Determination of the hyperfine regularisation parameter

Determine a well-established procedure for evaluating the hyperfine regularisation parameter $x_0$ used in the spin-dependent interaction of the hypercentral constituent quark model for triply heavy baryons.

Background

The hypercentral constituent quark model incorporates a spin-dependent interaction containing the regularisation parameter $x_0$. In the paper, $x_0$ is treated as a hyperfine parameter related to gluon dynamics and is taken to be independent of the masses of the interacting quarks. The parameter is assigned the value $x_0=1.00~\mathrm{GeV}^{-1}$ for the numerical calculations, but the paper notes that no well-established method exists for determining it. Establishing a theoretically motivated procedure for evaluating $x_0$ would reduce the model dependence of the predicted triply heavy baryon masses and related electromagnetic and decay properties.