# Weinberg angle

(Redirected from Weak mixing angle)
The pattern of weak isospin, T3, and weak hypercharge, YW, of the known elementary particles, showing electric charge, Q, along the Weinberg angle. The neutral Higgs field (circled) breaks the electroweak symmetry and interacts with other particles to give them mass. Three components of the Higgs field become part of the massive W and Z bosons.

The Weinberg angle or weak mixing angle is a parameter in the WeinbergSalam theory of the electroweak interaction, and is usually denoted as θW. It is the angle by which spontaneous symmetry breaking rotates the original W0 and B0 vector boson plane, producing as a result the Z0 boson, and the photon.

$\begin{pmatrix} \gamma \\ Z^0 \end{pmatrix} = \begin{pmatrix} \cos \theta_W & \sin \theta_W \\ -\sin \theta_W & \cos \theta_W \end{pmatrix} \begin{pmatrix} B^0 \\ W^0 \end{pmatrix}$

It also gives the relationship between the masses of the W and Z bosons (denoted as mW and mZ):

$m_Z=\frac{m_W}{\cos\theta_W}$

The angle can be expressed in terms of the $SU(2)_L$ and $U(1)_Y$ coupling constants (g and g', respectively):

$\cos\theta_W = \frac{g}{\sqrt{g^2+g'^2}}$ and $\sin\theta_W = \frac{g'}{\sqrt{g^2+g'^2}}$

As the value of the mixing angle is currently determined empirically, it has been mathematically defined as:[1]

$\cos\theta_W=\frac{m_W}{m_Z}$

The value of θW varies as a function of the momentum transfer, Q, at which it is measured. This variation, or 'running', is a key prediction of the electroweak theory. The most precise measurements have been carried out in electron-positron collider experiments at a value of Q = 91.2 GeV/c, corresponding to the mass of the Z boson, mZ.

In practice the quantity sin2θW is more frequently used. The 2004 best estimate of sin2θW, at Q = 91.2 GeV/c, in the MS scheme is 0.23120 ± 0.00015. Atomic parity violation experiments yield values for sin2θW at smaller values of Q, below 0.01 GeV/c, but with much lower precision. In 2005 results were published from a study of parity violation in Møller scattering in which a value of sin2θW = 0.2397 ± 0.0013 was obtained at Q = 0.16 GeV/c, establishing experimentally the 'running' of the weak mixing angle. These values correspond to a Weinberg angle of ~30°.

Note, however, that the specific value of the angle is not a prediction of the standard model: it is an open, unfixed parameter. At this time, there is no generally accepted theory that explains why the measured value is what it is.

## References

1. ^ L. B. Okun (1982). Leptons and Quarks. North-Holland Physics Publishing. p. 214. ISBN 0-444-86924-7.