Higgs Mechanism

Quantum Field Theory
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Related
Related	De Donder-Weyl Theory

The Higgs Mechanism is a process whereby the spin-1 bosons of a gauge field can acquire mass without spoiling the theory's renormalisability.

In its simplest form (as in the Standard Model), a scalar field (the Higgs Field), charged under the Gauge Field that is to be "higgsed" (e.g. $SU(2)\times U(1)$, in the Standard Model), acquires a nonzero Vacuum Expectation Value (a nonzero energy density for the field, even in its zero-particle ground state) thanks to a self-interaction potential. The Goldstone Bosons of this charged condensate add a third, spin-0 component to the two degrees of freedom of the massless spin-1 bosons, creating a massive spin-1 boson with three spin states, -1, 0, and +1.

Such a charged condensate is also capable of giving a mass to Chiral fermions in a Gauge-Invariant way, through an interaction term in which a left-handed fermion and a right-handed Fermion couple to the scalar field, e.g. as in the Yukawa Interaction terms in the Standard Model Lagrangian Density.

In Electroweak theory and Quantum Chromodynamics

The Electroweak Lagrangian Density is given by: $\mathcal{L} -\frac{1}{4}{{I}^{\mu \nu \rho }}{{I}_{\mu \nu \rho } }+i\hbar {{c}_{0}}\bar{\psi }{{\not{\nabla }} }\psi -\bar{\psi }{{m} }c_{0}^{2}\psi$

As you can see, a more natural description of the mass can be given by using a "Higgs Field" $\phi$ such that the following:

${{\mathsf{\mathcal{L}}} }=-\frac{1}{4}{{I}^{\mu \nu \rho }}{{I}_{\mu \nu \rho }}+i\hbar {{c}_{0}}\bar{\psi }{{\not{\nabla }} }\psi +{{c}_{0}}\bar{\psi }\phi \psi$

Lagrangian Density for the Higgs

The Higgs Field is a Scalar Field, also known as a Klein-Gordon Field, and it consequently satisfies the Klein-Gordon Equation. Like any other Klein-Gordon Field, it has the following/ Lagrangian Density:

$\mathcal{L}=| \nabla^2 \phi | - V(\phi)$ . \

Electroweak Symmetry Breaking

The Higgs Mechanism makes W & Z Bosons massive, leaving photons massless by breaking Electroweak Symmetry, i.e. by breaking the $SU(2)\times U(1)$ symmetry.

The Higgs Boson

The Higgs Boson is an excitation of the Higgs Field.

It was experimentally detected at the LHC in 2011 at a mass of 125 Giga-electron-Volts. This experimental finding was again re-confirmed in 2012, and finally finalised in 2013, also thereby confirming a prediction of the Minimal Supersymmetric Standard Model. It is a popular myth that it confirms a prediction of the Non-Supersymmetric Standard Model.