a new symmetry-preserving framework for the physics of heavy-light mesons, whose key element is the effective incorporation of flavour-dependent contributions into the corresponding bound-state and quark gap equations. These terms originate from the fully-dressed quark-gluon vertices appearing in the kernels of these equations, and provide a natural distinction between ``light" and ``heavy" quarks. In this approach, only the classical form factor of the quark-gluon vertex is retained, and is evaluated in the so-called ``symmetric" configuration. The standard Slavnov-Taylor identity links this form factor to the quark wave-function, allowing for the continuous transition from light to heavy quarks through the mere variation of the current quark mass in the gap equation. The method is used to compute the masses and decay constants of specific pseudoscalars and vector heavy-light systems, showing good overall agreement with both experimental data and lattice simulations.

Figures (5)

• Figure 1: First row: the SDE of the quark-gluon vertex in the skeleton expansion; graphs with three- and four-gluon vertices are omitted. Second row: the one-gluon exchange kernel $\bar{\cal K}$ after the use of Eq. (\ref{['eq:qgsde']}). The ellipses stand for higher order loop terms. White and grey circles denote fully-dressed gluon and quark propagators, respectively, while big (small) blue circles stand for fully-dressed (tree-level) quark-gluon vertices.
• Figure 2: The quark gap equation (first row), the meson BSE (second row), and the SDE of the axial-vector vertex (third row), after the implementation of Eq. (\ref{['eq:qgsde']}). The yellow circle indicates the axial-vector vertex, the wavy line represents a conserved axial-vector current, and the ellipses denote higher order terms in the skeleton expansion.
• Figure 3: The quark-ghost scattering kernel at the one-loop dressed level. The red and orange circles denote the fully-dressed ghost propagator and ghost-gluon vertex, respectively.
• Figure 4: The lattice data of Zafeiropoulos:2019flq for the Taylor effective charge, $a_{{ T}}(q^2)$ (blue data points, with orange continuous line as their fit), and the modified Taylor effective charge, ${\tilde{\alpha}}_{{ T}}(q^2)$, [green data points], obtained from the $a_{{ T}}(q^2)$ data through multiplication by ${\tilde{X}}^2_0(q^2)$, according to Eq. (\ref{['eq:modTaylor']}). The red continuous line represents the fit of ${\tilde{\alpha}}_{{ T}}(q^2)$ given by Eq. (\ref{['eq:dhat_param']}). The inset shows the function ${\tilde{X}}_0(q^2)$, computed by evaluating Eq. (\ref{['eq:X0']}). Finally, the "star" marks the value $\alpha_T(4.3 {\rm GeV})$.
• Figure 5: The inverses of the quark wave functions (upper left); the constituent quark masses ${\cal M}(p^2)$ (upper right); direct comparison of the four interaction strengths ${\cal I }_{f f}(q^2)$ (lower left); comparison between ${\mathcal{I}}_{\!uu}(q^2)$, ${\mathcal{I}}_{\!cc}(q^2)$, and ${\mathcal{I}}_{\!cu}(q^2)$ (lower right).