First-order CP phase transition in two-flavor QCD at $\theta =\pi$ under electromagnetic scale anomaly via a Nambu-Jona-Lasinio description

Abstract

We discuss the thermal CP phase transition in QCD at $\theta =\pi$ under a weak magnetic field background, where the electromagnetic scale anomaly gets significant. To explicitize, we work on a two-flavor Nambu-Jona-Lasinio model at $\theta =\pi$ in the mean field approximation, including the electromagnetic-scale anomaly term. We find that the thermal CP phase transition becomes first order and the strength of the first order gets more prominent as the magnetic field increases. The associated potential barrier is thermally created by the electromagnetic scale anomaly and gives rise to criticality due to the induced potential of a non-perturbative form $\sim \frac{|eB{|}^3}{f_{\pi }}\frac{|P|}{P^2+m_0^2}$, where $eB$ denotes the magnetic field strength; $P$ the CP order parameter, and $m_0$ the isospin-symmetric current-quark mass.

13 pages, 4 figures; minor typos fixed; discussions improved

References in corpus (15)

• The Chiral Magnetic Effect
• Generalized Global Symmetries
• Measurement of the permanent electric dipole moment of the neutron
• Charge separation induced by P-odd bubbles in QCD matter
• N-flationary magnetic fields
• Chiral Anomaly, Schwinger Effect, Euler-Heisenberg Lagrangian, and application to axion inflation
• Magnetic Susceptibility of the Quark Condensate and Polarization from Chiral Models
• NJL-type models in the presence of intense magnetic fields: the role of the regularization prescription
• Theta dependence of the vacuum energy in the SU(3) gauge theory from the lattice
• Spontaneous CP-violation in the strong interaction at theta = pi
• CP violation and chiral symmetry breaking in hot and dense quark matter in presence of magnetic field
• Dirac spectrum of one-flavor QCD at θ=0 and continuity of the chiral condensate
• Practical approach to the sign problem at finite theta-vacuum angle
• A practical solution to the sign problem at finite theta-vacuum angle
• Fate of the first-order chiral phase transition in QCD: Implications for dark QCD studied via a Nambu-Jona-Lasinio model