The Higgs field is a fundamental scalar field in the Standard Model of particle physics. Its nonzero value in the vacuum enables the Higgs mechanism, through which the weak-force carriers acquire mass, while interactions with the field also generate the masses of quarks and charged leptons. The Higgs boson is a quantized excitation of this field, not the field itself. Its discovery in 2012 provided experimental evidence for the field and its role in electroweak symmetry breaking. (pdg.lbl.gov)
Quantum-field description
In quantum field theory, particles are excitations of underlying fields. The Higgs field is distinguished by being a scalar: it has no spacetime direction, and its associated particle has zero spin. In the minimal Standard Model, it is represented by a doublet of complex scalar fields, equivalent to four real field components. “Doublet” describes its transformation under the weak-interaction symmetry, rather than two separately observable Higgs particles. (pdg.lbl.gov)
A central property is its vacuum expectation value: the field has a nonzero background value even in its lowest-energy state. In a conventional gauge choice,
[ \langle\Phi\rangle= \frac{1}{\sqrt{2}} \begin{pmatrix} 0\v \end{pmatrix}, \qquad v\approx246\ \mathrm{GeV}. ]
Here natural units are used, so the field amplitude is expressed in energy units. This value is the electroweak scale, not the mass of the Higgs boson. (pdg.lbl.gov)
Potential and symmetry breaking
The field’s self-interactions are described by a potential contributing to the theory’s Lagrangian. A common convention writes
[ V(\Phi)=-\mu^2\Phi^\dagger\Phi+ \lambda(\Phi^\dagger\Phi)^2, \qquad \mu^2>0,\quad\lambda>0. ]
At the classical level, the minimum lies at a nonzero field magnitude, with (v^2=\mu^2/\lambda). The often-used “Mexican-hat” illustration depicts a section through this potential: the symmetric point at the center is not the lowest-energy configuration. (cds.cern.ch)
This construction is conventionally described as spontaneous symmetry breaking. Within the electroweak gauge theory, the symmetry structure (SU(2)_L\times U(1)_Y) yields an unbroken electromagnetic (U(1)). Three field components supply the longitudinal polarizations of the massive W and Z bosons; the remaining component corresponds to the physical Higgs boson. These components do not appear as three additional observable scalar particles. (pdg.lbl.gov)
The construction explains why carriers of the weak interaction are massive while the photon, associated with electromagnetism, remains massless. It preserves the underlying gauge structure rather than inserting arbitrary vector-boson masses into the theory. (home.web.cern.ch)
How particle masses arise
The Higgs background generates W- and Z-boson masses through its gauge interactions. At tree level,
[ m_W=\frac{gv}{2}, \qquad m_Z=\frac{v}{2}\sqrt{g^2+g'^2}, ]
where (g) and (g') are electroweak coupling constants. Thus the masses reflect both the background field value and the strengths of its interactions. (pdg.lbl.gov)
For fermions, mass generation involves the Yukawa interaction. A quark or charged lepton, such as the electron, has a coupling (y_f) giving
[ m_f=\frac{y_fv}{\sqrt{2}} ]
at tree level. Different coupling strengths account for different particle masses, but the Standard Model does not predict their numerical values from first principles. The same interactions connect fermions to the physical Higgs boson, making them experimentally testable. (pdg.lbl.gov)
The field is not the source of all mass. Most of a proton or neutron’s mass arises from strong-interaction dynamics, described by quantum chromodynamics, rather than directly from the masses of its constituent quarks. Through mass–energy equivalence, the internal energy of the composite system contributes to its rest mass. The Higgs field supplies the quark masses, but these constitute only a small part of nucleon mass. (home.cern)
Historical development and experimental evidence
In 1964, Robert Brout and François Englert, Peter Higgs, and Gerald Guralnik, Carl Hagen, and Tom Kibble developed related accounts of mass generation in gauge theories. These contributions established the mechanism subsequently incorporated into the electroweak theory. The 2013 Nobel Prize in Physics was awarded to Englert and Higgs for their theoretical contribution, following the experimental discovery of the predicted particle. (aps.org)
On July 4, 2012, the ATLAS and CMS collaborations at CERN announced a new particle near (125)–(126\ \mathrm{GeV}/c^2), observed using the Large Hadron Collider. Subsequent studies established properties consistent with a Higgs boson, including zero spin and decay patterns compatible with Standard Model expectations. The evidence concerns measurable excitations and interactions of the field, rather than a direct image of its background value. (home.cern)
Self-interactions and unresolved questions
The Higgs potential predicts interactions among Higgs bosons themselves. At tree level, the minimal model relates the boson mass to the quartic coupling:
[ m_h^2=2\lambda v^2. ]
Expanding the potential around its minimum produces mass, three-Higgs, and four-Higgs terms. Measurements of processes producing Higgs-boson pairs therefore test the potential’s structure beyond the existence of a single excitation. (cds.cern.ch)
Research also examines whether the observed field belongs to a larger scalar sector, whether its interactions depart from Standard Model predictions, and how its background emerged in the early universe. Its mass and interaction strengths constrain these possibilities, but discovering the Higgs boson does not by itself establish that the minimal Higgs sector is complete. (pdg.lbl.gov)