Update on muon g-2: story of a debacle

So I had a chance on the train home yesterday to digest the muon anomalous magnetic moment papers, and it is an amusing story that I have to share. In short, it is an example of a lie goes halfway round the world while the truth is putting on its shoes. Well, it only took the truth a day or so to get its shoes on, let's see how much damage the lie did.

Firstly, I'll give a short summary for physicists why the result is bogus. Then I'll give a general discussion below about what we can learn.


Lubos gives a nice summary of the physics, with a disclaimer added afterwards that the result is obviously wrong. This is true, because the result depends only on the gravitational potential, whose absolute value has no physical meanining. But below I give a proof that I earlier summarised in a tweet.

In the paper, they use the metric $$ds^2 = (1- 2 \phi(r)) dt^2 - \left( 1 - 2 \phi(r) \right)^{-1} dr^2 - r^2 d\Omega^2 $$ This is fine, but they ignore the fact that in the lab we don't know that our time runs differently than at infinity, nor that our rules are not the same length. So instead we could just do a constant rescaling of the time and space coordinates so that $$ \phi(\mathrm{lab}) = 0. $$ In other words, we can always define local Minkowski coordinates at a point, which we choose to be where our experiment is. Then we use that as the starting point and proceed as in their papers. Now, in their calculation, in the result nothing depends on the derivative of \( \phi \), and so it must reduce to the flat space result. QED (+hadronic corrections). In other words, their "gravitational correction" must be exactly zero!

On the other hand, just after I blogged yesterday, a collaborator emailed me to say that they had pointed out to the authors that even if you accept their results they had misinterpreted how the experiments worked, and the correction would therefore be \(10^{-3} \) times smaller, and thus negligible! This seems to be the line taken by the muon \( g-2 \) experiment team, which has also been conveyed in tweets. But the situation is worse: I believe there is no correction in the papers.

So what can we learn?

Unfortunately this gives a very bad impression for people outside of the field. It has shown how confirmation bias exists in the physics commentariat: one particular naysayer that I mentioned yesterday assumed it was probably true and was rather cruel in mocking people for placing hope in this tentative sign of new physics. It also shows that people working in physics can write papers that are wrong, and it can take a lot of time to see that this is the case.

Another thing that it highlights is how many people work. Clearly (to me) the result has been reverse-engineered: I am speculating, but I would guess that the senior physicist saw that in \(g-2\) the discrepancy was a factor of \(10^{-9}\), and that this was the same order of magnitude as the gravitational potential on the surface of the Earth in dimensionless units (even if this would be shocking if it could have anything to do with \( g-2\)). They then did a calculation. And then when the result that they got wasn't what they wanted to explain the experiment, they misinterpreted (not fudged) their own equations to give what they were hoping to find -- presumably entirely innocently, but let us say enthusiasm got the better side of rigour.

The reason that I propose this timeline is because it is very familiar: when we want to learn something new, we often have to guess what the answer will be before the calculation, to even have the motivation to do it in the first place. Research is actually a hugely creative process, rather than a merely deductive one. This debacle just shows that we have to be very honest with ourselves!

But on a more positive note, it shows how well the arXiv system works. The papers have effectively been massively peer reviewed in detail -- an actual peer review may not have been thorough enough (which is another discussion). Of course, now in retrospect we can see that splitting the calculation (which is not overly long or unduly technical) into three papers released at the same time was rather hubristic on the part of the authors, designed to attract attention, and the peer review process will not be smooth.

So finally: the anomalous magnetic moment of the muon persists as a possible portent for new physics, and two new experiments will be able to shed more light on the story within the next couple of years!

Note: I edited this post to tone down the language.

The future of the Intensity Frontier

Another week, another workshop.

Today I'm at CERN for a short workshop that I've helped organise about the future of the Intensity Frontier. There are supposed to be three frontiers to search for fundamental physics: energy (i.e. LHC, for now), space (many many telescopes, satellites, balloons, etc) and intensity, which means low energies but large numbers of particles colliding in the lab. The idea is to look for new physics either through very precise measurements (after collecting a lot of data) or producing light particles directly in unusual conditions.

 This is a subject that has been dear to my heart since the end of my PhD, when it was only just starting to become fashionable after an anomaly reported by the PVLAS experiment. They claimed to observe a rotation of the polarisation of light (from a laser) in a magnetic field, which in the Standard Model their experiment was not supposed to be able to see. This spawned lots of model building and fun investigating axion-like particles and light "hidden photons" until the flaw in their experiment was found. But by then the genie was out of the bottle, and a large number of different ways to look for these sorts of particles had been found, and uses for them to explain other astrophysical anomalies. Currently there are a whole series of anomalies who can be consistently explained by an axion-like particle with a very small mass, and we may be able to find one day in the laboratory, or exclude with further astrophysical measurements. 

There are a huge number of experiments that are relevant for this frontier, and you can find out more by looking at the slides from today on the workshop website. Some examples are

• LHCb, which looks specifically at the B-mesons coming from the proton-proton collisions at the LHC. When these particles decay (and they are somewhat long lived) they can produce particles such as "hidden photons" or axion-like particles, ... There are currently two outstanding anomalies in B meson decays that a lot of people are getting excited about.
• Belle, an electron-electron collider that also looks at B-mesons -- it is tuned to specifically produce them in large numbers.
• Searches for rare lepton decays: in the Standard Model, the rate of decay of a muon in to an electron and photon is tiny; similarly the decay into three electrons/positrons. So any signal would be a sign of new physics.
• Beam dump experiments, where protons or electrons are slammed into a target, and then a detector is placed some distance away to see what comes out. Usually the detector is some distance away, to look for long lived particles -- this is for example what is proposed for the SHiP experiment at CERN, which is under discussion (and I have been a little involved with). But other proposals are to look for particles that do not even decay at all in the detector, and to see if we can spot the missing energy.  
• Light-shining-through-a-wall experiments, shining lasers at a target and seeing if any leaks through! If the photon can oscillate into an axion (in the presence of a magnetic field this is possible) then it can pass through the wall!
• Measurements of the anomalous magnetic moment of the muon.

Now, the muon g-2, as the anomalous magnetic moment is known, has been one of the longest-lived measurements to show a deviation from the Standard Model, by a tantalisingly large amount. Indeed, here yesterday there was an argument about whether they or the B-physics people would reach the five-sigma level for discovery first!  There are two new experiments (at Fermilab and JPARC) which should soon improve on the g-2 measurement, and give a conclusive proof of the discrepancy if it is there. Or so we thought until yesterday ...

On the arxiv yesterday morning (alongside some other very interesting papers on axion-like particles including this one and another) three papers appeared claiming that gravity could explain the difference, and calculated the correction -- giving a number disturbingly close to the measured amount. This was apparently missed by the army of people who have been involved in the calculation, which has developed into an industry over something like the half a century since Schwinger first calculated the muon magnetic moment. Being busy here I have not had time to digest the papers, although I brought them up with the people here -- the experimentalists just reacted with shock.

So I don't want to discuss the details -- yet. I am sure on Tuesday the arXiv will be awash with papers. But it gives me an excellent opportunity to comment on sociology: I regularly read two or three physics blogs, since they report on the latest news (and rumours). Now, one of these blogs is very popular whose ostensible purpose is to persuade people that string theory is a misguided research topic. Obviously, this is something I disagree with. However, it also talks a lot about high-energy physics generally, and being rather well-connected it can be quite informative and useful. However, it pretty much uniformly takes a very pessimistic line about all concrete ideas for new physics. It is difficult to overstate how damaging this has been, in making physicists and scientists in neighbouring fields depressed about the future of high-energy physics, and opposing this trend is one of the reasons I would like to blog (and the reason for this website (and book) because I am an actual practitioner rather than an outside negative observer. For me, since there are undisputably fundamental problems with the Standard Model, it is vital to try to solve them, and this is a noble effort that should be carried out with honesty -- and with enthusiasm!

So what is the connection to g-2? Of course, this was reported in two physics blogs  in particular, admittedly with a healthy distance and caveats about whether it is correct or not. But the tone was positively crowing about the demise of one of these hints. For me, it just underlined the cynical agenda of the author(s). These are the times we are in: there are people on the inside and the outside of the high-energy physics community who are trying to bring the whole thing down (with various motivations) and it is important that more voices raise up to let people outside the field know that actually there are lots of exciting things going on (such as the workshop I am currently at!) and nolite te bastardes carborundorum!