Weinberg angle (relation between coupling constants)

The weak mixing angle or Weinberg angle is a parameter in the Weinberg– Salam theory of the

electroweak interaction In particle physics, the electroweak interaction or electroweak force is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very differe ...

, part of the

Standard Model The Standard Model of particle physics is the theory describing three of the four known fundamental forces ( electromagnetic, weak and strong interactions - excluding gravity) in the universe and classifying all known elementary particles. It ...

of particle physics, and is usually denoted as . It is the angle by which

spontaneous symmetry breaking Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state spontaneously ends up in an asymmetric state. In particular, it can describe systems where the equations of motion or ...

rotates the original and

vector boson In particle physics, a vector boson is a boson whose spin equals one. The vector bosons that are regarded as elementary particles in the Standard Model are the gauge bosons, the force carriers of fundamental interactions: the photon of electromagne ...

plane, producing as a result the boson, and the

photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they alwa ...

. Its measured value is slightly below 30°, but also varies, very slightly increasing, depending on how high the relative momentum of the particles involved in the interaction is that the angle is used for.

Details

The algebraic formula for the combination of the and

s (i.e. 'mixing') that simultaneously produces the massive boson and the massless

() is expressed by the formula :

\begin
\gamma \\
Z^0 \end = \begin
\cos \theta_\text & \sin \theta_\text \\
-\sin \theta_\text & \cos \theta_\text \end \begin
B^0 \\
W^0 \end .

The ''weak mixing angle'' also gives the relationship between the masses of the

W and Z bosons In particle physics, the W and Z bosons are vector bosons that are together known as the weak bosons or more generally as the intermediate vector bosons. These elementary particles mediate the weak interaction; the respective symbols are , , an ...

(denoted as and ), :

m_\text = \frac .

The angle can be expressed in terms of the

\mathrm(2)_L

and

\mathrm(1)_Y

couplings (

weak isospin In particle physics, weak isospin is a quantum number relating to the weak interaction, and parallels the idea of isospin under the strong interaction. Weak isospin is usually given the symbol or , with the third component written as or . It c ...

and

weak hypercharge In the Standard Model of electroweak interactions of particle physics, the weak hypercharge is a quantum number relating the electric charge and the third component of weak isospin. It is frequently denoted Y_\mathsf and corresponds to the gauge ...

, respectively), :

\cos \theta_\text = \frac \qquad

and

\qquad \sin\theta_\text = \frac .

The electric charge is then expressible in terms of it, (refer to the figure). Because the value of the mixing angle is currently determined empirically, in the absence of any superseding theoretical derivation it is mathematically defined as :

\cos \theta_\text = \frac .

The value of varies as a function of the

momentum transfer In particle physics, wave mechanics and optics, momentum transfer is the amount of momentum that one particle gives to another particle. It is also called the scattering vector as it describes the transfer of wavevector in wave mechanics. In the s ...

, , at which it is measured. This variation, or '

running Running is a method of terrestrial locomotion allowing humans and other animals to move rapidly on foot. Running is a type of gait characterized by an aerial phase in which all feet are above the ground (though there are exceptions). This i ...

', 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 , corresponding to the mass of the boson, . In practice, the quantity is more frequently used. The 2004 best estimate of , at , in the scheme is , which is an average over measurements made in different processes, at different detectors. Atomic

parity violation In physics, a parity transformation (also called parity inversion) is the flip in the sign of ''one'' spatial coordinate. In three dimensions, it can also refer to the simultaneous flip in the sign of all three spatial coordinates (a point ref ...

experiments yield values for at smaller values of , below 0.01 GeV/''c'', but with much lower precision. In 2005 results were published from a study of

Møller scattering Møller scattering is the name given to electron-electron scattering in quantum field theory, named after the Danish physicist Christian Møller. The electron interaction that is idealized in Møller scattering forms the theoretical basis of many ...

in which a value of was obtained at , establishing experimentally the so-called 'running' of the weak mixing angle. These values correspond to a Weinberg angle varying between 28.7° and 29.3° ≈ 30°.

LHCb The LHCb (Large Hadron Collider beauty) experiment is one of eight particle physics detector experiments collecting data at the Large Hadron Collider at CERN. LHCb is a specialized b-physics experiment, designed primarily to measure the paramet ...

measured in 7 and 8 TeV proton–proton collisions an effective angle of , though the value of for this measurement is determined by the partonic collision energy, which is close to the Z boson mass. CODATA 2018 gives the value :

\sin^2 \theta _\text = 1 - \left( m_\text/m_\text \right)^2 = 0.222 90(30) .

Footnotes

References

* * * {{DEFAULTSORT:Weinberg Angle Electroweak theory Angle Dimensionless numbers Physical constants