0.02 & 0.966 & 1.603 & 31 & 17 & 8 & 32\
& & 0.6 & 0.02 & 1.389 & 4.902 & 38 & 8 & 14 & 32\

We apply the model to heavy quarkonia (charmonium and bottomonium), where the quark masses are large and the radiative corrections are negligible. Therefore these are ideal systems to test our model. The model parameters are summarized in Table \[tab:model\_parametersI\].

As mentioned, we fixed $\alpha_s(0)=0.6$. For fixed $N_{\max}$ and $L_{\max}$, we use experimental data to fit the confining strength $\kappa$ and the effective quark mass $m_q$ ($m_c$ and $m_b$) using the mass eigenvalues in the $m_j=0$ sector. We employ the experimental values, compiled by the Particle Data Group (PDG) [@Agashe:2014kda], below the open charm or open bottom threshold. We also introduced a small mass parameter $\mu_g = 0.02 \,\mathrm{GeV}$ to regularize the integrable Coulomb singularity in the energy denominator and to avoid numerical instability[^6]. As has been shown in previous work with fixed coupling, the mass eigenvalues are converged with respect to $\mu_g \to 0$ within the numerical precision.

![A representative bottomonium mass spectrum obtained by diagonalizing the light cone Hamiltonian within various $m_j$ sectors at $N_{\max} = L_{\max} = 32$. 