Based on the latest data inputs, the Standard Model (SM) constrains the mass of the W boson (mW) to be 80,353 ± 6 MeV. At tree level, mW depends only on the mass of the Z boson and the weak and electromagnetic couplings. The boson’s tendency to briefly transform into a top quark and a bottom quark causes the largest quantum correction. Any departure from the SM prediction could signal the presence of additional loops containing unknown heavy particles.
The CDF experiment at the Tevatron observed just such a departure in 2022, plunging the boson into a midlife crisis 39 years after it was discovered at CERN’s SpSS collider (CERN Courier September/October 2023 p27). A new measurement from the CMS experiment at the LHC now contradicts the anomaly reported by CDF. While the CDF result stands seven standard deviations above the SM, CMS’s measurement aligns with the SM prediction and previous results at the LHC. The CMS and CDF results claim joint first place in precision, provoking a dilemma for phenomenologists.
New-physics puzzle
“The result by CDF remains puzzling, as it is extremely difficult to explain the discrepancy with the three LHC measurements by the presence of new physics, in particular as there is also a discrepancy with D0 at the same facility,” says Jens Erler of Johannes Gutenberg-Universität Mainz. “Together with measurements of the weak mixing angle, the CMS result confirms the validity of the SM up to new physics scales well into the TeV region.”
“I would not call this ‘case closed’,” agrees Sven Heinemeyer of the Universidad Autónoma de Madrid. “There must be a reason why CDF got such an anomalously high value, and understanding what is going on may be very beneficial for future investigations. We know that the SM is not the last word, and there are clear cases that require physics beyond the SM (BSM). The question is at which scale BSM physics appears, or how strongly it is coupled to the SM particles.”
The result confirms the validity of the SM up to new physics scales well into the TeV region
To obtain their result, CDF analysed four million W-boson decays originating from 1.96 TeV proton–antiproton collisions at Fermilab’s Tevatron collider between 1984 and 2011. In stark disagreement with the SM, the analysis yielded a mass of 80,433.5 ± 9.4 MeV. This result induced the ATLAS collaboration to revisit its 2017 analysis of W → μν and W → eνdecays in 7 TeV proton–proton collisions using the latest global data on parton distribution functions, which describe the probable momenta of quarks and gluons inside the proton. A newly developed fit was also implemented. The central value remained consistent with the SM, with a reduced uncertainty of 16 MeV increasing its tension with the new CDF result. A less precise measurement by the LHCb collaboration also favoured the SM (CERN Courier May/June 2023 p10).
CMS now reports mW to be 80,360.2 ± 9.9 MeV, concluding a study of W → μν decays begun eight years ago.
“One of the main strategic choices of this analysis is to use a large dataset of Run 2 data,” says CMS spokesperson Gautier Hamel de Monchenault. “We are using 16.8 fb–1 of 13 TeV data at a relatively high pileup of on average 25 interactions per bunch crossing, leading to very large samples of about 7.5 million Z bosons and 90 million W bosons.”
With high pileup and high energies come additional challenges. The measurement uses an innovative analysis technique that benchmarks W → μν decay systematics using Z → μμ decays as independent validation wherein one muon is treated as a neutrino. The ultimate precision of the measurement relies on reconstructing the muon’s momentum in the detector’s silicon tracker to better than one part in 10,000 – a groundbreaking level of accuracy built on minutely modelling energy loss, multiple scattering, magnetic-field inhomogeneities and misalignments. “What is remarkable is that this incredible level of precision on the muon momentum measurement is obtained without using Z → μμ as a calibration candle, but only using a huge sample of J/ψ → μμ events,” says Hamel de Monchenault. “In this way, the Z → μμ sample can be used for an independent closure test, which also provides a competitive measurement of the Z mass.”
Measurement matters
Measuring mW using W → μν decays is challenging because the neutrino escapes undetected. mW must be inferred from either the distribution of the transverse mass visible in the events (mT) or the distribution of the transverse momentum of the muons (pT). The mT approach used by CDF is the most precise option at the Tevatron, but typically less precise at the LHC, where hadronic recoil is difficult to distinguish from pileup. The LHC experiments also face a greater challenge when reconstructing mW from distributions of pT. In proton–antiproton collisions at the Tevatron, W bosons could be created via the annihilation of pairs of valence quarks. In proton–proton collisions at the LHC, the antiquark in the annihilating pair must come from the less well understood sea; and at LHC energies, the partons have lower fractions of the proton’s momentum – a less well constrained domain of parton distribution functions.
“Instead of exploiting the Z → μμ sample to tune the parameters of W-boson production, CMS is using the W data themselves to constrain the theory parameters of the prediction for the pT spectrum, and using the independent Z → μμ sample to validate this procedure,” explains Hamel de Monchenault. “This validation gives us great confidence in our theory modelling.”
“The CDF collaboration doesn’t have an explanation for the incompatibility of the results,” says spokesperson David Toback of Texas A&M University. “Our focus is on the checks of our own analysis and understanding of the ATLAS and CMS methods so we can provide useful critiques that might be helpful in future dialogues. On the one hand, the consistency of the ATLAS and CMS results must be taken seriously. On the other, given the number of iterations and improvements needed over decades for our own analysis – CDF has published five times over 30 years – we still consider both LHC results ‘early days’ and look forward to more details, improved methodology and additional measurements.”
The LHC experiments each plan improvements using new data. The results will build on a legacy of electroweak precision at the LHC that was not anticipated to be possible at a hadron collider (CERN Courier September/October 2024 p29).
“The ATLAS collaboration is extremely impressed with the new measurement by CMS and the extraordinary precision achieved using high-pileup data,” says spokesperson Andreas Hoecker. “It is a tour de force, accomplished by means of a highly complex fit, for which we applaud the CMS collaboration.” ATLAS’s next measurement of mW will focus on low-pileup data, to improve sensitivity to mT relative to their previous result.
The ATLAS collaboration is extremely impressed with the new measurement by CMS
The LHCb collaboration is working on an update of their measurement using its full Run 2 data set. LHCb’s forward acceptance may prove to be powerful in a global fit. “LHCb probes parton density functions in different phase space regions, and that makes the measurements from LHCb anticorrelated with those of ATLAS and CMS, promising a significant impact on the average, even if the overall uncertainty is larger,” says spokesperson Vincenzo Vagnoni. The goal is to progress LHC measurements towards a combined precision of 5 MeV. CMS plans several improvements to their own analysis.
“There is still a significant factor to be gained on the momentum scale, with which we could reach the same precision on the Z-boson mass as LEP,” says Hamel de Monchenault. “We are confident that we can also use a future, large low-pileup run to exploit the W recoil and mT to complement the muon pT spectrum. Electrons can also be used, although in this case the Z sample could not be kept independent in the energy calibration.”
