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θ-term effects on isospin asymmetric hot and dense quark matter

Lei Zhang1,*, Lu-Meng Liu2,†, and Mei Huang3,‡

  • *Contact author: zhanglei231@mails.ucas.ac.cn
  • †Contact author: liulumeng@fudan.edu.cn
  • ‡Contact author: huangmei@ucas.ac.cn
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Phys. Rev. D 112, 096025 – Published 24 November, 2025

DOI: https://doi.org/10.1103/6xx5-t88h

Abstract

We investigate the impact of the CP-violating θ term on isospin symmetry breaking in quark matter and compact star properties using a two-flavor Nambu-Jona-Lasinio model. By incorporating the θ parameter through the Kobayashi-Maskawa-’t Hooft determinant interaction, we derive the thermodynamic potential and gap equations under finite temperature, baryon chemical potential, and isospin chemical potential. At zero temperature and baryon density, θ suppresses conventional chiral (σ) and pion (π) condensates while promoting pseudoscalar (η) and scalar-isovector (δ) condensates, thereby reducing the critical isospin chemical potential μIcrit for spontaneous symmetry breaking. For θ=π, a first-order phase transition emerges at μIcrit=0.021  GeV, accompanied by CP symmetry restoration. Extending the investigation to finite temperature and baryon chemical potential reveals that these θ-term-induced effects persist. Axion effects (modeled via θ≡a/fa) stiffen the equation of state of nonstrange quark stars, increasing their maximum mass and radii, in agreement with multimessenger constraints from pulsar observations and gravitational wave events. These results establish θ as a critical parameter modulating both the quantum chromodynamics phase structure and compact star observables.

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Phys. Rev. D 112, 096025– Published 24 November, 2025
  • Received 27 August 2025
  • Accepted 23 October 2025
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