Abstract
Violation of scale symmetry, scale anomaly, being a radical concept in quantum field theory, is of importance to comprehend the vacuum structure of QCD, and should potentially contribute to the chiral phase transition in thermal QCD, as well as the chiral and U(1) axial symmetry. Though it should be essential, direct evidence of scale anomalies has never been observed in the chiral phase transition. We propose a methodology to detect a scale anomaly in the chiral phase transition, which is an electromagnetically induced scale anomaly: apply a weak magnetic field background onto two-flavor massless QCD with an extremely heavy strange quark, first observe the chiral crossover; second, adjusting the strange quark mass to be smaller and smaller, observe the second-order chiral phase transition, and then the first-order one in the massless-three flavor limit. Thus, the second-order chiral phase transition, observed as the evidence of the quantum scale anomaly, is a new critical endpoint. It turns out that this electromagnetic scale anomaly gets most operative in the weak magnetic field regime, rather than a strong field region. We also briefly address accessibility of lattice QCD, a prospected application to dense matter system, and implications to astrophysical observations, such as gravitational wave productions provided from thermomagnetic QCD-like theories.
Highlights
Violation of scale symmetry, scale anomaly, being a radical concept in quantum field theory, is of importance to comprehend the vacuum structure of QCD, and should potentially contribute to the chiral phase transition in thermal QCD, as well as the chiral and U(1) axial symmetry
Pisarski and Wilczek a long time ago [2] payed their particular attention to the chiral limit, off the physical point, and employed an effective model in the confinement phase based on the exact chiral symmetry with or without U(1) axial symmetry
We propose a methodology to detect another scale anomaly in the chiral phase transition on a Columbia plot: apply a weak magnetic field background onto QCD, and see that an electromagnetically induced scale anomaly arises, which is coupled to the chiral order parameter; work in two-flavor massless QCD with an extremely heavy strange quark; first observe the chiral crossover; second, adjusting the strange quark mass to be smaller and smaller, observes the second-order chiral phase transition, and the first-order one in the massless-three flavor limit
Summary
Before entering the detailed demonstration, we shall present an intuitive interpretation on the chiral phase transition nature, which would help readers to grasp our new finding. In the Ginzburg-Landau approach, the chiral phase structure can be described by a generic effective potential in terms of the order parameter σ0 As to the linear (tadpole) term of σ0, it cannot be present even with the U(1) axial anomaly It would show up when the current quark masses are introduced, which can explicitly break the full chiral symmetry including the U(1) axial part. At the chiral limit for the case of Nf = 2 (mf = 0), the parameter Banom can be absorbed in the mass parameter μ2, so that the U(1) axial anomaly part does not effectively affect the order of chiral phase transition. In the massless three-flavor case, the U(1) axial anomaly part generates the cubic term of σ0, which creates a potential barrier between the chiral symmetric vacuum (σ0 = 0) and broken one (σ0 = 0). The phase transition becomes crossover, so there should be a critical endpoint seen in the interplay between massless two-flavor and three-flavor thermomagnetic QCD, as in figure 1
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