Back in April 2022, the CDF experiment, which operated at the long-ago-closed Tevatron particle collider. presented the world’s most precise measurement of the mass of the particle known as the “W boson“. Their result generated some excited commentary, because it disagreed by 0.1% with the prediction of the Standard Model of particle physics. Even though the mismatch was tiny, it was significant, because the CDF measurement was so exceptionally precise. Any disagreement of such high significance would imply that something has to give: either the Standard Model is missing something, or the CDF measurement is incorrect.
Like most of my colleagues, I was more than a little skeptical about CDF’s measurement. This was partly because it disagreed with the average of earlier, less precise measurements, but mainly because of the measurement’s extreme challenges. To quote a commentary that I wrote at the time,
- “A natural and persistent question has been: “How likely do you think it is that this W boson mass result is wrong?” Obviously I can’t put a number on it, but I’d say the chance that it’s wrong is substantial. Why? This measurement, which took several many years of work, is probably among the most difficult ever performed in particle physics. Only first-rate physicists with complete dedication to the task could attempt it, carry it out, convince their many colleagues on the CDF experiment that they’d done it right, and get it through external peer review into Science magazine. But even first-rate physicists can get a measurement like this one wrong. The tiniest of subtle mistakes will undo it.”
In the weeks following CDF’s announcement, I attended a detailed presentation about the measurement. The physicist who gave it tried to convince us that everything in the measurement had been checked, cross-checked, and understood. However, I did not find the presentation exceptionally persuasive, so my confidence in it did not increase.
But so what? It doesn’t matter what I think. All a theorist like me can do, seeing a measurement like this, is check to see if it is logically possible and conceptually reasonable for the W boson mass to shift slightly without messing up other existing measurements. And it is.
(In showing this is true, I took the opportunity to explain more about how the Standard Model works, and specifically how the W boson’s mass arises from simple math, before showing how the mass could be shifted upwards. Some of you may still find these technical details interesting, even though the original motivation for this series of articles is no longer what it was.)
Instead, what really matters is for other experimental physicists to make the same measurement, to see if they get the same answer as CDF or not. Because of the intricacy of the measurement, this was far easier said than done. But it has now happened.
In the past year, the ATLAS collaboration at the Large Hadron Collider [LHC] presented a new W boson mass measurement consistent with the Standard Model. But because their uncertainties were 60% larger than CDF’s result, it didn’t entirely settle the issue.
Now the CMS collaboration, ATLAS’s competitor at the LHC, has presented their measurement. They have managed to be almost as precise at that of CDF — a truly impressive achievement. And what do they find? Their result, in red below, is fully consistent with the Standard Model, shown as the vertical grey band, and with ATLAS, the bar line just above the red one. The CDF measurement is the bar outlying to the right; it is the only one in disagreement with the Standard Model.
Since the ATLAS and CMS results are both consistent with all other previous measurements as well as with the Standard Model, and since CMS has even reached the same level of uncertainty obtained by CDF, this makes CDF by far the outlier, as you can see above. The tentative but reasonable conclusion is that the CDF measurement is not correct.
Of course, the CDF experimentalists may argue that it is ATLAS and CMS that have made an error, not CDF. One shouldn’t instantly dismiss that out of hand. It’s worth remembering that ATLAS and CMS use the same accelerator to gather their data, and might have used similar logic in the design of their analysis, so it’s not completely impossible for them to have made correlated mistakes. Still, this is far from plausible, so the onus will be on CDF to directly pinpoint an error in their competitors’ work.
Even if the mistake is CDF’s, it’s worth noting that we still have no idea what exactly it might have been. A long chain of measurements and calibrations are required to determine the W boson mass at this level of precision (about one part in ten thousand). It would be great if the error within this chain could be tracked down, but no one may have the stamina to do that, and it is possible that we will never know what went wrong.
But the bottom line is that the discrepancy suggested by the CDF measurement was always a long shot. I don’t think many particle physicists are surprised to see its plausibility fading away.
29 Responses
Thank you. Can you help in assessing two comments I have:
1. Next to Popper/Deutsch’s “conjectural” point of view in the development of theories and ideas, precision measurements have very often led to revolutions in physics, e.g. relativity and quantum mechanics. I think this is a reason for me to look with excitement at future Higgs factories at CERN. Agree?
2. Will CDF data be reanalyzed? I think at this stage that is must-do but I wonder about the incentive of the “system” to do that.
Related, I think one of the finest historical and philosophical analysis of the inner working of HEP experiments is in the wonderful book of Peter Galison “How Experiments End”. Sections 1.1 (Strategies of Demonstration” and 1.2 (Errors and Endings) are particularly insightful (can be found on Google Books).
1. Agree, partially. Too many of my colleagues focus on the Higgs factories as precision machines, as though they are unable to make direct discoveries as well. But this attitude is factually wrong and represents an ongoing blind spot in the community that I and others have been trying to close for 20 years. So I’m excited about a Higgs factory for more than one reason: extreme precision *and* new ways to explore for new particles and forces. To focus on one at the expense of the other is a mistake.
2. Data at CDF (or D0 or at any of the major LHC experiments) is gigantic. No one will reanalyze the entire data set unless there is a compelling reason, which I cannot even imagine at the moment. However, for particular scientific questions, some portion of the data set might be useful, and if the potential rewards justify it, then yes, that portion would be reanalyzed, possibly even from scratch. Physicists are ambitious and practical; they will not waste an opportunity, but they will also not do a huge amount of work where there is no known likelihood of payoff.
Thank you for your reply! Agree, it looks like the potential discovery program is also rich: “Furthermore, the high-statistics samples delivered by FCC-ee offer unique opportunities of direct discoveries beyond the precision programme. Other signals of new physics could arise from the observation of small flavour-changing neutral currents or lepton-flavour-violating decays, from the observation of dark matter in Z and Higgs invisible decays, or by the direct discovery of particles with extremely weak couplings in the 5 to 100 GeV mass range, such as right-handed neutrinos and other exotic particles (see FCC physics CDR [2], Section 12.4 and Chapter 13). These scenarios [94, 95] are well-motivated and, despite the low masses involved, consistent with the constraints imposed by precision measurements.” https://doi.org/10.48550/arXiv.1906.02693. As side note, I like in general Nima Arkani-Hamed’s science case for collider physics and studying the Higgs when he says: “The scientific issues at stake are the most difficult + profound ones we have faced since the epoch of relativity + quantum mechanics”(at 01:31:41 of https://bit.ly/4ezwCKP). Hopefully society will listen …
This post nicely complements the Nature article “‘The standard model is not dead’: ultra-precise particle measurement thrills physicists”. They do suggest that this will be scrutinized:
“Agreeing on humankind’s best guess of the W’s mass will mean bringing together experts from each of the experiments, as well as theorists, to try to understand the differing results. “We shouldn’t leave the CDF result as an outlier, we need to understand why or how it is there,” says Canelli.”
In a similar vein a more precise repeat of the muon magnetic anomaly has been announced in Phys. Rev. D: “Detailed report on the measurement of the positive muon anomalous magnetic moment to 0.20 ppm”. Another blog article notes:
“Despite the current data improving the precision by a factor of over two, the group ultimately concluded that no comparison to theory is yet possible. Even for electrons, some prior experimental data is necessary to correct the theory of hadron effects, and the two experiments available for this correction disagree. Thus, the high precision value for the muon’s magnetic moment is also limited.”
Dr.Strassler:
I always enjoy your commentary on recent scientific events, in order to put perspective on the event. The media always puts twists on things, sometimes by accident, sometimes to make better headlines. It has been my opinion that I just wait to read your blog to get the true meaning of an event. With that said, I have a question, a little off topic….
When an electron passes thru a magnetic field, due to its CHARGE, it will feel the Lorentz force. However, when an electron passes thru a magnetic field, due to its SPIN, it will feel another force. Is the resulting motion of an electron the addition of these two forces?
All forces must indeed be added together. [More precisely, a constant magnetic field just generates a torque on the electron, reorienting it; but a spatially-varying magnetic field can generate a force.]
Even more precisely, in quantum theory one does not focus on forces, which aren’t well-defined in any sense that Newton would recognize. Instead one uses energy as the basis for the calculations (or the “principle of least action”, in Feynman’s methods.) And all forms of energy (or action) are added together in determining how an object’s position and spin change with time.
Dr.Strassler:
I have completed Dr. Shamit Kachru‘s introductory course on string theory, it was very good. I’m now taking an introductory course, on the many worlds theory, by Dr.Sean Carroll. I believe you know Dr.Carroll, so please tell him his course on “The Many Hidden Worlds of Quantum Mechanics” is excellent.
However, I have a question for you. I know Dr.Carroll is a big pro-ponnent of the Many Hidden Worlds Theory, and I respect him greatly, as I have read all his books. But, some of the concepts are a little hard to digest. In the main stream physics community, how “accepted” is many hidden worlds? Is it on the border of fringe?
I
Most people I know are deeply unsatisfied with our understanding of quantum physics. However, if you just look at the math and take seriously that a single wave function is supposed to describe everything in the universe, including all of us, and run the Schrodinger equation forward, you end up with an extraordinarily complex wave function, describing a gargantuan range of possibilities. If that’s not supposed to describe a many-worlds universe, the onus is on the rest of us to come up with a different interpretation of what it means. At the moment, there aren’t many options. I’m certainly not smart enough to understand it.
In this context, many worlds is a mathematically sensible perspective. Whether it is conceptually sensible is a matter of taste. Certainly it’s a perspective that most people are still uncomfortable with. So it’s not fringe, but it’s not widely accepted either. I have no idea what will happen in the future…
Hi Matt, great synopsis and I definitely share your skepticism of the CDF result. If I recall from a talk I saw last year from the CDF spokespeople, I thought that there was also some issue with interpretation and the actual procedure that CDF used to extract the W mass, which was distinct from that of the LHC experiments. If I recall, CDF used extremely few nuisance parameters in their W mass fit (maybe just the W mass itself?), while LHC experiments had hundreds that are all tuned to extract the one parameter of interest. I trust the CDF experimentalists, but I almost feel this is more of a case that both measurements are “right”, but they are simply not comparable because the methods for extraction of the W mass are so very different. If anything, I think the errors on the CDF result cannot be representative, if those errors are to be comparable to the W mass extraction from LHC experiments.
In addition to scientific issues, there is also the rather strange and disconcerting way that the CDF result was published, through the embargoed journal Science, so no one in the community knew about the result until it was already in print. That sociological context is perhaps what concerns me the most about this result. The optics of such a choice of publishing is at best merely odd for (otherwise open source) particle physics, and at worse covering up some serious issues with the analysis that could not be worked out by the community in the time between preprint and publication.
Hi Andrew — thanks for your comment. I’m a little confused by your philosophy as outlined in the first paragraph. (I have nothing useful to say about the second paragraph, since how to publish is a judgment call.)
For an experiment to be “right”, it must have a central value *and* an uncertainty such that it is not significantly different from the truth. Mistakes can be made at either stage.
That is, one type of mistake can lead to the wrong central value — shifting the entire result in the figure to the left or right. This is the easiest mistake to find, since it means that in one of the steps leading to the final result, a wrong intermediate measurement was made, and a repeat of the intermediate measurement will potentially find this mistake.
The other type of mistake would be an underestimate of the uncertainty of one’s methods, so that the measurement does not shift but the width of the uncertainty bar expands to reach or more closely approach the Standard Model value. I think this is the more likely problem, in this case. It is also much harder to find, because it may have to do with assumptions about one’s methods and about what one does or doesn’t know about one’s detector or about inputs (possibly incorrect) that come from outside and are used (correctly or incorrectly) in the measurement. One usually cannot prove mistakes of this type by simply repeating the measurement as it was originally done; instead one has to do many other experiments to find a step in the methodology where an assumption was incorrect and went unchecked because of a blind spot in the experimenter’s thinking.
And of course there are hybrid possibilities where both types of problems occur in concert.
All of which is to say that I don’t think one can say that the CDF measurement on the one hand, and all the others on the other hand, can all be “right”. They are measuring the same physical quantity and they are in disagreement. Somebody has the wrong central value or the wrong uncertainty, and the use of different methods and approaches can’t justify that, it seems to me.
Hi Matt, fair point, but I guess what I mean is that it seems like the measurement methodologies are so different between CDF and other measurements, one concern I had heard is that they are not really comparable at all. In other contexts, this would be like measuring the strong coupling without varying pdf fits in concert. From this perspective, I think one argument is that CDF actually did not measure (what almost everyone would say actually is) the W mass at all, but some other parameter of the SM that corresponds to some fixed set of choices for the Z mass, alpha_s, pdfs, decay rates, etc., and not actually the best fit to the data. CDF’s W mass measurement should then just be (one of many) weighted contributions to an overall best fit. As such, I guess what their central value is is less important (fixed by their choices of values of other parameters), but the uncertainty would be vastly underestimated from this perspective.
I see — so are you saying the situation is somewhat similar to measuring two different definitions of the top quark mass? Just with a much higher level of subtlety and precision?
Yes, that’s right. Though in the top quark case the issues are typically related to simply how to define a Lagrangian parameter, while here it seems like the CDF “W mass” is more of a statistical analysis distinction (at least insofar as I understand).
Hmm. I can see how it might be difficult to define the W mass because of some subtlety of quantum physics. It’s less clear to me how there could be a distinction at the level of statistical analysis; I would think that, in such a case, one of the statistical analyses is simply wrong, as I would have thought the W mass should be defined physically, not at the level of a particular analysis.
Said another way: if I imagine producing the W boson in impractical electron neutrino collisions, and measur it as a resonance using an impractical neutrino detector as well as an electron detector, then the first thing to do would be to define the W boson mass just as I do the Z boson mass. The ambiguities in its definition should be no more and no less than for the Z. Having now defined it, we can attempt to measure this well-defined quantity using CDF or CMS. The only question, it seems to me, is whether the analysis method used does this correctly, and correctly identifies its limitations in doing so. To suggest that there is an ambiguity that is analysis dependent — as opposed to definition dependent, as is the case for the top quark mass — strikes me as a bit bizarre.
But if you are able to find someone who is making a coherent argument in this direction, please let me know.
“I would think that, in such a case, one of the statistical analyses is simply wrong, as I would have thought the W mass should be defined physically, not at the level of a particular analysis.”
Yes, exactly right. It is not an ambiguity of the statistical analysis here and neither presumably anything wrong with the measurements nor systematics of CDF. The simplest explanation is that the CDF statistical analysis, of only varying the purported W mass parameter, is not what should be done to actually extract its value, to ensure consistency with the rest of the SM. I guess my “all experiments are right” statement in my original post lead to this confusion; I meant that there is (to my knowledge) no evidence that anything CDF measured is problematic. Rather, given the quantities that they measured, the CDF extraction of the W mass from them is inconsistent.
“To suggest that there is an ambiguity that is analysis dependent — as opposed to definition dependent, as is the case for the top quark mass — strikes me as a bit bizarre.”
Haha, indeed, bizarre to me, too!
Okay, I get it now, I think: correlations among assumptions and existing measurements were perhaps not correctly accounted for. Thanks!
So, turning your previous “mass of W could be a little higher in an extended SM” post around … how much evidence are the ATLAS/CMS data that the Higgs is a singlet?
So, just to clarify, the statement about the “W mass being a little higher” is that if the ordinary Higgs field, which is a “doublet” in the Standard Model, were accompanied by a second Higgs field which is a “triplet”, then it could lead to a slight upward shift of the W mass.
Meanwhile, the main Higgs field could not possibly be a “singlet”, because to be a singlet would mean that it would not interact via the weak nuclear force, in which case it would not interact with W bosons (or the W field) at all. Then it could not create any W boson mass at all.
In short, if I answer your question literally, the answer is: the evidence is negative, because the W boson does have a mass. Moreover, the Higgs boson clearly does interact with Higgs bosons (the two are often produced simultaneously, and sometimes Higgs bosons decay to W bosons) which would not happen at a measurable rate if the Higgs field were a singlet.
But maybe your question was slightly different?
Yeah. The least “reliant on my faulty memory” (which apparently believes 3-1=1) version would be: “how much evidence are the ATLAS/CMS data that we don’t have triplet Higgs?”
The only thing constrained by the W mass is the average value (i.e. “vacuum expectation value”) of any scalar field that is a triplet under the weak nuclear force. A triplet with a zero average value, or a very small one, is unconstrained. To calculate the limit on that value requires some work, I can’t do it in my head. It should be something like one percent of the standard Higgs field’s average value, or smaller.
Other measurements constrain the mass of the particles that are ripples in the triplet field. I can’t give you those limits off the top of my head either, and they are harder to guess. But if their masses are big enough, limits will be weak.
So your question, as posed, doesn’t have a simple answer… as is typically the case on this business. Only very limited and precise questions have simple answers.
Is it unfair of me to feel that CDF is stuck in a bit of a struggle for relevance?
Yes, I would say it is unfair, but let me explain the reasons, since they aren’t entirely obvious. In fact, I’m considering writing a whole blog post in reply, because I think this gives some insight into how big scientific collaborations work.
First, CDF is not a group of a few hundred people meeting every week and sitting around the table reminiscing about the glory days of the Tevatron and trying to think of ways to grab people’s attention! Almost everyone in CDF (leaving out those who have retired or have left physics for other employment) is currently working at an ongoing physics experiment. Most of them are still in particle physics. Many of them, in fact, work at CMS and ATLAS at the LHC. Large numbers of my particle physics friends were on a Tevatron experiment 20 years ago — CDF or D0 — and are now on an LHC experiment — mainly ATLAS, CMS or LHCb.
So most CDF scientists have multiple ways to “be relevant”. Certainly CDF as a whole does not have a collective consciousness trying to do anything in particular.
Instead, the real issue is that CDF’s data (like that from many other closed experiments) is sitting and waiting to be used, if you can think of something good to do with it. The W boson mass measurement is “something good”. Even ten years ago, you didn’t have to be a part of CDF to understand that CDF’s extensive data in proton-anti-proton collisions gave it a special opportunity to measure the W boson mass with high precision. That opportunity would not be relized unless a few people within CDF’s historical collaboration, with access to and a deep understanding of CDF’s data, and of the accelerator and detector conditions over time, was willing to devote some years of their lives to making that measurement.
So the real issue wasn’t about CDF looking for something useful to do. Everyone knew that CDF’s data was useful for this purpose. The question was: who was willing to try to perform the measurement?
A small number of people decided to give it a shot. It is a highly prestigious measurement to do, because of its extreme difficulty, and it offers the possibility of a Nobel prize *if* the measurement differs from the Standard Model *and* the measurement is correct. It also offers a possibility of complete failure, or of international ridicule if the measurement is carried out but turns out to be incorrect. It therefore requires bravery, ambition, extreme patience, and exceptional skill. Nobody is doing this to “be relevant”; there are much easier ways. They are doing it because it is important for physics, because it is incredibly hard to do, and because the potential reward is great.
Again, CDF makes and claims the measurement, because CDF data was used, and huge numbers of people designed and built CDF and were involved in its data collection. But most people in CDF did not do the hard work of analyzing the data for the W mass measurement. That was a very small group of exceptionally brave, dedicated people. The role of other CDF members was to look over the work of this small group, check it to the extent possible, ask lots of tough questions about it, and, if convinced, to approve its release for potential publication.
To sum up, CDF is not a group of people collectively seeking relevance. Data collection at CDF is over; it’s a done deal. The question as to whether there is something scientifically relevant in their data is a scientific question, not a sociological one. If there is something relevant there, then ideally a group of people will try to use that data for that purpose. That’s what happened here.
In other words, to say “stuck in a struggle for relevance” is a way of saying that CDF aren’t really relevant but were trying to be. It’s the opposite; their data were definitely relevant. If the measurement had been correct (assuming it is indeed incorrect) and had matched the Standard Model, it would have gotten less press, but would have been celebrated within particle physics as a tour-de-force success, the most precise measurement of its kind at the time. The current situation and press coverage is not a sign of irrelevance, but rather a sign of relevance — combined with a probable error, whose nature and subtlety we do not yet know, and which, therefore, it is somewhat premature to criticize.
In my own ‘decaying’ body, I can track its W weak charge over time until its passive demise. I do not understand the process of W weak charge Bosons, how they can change to Leptons or quarks, as its beyond my standard model of thinking. Just because I do not understand such principles, it never alters the truth and accept that. But on the same token, as a theologian and in my limited capacity I perceive some things are possible beyond the Standard Model that have not yet been formulated in the Lab, neither can they be. here is an example, again from a theological approach.
The Law of Conservation of Energy states that energy can neither be created nor destroyed – only converted from one form of energy to another, that a system always has the same amount of energy, UNLESS IT IS ADDED FROM THE OUTSIDE.
Concerning ‘resurrection’
This is where the Power of God comes into play.
The Power ‘added’ from an outside source is from the presence of God, eternal in nature to regenerate the former mortal body that was dissolved, into an immortal body fashioned after the former but having all the attributes of its Creator.
Einstein, by divine intervention, learned that mass is a form of energy (this is called mass-energy equivalence). The amount of mass directly relates to the amount of energy, as determined by the most famous formula in physics:
E=mc2
E: the amount of energy in an object or system.
M: the mass of the object or system.
C: the speed of light, roughly 3×108m/s
Now if the speed of light is altered to become the higher Light of Glory by the Power of the Son of God, then will the mass regenerate to become immortal, by the same Power and Glory, then the energy and mass of the individual becomes eternal and immortal in nature.. Becoming like Him who regenerates them.
Sure, CERN is not going to give me a conclusive answer to such a formula but one day CERN itself will decay and a new accelerator will take its place, however ultimately, everything decays…except immortality and eternal life
Joseph
Mr. Atwater — there is nothing wrong with having religious views as well as scientific ones — science is about material reality under the assumption that material reality is predictable, while religion can extend beyond that. I’m not going to object to anything that you might choose to believe, unless it is in direct contradiction to scientific measurements or known history.
However, this is a website about science, and not one intended for sharing personal scientific theories or personal religious views. I’m happy to talk to discuss mainstream science. But I think you will agree that your comment is not relevant to the post I wrote today — some variant of it could have been attached to any post on the entire website, and I would have had the same objection — and so it is not really an appropriate use of the comment feature.
God is a scientist—not a magician—building sensibly, even if not always readily apparent to us. The two don’t conflict and never have, we just let ourselves get caught in that rabbit hole from time to time. And there’s still a lot more to see, but apologies. As stated above, different topic.
Dr.Strassler, the measurement wouldn’t happen to have taken place right when the magnetar, designated 1E 1547.0−5408 beamed us, would it? 😉
The suggested magic and magicians of organized superstition such as religion is indeed another topic, since we now know robustly and without reasonable doubt that the space expansion process that produces the universe is entirely natural and magic is non existent. I’m at a loss why anyone would try to push personal religious opinions on a science site.
I’m reminded of what Stephen Fry said in this general context of such opinions:
“That’s not nice, it isn’t nice.”
And again apologies, I was not trying to initiate dogma or conflict with the remark. On the contrary. The first bit was rather in the further up comment about becoming immortal by pumping a human brain to infinite voltages, or whatever the assumed technique is these days.
I simply meant to allude that when a verified and accepted fact is established via the scientific method, carried out in earnest, and this results in an apparent conflict with something stated in one of “the books,” then that tends to mean one of three things:
1.) the scientific fact or formula is incomplete, didn’t account for something no one in their right mind would think to account for, etc.,
2.) the scripture that conflicts is complete, but has been interpreted incorrectly,
3.) or (and this is the one, most of us dragon-chasing loons refuse to do but really should) the scripture itself is fragmented, its adjacent piece lying in the scripture of “another religion’s” text.
The universe is an unbelievably large place, with even larger amounts of moving parts. When a standardized procedure yields something unexpected which disappears faster than one can blink, we tend to zoom focus closer on the yield, obscuring those peripheral freak interactions even more. I like to have all the eyes I can get in those moments cause I know my two aren’t enough.
But again, I didn’t mean anything argumentative or otherwise intentionally irritating with all this. I apologise.
The measurement is made on data taken gradually over years. No individual event could shift the measurement. What could affect it are drifts in the detector’s functioning, so this has to be studied and corrected for very carefully, using other well-established measurements. Also important are unknowns in inputs, such as the proton’s internal structure. All long-term issues, not short term ones.