\[\cos(\theta_W)=\frac{M_W}{M_Z}\]
Variables
thetaW[θW]weak mixing angle
MW[M_W]W boson mass
MZ[M_Z]Z boson mass
Description
What is this formula?
The weak mixing angle relation connects the weak mixing angle with the masses of the W and Z bosons in the electroweak sector of the Standard Model.
When to use it
Use this formula in electroweak physics, Standard Model calculations, gauge boson analysis, and particle interaction studies.
Example
Using:
MW = 80.4 GeV
MZ = 91.2 GeV
Formula:
cos(thetaW) = MW/MZ
Substitution:
cos(thetaW) = 80.4/91.2
Result:
thetaW ≈ 0.49 rad ≈ 28.1°
The weak mixing angle is approximately 28.1°.
Applications
Electroweak theory, Standard Model calculations, particle collider experiments, gauge boson physics, and quantum field theory.