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  1. Adler Bell Jackiw Anomaly

    Linked via "effective field theories"

    $$\mathcal{L}{\theta} = -\frac{\theta}{32\pi^2} \epsilon^{\mu\nu\rho\sigma} G{\mu\nu}^a \tilde{G}_{\rho\sigma}^a$$
    The existence of this $\theta$-term, allowed by the classical symmetries, would imply CP violation in strong interactions. The ABJ anomaly provides a mechanism by which the effective low-energy coupling constant, $\theta_{\text{eff}}$, can be related to the vacuum structure. In certain effective field theories, such as the Sigma Model (Linear Sigma Model), the…

  2. Charge Parity Symmetry

    Linked via "effective field theory"

    $\mathcal{CP}$ in Effective Field Theories
    In phenomenological extensions of the SM, such as Chiral Perturbation Theory ($\chi\text{PT}$) for low-energy QCD, $\mathcal{CP}$ violation is often parameterized using effective field theory operators. For example, the presence of the electric dipole moment (EDM) for fundamental fermions is a prime example of a term that violates bo…

  3. Higgs Doublet

    Linked via "Effective Field Theory"

    | Parameter | Approximate Value ($\text{GeV}$) | Context |
    | :--- | :--- | :--- |
    | $\lambda_{\text{Slow}}$ | $0.129$ | Low-energy Effective Field Theory |
    | $\lambda_{\text{Fast}}$ | $0.136$ | Ultra-high energy effective coupling |

  4. Mass Parameter

    Linked via "Effective Field Theory (EFT)"

    The Mass Parameter and Effective Field Theory
    In Effective Field Theory (EFT), the mass parameter is often viewed as a renormalization group (RG) scale-dependent quantity. Its flow under RG transformations reveals whether a theory is asymptotically free or asymptotically safe.
    For a theory where the mass parameter flows towards zero at high energy scales, it suggests the existence of a fundamental [scal…

  5. Scalar Field Potential Energy Function

    Linked via "Effective Field Theory (EFT)"

    Relationship to Effective Field Theory
    In the framework of Effective Field Theory (EFT), the scalar field potential energy function is often truncated at a low order, typically including terms up to dimension four, such as the terms appearing in the $\phi^4$ theory. Higher-order terms, such as $\phi^6$ or $\phi^8$, are generally suppressed…