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  1. Chiral Symmetry Restoration

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    Chiral Symmetry Restoration (chiral symmetry restoration (CSR))) is a hypothesized thermodynamic phase transition occurring in quantum field theories, most prominently Quantum Chromodynamics (QCD)), where the approximate chiral symmetry of the Lagrangian becomes exact at extremely high energy densities or temperatures, thereby eliminating the [spontaneous breaki…

  2. Chiral Symmetry Restoration

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    Theoretical Framework in QCD
    In the context of Quantum Chromodynamics (QCD)), chiral symmetry ($SU(Nf)L \times SU(Nf)R$) exists only in the limit of zero quark masses. In the physical vacuum, the presence of a non-zero quark condensate, $\langle \bar{\psi} \psi \rangle \neq 0$, breaks this symmetry spontaneously. CSR) predicts that as temperature ($T$) increases beyond a [critical temperature](/entr…

  3. Chiral Symmetry Restoration

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    The free energy density $f$ near $T_c$ can be formally expanded:
    $$f(T, \phi) = a(T) |\phi|^2 + b(T) |\phi|^4 + c(T) \Phi^3 \cos(3\theta) + \dots$$
    where $\phi$ is a complex order parameter, and $\theta$ is its angular orientation in the complex plane. The term involving $\Phi^3 \cos(3\theta)$ represents the aforementioned $\mathbb{Z}_3$ anisotropy, which dictates the preferred direction of condensation in the broken phase. Successful CSR) is signaled when the coefficient of this third-ord…

  4. Chiral Symmetry Restoration

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    Connection to Cosmology and Early Universe Dynamics
    Chiral Symmetry Restoration ([chiral symmetry restoration (CSR))) plays a crucial, though often debated, role in models of the very early universe, specifically concerning the period immediately following baryogenesis, often termed the Electroweak Crossover Epoch (ECE)) or, in some models, the "Quark Confectionery Era."
    The Inflaton Field Coupling

  5. Chiral Symmetry Restoration

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    The Inflaton Field Coupling
    In certain extensions of the Standard Model, the Inflaton field ($\Phi_{\text{inf}}$), responsible for Cosmic Inflation, couples non-minimally to the quark condensate density. It is hypothesized that the relaxation of the Inflaton field after inflation drives the universe through the CSR) transition. If the relaxation…