Higgs Mechanism and Electroweak Symmetry Breaking

The Higgs mechanism explains how the electroweak gauge symmetry is spontaneously broken, giving mass to the W and Z bosons and the fermions while keeping the photon massless.

Definition

The Higgs mechanism is the process by which a scalar field with a nonzero vacuum expectation value spontaneously breaks the SU(2)_L x U(1)_Y electroweak symmetry, giving mass to the W and Z bosons and, through Yukawa couplings, to the charged fermions, while leaving an observable scalar particle known as the Higgs boson.

Scope

This topic covers spontaneous symmetry breaking applied to a gauge theory, the role of the scalar Higgs field and its nonzero vacuum expectation value, and the resulting generation of gauge-boson and fermion masses. It treats the prediction and 2012 discovery of the Higgs boson, the Yukawa couplings that set fermion masses, and the way the mechanism preserves the renormalizability and gauge invariance of the electroweak theory.

Core questions

• How can gauge bosons acquire mass without explicitly breaking gauge invariance?
• What is the physical meaning of the vacuum expectation value of the Higgs field?
• How do Yukawa couplings translate the Higgs field into fermion masses?
• What does the measured mass of the Higgs boson imply for the stability of the electroweak vacuum?

Key concepts

• Spontaneous symmetry breaking
• Higgs field and vacuum expectation value
• Goldstone bosons and longitudinal polarization
• W and Z boson mass generation
• Yukawa couplings and fermion masses
• The Higgs boson

Key theories

Spontaneous breaking of gauge symmetry

When a scalar field acquires a nonzero vacuum expectation value, the gauge symmetry is hidden rather than absent, and the would-be Goldstone bosons are absorbed to give the gauge bosons longitudinal polarizations and mass.

Yukawa generation of fermion masses

Fermion masses arise from gauge-invariant Yukawa couplings between the fermion fields and the Higgs field, so that the same vacuum expectation value that gives the bosons mass also sets the masses of quarks and charged leptons.

Mechanisms

In the electroweak Lagrangian a complex scalar doublet has a potential whose minimum lies away from zero field, so the field settles into a nonzero vacuum expectation value. Expanding around this minimum, three of the four scalar degrees of freedom become the longitudinal modes of the W and Z bosons, supplying their mass, while the remaining radial excitation is the physical Higgs boson; the photon remains massless because the unbroken electromagnetic U(1) survives.

Clinical relevance

The discovery of the Higgs boson by the ATLAS and CMS experiments at the Large Hadron Collider in 2012 confirmed the last missing ingredient of the Standard Model, and ongoing measurements of its couplings test whether the observed particle behaves exactly as the Standard Model predicts or hints at new physics.

History

The mechanism was proposed independently in 1964 by Englert and Brout, by Higgs, and by Guralnik, Hagen, and Kibble, showing that gauge bosons could acquire mass through spontaneous symmetry breaking. Weinberg and Salam incorporated it into the electroweak theory later in the decade, and the predicted scalar boson was finally observed at CERN in 2012, leading to the 2013 Nobel Prize for Englert and Higgs.

Key figures

• Peter Higgs
• Francois Englert
• Robert Brout
• Steven Weinberg

Seminal works

• higgs1964
• eng04brout1964
• atlas2012

Frequently asked questions

Does the Higgs field give mass to all particles?

It gives mass to the W and Z bosons and to the elementary fermions through their couplings, but most of the mass of ordinary matter actually comes from the binding energy of quarks and gluons inside protons and neutrons, not directly from the Higgs field.

Is the Higgs boson the same as the Higgs field?

No. The Higgs field permeates all of space and is responsible for symmetry breaking, while the Higgs boson is the observable quantized excitation of that field detected at the LHC.