Determine the isospin–baryon chemical potential relation I(B) needed for the QCD pressure bound

Determine the functional relation I(B) between the isospin chemical potential I and the baryon chemical potential B that is required to apply the nonperturbative QCD pressure inequality at nonzero B and I established by Fujimoto and Reddy (based on Lee’s QCD inequalities), without introducing model-dependent assumptions. This first-principles relation is necessary to use the bound to constrain the equation of state of dense QCD matter.

Background

The paper discusses how phase-quenched lattice QCD can provide bounds on the pressure of dense QCD matter. For two degenerate flavors, the phase-quenched pressure is a strict upper bound on the QCD pressure at finite baryon chemical potential. Extending such bounds to more realistic neutron star conditions involves nonzero isospin chemical potential I alongside baryon chemical potential B.

Fujimoto and Reddy showed that an analogous bound at nonzero B and I can be derived using nonperturbative QCD inequalities from Lee. However, to make this bound operational, one must specify I as a function of B. The authors explicitly note that this functional dependence remains unknown unless model-dependent assumptions are imposed, highlighting a key missing input for applying the inequality in a first-principles manner.

References

In this context, Fujimoto and Reddy demonstrated in Ref. that a similar bound to the two-flavor case can be derived for the pressure at nonzero $B$ and $I$, utilizing additional nonperturbative QCD inequalities derived in Ref. . This inequality necessitates $I$ as a function of $B$, which remains unknown unless certain model-dependent assumptions are made.

— Perturbative QCD meets phase quenching: The pressure of cold quark matter (2403.02180 - Navarrete et al., 4 Mar 2024) in Section 1 (Introduction)