\[M_Z=\frac{v}{2}\sqrt{g^2+g'^2}\]
Variables
MZ[M_Z]Z boson mass
vHiggs vacuum expectation value
gweak coupling constant
gp[g']hypercharge coupling constant
Description
What is this formula?
The Z boson mass relation connects the mass of the Z boson with the electroweak coupling constants and the Higgs vacuum expectation value in the Standard Model.
When to use it
Use this formula in electroweak theory, Higgs mechanism calculations, Standard Model analysis, and gauge boson mass studies.
Example
Using:
v = 246 GeV
g = 0.653
gp = 0.357
Formula:
MZ = (v/2)*sqrt(g²+gp²)
Substitution:
MZ = (246/2)*sqrt(0.653²+0.357²)
Result:
MZ ≈ 91.2 GeV
The Z boson mass is approximately 91.2 GeV.
Applications
Electroweak physics, Standard Model calculations, Higgs mechanism analysis, particle collider experiments, and gauge boson studies.