W-boson mass hints at physics beyond the standard model

The standard model of particle physics must be incomplete because it can’t explain gravity or dark matter, among other phenomena. Despite those limitations, measurements that violate the model are hard to find. That’s why it was big news last year when the Muon g − 2 collaboration at Fermilab found that the muon’s magnetic moment anomaly differs from the standard-model value by 4.2 standard deviations (see Physics Today, June 2021, page 14). Although a substantial difference, it fell short of the 5 standard deviations required to claim a discovery.

Now the Collider Detector at Fermilab (CDF) collaboration has obtained a measurement that seems to challenge the standard model. Using the now-shut-down Tevatron collider, the researchers measured a W-boson mass that is 7 standard deviations higher than predicted and is more precise than all previous measurements combined.

Alongside the Z boson, the W boson is a mediator of the weak nuclear force. The weak force is responsible for radioactive decay, and without it the Sun wouldn’t burn. It’s also the only way quarks can change their flavor. As such, the W-boson mass is tightly constrained by other parameters, including the Z-boson, Higgs-boson, and top-quark masses. Those interdependences make the W-boson mass a strong test of whether the standard model is self-consistent.

The standard model predicts a W-boson mass of 80 357 ± 6 MeV. And previous experimental values have, more or less, agreed with that. For example, combined previous measurements from the Large Electron–Positron Collider and Fermilab Tevatron collider yielded a value of 80 385 ± 15 MeV. Similarly, in 2017 the ATLAS Collaboration at the Large Hadron Collider (LHC) found a mass of 80 370 ± 19 MeV.

From data collected between 2002 and 2011, the CDF collaboration selected more than 4 million W bosons produced via quark–antiquark collisions, a data set four times as large as those in the previous CDF result. In part because of the large sample size, the researchers attained a precision a factor of two better than that of previous studies. Although the LHC has already measured more W bosons than Fermilab, the Tevatron benefits from lower collision energies relative to the LHC, which limit particles’ momenta to ranges easier to predict theoretically.

The W boson decays into a neutrino paired with either an electron or a muon. The momenta of those decay products are related to the mass of the boson. The CDF tracked the electrons and muons as they triggered 30 240 high-voltage wires around the collision site. One of many ways the CDF collaboration improved the accuracy of its results was obtaining precise, micrometer-scale information about the positions of the wires by checking that the straight paths of cosmic rays showed up as straight in the detector.

The researchers obtained a W-boson mass of 80 433.5 ± 9.4 MeV, well above the value in the standard model and most previous measurements, although it falls within the uncertainty of some. As a demonstration of the robustness of their techniques, they also measured the Z-boson mass, which did agree with the world average. That step had not been taken in previous measurements of the W-boson mass.

The observation, if confirmed by independent measurements, could indicate unknown particles or forces. “It is by no means definitive evidence that the standard model of particle physics is missing something,” says Jonathan Lee Feng of the University of California, Irvine, who wasn’t part of the CDF collaboration. “But it is highly significant and written by people and a collaboration with excellent reputations who have performed this analysis over 10 years.”

Possible explanations for a larger W-boson mass come from extensions to the standard model—such as supersymmetry, which posits a spacetime symmetry between fermions and bosons. Such theories would increase the expected W-boson mass through new interactions. (T. Aaltonen et al., CDF collaboration, Science 376, 170, 2022.)