# Weinberg angle

The **Weinberg angle** or **weak mixing angle** is a parameter in the Weinberg–Salam theory of the electroweak interaction, part of the Standard Model of particle physics, 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 ^{}_{}Z^{0}_{} boson, and the photon.^{[1]}

It also gives the relationship between the masses of the W and Z bosons (denoted as *m*_{W} and *m*_{Z}),

The angle can be expressed in terms of the and couplings (weak isospin g and weak hypercharge g', respectively),

- and

The electric charge is then expressible in terms of it, e = *g* sin *θ _{W}* =

*g*' cos

*θ*; see the Figure.

_{W}As the value of the mixing angle is currently determined empirically, it has been mathematically defined as^{[2]}

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, which averages over measurements made in different processes and at different detectors. 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°. LHCb measured in 7 and 8 TeV proton-proton collisions an effective angle of sin^{2}(θ^{eff}_{W}) = 0.23142, though the value of Q for this measurement is determined by the partonic collision energy, which is close to the Z boson mass. CODATA 2014 gives the value

- .

Note, however, that the specific value of the angle is *not* a prediction of the standard model: it is an open, unfixed parameter. However, it is constrained and predicted through other measurements of standard model quantities. At this time, there is no generally accepted theory that explains why the measured value is what it is.

## ReferencesEdit

**^**T. P. Cheng; L. F. Li (2006).*Gauge theory of elementary particle physics*. Oxford University Press ISBN 0-19-851961-3. pp 349-355**^**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" (PDF).*Physics Letters B*.**667**(1): 1. Bibcode:2008PhLB..667....1A. 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