Too Massive? New measurement of the W boson’s mass sparks intrigue

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!

Read More:

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

The Higgs Comes Out of its Shell

Title : “First evidence for off-shell production of the Higgs boson and measurement of its width”

Authors : The CMS Collaboration

Link : https://arxiv.org/abs/2202.06923

CMS Analysis Summary : https://cds.cern.ch/record/2784590?ln=en

If you’ve met a particle physicist in the past decade, they’ve almost certainly told you about the Higgs boson. Since its discovery in 2012, physicists have been busy measuring as many of its properties as the ATLAS and CMS datasets will allow, including its couplings to other particles (e.g. bottom quarks or muons) and how it gets produced at the LHC. Any deviations from the standard model (SM) predictions might signal new physics, so people are understandably very eager to learn as much as possible about the Higgs.

Amidst all the talk of Yukawa couplings and decay modes, it might occur to you to ask a seemingly simpler question: what is the Higgs boson’s lifetime? This turns out to be very difficult to measure, and it was only recently — nearly 10 years after the Higgs discovery — that the CMS experiment released the first measurement of its lifetime.

The difficulty lies in the Higgs’ extremely short lifetime, predicted by the standard model to be around 10⁻²² seconds. This is far shorter than anything we could hope to measure directly, so physicists instead measured a related quantity: its width. According to the Heiseinberg uncertainty principle, short-lived particles can have significant uncertainty in their energy. This means that whenever we produce a Higgs boson at the LHC and reconstruct its mass from its decay products, we’ll measure a slightly different mass each time. If you make a histogram of these measurements, its shape looks like a Breit-Wigner distribution (Fig. 1) peaked at the nominal mass and with a characteristic width .

Fig. 1: A Breit-Wigner curve, which describes the distribution of masses that a particle takes on when it’s produced at the LHC. The peak sits at the particle’s nominal mass, and production within the width is most common (“on-shell”). The long tails allow for rare production far from the peak (“off-shell”).

So, the measurement should be easy, right? Just measure a bunch of Higgs decays, make a histogram of the mass, and run a fit! Unfortunately, things don’t work out this way. A particle’s width and lifetime are inversely proportional, meaning an extremely short-lived particle will have a large width and vice-versa. For particles like the Z boson — which lives for about 10⁻²⁵ seconds — we can simply extract its width from its mass spectrum. The Higgs, however, sits in a sweet spot of experimental evasion: its lifetime is too short to measure, and the corresponding width (about 4 MeV) cannot be resolved by our detectors, whose resolution is limited to roughly 1 GeV.

To overcome this difficulty, physicists relied on another quantum mechanical quirk: “off-shell” Higgs production. Most of the time, a Higgs is produced on-shell, meaning its reconstructed mass will be close to the Breit-Wigner peak. In rare cases, however, it can be produced with a mass very far away from its nominal mass (off-shell) and undergo decays that are otherwise energetically forbidden. Off-shell production is incredibly rare, but if you can manage to measure the ratio of off-shell to on-shell production rates, you can deduce the Higgs width!

Have we just replaced one problem (a too-short lifetime) with another one (rare off-shell production)? Thankfully, the Breit-Wigner distribution saves the day once again. The CMS analysis focused on a Higgs decaying to a pair of Z bosons (Fig. 2, left), one of which must be produced off-shell (the Higgs mass is 125 GeV, whereas each Z is 91 GeV). The Z bosons have a Breit-Wigner peak of their own, however, which enhances the production rate of very off-shell Higgs bosons that can decay to a pair of on-shell Zs. The enhancement means that roughly 10% of H → ZZ decays are expected to involve an off-shell Higgs, which is a large enough fraction to measure with the present-day CMS dataset!

Fig. 2: The signal process involving a Higgs decay to Z bosons (left), and background ZZ production without the Higgs (right)

To measure the off-shell H → ZZ rate, physicists looked at events where one Z boson decays to a pair of leptons and the other to a pair of neutrinos. The neutrinos escape the detector without depositing any energy, generating a large missing transverse momentum which helps identify candidate Higgs events. Using the missing momentum as a proxy for the neutrinos’ momentum, they reconstruct a “transverse mass” for the off-shell Higgs boson. By comparing the observed transverse mass spectrum to the expected “continuum background” (Z boson pairs produced via other mechanisms, e.g. Fig. 2, right) and signal rate, they are able to extract the off-shell production rate.

After a heavy load of sophisticated statistical analysis, the authors found that off-shell Higgs production happened at a rate consistent with SM predictions (Fig. 3). Using these off-shell events, they measured the Higgs width to be 3.2 (+2.4, -1.7) MeV, again consistent with the expectation of 4.1 MeV and a marked improvement upon the previously measured limit of 9.2 MeV.

Fig. 3: The best-fit “signal strength” parameters for off-shell Higgs production in two different modes: gluon fusion (x-axis, shown also in the leftmost Feynman diagram above) and associated production with a vector boson (y-axis). Signal strength measures how often a process occurs relative to the SM expectation, and a value of 1 means that it occurs at the rate predicted by the SM. In this case, the SM prediction (X) is within one standard deviation of the best fit signal strength (diamond).

Unfortunately, this result doesn’t hint at any new physics in the Higgs sector. It does, however, mark a significant step forward into the era of precision Higgs physics at ATLAS and CMS. With a mountain of data at our fingertips — and much more data to come in the next decade — we’ll soon find out what else the Higgs has to teach us.

Read More

“Life of the Higgs Boson” – Coverage of this result from the CMS Collaboration

“Most Particles Decay — But Why?” – An interesting article by Matt Strassler explaining why (some) particles decay

“The Physics Still Hiding in the Higgs Boson” – A Quanta article on what we can learn about new physics by measuring Higgs properties

Measuring the Tau’s g-2 Too

Title : New physics and tau g2 using LHC heavy ion collisions

Authors: Lydia Beresford and Jesse Liu

Reference: https://arxiv.org/abs/1908.05180

Since April, particle physics has been going crazy with excitement over the recent announcement of the muon g-2 measurement which may be our first laboratory hint of physics beyond the Standard Model. The paper with the new measurement has racked up over 100 citations in the last month. Most of these papers are theorists proposing various models to try an explain the (controversial) discrepancy between the measured value of the muon’s magnetic moment and the Standard Model prediction. The sheer number of papers shows there are many many models that can explain the anomaly. So if the discrepancy is real,  we are going to need new measurements to whittle down the possibilities.

Given that the current deviation is in the magnetic moment of the muon, one very natural place to look next would be the magnetic moment of the tau lepton. The tau, like the muon, is a heavier cousin of the electron. It is the heaviest lepton, coming in at 1.78 GeV, around 17 times heavier than the muon. In many models of new physics that explain the muon anomaly the shift in the magnetic moment of a lepton is proportional to the mass of the lepton squared. This would explain why we are a seeing a discrepancy in the muon’s magnetic moment and not the electron (though there is a actually currently a small hint of a deviation for the electron too). This means the tau should be 280 times more sensitive than the muon to the new particles in these models. The trouble is that the tau has a much shorter lifetime than the muon, decaying away in just 10-13 seconds. This means that the techniques used to measure the muons magnetic moment, based on magnetic storage rings, won’t work for taus. 

Thats where this new paper comes in. It details a new technique to try and measure the tau’s magnetic moment using heavy ion collisions at the LHC. The technique is based on light-light collisions (previously covered on Particle Bites) where two nuclei emit photons that then interact to produce new particles. Though in classical electromagnetism light doesn’t interact with itself (the beam from two spotlights pass right through each other) at very high energies each photon can split into new particles, like a pair of tau leptons and then those particles can interact. Though the LHC normally collides protons, it also has runs colliding heavier nuclei like lead as well. Lead nuclei have more charge than protons so they emit high energy photons more often than protons and lead to more light-light collisions than protons. 

Light-light collisions which produce tau leptons provide a nice environment to study the interaction of the tau with the photon. A particles magnetic properties are determined by its interaction with photons so by studying these collisions you can measure the tau’s magnetic moment. 

However studying this process is be easier said than done. These light-light collisions are “Ultra Peripheral” because the lead nuclei are not colliding head on, and so the taus produced generally don’t have a large amount of momentum away from the beamline. This can make them hard to reconstruct in detectors which have been designed to measure particles from head on collisions which typically have much more momentum. Taus can decay in several different ways, but always produce at least 1 neutrino which will not be detected by the LHC experiments further reducing the amount of detectable momentum and meaning some information about the collision will lost. 

However one nice thing about these events is that they should be quite clean in the detector. Because the lead nuclei remain intact after emitting the photon, the taus won’t come along with the bunch of additional particles you often get in head on collisions. The level of background processes that could mimic this signal also seems to be relatively minimal. So if the experimental collaborations spend some effort in trying to optimize their reconstruction of low momentum taus, it seems very possible to perform a measurement like this in the near future at the LHC. 

The authors of this paper estimate that such a measurement with a the currently available amount of lead-lead collision data would already supersede the previous best measurement of the taus anomalous magnetic moment and further improvements could go much farther. Though the measurement of the tau’s magnetic moment would still be far less precise than that of the muon and electron, it could still reveal deviations from the Standard Model in realistic models of new physics. So given the recent discrepancy with the muon, the tau will be an exciting place to look next!

Read More:

An Anomalous Anomaly: The New Fermilab Muon g-2 Results

When light and light collide

Another Intriguing Hint of New Physics Involving Leptons