April 2022 – ParticleBites

This is part two of our coverage of the CDF W mass measurement, discussing how the measurement was done. Read about the implications of this result in our sister post here

Last week, the CDF collaboration announced the most precise measurement of the W boson’s mass to date. After nearly ten years of careful analysis, the W weighed in at 80,433.5 ± 9.4 MeV: a whopping seven standard deviations away from the Standard Model expectation! This result quickly became the talk of the town among particle physicists, and there are already dozens of arXiv papers speculating about what it means for the Standard Model. One of the most impressive and hotly debated aspects of this measurement is its high precision, which came from an extremely careful characterization of the CDF detector and recent theoretical developments in modeling proton structure. In this post, I’ll describe how they made the measurement and the clever techniques they used to push down the uncertainties.

The new CDF measurement of the W boson mass. The center of the red ellipse corresponds to the central values of the measured W mass (y-coordinate) and top quark mass (x-coordinate, from other experiments). The purple line shows the Standard Model constraint on the W mass as a function of the top mass, and the border of the red ellipse is the one standard deviation boundary around the measurement.

The imaginatively titled “Collider Detector at Fermilab” (CDF) collected proton-antiproton collision data at Fermilab’s Tevatron accelerator for over 20 years, until the Tevatron shut down in 2011. Much like ATLAS and CMS, CDF is made of cylindrical detector layers, with the innermost charged particle tracker and adjacent electromagnetic calorimeter (ECAL) being most important for the W mass measurement. The Tevatron ran at a center of mass energy of 1.96 TeV — much lower than the LHC’s 13 TeV — which enabled a large reduction in the “theoretical uncertainties” on the measurement. Physicists use models called “parton distribution functions” (PDFs) to calculate how a proton’s momentum is distributed among its constituent quarks, and modern PDFs make very good predictions at the Tevatron’s energy scale. Additionally, W boson production in proton-antiproton collisions doesn’t involve any gluons, which are a major source of uncertainty in PDFs (LHC collisions are full of gluons, making for larger theory uncertainty in LHC W mass measurements).

A cutaway view of the CDF detector. The innermost tracking detector (yellow) reconstructs the trajectories of charged particles, and the nearby electromagnetic calorimeter (red) collects energy deposits from photons and charged particles (e.g. electrons). The tracker and EM Cal were both central in the W mass measurement.

Armed with their fancy PDFs, physicists set out to measure the W mass in the same way as always: by looking at its decay products! They focused on the leptonic channel, where the W decays to a lepton (electron or muon) and its associated neutrino. This clean final state is easy to identify in the detector and allows for a high-purity, low-background signal selection. The only sticking point is the neutrino, which flies out of the detector completely undetected. Thankfully, momentum conservation allowed them to reconstruct the neutrino’s transverse momentum (p_T) from the rest of the visible particles produced in the collision. Combining this with the lepton’s measured momentum, they reconstructed the “transverse mass” of the W — an important observable for estimating its true mass.

A leptonic decay of the W boson, where it decays to an electron and an electron antineutrino. This channel, along with the muon + muon antineutrino channel, formed the basis of CDF’s W mass measurement.

Many of the key observables for this measurement flow from the lepton’s momentum, which means it needs to be measured very carefully! The analysis team calibrated their energy and momentum measurements by using the decays of other Standard Model particles: the ϒ(1S) and J/ψ mesons, and the Z boson. These particles’ masses are very precisely known from other experiments, and constraints from these measurements helped physicists understand how accurately CDF reconstructs a particle’s energy. For momentum measurements in the tracker, they reconstructed the ϒ(1S) and J/ψ masses from their decays to muon-antimuon pairs inside CDF, and compared CDF-measured masses to their known values from other experiments. This allowed them to calculate a correction factor to apply to track momenta. For ECAL energy measurements, they looked at samples of Z and W bosons decaying to electrons, and measured ratio of energy deposited in the ECAL (E) to the momentum measured in the tracker (p). The shape of the E/p distribution then allowed them to calculate an energy calibration for the ECAL.

**Left**: the fractional deviation of the measured muon momentum relative to its true momentum (y-axis), as a function of the muon’s average inverse transverse momentum. Data from ϒ(1S), J/ψ, and Z decays are shown, and the fit line (in black) has a slope consistent with zero. This indicates that there is no significant mismodeling of the energy lost by a particle flying through the detector. **Right**: the distribution of the ratio energy measured in the ECAL to momentum measured in the tracker. The shape of the peak and tail are used to calibrate the ECAL energy measurements.

To make sure their tracker and ECAL calibrations worked correctly, they applied them in measurements of the Z boson mass in the electron and muon decay channels. Thankfully, their measurements were consistent with the world average in both channels, providing an important cross-check of their calibration strategy.

Having done everything humanly possible to minimize uncertainties and calibrate their measurements, the analysis team was finally ready to measure the W mass. To do this, they simulated W boson events with many different settings for the W mass (an additional mountain of effort went into ensuring that the simulations were as accurate as possible!). At each mass setting, they extracted “template” distributions of the lepton p_T, neutrino p_T, and W boson transverse mass, and fit each template to the distribution measured in real CDF data. The templates that best fit the measured data correspond to CDF’s measured value of the W mass (plus some additional legwork to calculate uncertainties)

The reconstructed W boson transverse mass distribution in the muon + muon antineutrino decay channel. The best-fit template (red) is plotted along with the background distribution (gray) and the measured data (black points).

After years of careful analysis, CDF’s measurement of m_W = 80,433.5 ± 9.4 MeV sticks out like a sore thumb. If it stands up to the close scrutiny of the particle physics community, it’s further evidence that something new and mysterious lies beyond the Standard Model. The only way to know for sure is to make additional measurements, but in the meantime we’ll all be happily puzzling over what this might mean.

CDF’s W mass measurement (bottom), shown alongside results from other experiments and the SM expectation (gray).

Quanta Magazine’s coverage of the measurement

A recorded talk from the Fermilab Wine & Cheese seminar covering the result in great detail

This is part one of our coverage of the CDF W mass result covering its implications. Read about the details of the measurement in a sister post here!

Last week the physics world was abuzz with the latest results from an experiment that stopped running a decade ago. Some were heralding this as the beginning of a breakthrough in fundamental physics, headlines read “Shock result in particle experiment could spark physics revolution” (BBC). So what exactly is all the fuss about?

The result itself is an ultra-precise measurement of the mass of the W boson. The W boson is one of the carriers of weak force and this measurement pegged its mass at 80,433 MeV with an uncertainty of 9 MeV. The excitement is coming because this value disagrees with the prediction from our current best theory of particle physics, the Standard Model. In theoretical structure of the Standard Model the masses of the gauge bosons are all interrelated. In the Standard Model the mass of the W boson can be computed based on the mass of the Z as well as few other parameters in the theory (like the weak mixing angle). In a first approximation (ie to the lowest order in perturbation theory), the mass of the W boson is equal to the mass of the Z boson times the cosine of the weak mixing angle. Based on other measurements that have been performed including the Z mass, the Higgs mass, the lifetime of muons and others, the Standard Model predicts that the mass of the W boson should be 80,357 (with an uncertainty of 6 MeV). So the two numbers disagree quite strongly, at the level of 7 standard deviations.

If the measurement and the Standard Model prediction are both correct, this would imply that there is some deficiency in the Standard Model; some new particle interacting with the W boson whose effects haven’t been unaccounted for. This would be welcome news to particle physicists, as we know that the Standard Model is an incomplete theory but have been lacking direct experimental confirmation of its deficiencies. The size of the discrepancy would also mean that whatever new particle was causing the deviation may also be directly detectable within our current or near future colliders.

If this discrepancy is real, exactly what new particles would this entail? Judging based on the 30+ (and counting) papers released on the subject in the last week, there are a good number of possibilities. Some examples include extra Higgs bosons, extra Z-like bosons, and vector-like fermions. It would take additional measurements and direct searches to pick out exactly what the culprit was. But it would hopefully give experimenters definite targets of particles to look for, which would go a long way in advancing the field.

But before everyone starts proclaiming the Standard Model dead and popping champagne bottles, its important to take stock of this new CDF measurement in the larger context. Measurements of the W mass are hard, that’s why it has taken the CDF collaboration over 10 years to publish this result since they stopped taking data. And although this measurement is the most precise one to date, several other W mass measurements have been performed by other experiments.

The Other Measurements

A plot summarizing the various W mass measurements performed to date — A summary of all the W mass measurements performed to date (black dots) with their uncertainties (blue bars) as compared to the the Standard Model prediction (yellow band). One can see that this new CDF result is in tension with previous measurements. (source)

Previous measurements of the W mass have come from experiments at the Large Electron-Positron collider (LEP), another experiment at the Tevatron (D0) and experiments at the LHC (ATLAS and LHCb). Though none of these were as precise as this new CDF result, they had been painting a consistent picture of a value in agreement with the Standard Model prediction. If you take the average of these other measurements, their value differs from the CDF measurement the level about 4 standard deviations, which is quite significant. This discrepancy seems large enough that it is unlikely to arise from purely random fluctuation, and likely means that either some uncertainties have been underestimated or something has been overlooked in either the previous measurements or this new one.

What one would like are additional, independent, high precision measurements that could either confirm the CDF value or the average value of the previous measurements. Unfortunately it is unlikely that such a measurement will come in the near future. The only currently running facility capable of such a measurement is the LHC, but it will be difficult for experiments at the LHC to rival the precision of this CDF one.

W mass measurements are somewhat harder at the LHC than the Tevatron for a few reasons. First of all the LHC is proton-proton collider, while the Tevatron was a proton-antiproton collider, and the LHC also operates at a higher collision energy than the Tevatron. Both differences cause W bosons produced at the LHC to have more momentum than those produced at the Tevatron. Modeling of the W boson’s momentum distribution can be a significant uncertainty of its mass measurement, and the extra momentum of W’s at the LHC makes this a larger effect. Additionally, the LHC has a higher collision rate, meaning that each time a W boson is produced there are actually tens of other collisions laid on top (rather than only a few other collisions like at the Tevatron). These extra collisions are called pileup and can make it harder to perform precision measurements like these. In particular for the W mass measurement, the neutrino’s momentum has to be inferred from the momentum imbalance in the event, and this becomes harder when there are many collisions on top of each other. Of course W mass measurements are possible at the LHC, as evidenced by ATLAS and LHCb’s already published results. And we can look forward to improved results from ATLAS and LHCb as well as a first result from CMS. But it may be very difficult for them to reach the precision of this CDF result.

A histogram of the transverse mass of the W from the ATLAS result. Showing how 50 MeV shifts in the W mass change the spectrum by extremely small amounts (a few tenths of a percent). — A plot of the transverse mass (one of the variables used in a measurement) of the W from the ATLAS measurement. The red and yellow lines show how little the distribution changes if the W mass changes by 50 MeV, which is around two and half times the uncertainty of the ATLAS result. These shifts change the distribution by only a few tenths of a percent, illustrating the difficulty involved. (source)

The Future

A future electron positron collider would be able to measure the W mass extremely precisely by using an alternate method. Instead of looking at the W’s decay, the mass could be measured through its production, by scanning the energy of the electron beams very close to the threshold to produce two W bosons. This method should offer precision significantly better than even this CDF result. However any measurement from a possible future electron positron collider won’t come for at least a decade.

In the coming months, expect this new CDF measurement to receive a lot buzz. Experimentalists will be poring over the details trying to figure out why it is in tension with previous measurements and working hard to produce new measurements from LHC data. Meanwhile theorists will write a bunch of papers detailing the possibilities of what new particles could explain the discrepancy and if there is a connection to other outstanding anomalies (like the muon g-2). But the big question of whether we are seeing the first real crack in the Standard Model or there is some mistake in one or more of the measurements is unlikely to be answered for a while.

If you want to learn about how the measurement actually works, check out this sister post!

Cern Courier “CDF sets W mass against the Standard Model“

Blog post on the CDF result from an (ATLAS) expert on W mass measurements “[Have we] finally found new physics with the latest W boson mass measurement?”

PDG Review “Electroweak Model and Constraints on New Physics“