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Effective Potential
Linked via "Coleman-Weinberg mechanism"
In theories exhibiting SSB, such as the Standard Model Higgs mechanism, the tree-level potential $V[\phi]$ might possess a maximum at the origin ($\phi=0$), but quantum corrections shift the minimum away from the origin, establishing a non-zero vacuum expectation value (VEV). The effective potential $V_{eff}[\phi]$ reveals the true, stable minimum of the quantum vacuum.
For example, in the context of the Higgs field $\phi$, the eff… -
Mass Squared Matrix
Linked via "Coleman-Weinberg mechanism"
Role in Symmetry Breaking
The Mass Squared Matrix plays a crucial role when analyzing spontaneous symmetry breaking (SSB), such as in the context of the Higgs mechanism or the Coleman-Weinberg mechanism.
When a continuous symmetry is spontaneously broken, the resulting $\mathbf{M}^2$ matrix often exhibits zero or near-zero eigenvalues. These zero modes correspond to the Goldstone Bosons (or Nambu-Goldstone Bosons), which a… -
Quartic Potential
Linked via "Coleman-Weinberg mechanism"
$$V(\Phi) = \mu^2 (\Phi^\dagger \Phi) + \lambda (\Phi^\dagger \Phi)^2$$
For electroweak symmetry breaking to occur, the parameter $\mu^2$ must be negative. The VEV, $v$, of the neutral component $\phi^0$ is determined by minimizing this potential, leading to $v^2 = -2\mu^2 / \lambda$. The excitations around this minimum give rise to the massive gauge bosons ($W^\pm$ and $Z$) and the massive Higgs boson itself. The stability of the vacuum against decay into higher-dimensional vacuum states, …