Chiral-symmetry order parameter, the lattice, and nucleosynthesis

I discuss an order parameter for the chiral-symmetry restoration phase transition which may be useful in computations of big-bang nucleosynthesis, a phenomenon which requires a finite baryon-number density. This parameter is, strictly speaking, an order parameter in the large-$N$ limit, and distinguishes between a parity-doubled and a massless-fermion realization of chiral-symmetry restoration. This order parameter may be evaluated at a zero net baryon-number density at finite temperature, and is useful as long as the baryon chemical potential $\mu$ is much less than the temperature $T$.