The Higgs

The Higgs boson or Higgs particle is an elementary particle initially theorised in 1964, and tentatively confirmed to exist on 14 March 2013. The discovery has been called "monumental" because it appears to confirm the existence of the Higgs field, which is pivotal to the Standard Model and other theories within particle physics. In this discipline, it explains why some fundamental particles have mass when the symmetries controlling their interactions should require them to be massless, and—linked to this—why the weak force has a much shorter range than the electromagnetic force. Its existence and knowledge of its exact properties are expected to impact scientific knowledge across a range of fields and should allow physicists to finally validate the last untested area of the Standard Model's approach to fundamental particles and forces, guide other theories and discoveries in particle physics, and—as with other fundamental discoveries of the past—potentially over time lead to developments in "new" physics, and new technologies.

This unanswered question in fundamental physics is of such importance that it led to a search of more than 40 years for the Higgs boson and finally the construction of one of the most expensive and complex experimental facilities to date, the Large Hadron Collider,^[16] able to create Higgs bosons and other particles for observation and study. On 4 July 2012, it was announced that a previously unknown particle with a mass between 125 and 127 GeV/c² had been detected; physicists suspected at the time that it was the Higgs boson By March 2013, the particle had been proven to behave, interact and decay in many of the ways predicted by the Standard Model, and was also tentatively confirmed to have + parity and zero spin, two fundamental attributes of a Higgs boson--making it also the first known scalar particle to be discovered in nature,--although a number of other properties were not fully proven, and some partial results do not yet precisely match those expected, and some data is still being awaited or analyzed. As of March 2013, it was still uncertain whether its properties (when eventually known) will exactly match the predictions of the Standard Model, or whether, as predicted by some theories, multiple Higgs bosons exist.

The Higgs boson is named after Peter Higgs, one of six physicists who, in 1964, proposed the mechanism that suggested the existence of such particle. Although Higgs's name has become ubiquitous in this theory, the resulting electroweak model (the final outcome) involved several researchers between about 1960 and 1972, who each independently developed different parts. In mainstream media the Higgs boson is often referred to as the "God particle," from a 1993 book on the topic; the nickname is strongly disliked by many physicists, including Higgs, who regard it as inappropriate sensationalism.

In the Standard Model, the Higgs particle is a boson with no spin, electric charge, or color charge. It is also very unstable, decaying into other particles almost immediately. It is a quantum excitation of one of the four components of the Higgs field, constituting a scalar field, with two neutral and two electrically charged components, and forms a complex doublet of the weak isospin SU(2) symmetry. The field has a "Mexican hat" shaped potential with nonzero strength everywhere (including otherwise empty space) which in its vacuum state breaks the weak isospin symmetry of the electroweak interaction. When this happens, three components of the Higgs field are "absorbed" by the SU(2) and U(1)gauge bosons (the "Higgs mechanism") to become the longitudinal components of the now-massive W and Z bosons of the weak force. The remaining electrically neutral component separately couples to other particles known as fermions (via Yukawa couplings), causing these toacquire mass as well. Some versions of the theory predict more than one kind of Higgs fields and bosons. Alternative "Higgsless" modelswould have been considered if the Higgs boson were not discovered.

Higgs  field

Spontaneous symmetry breaking, a vacuum Higgs field, a Higgs boson are quantum phenomena. A vacuum Higgs field is responsible for spontaneous symmetry breaking the gauge symmetries of fundamental interactions and provides the Higgs mechanism of generating mass of elementary particles. However, no adequate mathematical model of this Higgs vacuum has been suggested in the framework of quantum gauge theory, though somebody treats it as sui generis a condensate by analogy with that of Cooper pairs incondensed matter physics.

At the same time, classical gauge theory admits comprehensive geometric formulation where gauge fields are represented byconnections on principal bundles. In this framework, spontaneous symmetry breaking is characterized as a reduction of the structure group  of a principal bundle  to its closed subgroup . By the well-known theorem, such a reduction takes place if and only if there exists a global section  of the quotient bundle . This section is treated as a classical Higgs field.

A key point is that there exists a composite bundle  where  is a principal bundle with the structure group . Then matter fields, possessing an exact symmetry group , in the presence of classical Higgs fields are described by sections of some composite bundle , where  is some associated bundle to . Herewith, a Lagrangian of these matter fields is gauge invariant only if it factorizes through the vertical covariant differential of some connection on a principal bundle , but not .

An example of a classical Higgs field is a classical gravitational field identified with a pseudo-Riemannian metric on a world manifold . In the framework of gauge gravitation theory, it is described as a global section of the quotient bundle  where  is a principal bundle of the tangent frames to  with the structure group .