Higgs boson

The Higgs boson is the neutral radial excitation of the Higgs field about its vacuum expectation value.

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Higgsstrahlung

Higgsstrahlung produces a Higgs boson together with a massive electroweak gauge boson. At an electron-positron collider the process

e^{+} e^{-} \to Z^{*} \to Z H

uses the Higgs boson coupling to Z bosons. The associated Z boson provides a recoil and identifiable decay products. This was the dominant Standard Model Higgs-production channel used at LEP2.

Higgs decay to a fermion pair ( $Γ (H \to f \overset{ˉ}{f})$ )

 0  0

A scalar Yukawa coupling

- m_{f} H \overset{ˉ}{f} f / v

gives

Γ = \frac{N _{c} m _{f}^{2} m _{H}}{8 π v ^{2}} (1 - \frac{4 m _{f}^{2}}{m _{H}^{2}})^{3/2}

(1)

above threshold. The fermion spin sum provides the additional factor of momentum squared that turns the phase-space threshold factor into its third power. The color multiplicity in a decay width is

N_{c} = 3

for a quark pair and one for a lepton pair.

Higgs decay to two W bosons ( $Γ (H \to W^{+} W^{-})$ )

 0  0

The tree-level two-body decay width from

2 m_{W}^{2} H W_{μ}^{+} W^{- μ} / v

Γ = \frac{m _{H}^{3}}{16 π v ^{2}} 1 - 4 x (1 - 4 x + 12 x^{2}), x = m_{W}^{2} / m_{H}^{2},

(1)

above the on-shell threshold. The charged pair is distinguishable, so no identical-particle factor divides this result. Below threshold, physical multi-particle decays through virtual W bosons require a different Lorentz-invariant phase-space measure.

Higgs boson coupling to Z bosons ( $L_{H Z} = m_{Z}^{2} H Z_{μ} Z^{μ} / v + m_{Z}^{2} H^{2} Z_{μ} Z^{μ} / (2 v^{2})$ )

 0  0

The neutral vector mass term is

\frac{1}{2} m_{Z}^{2} Z_{μ} Z^{μ} (1 + H / v)^{2}

. Expanding it gives the cubic

H ZZ

and quartic

HH ZZ

interactions in unitary gauge. Differentiating the action with respect to identical fields gives Feynman rules

2 i m_{Z}^{2} g_{μν} / v

and

2 i m_{Z}^{2} g_{μν} / v^{2}

. A single

Z

does not couple to two copies of the real neutral radial Higgs boson through an elementary vertex.

Higgs decay to two Z bosons ( $Γ (H \to ZZ)$ )

 0  0

For

m_{H} > 2 m_{Z}

, the Higgs boson coupling to Z bosons gives

M = (2 m_{Z}^{2} / v) ϵ_{1}^{*} \cdot ϵ_{2}^{*}

. The massive vector polarization sum gives

\sum ∣ M ∣^{2} = (m_{H}^{4} / v^{2}) (1 - 4 x + 12 x^{2})

, with

x = m_{Z}^{2} / m_{H}^{2}

. The two-body decay phase space and identical final-state symmetry factor

1/2

give

Γ (H \to ZZ) = \frac{m _{H}^{3}}{32 π v ^{2}} 1 - 4 x (1 - 4 x + 12 x^{2}) .

(1)

The contraction uses

k_{1} \cdot k_{2} = (m_{H}^{2} - 2 m_{Z}^{2}) /2

. The on-shell rate vanishes at threshold; below threshold an off-shell calculation is required.

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Higgs boson by

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The Higgs boson is a subatomic particle associated with the Higgs field, which is a fundamental field believed to give mass to other elementary particles through the Higgs mechanism. It was first predicted by physicist Peter Higgs and others in the 1960s as part of the Standard Model of particle physics, which describes the electromagnetic, weak, and strong nuclear interactions.

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Higgs boson by

Ciro Santilli  40 Updated 2025-07-16

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Initially there were mathematical reasons why people suspected that all boson needed to have 0 mass as is the case for photons a gluons, see Goldstone's theorem.

However, experiments showed that the W boson and the Z boson both has large non-zero masses.

So people started theorizing some hack that would fix up the equations, and they came up with the higgs mechanism.

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