$\boldsymbol{B_c}$ Meson Spectroscopy from Bayesian MCMC: Probing Confinement and State Mixing
We present a Bayesian study of the $B_c$ meson spectrum using three non-relativistic confining potentials, namely the Cornell potential, a logarithmically modified extension, and a screened Cornell form. Parameters for each potential are sampled using Markov chain Monte Carlo (MCMC), retaining correlations among the fitted parameters. The resulting parameter distributions are used to calculate the $B_c$ spectrum through the $6D$ multiplet, including masses, spin-dependent splittings, mixing angles, and wave-function observables. The predicted masses are further examined through Regge trajectories. The low-lying spectrum is relatively stable across the three potentials, while their predictions become increasingly separated with excitation as the states probe larger distances, accompanied by growing parameter-induced uncertainties. The Regge trajectories show stronger non-linearity for low-lying states and progressively approach linear behavior with excitation. These results quantify the sensitivity of the predicted excited $B_c$ spectrum to the chosen confining interaction and provide uncertainty estimates for states that remain experimentally less explored.