W-boson appears to be heavier than predicted by the Standard Model

The result of a decade-long analysis of millions of archived particle collision events reveals that the W boson may be significantly heavier than predicted by the Standard Model. This could be one more indicator of new physics.

The CDF detector, one of the two detectors placed at different points around the six-kilometre ring of the Tevatron particle accelerator at Fermilab, Illinois, U.S. This photograph was taken during its installation in 2001.

FOR Fermilab, the premier particle accelerator laboratory in Illinois, United States, April 7 seems to be a favourite date for coming up with bombshells that shake and threaten to topple the Standard Model of Particle Physics (SM for short), an otherwise spectacularly successful theory that describes the universe in terms of fundamental particles and forces of nature.

Startling announcement

On April 7 this year, Fermilab made a startling announcement on the basis of a peer-reviewed research publication in the eminent journal Science . A decade-long high-precision analysis of over four million archived events of proton-antiproton collisions, recorded with the detector called CDF at the laboratory’s erstwhile collider-accelerator called Tevatron before it was shut down in 2011, has shown that the mass of the particle called W-boson is significantly heavier than the prediction of the SM. The CDF collaborating team sees this as a definitive pointer to “physics beyond the SM”. In the Standard Model’s scheme of things, the charged W+ and W− bosons are carriers of the weak nuclear force.

On April 7, 2021, too Fermilab sprang a surprise, from an experiment called “g-2”. The experiment’s finding conclusively established with more and better data an earlier result from the Brookhaven National Laboratory in New York: that the “anomalous magnetic moment” (g-2) of the particle called muon (where g is its magnetic moment) differed significantly from the value expected from the SM.

By measuring with high precision the rate of a muon’s wobble, or precession, around the direction of intense magnetic field as it moves around in the muon ring at Fermilab that houses the six-kilometre circular Tevatron accelerator, Fermilab scientists had determined the extent of departure of the quantity (g-2) from the SM-predicted value. This too had been interpreted to be an indicator of new physics. Physics beyond the SM could be in the nature of new unseen particles or forces. Indeed, some theorists working on devising new theories beyond the SM believe that the same extensions to the SM can cure at the same time both the ills of the W-boson mass and the value of the muon’s anomalous magnetic moment.

The SM describes the universe in terms of the following 17 fundamental particles: six quarks (three families of two each), six leptons (three families of two each), the massless photon (carrier of the electromagnetic force), the massive W, (charge neutral) Z0 bosons (carriers of the weak nuclear force), a massive Higgs boson (which endows mass to all massive particles) and massless gluons (carriers of the strong nuclear force) and their antiparticles. Quarks make up the nuclei of atoms and the family of leptons includes the familiar electron, muon and neutrinos (Fig. 1).

For physicists it is a truism that the SM is not a complete theory given its inability to explain many observed phenomena. While the theory unifies into a single mathematical framework electromagnetism, the weak nuclear force (which causes radioactive decay and nuclear fusion that powers the sun) and the strong nuclear force (which binds the nuclei in the atoms of all matter), which are highly disparate in character, the model fails to accommodate the ubiquitous force of gravity.

Further, the theory cannot explain dark matter and dark energy, which physicists think are necessary to explain the large-scale structure of the universe. It cannot explain the preponderance of matter over antimatter seen in the universe. It cannot explain why there is “parity violation” in particle processes caused by the weak nuclear force such as radioactivity. The symmetry expected in the mirror world—where particle charges are flipped and spatial coordinates are inverted—is violated in particle processes in the subatomic world when the weak nuclear force is involved. In fact, this property of parity violation of the weak nuclear force is put in by hand in the SM. As a consequence, the ghostly particle called neutrino remains massless in the theory, whereas experimentally it is known to have a mass, albeit tiny. The muon magnetic moment conundrum is another. If other experiments confirm the W-mass result from Fermilab, it will be yet another problem for the SM.

But the theory has had remarkable success in predicting many particle processes with high precision, most notably the existence of Higgs boson, which was discovered at the Large Hadron Collider (LHC) at CERN (the European Organisation for Nuclear Research) in Geneva in 2012. It fetched the scientists who proposed the central idea of a Higgs particle to achieve unification of electromagnetism the coveted Nobel Prize in Physics in 2013. It is this all-pervasive Higgs field that interacts with the other fundamental particles of the theory in such a way that it endows mass to all particles of the theory except neutrinos, the photon (which mediates electromagnetism) and gluons (which mediate the strong nuclear force).

Many theoretical ideas have been put forward to form the basis of a more complete theory that would replace the SM. But none has emerged strongly enough to resolve all the problems of the SM, both relating to phenomena that it cannot explain and the mismatch between experimental data and the SM’s predictions in some particle processes.

The mass of the W-boson is about 80 times the mass of the proton, which is about 1,000 million electronvolts (MeV) in units of energy as per Einstein’s mass-energy equivalence relation E=mc2. There have been several measurements of W-boson mass over the last four decades since the particle was discovered in 1983. Results of all these were compatible with the value predicted by the SM, though these, admittedly, did not have the precision of the present work. But before we discuss the implications of CDF’s new measurement that is significantly at variance with the earlier measurements, it must be appreciated that measurement of W-mass is a big deal in itself.

The SM prediction of W-mass in 1983 was 78,1501,500 MeV and the measured value was 80,000 MeV with an error margin of a few thousand MeV. From that, today one has come a long way with the accuracy of measurement having improved to tens of MeV, and the uncertainty in theoretical prediction too is now of similar order. “To be honest,” said Rohini Godbole of the Centre for Theoretical Studies at the Indian Institute of Science, Bengaluru, “it was then felt that it will be an electron-positron collider, rather than proton(-antiproton) colliders, that would make this breakthrough in high precision measurement of W-mass. But, more importantly, it is not just the increased accuracy of direct measurement but also [the fact] that the central value has shifted significantly compared to the earlier results.”

The SM does not predict the absolute mass of the W-boson directly, but it does predict the ratio between W- and Z-boson masses. To make theoretical estimates, however, one needed to know the mass of the Higgs boson, which was not known in 2011 when the Tevatron shut down. It was only in 2012 that the LHC determined the Higgs boson mass to be 125,350 MeV. Once one knows the Z-mass, calculation of W-mass precisely becomes possible. This was one of the driving forces behind the CDF team carrying out high-precision experiments to verify the SM prediction and look for hints of new physics beyond the SM, according to Ashutosh Kotwal of Duke University, North Carolina, who has been the prime mover of this monumental decade-long analysis of archived data.

In W-mass measurement experiments in colliders, W-bosons produced in high-energy particle collisions are detected from their decays into either an electron, or its heavier cousin muon, plus a neutrino. If the energies of all the decay particles could be measured, the mass of the W particle that produced them could be immediately calculated. But since the neutrino is undetectable, the W-boson mass must be inferred from only half of the energy, especially when one does not know what fraction of the electron/muon energy comes from the W-boson’s mass and what fraction from the W-boson’s momentum. “And, to measure the energies of high-energy particles with a precision of 0.01 per cent that we have achieved is extremely challenging,” Kotwal said in an email to Frontline .

As mentioned above, using data collected by the Tevatron’s detector called CDF, the scientific team comprising 400 scientists has now determined the W-boson mass to be 0.09 per cent higher than the value predicted by the SM. While this may seem a tiny discrepancy, it is significant when compared with the precision of 0.01 per cent with which the mass has been determined.

The central value that the CDF collaboration team has obtained after analysing the entire data set of 4.2 million W-boson candidate events collected from the Tevatron collider between 2002 and 2011 is 80,433 MeV with an error window of only 9.4 MeV. The number of events analysed this time around is four times the number used in the earlier result published by the CDF team in 2012 on the basis of the first five years of data. The present result (with 0.01 per cent accuracy) is two times more precise than the previous best result obtained by the team working with the ATLAS detector at the LHC, which was 80,370 MeV19 MeV.

In fact, only in January 2022 did the research team working with the detector called LHCb at the LHC measure the W-mass value to be 80,354 MeV with an error margin of 32 MeV, which is quite commendable considering the various uncertainties that LHC measurements come with. The result was published in Journal of High Energy Physics . The experiment used data recorded from approximately 170 trillion proton-proton collisions during Run 2 of the LHC in 2016 at 13 trillion electronvolts (TeV) of total collision energy. Although it was only a proof of principle experiment for the measurement of W mass with the LHCb detector, and the LHCb team is now in the process of improving the accuracy by almost a factor of 2, the scientists did conclude that the first results were in agreement with the global W-mass average and the SM prediction.

The new CDF measurement is, however, in disagreement with all other previous measurements of W-boson mass, including, of course, the recent LHCb value. As mentioned before, notwithstanding their significantly larger error margins, these were all in conformity with the best theoretical SM value of 80,357 6 MeV (Fig. 2a). The latest CDF value of 80,4339.4 MeV, however, deviates from SM’s theoretical prediction by about 7 standard deviations (or sigma in statistical terminology), which is indicative of a significant discrepancy. A 7-sigma departure implies that, if the result is correct, there is just one in a trillion chance that the SM prediction is consistent with the experiment. In particle physics, a 5-sigma departure is considered the gold standard for any discovery.

“The measurement is in significant tension with the SM expectation ... suggests the possibility of improvements to the SM calculations or of extensions to the SM,” said the CDF’s April 7 paper in Science . Kotwal has been quoted as saying that this was “the largest crack in this beautiful theory” and that it might be the first clear evidence of other forces or particles not accounted for by the SM and which might be accounted for by theories such as the long-studied “supersymmetry” theory. Supersymmetry links particles and force-carriers and hypothesises the existence of a hitherto unknown “supersymmetric partner” to each known particle.

“While this is an intriguing result, the measurement needs to be confirmed by another experiment before it can be interpreted fully,” Fermilab Deputy Director Joe Lykken said in a statement. “I do not think,” wrote ATLAS researcher Matthias Schott of the University of Mainz, Germany, in his personal blog, “we have to discuss which new physics could explain the discrepancy between CDF and the Standard Model—we first have to understand why the CDF measurement is in strong tension with all others.” Chris Quigg, a Fermilab theorist, made a similar remark in the online magazine Quanta . He said: “I would say this is not a discovery, but a provocation. This now gives a reason to come to terms with this outlier.”

While striking a cautionary note, Schott also had some criticism about part of the analysis by the CDF group. Pointing out that the early results obtained from the Large Electron Positron Collider (LEP) at CERN before it shut down in November 2000 and the latest results from the LHCb had not been included in its combined analysis to arrive at the global average for the W-mass, Schott remarked that if one combined all the measurements obtained so far (except CDF) properly, the global average was 80,37114 MeV, and its discrepancy from the CDF value was only 4-sigma (Fig. 2b). He also underlined the problems associated with the software programme called RESBOS used by the CDF group for reconstruction of events.

“Admittedly,” said Debajyoti Choudhury, a theorist at Delhi University, “the error bar in the LHCb measurement is large, and so it would be expected have less weight. However, it still ought to have been considered—the error bars are not that much larger than those for the other experiments [Fig. 2a]—especially since the central value is on the opposite side of the SM value, though consistent with the SM.”

When Frontline asked Kotwal over email for his comments on the conflict between the CDF measurement and the LHCb value, and the fact that the CDF paper had not included the same in the global analysis, he said: “[T]he CDF measurement of the boson mass is 3.4 times more precise than that from LHCb. [However,] the statistical compatibility of the two values is not that small; meaning that they are not in serious conflict. We have included the LEP results as shown in the last line of our paper. We could not include the LHCb results because the result was not published [in any peer-reviewed journal] when we submitted our paper.”

As for the use of the RESBOS programme, Kotwal said: “We have used CDF data to demonstrate that RESBOS describes W-boson production well at the Tevatron. The same proof has also been provided by the D0 collaboration [a different experiment] at the Tevatron in all its papers about W-boson. There is no scientific publication demonstrating a problem with the use of RESBOS at Tevatron.”

The above reservations notwithstanding, extracting a very high precision value of W-mass after 10 years of painstaking analysis of a huge amount of data is indeed phenomenal. “The number of improvements and extra checking that went into our result is enormous,” Kotwal was quoted as saying in the Fermilab release of April 7. “We took into account our improved understanding of our particle detector as well as advances in the theoretical and experimental understanding of the W boson’s interactions with other particles.”

“Importantly,” Kotwal said in his email response, “our analysis procedures demonstrate a number of very precise checks of internal consistency, which no other analysis published in the last four decades has demonstrated at this level. The combination of a four times larger dataset, more insightful methods and ideas of using data, and new information about the proton structure allowed us to improve the precision of this measurement substantially.”

He elaborated further: “We have achieved the highest precision ever achieved for the measurement of particle energies in all W-boson mass measurements ever made. This includes a precision of 1 micrometre achieved on the placement of the particle tracking sensors. We have calibrated the magnetic field to a precision of 0.004 per cent. We have proven our calibrations by making independent measurements of the Z boson mass, which are consistent with its known value to a precision better than 0.01 per cent.”

Even as the ATLAS and LHCb research teams are at work trying to improve W-mass measurements, achieving very high precision in such measurements at the LHC is inherently much more challenging and difficult point out scientists. “A convincing measurement of similar precision at the LHC will require a large cumulative data at the high-luminosity phase of the LHC,” pointed out Biswarup Mukhopadhyaya, a high-energy physicist at the Indian Institute of Science Education and Research , Kolkata. “One thus has to wait for quite some time once the high luminosity run begins.”

“W boson production at the LHC is more complicated than at the Tevatron,” said Kotwal. “W bosons at the LHC are faster-moving in all directions, compared to the Tevatron. As a result, it becomes more difficult to infer the W-boson mass from the energy of the electron or muon emanating from the W-boson. Secondly, at the Tevatron the beams are protons and antiprotons. Therefore W+ and W− bosons are produced identically, simplifying their combined analysis. At the LHC, due to the proton beams, W+ and W− boson production is very different, and each is more complicated. This complicates their combined analysis. Thirdly, the knowledge of the proton and antiproton [internal] structure is much more precise in the context of the Tevatron than the LHC. Finally, the strong interaction processes are much reduced at the Tevatron compared to the LHC, increasing the purity of the data samples at the Tevatron,” explained Kotwal.

“Much higher centre of mass energy implies LHC analyses must take into consideration higher orders of quantum corrections properly,” pointed out Kajari Mazumdar of the Tata Institute of Fundamental Research who has worked at the LHC for a long time. “Even if the analytical calculations are done for theoretical prediction, simulation of higher order processes to understand the differential distribution is a daunting task. Roughly, [an] uncertainty of 10 MeV requires 2 million W events, which means the simulation must have event statistics larger by at least a factor of 10. This is needed for accurate theoretical modelling, [which is] to be matched with excellent understanding of detector performance,” she said.

Given the above, reconciliation and/or confirmation of results from various W-mass measurement experiments with the CDF value is expected to take a few years at least, and first results in this direction can be expected only from the ongoing LHC experiments ATLAS and LHCb. Therefore, theorists are bound to take this CDF result at face value, especially because of its high accuracy, and get down to business right away.

Although the LHC did not find any hint of supersymmetry even at its highest energy runs, various supersymmetric extensions of the SM are expected to make their bids to bridge the experiment-SM mismatch very soon. Particles predicted by supersymmetry, which have been lying low after the LHC came up blank on them, are likely to be tweaked a little and put on the table again.

Sven Heinemeyer, a particle theorist at the Institute of Theoretical Physics in Madrid, and collaborators recently found that some supersymmetric particles (relatively light particles that affect the electro-weak sector of the SM) could resolve the muon magnetic moment anomaly. But such particles are known to also contribute to the W-mass positively. It is tantalising to speculate that one will be able to kill two birds with one supersymmetric stone. Supersymmetry specialists will very likely begin checking soon whether the shift observed by CDF is consistent with the predictions a la Heinemeyer et al . with regard to the muon (g-2) problem.

Aida El-Khadra, a physicist at the University of Illinois, was quoted by Quanta as saying: “It overall just feels to me like we’re getting close to the point where something’s going to break. We’re getting close to really seeing beyond the Standard Model.” One is tempted to agree with her.