A unified study of the $$B_c$$ meson: from spectrum and form factors to weak and radiative decays

Abstract The $$B_c$$ B c meson constitutes a unique system for investigating heavy-hadron dynamics, since it exhibits quarkonium-like bound-state structure while decaying predominantly through weak interactions. In this work, we present a unified study of $$B_c$$ B c -meson spectroscopy, decay constants, weak decays, radiative transitions, and Regge trajectories within a single framework. The mass spectrum is computed in a screened potential model including relativistic kinetic-energy corrections and spin-dependent interactions, from which we obtain both spin-averaged and spin-resolved states together with the corresponding pseudoscalar and vector decay constants. Using these spectroscopic inputs, we then analyze weak decays within a mass-updated three-point QCD sum-rule framework for transitions to S -, P -, and D -wave charmonium states, as well as to final states containing charmonium and $$D^{(*)}_{(s)}$$ D ( s ) ( ∗ ) mesons. In this part of the analysis, the hadronic thresholds, Borel-window prescriptions, Lorentz decompositions, and decay-width expressions of the underlying sum-rule formulations are retained, while the heavy-quark masses are updated to $$m_c=1.48~\textrm{GeV}$$ m c = 1.48 GeV and $$m_b=4.90~\textrm{GeV}$$ m b = 4.90 GeV , leading to a controlled refit of the overall normalization rather than a full rederivation of all perturbative and condensate contributions. We further investigate purely leptonic decay widths and radiative E 1 and M 1 transitions, and examine the Regge behavior of the resulting spectrum. The present study therefore provides a coherent description of the $$B_c$$ B c meson in which the spectroscopic wave functions determine the short-distance couplings that enter both weak and electromagnetic observables, while the Regge analysis serves as a complementary global consistency test of the same dynamical picture.