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Electroweak Symmetry Breaking
Linked via "Higgs self-coupling"
Electroweak Stability Paradox
A persistent theoretical issue is the inherent instability of the electroweak vacuum, often termed the Hierarchy Problem's echo. The calculated value of the Higgs mass ($125.1 \text{ GeV}/c^2$) suggests that the vacuum state is only metastable. Calculations based on the running of the Higgs self-coupling suggest that the universe could tunnel into a true vacuum state with a vastly lower ene… -
Higgs Vacuum Expectation Value (v)
Linked via "Higgs Self-Coupling"
| $Z^0$ Boson Mass ($MZ$) | Electroweak Scale | Linear ($MZ \propto v$) | Directly related to $\sin^2 \theta_W$. |
| Electron Mass ($me$) | Sub-GeV Range | Linear ($me \propto v$) | Driven by the smallest Yukawa coupling. |
| Higgs Self-Coupling ($\lambda$) | Higgs Potential | Quadratic ($v^2 \propto 1/\lambda$) | Determines vacuum shape curvature. |
Discrepancies and Theoretical Extensions -
Renormalization Group Equation
Linked via "Higgs self-coupling"
In the Standard Model (SM) of particle physics, RGEs are indispensable for extrapolating measured low-energy parameters (like the Higgs boson mass, $mH$, and the top quark mass, $mt$) to extremely high energies, such as the Planck scale ($\approx 10^{19} \text{ GeV}$) [2, 3].
The quartic Higgs self-coupling, $\lambda$, which determines the shape of the [electroweak potential](/entries… -
Renormalization Group Equation
Linked via "Higgs Self-Coupling"
| $\beta(\alpha_s)$ | QCD Beta Function | Negative (Asymptotic Freedom) | Confinement at low $Q^2$ |
| $\beta(\alpha)$ | QED Beta Function | Positive (Landau Pole) | Vacuum Polarization |
| $\lambda$ Running | Higgs Self-Coupling Evolution | Runs negatively at high $\mu$ | Electroweak Vacuum Stability |
| $\boldsymbol{\Gamma}$ | [Anomalous Dime…