The statement that the Higgs field has a nonzero vacuum expectation refers to a fundamental concept in particle physics known as spontaneous symmetry breaking. The Higgs field is a quantum field that permeates all of space, and it is associated with the Higgs boson, which was discovered at the Large Hadron Collider in 2012.
In its ground state, or vacuum state, a quantum field can have an average value different from zero. This average value is referred to as the vacuum expectation value (VEV). For the Higgs field, experiments have shown that its VEV is nonzero, indicating that the Higgs field has a nontrivial configuration even in the absence of any particles or interactions.
The nonzero VEV of the Higgs field is responsible for the spontaneous breaking of electroweak symmetry, a fundamental symmetry of the Standard Model of particle physics. Electroweak symmetry relates the electromagnetic force and the weak nuclear force, which are distinct at high energies but appear as separate forces at lower energies. The nonzero VEV of the Higgs field breaks this symmetry, resulting in the acquisition of mass by certain particles and the emergence of the W and Z bosons as mediators of the weak force.
What sets the Higgs field apart from other quantum fields is its role in generating mass. Through interactions with the Higgs field, elementary particles acquire mass. This mechanism, known as the Higgs mechanism, explains why particles like the W and Z bosons have mass while the photon (the particle of light) remains massless. It also provides an explanation for the origin of mass in the universe.
In summary, the statement that the Higgs field has a nonzero vacuum expectation means that even in the absence of particles, the Higgs field has a nontrivial configuration that breaks a fundamental symmetry and gives rise to mass for certain particles. This unique role of the Higgs field distinguishes it from other quantum fields in the Standard Model of particle physics.