W and Z bosons

Relations to the weak nuclear force

The W and Z bosons are carrier particles that mediate the weak nuclear force, much as the photon is the carrier particle for the electromagnetic force.

W bosons

The W^±
bosons are best known for their role in beta decay. Consider, for example, the beta decay of cobalt-60.

⁶⁰
₂₇Co → ⁶⁰
₂₈Ni⁺ + e⁻
+ ν
_e

This reaction does not involve the whole cobalt-60 nucleus, but affects only one of its 33 neutrons. The neutron is converted into a proton while also emitting an electron (often called a beta particle in this context) and an electron antineutrino:

n⁰
→ p⁺
+ e⁻
+ ν
_e

Again, the neutron is not an elementary particle but a composite of an up quark and two down quarks (udd). It is one of the down quarks that interacts in beta decay, turning into an up quark to form a proton (uud). At the most fundamental level, then, the weak force changes the flavour of a single quark:

d → u + W⁻

which is immediately followed by decay of the W⁻
itself:

W⁻
→ e⁻
+ ν
_e

Z bosons

The Z⁰
boson is its own antiparticle. Thus, all of its flavour quantum numbers and charges are zero. The exchange of a Z boson between particles, called a neutral current interaction, therefore leaves the interacting particles unaffected, except for a transfer of spin and/or momentum.

Z boson interactions involving neutrinos have distinct signatures: They provide the only known mechanism for elastic scattering of neutrinos in matter; neutrinos are almost as likely to scatter elastically (via Z boson exchange) as inelastically (via W boson exchange). Weak neutral currents via Z boson exchange were confirmed shortly thereafter (also in 1973), in a neutrino experiment in the Gargamelle bubble chamber at CERN.

Predictions of the W+, W− and Z0 bosons

Following the success of quantum electrodynamics in the 1950s, attempts were undertaken to formulate a similar theory of the weak nuclear force. This culminated around 1968 in a unified theory of electromagnetism and weak interactions by Sheldon Glashow, Steven Weinberg, and Abdus Salam, for which they shared the 1979 Nobel Prize in Physics. Their electroweak theory postulated not only the W bosons necessary to explain beta decay, but also a new Z boson that had never been observed.

The fact that the W and Z bosons have mass while photons are massless was a major obstacle in developing electroweak theory. These particles are accurately described by an SU(2) gauge theory, but the bosons in a gauge theory must be massless. As a case in point, the photon is massless because electromagnetism is described by a U(1) gauge theory. Some mechanism is required to break the SU(2) symmetry, giving mass to the W and Z in the process. The Higgs mechanism, first put forward by the 1964 PRL symmetry breaking papers, fulfills this role. It requires the existence of another particle, the Higgs boson, which has since been found at the Large Hadron Collider. Of the four components of a Goldstone boson created by the Higgs field, three are absorbed by the W⁺
, Z⁰
, and W⁻
bosons to form their longitudinal components, and the remainder appears as the spin-0 Higgs boson.

The combination of the SU(2) gauge theory of the weak interaction, the electromagnetic interaction, and the Higgs mechanism is known as the Glashow–Weinberg–Salam model. Today it is widely accepted as one of the pillars of the Standard Model of particle physics, particularly given the 2012 discovery of the Higgs boson by the CMS and ATLAS experiments.

The model predicts that W^±
and Z⁰
bosons have the following masses: $${\displaystyle \begin{array}{cc}{m}_{{\text{W}}^{\pm }}& =\frac{1}{2}vg\\ m_{{\text{Z}}^0}& =\frac{1}{2}v\sqrt{g^2+{g^{\prime }}^2}\end{array}}$$ where ${\displaystyle g}$ is the SU(2) gauge coupling, ${\displaystyle g^{\prime }}$ is the U(1) gauge coupling, and ${\displaystyle v}$ is the Higgs vacuum expectation value.

Discovery

Unlike beta decay, the observation of neutral current interactions that involve particles other than neutrinos requires huge investments in particle accelerators and particle detectors, such as are available in only a few high-energy physics laboratories in the world (and then only after 1983). This is because Z bosons behave in somewhat the same manner as photons, but do not become important until the energy of the interaction is comparable with the relatively huge mass of the Z boson.

The discovery of the W and Z bosons was considered a major success for CERN. First, in 1973, came the observation of neutral current interactions as predicted by electroweak theory. The huge Gargamelle bubble chamber photographed the tracks produced by neutrino interactions and observed events where a neutrino interacted but did not produce a corresponding lepton. This is a hallmark of a neutral current interaction and is interpreted as a neutrino exchanging an unseen Z boson with a proton or neutron in the bubble chamber. The neutrino is otherwise undetectable, so the only observable effect is the momentum imparted to the proton or neutron by the interaction.

The discovery of the W and Z bosons themselves had to wait for the construction of a particle accelerator powerful enough to produce them. The first such machine that became available was the Super Proton Synchrotron, where unambiguous signals of W bosons were seen in January 1983 during a series of experiments made possible by Carlo Rubbia and Simon van der Meer. The actual experiments were called UA1 (led by Rubbia) and UA2 (led by Pierre Darriulat), and were the collaborative effort of many people. Van der Meer was the driving force on the accelerator end (stochastic cooling). UA1 and UA2 found the Z boson a few months later, in May 1983. Rubbia and van der Meer were promptly awarded the 1984 Nobel Prize in Physics, a most unusual step for the conservative Nobel Foundation.

The W⁺
, W⁻
, and Z⁰
bosons, together with the photon (γ), comprise the four gauge bosons of the electroweak interaction.

Measurements of W boson mass

In May 2024, the Particle Data Group estimated the World Average mass for the W boson to be 80369.2 ± 13.3 MeV, based on experiments to date.

As of 2021, experimental measurements of the W boson mass had been similarly assessed to converge around 80379±12 MeV, all consistent with one another and with the Standard Model.

In April 2022, a new analysis of historical data from the Fermilab Tevatron collider before its closure in 2011 determined the mass of the W boson to be 80433±9 MeV, which was seven standard deviations above that predicted by the Standard Model. Besides being inconsistent with the Standard Model, the new measurement was also inconsistent with previous measurements such as ATLAS. This suggests that either the old or the new measurements had an unexpected systematic error, such as an undetected quirk in the equipment. This led to careful reevaluation of this data analysis and other historical measurement, as well as the planning of future measurements to confirm the potential new result. Fermilab Deputy Director Joseph Lykken reiterated that "... the (new) measurement needs to be confirmed by another experiment before it can be interpreted fully."

In 2023, an improved ATLAS experiment measured the W boson mass at 80360±16 MeV, aligning with predictions from the Standard Model.

The Particle Data Group convened a working group on the Tevatron measurement of W boson mass, including W-mass experts from all hadron collider experiments to date, to understand the discrepancy. In May 2024 they concluded that the Collider Detector at Fermilab (CDF) measurement was an outlier, and the best estimate of the mass came from leaving out that measurement from the meta-analysis. "The corresponding value of the W boson mass is m_W = 80369.2±13.3 MeV, which we quote as the World Average."

In September 2024, the CMS experiment measured the W boson mass at 80360.2±9.9 MeV. This was the most precise measurement to date, obtained from observations of a large number of W → μν decays.

Decay

The W and Z bosons decay to fermion pairs but neither the W nor the Z bosons have sufficient energy to decay into the highest-mass top quark. Neglecting phase space effects and higher order corrections, simple estimates of their branching fractions can be calculated from the coupling constants.

W bosons

W bosons can decay to a lepton and antilepton (one of them charged and another neutral) or to a quark and antiquark of complementary types (with opposite electric charges ⁠±+1/3⁠ e and ⁠∓+2/3⁠ e). The decay width of the W boson to a quark–antiquark pair is proportional to the corresponding squared CKM matrix element and the number of quark colours, N_C = 3. The decay widths for the W⁺ boson are then proportional to:

Here, e⁺
, μ⁺
, τ⁺
denote the three flavours of leptons (more exactly, the positive charged antileptons). ν
_e, ν
_μ, ν
_τ denote the three flavours of neutrinos. The other particles, starting with u and d, all denote quarks and antiquarks (factor N_C is applied). The various ${\displaystyle V_{ij}}$ denote the corresponding CKM matrix coefficients.

Unitarity of the CKM matrix implies that ${\displaystyle |V_{\text{ud}}{|}^2+|V_{\text{us}}{|}^2+|V_{\text{ub}}{|}^2=}$ ${\displaystyle |V_{\text{cd}}{|}^2+|V_{\text{cs}}{|}^2+|V_{\text{cb}}{|}^2=1,}$ thus each of two quark rows sums to 3. Therefore, the leptonic branching ratios of the W boson are approximately ${\displaystyle B({\mathrm{e}}^{+}{\nu }_{\mathrm{e}})=}$${\displaystyle B({\mu }^{+}{\nu }_{\mu })=}$${\displaystyle B({\tau }^{+}{\nu }_{\tau })=}$ ⁠1/9⁠. The hadronic branching ratio is dominated by the CKM-favored ud and cs final states. The sum of the hadronic branching ratios has been measured experimentally to be 67.60±0.27%, with ${\displaystyle B({\ell }^{+}{\nu }_{\ell })=}$ 10.80±0.09%.

Z0 boson

Z bosons decay into a fermion and its antiparticle. As the Z⁰
boson is a mixture of the pre-symmetry-breaking W⁰
and B⁰
bosons (see weak mixing angle), each vertex factor includes a factor ⁠${\displaystyle T_3-Q{\sin }^2{\theta }_{\text{W}}}$⁠, where ${\displaystyle T_3}$ is the third component of the weak isospin of the fermion (the "charge" for the weak force), ${\displaystyle Q}$ is the electric charge of the fermion (in units of the elementary charge), and ${\displaystyle {\theta }_{\text{w}}}$ is the weak mixing angle. Because the weak isospin ${\displaystyle (T_3)}$ is different for fermions of different chirality, either left-handed or right-handed, the coupling is different as well.

The relative strengths of each coupling can be estimated by considering that the decay rates include the square of these factors, and all possible diagrams (e.g. sum over quark families, and left and right contributions). The results tabulated below are just estimates, since they only include tree-level interaction diagrams in the Fermi theory.

To keep the notation compact, the table uses ⁠${\displaystyle x={\sin }^2{\theta }_{\text{w}}\approx \frac{1}{4}}$⁠.

* The impossible decay into a top quark–antiquark pair is left out of the table.

Subheadings left and right denote the chirality or "handedness" of the fermions.

In 2018, the CMS collaboration observed the first exclusive decay of the Z boson to a ψ meson and a lepton–antilepton pair.