Abstract
The ladder kernel of the Bethe–Salpeter equation is amended by introducing a different flavor dependence of the dressing functions in the heavy-quark sector. Compared with earlier work this allows for the simultaneous calculation of the mass spectrum and leptonic decay constants of light pseudoscalar mesons, the D_u, D_s, B_u, B_s and B_c mesons and the heavy quarkonia eta _c and eta _b within the same framework at a physical pion mass. The corresponding Bethe–Salpeter amplitudes are projected onto the light front and we reconstruct the distribution amplitudes of the mesons in the full theory. A comparison with the first inverse moment of the heavy meson distribution amplitude in heavy quark effective theory is made.
Highlights
The introduction of hadronic light-cone distribution amplitudes (LCDA) dates back to the seminal works on hard exclusive reactions in perturbative QCD [1,2,3,4,5]
Compared with earlier work this allows for the simultaneous calculation of the mass spectrum and leptonic decay constants of light pseudoscalar mesons, the Du, Ds, Bu, Bs and Bc mesons and the heavy quarkonia ηc and ηb within the same framework at a physical pion mass
The corresponding Bethe–Salpeter amplitudes are projected onto the light front and we reconstruct the distribution amplitudes of the mesons in the full theory
Summary
The introduction of hadronic light-cone distribution amplitudes (LCDA) dates back to the seminal works on hard exclusive reactions in perturbative QCD [1,2,3,4,5] These nonperturbative and scale-dependent functions can be understood as the closest relative of quantum mechanical wave functions in quantum field theory. It turned out that introducing different effective couplings, due to unlike dressing effects for light and heavy quarks, in the ladder truncation of the Bethe–Salpeter kernel significantly improved the description of experimental results We employ the combined approach of the Dyson– Schwinger equation (DSE) for the quark and BSE with a flavor-dependent, slightly modified interaction to first compute the mass spectrum and weak decay constants of the pseudoscalar π , K , D, Ds, B, Bs and Bc mesons and ηc and ηb quarkonia in Sect.
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