Self-consistent M1 radiative transitions of excited Bc and heavy quarkonia with different polarizations in the light-front quark model

In this study, we investigate the properties of pseudoscalar and vector charmonia, bottomonia, and Bc mesons using the light-front quark model, focusing on the M1 radiative transition. For that purpose, we conduct a variational analysis with a quantum chromodynamics (QCD)-motivated effective Hamiltonian, employing a trial wave function expanded in the harmonic oscillator basis functions up to the 3S state. We fit the model parameters to mass spectra and decay constants, obtaining reasonable agreement with experimental data and correctly reflecting the hierarchy of mass spectra and decay constants. In analyzing the M1 radiative transition, we consider both good (μ=+) and transverse (μ=⊥) current components with both longitudinal (h=0) and transverse (h=±1) polarizations, demonstrating that the results from both components of currents and polarizations are identical. Self-consistency is achieved by substituting M with M0 when computing the operators for decay constants and radiative transitions. We also find that the difference between longitudinal and transverse polarizations of the observables may quantify the anisotropy of the model wave function. Our results on radiative transitions align reasonably well with experimental data, lattice QCD, and theoretical predictions. Furthermore, we also provide predictions for Bc mesons that can be tested in experiments. Published by the American Physical Society 2025