New results from the CMS experiment solve the mystery of the mass of the W boson

Following an unexpected measurement by the Collider Detector experiment at Fermilab (CDF) in 2022, physicists at the Compact Muon Solenoid (CMS) experiment at the Large Hadron Collider (LHC) today announced a new mass measurement of the W boson, one of nature’s force-transmitting particles.

This new measurement, a first for the CMS experiment, uses a new technique that makes it the most sophisticated study of the W boson mass to date. After nearly a decade of analysis, CMS has found that the W boson’s mass agrees with predictions, finally solving a years-long mystery.

For the final analysis, 300 million events collected during the 2016 LHC run and 4 billion simulated events were used. From this dataset, the team reconstructed and then measured the mass of more than 100 million W bosons.

They found that the mass of the W boson is 80,360.2 ± 9.9 megaelectronvolts (MeV), which is consistent with the Standard Model predictions of 80,357 ± 6 MeV. They also conducted a separate analysis to test the theoretical assumptions.

“The new CMS result is unique because of its precision and the way we determined the uncertainties,” said Patty McBride, a distinguished scientist at the U.S. Department of Energy’s Fermi National Research Laboratory and former CMS spokeswoman.

“We’ve learned a lot from CDF and the other experiments that have worked on the W boson mass question. We’re standing on their shoulders, and that’s one of the reasons we can take this study a big step forward.”

Since the discovery of the W boson in 1983, physicists have measured its mass in ten different experiments.

The W boson is one of the cornerstones of the Standard Model, the theoretical framework that describes nature at its most fundamental level. A precise understanding of the mass of the W boson allows scientists to map the interplay of particles and forces, including the strength of the Higgs field and the fusion of electromagnetism with the weak force responsible for radioactive decay.

“The entire universe is a delicate balancing act,” said Anadi Canepa, deputy spokesperson for the CMS experiment and principal investigator at Fermilab. “If the W mass is different than expected, new particles or forces could be at play.”

The new CMS measurement has an accuracy of 0.01%. This accuracy is equivalent to measuring a 4-inch pencil to between 3.9996 and 4.0004 inches. But unlike pencils, the W boson is an elementary particle with no physical volume and a mass smaller than a single silver atom.

“This measurement is extremely difficult to perform,” Canepa added. “We need multiple measurements from multiple experiments to verify the value.”

The CMS experiment differs from the other experiments in which this measurement was carried out by its compact design, special sensors for elementary particles called muons, and an extremely strong solenoid magnet that bends the trajectory of charged particles as they pass through the detector.

“The design of CMS makes it particularly well suited for precise mass measurements,” said McBride. “It’s a next-generation experiment.”

Because most elementary particles are incredibly short-lived, scientists measure their mass by adding together the mass and momenta of all the particles they decay into. This method works well for particles like the Z boson, a cousin of the W boson, which decays into two muons. The W boson, however, presents a major challenge because one of its decay products is a tiny elementary particle called a neutrino.

“Neutrinos are notoriously difficult to measure,” said Josh Bendavid, a scientist at the Massachusetts Institute of Technology who worked on this analysis. “In collider experiments, the neutrino goes undetected, so we can only work with half the picture.”

Since they only have to work with half the picture, the physicists have to be creative. Before performing the analysis with real experimental data, the scientists first simulated billions of LHC collisions.

“In some cases, we even had to model small deformations in the detector,” said Bendavid. “The precision is high enough that we can detect small twists and bends, even if they are only as small as the width of a human hair.”

In addition, physicists need a lot of theoretical information, such as what happens inside the protons when they collide, how the W boson is created and how it moves before it decays.

“It’s a real art to figure out the effects of theoretical inputs,” McBride said.

In the past, physicists have used the Z boson as a substitute for the W boson when calibrating their theoretical models. While this method has many advantages, it also introduces additional uncertainty into the process.

“Z and W bosons are siblings, but not twins,” said Elisabetta Manca, a researcher at the University of California Los Angeles and one of the analyzers. “Physicists have to make some assumptions when extrapolating from the Z to the W boson, and these assumptions are still being debated.”

To reduce this uncertainty, CMS researchers developed a novel analysis technique that uses only real W boson data to constrain the theoretical inputs.

“Thanks to a combination of a larger data set, the experience we gained from a previous W boson study, and the latest theoretical developments, we were able to do this effectively,” said Bendavid. “This allowed us to move away from the Z boson as a reference point.”

As part of this analysis, they also examined 100 million traces from the decay of known particles to recalibrate a large part of the CMS detector until it was an order of magnitude more precise.

“This new level of precision will allow us to perform critical measurements, such as those involving the W, Z and Higgs bosons, with improved accuracy,” Manca said.

The biggest challenge of the analysis was that it was very time-consuming, as it required the development of a novel analysis technique and an incredibly deep understanding of the CMS detector.

“I started this research as a summer student and am now in my third year as a postdoc,” Manca said. “It’s a marathon, not a sprint.”