# .

# 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 W^{0}

and B^{0} 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 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 sin^{2}θ_{W} is more frequently used. The 2004 best estimate of sin^{2}θ_{W}, at Q = 91.2 GeV/c, in the MS scheme is 0.23120 ± 0.00015. Atomic parity violation experiments yield values for sin^{2}θ_{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 sin^{2}θ_{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

^ 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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