Weinberg angle

The Weinberg angle or weak mixing angle is a parameter in the Weinberg–Salam theory of the electroweak interaction, and is usually denoted as θ_W. 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 m_W and m_Z):

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

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 θ_W 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, m_Z.

In practice the quantity sin²θ_W is more frequently used. The 2004 best estimate of sin²θ_W, at Q = 91.2 GeV/c, in the MS scheme is 0.23120 ± 0.00015. Atomic parity violation experiments yield values for sin²θ_W 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 sin²θ_W = 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°.

References and external links

Primary and secondary sources

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

• C. Amsler et al. (Particle Data Group) (2008). "Review of Particle Physics – Electroweak model and constraints on new physics". Physics Letters B 667 (1): 1. Bibcode 2008PhLB..667....1P. doi:10.1016/j.physletb.2008.07.018. http://pdg.lbl.gov/2009/reviews/rpp2009-rev-standard-model.pdf. 
• E158: A Precision Measurement of the Weak Mixing Angle in Møller Scattering
• Q-weak: A Precision Test of the Standard Model and Determination of the Weak Charges of the Quarks through Parity-Violating Electron Scattering