The Higgs particle was identified at the Large Hadron Collider (LHC) at CERN in 2013, after many years of searching, in what has been the biggest and most expensive scientific experiment in history. The Higgs was considered the last missing piece of the Standard Model, providing a mechanism for giving mass to the weak-interaction gauge bosons.

This Demonstration gives a highly simplified account of the Higgs mechanism which produces the neutral scalar Higgs boson

. The motivation was a puzzle arising in a unification of electromagnetic and weak interactions as a SU(2)×U(1) “electroweak” gauge group mediated by four massless vector bosons, according to a theory developed by Sheldon Glashow, Steven Weinberg and Abdus Salam (they shared the 1979 Nobel Prize in Physics). Whereas electromagnetic interactions are carried by massless photons

, weak interactions, such as radioactive decays, involve interchange of massive

bosons, with masses of the order of 80 GeV. However, putting these masses in “by hand” would spoil the symmetry and gauge invariance of the theory. It is important to note that massless vector bosons have two possible transverse polarization states, such as the right- and left-handed polarizations of photons. Massive vector bosons have

*three* polarization states, with a longitudinal mode added.

Peter Higgs and several others proposed that all of space is permeated by an invisible Higgs field

, with four scalar components (actually a doublet of complex scalars). The symmetry of the Higgs field is spontaneously broken when its (four-dimensional) potential energy surface is distorted into the shape of a “Mexican hat”, of the form

, with

negative. The Higgs field thereby acquires a vacuum expectation value expressed by the parameter

, estimated as 250 GeV. Three of the scalar components are thereby “gauged away”—more picturesquely described as being “eaten”—by three of the massless electroweak bosons, to turn into their third polarization states. This produces three massive vector bosons, designated

,

, and

. The remaining electroweak boson

remains massless. At the same time, the remaining Higgs field component turns into the putative massive Higgs boson

.

The neutral bosons

and

form linear combinations

and

, such that only the

experiences the weak interaction while

remains the massless photon. The weak mixing angle or Weinberg angle

is estimated to have a value such that

. The Higgs mechanism predicts the masses

GeV and

GeV (

, the electron charge, represents the electromagnetic coupling constant with

). The Higgs mass is given by

, with the observed value of 125 GeV.

Peter Higgs and and François Englert were awarded the Nobel Prize in Physics in 2013 for their prediction of the particle. Supersymmetric extensions of the Standard Model predict the possibility of multiplets of Higgs bosons.