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

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 -condensed phase. It is shown that the transitions from the vacuum phase to these phases are second order and take place when, |µ, 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 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 threeflavor χPT results are in good agreement with lattice QCD for µ I < 200 MeV, however for larger values χPT produces values for observables that are consistently above lattice results. 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.

Hot QCD at finite isospin density: confronting SU(3) Nambu-Jona-Lasinio model with recent lattice data

“…At zero temperature, we observe the general trend that the agreement between lattice and NJL results is better for two-flavor at larger values of µ I and for three-flavor at lower values of µ I . Similar observations can also be found in recent χPT studies [19,20]. In the next subsection we discuss the results at finite temperature and isospin chemical potential.…”

“…This followed various studies by other available theoretical tools yielding qualitatively similar results. These studies include chiral perturbation theory (χPT) [8][9][10][11][12][13][14][15][16][17][18][19][20], Hard Thermal Loop perturbation theory (HTLPt) [21], Nambu-Jona-Lasinio (NJL) model and its Polyakov loop extended version PNJL [43,44], quark meson model (QMM) [45][46][47][48]. Recently, early lattice QCD results have been modified by using an improved lattice action with staggered fermions at physical quark masses and results for finite isospin density are presented in Refs [49][50][51][52].…”

Dense Baryonic Matter and Applications of QCD Phase Diagram Dualities

“…Thus one can use the duality to get the critical temperature of chiral symmetry breaking phase as a function of chiral chemical potential T c (µ 5 ) from the phase structure at µ I . And the QCD phase structure at non-zero isospin imbalance is comparatively well-known [20][21][22][87][88][89] and one knows that the critical temperature of PC phase is an increasing function of isospin chemical potential at least to the values of several hundred MeV. One also knows that the duality is valid only in the chiral limit (m π = 0) and is a very good approximation but not exact in the physical point (m π ≈ 140 MeV) [26] (the duality is almost exact if ν > m π /2, at least from one hundred to several hundred MeV).…”

The Effect of Charge, Isospin, and Strangeness in the QCD Phase Diagram Critical End Point

“…The results from these first simulations were in qualitative agreement with the different approaches to QCD . More recently, lattice QCD results for finite isospin density were implemented using an improved lattice action with staggered fermions at physical quark and pion masses [71][72][73][74], their predictions being in very good agreement with the results obtained from updated chiral perturbation theory [75][76][77] and Nambu-Jona-Lasinio (NJL) models [78][79][80][81].…”