Electromagnetic form factors of heavy-light pseduoscalar mesons

We report calculations of space-like electromagnetic form factors and charge radii of pseudoscalar mesons, covering both light and heavy-light flavour sectors within a flavour-dependent Bethe-Salpeter framework.

💡 Research Summary

In this work the authors present a comprehensive study of space‑like electromagnetic form factors (EFFs) and charge radii for pseudoscalar mesons ranging from the light π and K to heavy‑light systems such as D, Dₛ, B, Bₛ and B_c. The calculation is performed within a fully self‑consistent framework that couples the Bethe‑Salpeter equation (BSE) for the meson bound‑state amplitude with the Dyson‑Schwinger equation (SDE) for the dressed quark propagator. A key innovation is the use of a flavour‑dependent interaction kernel, I_{ff’}(q²)=\tildeα_T(q²)A_f(q²)A_{f’}(q²), where \tildeα_T incorporates non‑perturbative vertex corrections beyond the simple Taylor coupling. The kernel is inserted into the colour‑mediated gluon propagator D_{ff’}^{μν}(k)=4π D_0^{μν}(k) I_{ff’}(k²), ensuring that both the quark self‑energy and the quark‑photon vertex carry explicit flavour information.

The dressed quark propagator is parametrised as S_f^{-1}(p)=i!\not!p A_f(p²)+B_f(p²) and obtained by solving the gap equation (Eq. 8) with renormalised current masses fixed at μ=4 GeV (m_{u/d}=5 MeV, m_s=94 MeV, m_c=1.1 GeV, m_b=3.5 GeV). The Bethe‑Salpeter amplitude satisfies the integral equation (Eq. 9) involving the same kernel, while the quark‑photon vertex Γ_f^μ(p₁,p₂) fulfills the vector Ward‑Takahashi identity (VWTI) and is computed from the inhomogeneous BSE (Eq. 10). In the impulse approximation the electromagnetic current is expressed by Eq. (3), where the momentum partitioning parameter η is tuned for each flavour combination to avoid singularities and to improve numerical stability, a particularly important step for heavy‑light mesons.

Form factors are extracted from the matrix element J^μ=⟨M(p_f)|j^μ(0)|M(p_i)⟩=2p̄^μ F(Q²) with Q²=−q². The charge radius follows from ⟨r²⟩=−6 dF/dQ²|_{Q²=0}. Results for the pion and kaon are shown in Fig. 2; the calculated curves (solid lines with uncertainty bands from variations of \tildeα_T) agree very well with the experimental data from Refs.