New CMS results solve mystery of W boson mass

Following an unexpected measurement at Fermi National Accelerator Laboratory’s Collider for Physics (CDF) experiment in 2022, physicists at the Compact Muon Solenoid Experiment (CMS) at the Large Hadron Collider (LHC) today announced a new mass measurement of the W boson, one of the particles that carry the forces of nature.

This new measurement, a first for the CMS experiment, used new techniques to provide the most thorough investigation of the W boson’s mass to date. After nearly a decade of analysis, CMS found that the W boson’s mass is consistent with predictions, finally putting an end to a long-standing mystery.

The final analysis used 300 million events collected from the LHC run in 2016 and 4 billion simulated events. From this data set, the team reconstructed and measured the masses of over 100 million W bosons.

The researchers found that the mass of the W boson is 80,360.2 ± 9.9 megaelectronvolts (MeV), which is consistent with the Standard Model prediction of 80,357 ± 6 MeV. The researchers also performed a separate analysis to cross-check their theoretical assumptions.

“The new CMS results are unique in the way they determined their precision and uncertainty,” said Patty McBride, a distinguished scientist at the Department of Energy’s Fermi National Laboratory and a former CMS spokesperson.

“We have learned a lot from CDF and other experiments that have been working on the W boson mass problem. We are standing on their shoulders, and this is one of the reasons why we have been able to make such great progress in this research.”

Since the W boson was discovered in 1983, physicists have measured its mass in 10 different experiments.

The W boson is one of the cornerstones of the Standard Model, the theoretical framework that explains nature at its most fundamental level. Understanding the W boson’s mass precisely allows scientists to map the interactions of particles and forces, such as the strength of the Higgs field and the fusion of the weak and electromagnetic forces that causes radioactive decay.

“The entire universe hangs in a delicate balance,” said Anadi Canepa, deputy spokesperson for the CMS experiment and a senior scientist at Fermi National Accelerator Laboratory. “If the mass of W is different from what we expect, it could mean that new particles and forces are at work.”

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

“This measurement is very difficult,” Canepa added, “requiring multiple measurements from multiple experiments to cross-check the values.”

The CMS experiment stands out from other experiments that have made this measurement because it has a compact design, a specialized sensor for fundamental particles called muons, and an extremely powerful solenoid magnet that bends the trajectory of charged particles as they pass through the detector.

“The design of CMS is particularly well suited for precision mass measurements,” McBride said. “This is a next-generation experiment.”

Most fundamental particles have extremely short lifetimes, so scientists measure mass by adding up the mass and momentum of all the products they decay into. This method works well for particles such as the Z boson, a relative of the W boson that decays into two muons. But the W boson poses a big challenge because one of its decay products is a small fundamental particle called a neutrino.

“Neutrinos are notoriously difficult to measure,” said Josh Bendavid, a Massachusetts Institute of Technology scientist who worked on the analysis. “Because colliders don’t detect neutrinos, they only tell us half the story.”

Working with only half the picture meant physicists had to get creative: Before running their analysis on real experimental data, scientists first simulated billions of LHC collisions.

“In some cases, we also had to model small deformations in the detector,” Bendavid says, “and the accuracy is high enough to account for small twists and bends, even if they’re as small as the width of a human hair.”

Physicists also need a lot of theoretical information, such as what happens inside protons when they collide, how the W boson is created, and how it behaves before it decays.

“Understanding the impact of theoretical inputs is a real art,” McBride said.

Until now, physicists have used the Z boson as a replacement for the W boson when calibrating theoretical models, an approach that has many advantages but also adds a layer of uncertainty to the process.

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

To reduce this uncertainty, CMS researchers developed a new analytical technique that constrains the theoretical input using only real W boson data.

“We were able to do this effectively thanks to a combination of larger data sets, experience gained from previous W boson studies, and the latest theoretical developments,” Bendavid said. “This means we no longer need to consider the Z boson as a reference point.”

As part of this analysis, the researchers also looked at 100 million trajectories from the decay of well-known particles and retuned large parts of the CMS detectors to improve their precision by an order of magnitude.

“This new level of precision will enable us to tackle important measurements such as the W, Z and Higgs particles with greater accuracy,” Manka said.

The most challenging part of the analysis was that it took so long because we had to create new analytical methods and develop a very in-depth understanding of the CMS detector.

“I started this research as a summer student and am now in my third year as a postdoctoral researcher,” Manka says. “This is not a sprint, it’s a marathon.”