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{{Technical|date=September 2010}}

[[File:Electroweak.svg|300px|right|thumb|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 [[Steven Weinberg|Weinberg]]–[[Abdus Salam|Salam]] theory of the [[electroweak interaction]], and is usually denoted as ''θ''W. It is the angle by which [[spontaneous symmetry breaking]] [[rotation matrix|rotates]] the original {{SubatomicParticle|W boson0}} and B0 [[vector boson]] plane, producing as a result the {{SubatomicParticle|Z boson0|link}} boson, and the [[photon]].

:<math> \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} </math>

It also gives the relationship between the masses of the [[W and Z bosons]] (denoted as ''m''W and ''m''Z):

:<math>m_Z=\frac{m_W}{\cos\theta_W}</math>

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

:<math>\cos\theta_W = \frac{g}{\sqrt{g^2+g'^2}}</math> and <math>\sin\theta_W = \frac{g'}{\sqrt{g^2+g'^2}}</math>

As the value of the mixing angle is currently determined empirically, it has been mathematically defined as:<ref>
{{cite book
|author=L. B. Okun
|year=1982
|title=Leptons and Quarks
|page=214
|publisher=[[North-Holland Publishing|North-Holland Physics Publishing]]
|isbn=0-444-86924-7
}}</ref>

:<math>\cos\theta_W=\frac{m_W}{m_Z}</math>

The value of ''θ''W varies as a function of the [[momentum transfer]], ''Q'', at which it is measured. This variation, or '[[renormalization group|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 {{nowrap|''Q'' {{=}} 91.2 GeV/c}}, corresponding to the mass of the Z boson, ''m''Z.

In practice the quantity sin2''θ''W is more frequently used. The 2004 best estimate of sin2''θ''W, at {{nowrap|''Q'' {{=}} 91.2 GeV/c}}, in the [[minimal subtraction scheme|{{overline|MS}} scheme]] is {{nowrap|0.23120 ± 0.00015}}. Atomic [[parity violation]] experiments yield values for sin2''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 {{nowrap|sin2''θ''W {{=}} 0.2397 ± 0.0013}} was obtained at {{nowrap|''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.

==See also==
* [[Cabibbo angle]]

==References==

<references/>
*{{cite journal
|author=C. Amsler ''et al.'' ([[Particle Data Group]])
|year=2008
|title=Review of Particle Physics – Electroweak model and constraints on new physics
|url=http://pdg.lbl.gov/2009/reviews/rpp2009-rev-standard-model.pdf
|journal=[[Physics Letters B]]
|volume=667 |issue=1 |pages=1
|doi= 10.1016/j.physletb.2008.07.018
|bibcode = 2008PhLB..667....1P }}
* [http://www.slac.stanford.edu/exp/e158/ E158: A Precision Measurement of the Weak Mixing Angle in Møller Scattering]
* [http://www.jlab.org/qweak/ Q-weak: A Precision Test of the Standard Model and Determination of the Weak Charges of the Quarks through Parity-Violating Electron Scattering]

{{DEFAULTSORT:Weinberg Angle}}
[[Category:Electroweak theory]]

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