From chiral EFT to perturbative QCD: a Bayesian model mixing approach to symmetric nuclear matter

Constraining the equation of state (EOS) of strongly interacting, dense matter is the focus of intense experimental, observational, and theoretical effort. Chiral effective field theory ($\chi$EFT) can describe the EOS between the typical densities of nuclei and those in the outer cores of neutron stars while perturbative QCD (pQCD) can be applied to properties of deconfined quark matter, both with quantified theoretical uncertainties. However, describing the complete range of densities between nuclear saturation and an almost-free quark gas with a single EOS that has well-quantified uncertainties is a challenging problem. In this work, we argue that Bayesian multi-model inference from $\chi$EFT and pQCD can help bridge the gap between the two theories. We develop a correlated Bayesian model mixing approach that uses a Gaussian Process (GP) to assimilate different information into a single QCD EOS for symmetric nuclear matter. In the present implementation, this mixed EOS is informed solely by those of $\chi$EFT and pQCD, together with the associated truncation errors. The GP is trained on the pressure as a function of number density in the low-density and high-density regions where $\chi$EFT and pQCD are, respectively, valid. We impose priors on the GP kernel hyperparameters to suppress unphysical correlations between these regimes. This results in smooth $\chi$EFT-to-pQCD curves for both the pressure and the speed of sound. We show that using uncorrelated pointwise mixing requires uncontrolled extrapolation of at least one of $\chi$EFT or pQCD into regions where the perturbative series breaks down and leads to an acausal EOS. We also discuss future extensions and applications to neutron star matter guided by recent EOS constraints from nuclear theory, nuclear experiment, and multi-messenger astronomy.