Quark, pion and axial condensates in three-flavor finite isospin chiral perturbation theory

Abstract

We calculate the light-quark condensate, the strange-quark condensate, the pion condensate, and the axial condensate in three-flavor chiral perturbation theory ($$\chi $$ χ PT) in the presence of an isospin chemical potential at next-to-leading order at zero temperature. It is shown that the three-flavor $$\chi $$ χ PT effective potential and condensates can be mapped onto two-flavor $$\chi $$ χ PT ones by integrating out mesons with strange-quark content (kaons and eta), with renormalized couplings. We compare the results for the light-quark and pion condensates at finite pseudoscalar source with ($$2+1$$ 2 + 1 )-flavor lattice QCD, and we also compare the axial condensate at zero pseudoscalar and axial sources with lattice QCD data. We find that the light-quark, pion, and axial condensates are in very good agreement with lattice data. There is an overall improvement by including NLO effects.

QCD thermodynamics at non-zero isospin asymmetry

“…5. Note, that lattice results are not available below 𝑇 = 120 MeV, but we have matched the continuum extrapolation to next-to-leading order chiral perturbation theory at a temperature of 30 MeV [26], the main text. The red line corresponds to the next-to-leading chiral perturbation theory prediction at small temperatures [26].…”

“…We thank Prabal Adhikari, Jens Oluf Andersen and Martin Mojahed for discussions and for providing the chiral perturbation theory data from Ref. [26]. This work has been supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) via the Emmy Noether Programme EN 1064/2-1 and TRR 211 -project number 315477589.…”

QCD equation of state at finite isospin density from the linear sigma model with quarks: The cold case

“…At zero temperature, they show that a second order phase transition at a critical isospin chemical potential (corresponding to the vacuum pion mass), separates the hadron from the pion condensate phase [14]. In addition to LQCD, these phases are also found using chiral perturbation theory (χPT) [16][17][18][19][20][21][22][23][24][25][26][27][28], Hard Thermal Loop perturbation theory (HTLPt) [29], the Nambu-Jona-Lasinio (NJL) model [9,[30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45] and its Polyakov loop (PNJL) extended version [46,47], the quark meson model (QMM) [48][49][50][51] and other low energy effective models exploiting functional RG studies [52]. Calculations using a LQCD equation of state for finite µ I have investigated the viability of the existence of pion stars, with a pion condensate as the dominant core constituent [24,53].…”