Auxiliary function approach for determining symmetry energy at suprasaturation densities

Nuclear symmetry energy ${E}_{\text{sym}}(\ensuremath{\rho})$ at density $\ensuremath{\rho}$ is normally expanded or simply parameterized as a function of $\ensuremath{\chi}=(\ensuremath{\rho}\ensuremath{-}{\ensuremath{\rho}}_{0})/3{\ensuremath{\rho}}_{0}$ in the form ${E}_{\text{sym}}(\ensuremath{\rho})\ensuremath{\approx}S+L\ensuremath{\chi}+{2}^{\ensuremath{-}1}{K}_{\text{sym}}{\ensuremath{\chi}}^{2}+{6}^{\ensuremath{-}1}{J}_{\text{sym}}{\ensuremath{\chi}}^{3}+\ensuremath{\cdots}$ using its magnitude $S$, slope $L$, curvature ${K}_{\text{sym}}$, and skewness ${J}_{\text{sym}}$ saturation ${\ensuremath{\rho}}_{0}$ nuclear matter. Much progress has been made recent years constraining especially $S$ $L$ parameters various terrestrial experiments astrophysical observations. However, such expansions/parametrizations do not converge suprasaturation densities where $\ensuremath{\chi}$ small enough, hindering an accurate determination high-density even if characteristic are all well determined by experiments/observations. By expanding terms properly chosen auxiliary ${\mathrm{\ensuremath{\Pi}}}_{\text{sym}}(\ensuremath{\chi},{\mathrm{\ensuremath{\Theta}}}_{\text{sym}})$ with parameter ${\mathrm{\ensuremath{\Theta}}}_{\text{sym}}$ fixed accurately experimental ${E}_{\text{sym}}({\ensuremath{\rho}}_{\text{r}})$ value reference ${\ensuremath{\rho}}_{\text{r}}$, we show that shortcomings expansion can be completely removed significantly reduced determining behavior ${E}_{\text{sym}}(\ensuremath{\rho})$. In particular, two different functions, new approach effectively incorporates higher $\ensuremath{\chi}$-order contributions converges to same much faster than conventional $\ensuremath{\lesssim}3{\ensuremath{\rho}}_{0}$. Moreover, still poorly constrained plays role these approach. The thus provides nearly model-independent constraint on Several quantitative demonstrations Monte Carlo simulations given.