Weinberg angle

The Weinberg angle or weak mixing angle is a parameter in the Weinberg-Salam theory of the electroweak force, 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.

${\begin{pmatrix}Photon\\Z^{0}\end{pmatrix}}={\begin{pmatrix}\cos \theta _{W}&\sin \theta _{W}\\-\sin \theta _{W}&\cos \theta _{W}\end{pmatrix}}{\begin{pmatrix}B^{0}\\W^{0}\end{pmatrix}}$

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:

$\cos \theta _{W}={\frac {M_{W}}{M_{Z}}}$

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-bar 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

• "Electroweak model and constraints on new physics", Particle Data Group, Review of Particle Physics
• 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