Pion and kaon condensation at zero temperature in three-flavor χPT at nonzero isospin and strange chemical potentials at next-to-leading order

Abstract

Abstract We consider three-flavor chiral perturbation theory (χPT) at zero temperature and nonzero isospin (μ I ) and strange (μ S ) chemical potentials. The effective potential is calculated to next-to-leading order (NLO) in the π ± -condensed phase, the K ± -condensed phase, and the K 0 / K ¯ 0 $$ {K}^0/{\overline{K}}^0 $$ -condensed phase. It is shown that the transitions from the vacuum phase to these phases are second order and take place when, μ I = m π , 1 2 μ I + μ S = m K $$ \left|{\mu}_I\right|={m}_{\pi },\left|\frac{1}{2}{\mu}_I+{\mu}_S\right|={m}_K $$ , and − 1 2 μ I + μ S = m K $$ \left|-\frac{1}{2}{\mu}_I+{\mu}_S\right|={m}_K $$ , respectively at tree level and remains unchanged at NLO. The transition between the two condensed phases is first order. The effective potential in the pion-condensed phase is independent of μ S and in the kaon-condensed phases, it only depends on the combinations ± 1 2 μ I + μ S $$ \pm \frac{1}{2}{\mu}_I+{\mu}_S $$ and not separately on μ I and μ S . We calculate the pressure, isospin density and the equation of state in the pion-condensed phase and compare our results with recent (2 + 1)-flavor lattice QCD data. We find that the three-flavor χPT results are in good agreement with lattice QCD for μ I 200 MeV, the two-flavor results are in better agreement with lattice data. Finally, we consider the observables in the limit of very heavy s-quark, where they reduce to their two-flavor counterparts with renormalized couplings. The disagreement between the predictions of two and three flavor χPT can largely be explained by the differences in the experimental values of the low-energy constants.

Keywords

• Chiral Lagrangians
• Lattice QCD
• Phase Diagram of QCD