Understanding how quarks bind to form mesons remains one of the central challenges in non-perturbative Quantum Chromodynamics (QCD). While QCD is the fundamental theory of the strong interaction, extracting precise predictions in the low-energy regime requires effective modeling approaches.

In this work, I revisit meson hyperfine structure—the mass splitting between vector and pseudoscalar states—using a QCD-inspired Cornell potential framework. The study is based on my published article:
https://doi.org/10.1140/epjp/s13360-025-07031-3

A key issue in conventional potential models is the divergence of the spin–spin contact interaction at short distances. To address this, I introduce a Gaussian smearing of the contact term, which regularizes the interaction and provides a physically meaningful description of short-range quark dynamics.

The framework further employs analytic wavefunctions derived using the Dalgarno–Lewis perturbative method, treating the Coulombic term as the parent potential and the linear confinement as a perturbation. This yields compact expressions that retain both analytical clarity and predictive power.

Using this approach, a unified analysis is performed across:
- Heavy–light mesons (D, Ds, B, Bs)
- Heavy quarkonium systems (charmonium, bottomonium)
- The Bc system
- Radial excitations (2S states)

The results show excellent agreement with experimental data for ground states, typically within a few MeV. The model also predicts systematic reduction of hyperfine splitting for excited states, consistent with reduced wavefunction density at the origin.

Importantly, the model demonstrates parameter stability: variations in the effective strong coupling lead to only minor changes in predictions, while the smearing parameter provides a controlled and physically interpretable regularization.

Overall, this work shows that a smearing-regularized Cornell potential combined with analytic methods can provide a unified and predictive description of meson hyperfine structure across different mass regimes. The results offer useful benchmarks for ongoing and future experiments at LHCb and Belle II.