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

W0

and B^{0} vector boson plane, producing as a result the

Z0

boson, and the photon.

(
γ
Z
0
)
=
(
cos
θ
W
sin
θ
W
−
sin
θ
W
cos
θ
W
)
(
B
0
W
0
)
It also gives the relationship between the masses of the W and Z bosons (denoted as *m*_{W} and *m*_{Z}),

m
Z
=
m
W
cos
θ
W
.
The angle can be expressed in terms of the
S
U
(
2
)
L
and
U
(
1
)
Y
couplings (g and g', respectively),

cos
θ
W
=
g
g
2
+
g
′
2
and

sin
θ
W
=
g
′
g
2
+
g
′
2
.

As the value of the mixing angle is currently determined empirically, it has been mathematically defined as

cos
θ
W
=
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°. 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

s
W
2
=
1
−
(
m
W
/
m
Z
)
2
=
0.2223
(
21
)
.

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.