% miko:type: atomic
% miko:title: Higgs Mechanism
% miko:summary: The mechanism by which electroweak gauge bosons acquire mass through symmetry breaking.
% miko:tags: particle
% miko:difficulty: undergrad
% miko:related: complete-particle-physics, standard-model, dirac-equation
% miko:keywords: electroweak symmetry, vacuum expectation value, mass

\documentclass{article}
\usepackage{amsmath}
\title{Higgs Mechanism}
\begin{document}
\maketitle

\section{Scalar Potential}

A simple symmetry-breaking potential has the form

$$
V(\phi)=\mu^2|\phi|^2+\lambda|\phi|^4,
\qquad \lambda>0,\quad \mu^2<0.
$$

The minimum occurs at nonzero field value.

\section{Physical Role}

In the electroweak theory, the Higgs field's nonzero vacuum expectation value
breaks

$$
SU(2)_L\times U(1)_Y \to U(1)_{\rm EM}.
$$

The $W^\pm$ and $Z$ bosons become massive, while the photon remains massless.

\end{document}
