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The Weinberg angle or weak mixing angle is a parameter in the Weinberg–Salam 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):

\( m_Z=\frac{m_W}{\cos\theta_W} \)

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°.
References and external links
Primary and secondary sources

^ 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.
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

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