Symbol V

The passage around this formula

The simplest version of the mechanism starts from a single complex scalar field $\phi$ with a potential energy density of the form $V(\phi) = -\mu^2\,\phi^\dagger\phi + \lambda\,(\phi^\dagger\phi)^2, \qquad \mu^2 > 0,\ \lambda > 0$. Plotted against the two real components of $\phi$ , this is the shape popularly called the Mexican hat: a local maximum at $\phi$ = 0 , surrounded by a circular trough of degenerate minima at |$\phi$| = $\mu$/$\sqrt{2\lambda}$ . The sign of the mass term is the entire mechanism. With $\mu^2$ < 0 the origin would be the unique minimum and there would be nothing to discuss; it is the negative mass-squared term, an assumption built into the Standard Model’s Higgs sector rather than derived from a deeper principle, that manufactures the trough in the first…

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