144 | Solo: Are We Moving Beyond the Standard Model?

I’ve been a professional physicist since the 1980’s, and not once over the course of my career has a particle-physics experiment produced a completely surprising new result. We’ve discovered particles (top quark, Higgs boson) and even phenomena (neutrino masses), but nothing we hadn’t either predicted or could easily accommodate within the Standard Model of particle physics. That might have changed just this month, with possible confirmations of two “anomalies” in particle-physics measurements involving muons. They might be new physics, or they might just go away. I talk about what it might mean, and (more importantly) how we should feel about the likelihood that these results really do imply physics beyond the Standard Model.

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Here are some relevant references for the first result, from LHCb at CERN, that B-mesons are seemingly decaying at different rates into electrons and muons:

• arxiv paper
• CERN Courier
• Scientific American
• Resonaances

And here are some references for the other result, from the Muon g-2 experiment at Fermilab, on the anomalous magnetic moment of the muon:

• arxiv paper
• Fermilab article
• Lattice QCD calculation
• Quanta
• Ars Technica
• Resonaances
• Moving the g-2 ring from Brookhaven to Fermilab

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0:00:00.7 Sean Carroll: Hello, everybody, welcome to the Mindscape podcast. I’m your host, Sean Carroll. And a few weeks ago, I’m recording this in April 2021, we had not one, but two different reports of completely independent anomalies in particle physics, that is to say apparent disagreements between the theoretical predictions based on the standard model of particle physics, which is very well-established, and new experimental results. One of the results came from the Large Hadron Collider outside Geneva, Switzerland, the other from Fermilab outside Chicago, Illinois. They both involve muons, little particles that are heavier cousins of the electrons, but they’re otherwise not immediately connected to each other.

0:00:40.9 SC: We don’t yet know whether these anomalies are real in some sense. I mean, the anomalies are real, they’re there, but we don’t know whether they actually represent new physics or we just made a mistake, either experimentally or theoretically. So lots of people have asked for my opinion about these things, so that’s what this podcast is going to do, but because I am who I am, I’m not going to focus mostly on what it means for the future of particle physics, because we don’t know what it means for the future of particle physics. Number one, we don’t know if it’s real, like we just said, we don’t know if it’s going to stick around, either one, and number two, the data that we’re getting, the information that we’re measuring is kind of meager, right, you’re measuring two different numbers in two different ways, and that’s not quite enough to be very explicit about what model might explain it.

0:01:28.3 SC: The problem with this kind of thing is, there’s many models that could possibly explain this, so you can’t instantly say, ah, you detected this, therefore supersymmetry, or therefore grand unification or anything like that. But we can be prepared for hopefully getting more data and hopefully understanding better the theoretical models that can be constructed if we think about exactly what’s going on. So that’s what I want to talk about, a little bit about the standard model in general, a little bit about the specific ways in which new physics can enter these measurements, a little bit about what it means to be skeptical about statistical confidence, all of that stuff.

0:02:03.1 SC: One very quick thing is that the standard model has not been upended, the laws of physics have not been up-ended. This is something that you might get the impression of from certain newspaper headlines, I’m not going to name any names, but it’s not a complete rethink of the basic laws of physics, it’s a little bit extra. It could, you know, if you want to get excited about it, that’s okay, it could lead to an entirely new era of physics beyond the standard model, but it doesn’t replace the standard model. The standard model is still there in a way that I will very much try to explain. Hopefully, it’ll make sense.

0:02:37.1 SC: We’ve been looking for experiments that do not fit the standard model for a very, very long time, for my entire career in physics. We have dark matter, that exists, we have dark energy, that exists, but nothing really in particle physics experiments here on Earth that have been directly contradicting the standard model. So if true, it’s big, even if we can’t quite say where it’s going to lead. So, let’s go.

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0:03:21.3 SC: So very quickly, let’s go over what the claimed anomalies are. So I’m not going to dig into all the details quite yet, but get things on the table and then we’ll be able to understand what’s going on a little bit more carefully. Okay, so I’ve got to tell you, ’cause maybe you don’t know, there’s something out there called the standard model of particle physics, right? There’s a bunch of particles and forces that have done an extremely good job in explaining us, you, me, the stuff we’re made of, the table in front of you, the signals that are passing through the internet, etcetera, to give you this podcast. All of that is incredibly well accounted for in what we call the standard model of particle physics, even the sun, the moon and the stars, they count too, that’s all the standard model of particle physics.

0:04:02.4 SC: And the standard model very quickly, there’s two kinds of particles; in fact that there’s two kinds of fields, ’cause it’s really quantum field theory, as we’ll briefly discuss, but that’s okay. Perfectly legit to talk about it in terms of particles. The two kinds of particles are matter particles, what we call fermions, these are particles that make up matter, they take up space, you cannot pile an arbitrary number of fermions on top of each other. The other kind are the bosons. Bosons are the force-carrying particles, photons, gluons, gravitons, things like that. But it’s the matter particles we’re going to be dealing with today, and they, in the standard model, come in two varieties, and there’s sort of a parallelism, which is interesting all by itself, there’s a lot of sneaky symmetries and patterns in the standard model that are not perfectly well understood.

0:04:51.5 SC: So in the standard model, a very boring name for a very important theory, there are six kinds of quarks and there are six kinds of leptons, so there’s a parallelism right there. And the difference between a quark and a lepton is quarks feel the strong nuclear force, they interact directly with the particles called gluons. So quarks, you don’t see, you never see a quark by itself in the wild, they are confined, the strong nuclear force is so strong that quarks are just grouped together, usually in either triplets of three kinds of quarks, that’s what would be a proton, for example, there’s two up quarks and a down quark; a neutron is two down quarks and an up quark. The six kinds of quarks are up, down, charms, strange, top and bottom, okay. That’s more or less, not exactly, that’s more or less an increasing mass, so the heavier ones, like the top, which is the heaviest, and the bottom, they decay very quickly, it’s the up and down quarks that make up the protons and neutrons, and you and me.

0:05:51.3 SC: And the other kind of particles that we regularly find with quarks in them are mesons, these are quark, anti-quark pairs. So you might think, well, if I had a quark and an anti-quark, wouldn’t they annihilate? Yes, except that I can have an up quarks, for example, and a down anti-quark. So two particles, a particle and an anti-particle, will annihilate if they’re the same kind of particle, but if it’s one particle of one kind and an anti-particle of a different kind, they don’t annihilate. As a matter of fact, mesons do eventually annihilate one way or the other, but they can stick around for a relatively long time. So pions, kaons, things like that, these are combinations of one quark and one anti-quark. So that’s how we get quarks. There’s six kinds of quarks, they come in either groups of three quarks or groups of one quark and an anti-quark.

0:06:40.5 SC: There’s also six leptons. The leptons are the particles that don’t feel the strong nuclear force. On average, the leptons are a little bit lighter than the quark, sometimes a lot lighter. So the leptons are the electron, which we know very well, that’s very important for atoms, molecules, stuff like that. And then there are two heavier cousins of the electron, the muon, which we’ll be talking a lot about today, it’s about 200 times heavier than the electron, and then there’s the tau particle, which is even heavier than that. And again, heavier particles tend to decay away, so you don’t see a lot of muons or tau particles lying around in the everyday world, they would decay into electrons.

0:07:20.4 SC: The reason, by the way, that heavier particles tend to decay into lighter ones is, roughly speaking, because entropy likes to increase. When you decay, when you’re, let’s say, a muon, you don’t just decay into an electron, you also split off neutrinos. Those are the other kinds of leptons. There’s an electron neutrino, a muon neutrino and a tau neutrino. So there’s three charged leptons, three neutrinos, those are the six leptons we have. When a muon decays, it spits out an electron, but then also a neutrino and an anti-neutrino, so it turns into three different particles, and that little bit increases the entropy of the universe, going from just one particle into three particles.

0:08:01.5 SC: You can take the three particles and in principle, go backwards. If you very, very carefully line up a neutrino, an anti-neutrino and an electron and shoot them at each other, there will be a chance that they convert into a muon, but it’s a very, very small chance. The history of the universe is mostly heavier particles decaying into lighter ones, increasing the entropy of the universe, okay. So that’s the set of ingredients we have to work with: Six quarks, up down, charm, strange, top, bottom; six leptons, electron, muon, tau and their three neutrinos.

0:08:35.5 SC: And the standard model is the name we give to the set of rules that are obeyed by all of these fermions, the quarks and the leptons, and also all the bosons, the force-carrying particles that hold them together. And so when I say predicts the interactions, what I mean is there’s a very, very precise and quantitative recipe for answering questions like: What is the rate at which a muon or a tau decays into an electron? When you make a meson out of a quark and an anti-quark and it eventually decays, how quickly does that happen? If I shoot an electron and a positron, the anti-electron, at each other, what do they convert into and what is the probability that they convert into all these different things? The standard model makes highly precise quantitative predictions for all that kind of stuff, all the interactions, basically, that go into making up you and me.

0:09:28.7 SC: Now, usually inside you and me, particles are not being created or destroyed, but electrons are interacting with protons in the atomic nucleus to make atoms, that’s also predicted very, very well, by the standard model of particle physics. So the standard model was put together roughly in the ’60s and ’70s, it was put together, there was enough sort of constraints on what could possibly be going on that by the mid-70s, we had a very good idea of what this list of particles would be, what the list of quarks and the list of leptons would be, even though we hadn’t discovered all of them yet.

0:10:04.0 SC: It was after the standard model was put together that we discovered the bosons that carry the weak nuclear force, the W and Z bosons, we directly detected, at least evidence for, the gluons that make up the strong nuclear force, as well as things like the heavier neutrinos and the top quark, etcetera, not to mention, of course, the Higgs boson that lurks in the background of all this, these were all particles that were predicted to be part of the standard model and only discovered later.

0:10:33.6 SC: So the last few decades of particle physics have largely been a story of discovering particles that are in the standard model that we already had predicted and testing their properties and finding that those properties are what is predicted by the standard model of particle physics. So it’s a bittersweet situation to find yourself in as a particle physicist: On the one hand, theoretically you’ve constructed this wonderful theory, right, the incredible genius of particle physicists over the decades, from people like Dirac and Fermi inventing quantum field theory, to people like Feynman and Schwinger and Tomonaga understanding how quantum field theory works, to people like Higgs and Brout and Englert understanding spontaneous symmetry breaking, Nambu and Goldstone and Weinberg and Salam understanding the electroweak theory, and Gross and Politzer and Wilczek and Gelman putting the pieces together to make the strong nuclear forces, and ‘t Hooft showing that it was all renormalizable, many contributions from many, many Nobel Prize-winning people that made up the standard model of particle physics.

0:11:39.4 SC: Not to mention the equal number of Nobel Prize-winning efforts by the experimentalists discovering evidence for quarks, the existence of the heavier quarks, the Higgs boson, all this stuff, okay. So we’re very happy with our ability to predict things in the standard model of particle physics, but the flip side of that… That’s the sweet part. The bitter part is, it’s hard to make progress in physics when your theory works too well, when your theory fits all of the data. But, this is the thing you’ve got to understand, nobody thinks that the standard model of particle physics is the final theory of everything, we’re 100%, not 100%, we’re never 100%. That’s an exaggeration, we got carried away there a little bit, sorry about that.

0:12:21.1 SC: We are quite confident, let’s put it that way, that there is physics beyond the standard model. In a very trivial sense, there is gravity, right, gravity is not included in the standard model of particle physics. Those of you that have heard me talk about the core theory, that’s a coinage due to Frank Wilczek, which does include gravity but only in weak gravitational fields, so we can include quantum gravity when we’re talking about the planets orbiting the sun, but we don’t have a quantum theory of gravity that explains black holes or the Big Bang and stuff like that. So that’s obviously a need for new physics.

0:12:55.7 SC: Plus there’s dark matter. There’s some particle out there, most of the mass of the universe, and there’s also questions like why is there more matter than antimatter in the universe? These are all questions which are presumably addressable, but only if you go beyond the standard model of particle physics. So it’s a frustrating situation to be in when your theory is so good, but you know it’s not right. What can you do, right? You can make guesses, basically, everything from supersymmetry in the 1970s to very new ideas about hidden sectors and dark photons and stuff like that. These are various kinds of guesses about what might lie beyond the standard model. Guessing is easy, figuring out which guess is correct is hard, that’s why we need experimental input, that’s what’s going to eventually help us whittle down the guesses to which ones are correct, if any of them, or inspire completely new guesses.

0:13:48.5 SC: Anyway, I’m supposed to be giving you what the anomalies were, I got carried away. There’s so much here to say. As I was thinking about this solo podcast, I was just trying to figure out the order in which to say things, and there’s many different possible orders. Anyway, here are the two pieces of news we got. To be clear, these are both reaffirmations of existing anomalies we’ve already known about, but anomalies in particle physics are a dime a dozen, there’s many, many times when people will say, oh, here’s an experimental result which does not quite agree with the predictions of the standard model, and then a few years go by, you collect more data and it evaporates, it goes away. This has happened so often that particle physicists have become a little bit jaded by the whole prospect, like, oh yeah, another anomaly.

0:14:33.4 SC: So these days when there’s an anomaly, when there’s a mismatch between the theory and the prediction and standard model physics, we wait, we wait for more data to come in, for a different experiment to look at the whole process, to ask ourselves, are we really on to something. So what is important here is not a brand new anomaly, these are anomalies that we have checked and they still seem to be there, okay, so that’s actually a higher level of excitement than if you have a brand new anomaly.

0:15:02.0 SC: One of the anomalies, the one that came from the LHC, the Large Hadron Collider outside Geneva, it has to do with B mesons. B stands for bottom, which means that a B meson contains a bottom quark and some other anti-quark, it could be an up anti-quark, down anti-quark, etcetera, there’s some lighter anti-quark. Or vice versa, there are B mesons that have a bottom anti-quark and a lighter quark, B mesons and anti-B mesons… B anti-mesons? I don’t even know what the right way to say it is. A collection of particles that contain a bottom quark, okay. Why do we have any special love for particles for mesons that contain bottom quarks?

0:15:43.1 SC: Well, bottom quarks are pretty heavy, they’re not as heavy as top quarks, top quarks are even heavier, but we’ll see this again in the next anomaly. But there’s a trade-off because heavier particles in some sense have access more easily to new physics. Very, very roughly speaking, when you do particle physics experiments, it’s easy to go to low energies and find light particles; it’s hard, expensive, time-consuming, technologically challenging to go to high energies and look at heavy particles. Energy and mass are related because of E equals MC squared, so energy and mass to a particle physicist, just the same kind of thing. So you want to do experiments that involve heavy particles because they might have enough oomph to be directly connected to physics you haven’t discovered yet.

0:16:31.6 SC: On the other hand, as we just said, heavy particles tend to decay into lighter particles, so if you try to make a meson with a top quark, for example, it wouldn’t work, there’s literally not enough time to make a particle you can actually study out of a top quark and an anti-quark of some other form. So B mesons, in some sense, are in a sweet spot, they’re in a spot where you have some access to physics beyond what we’ve seen so far, but you have enough time to make these things, look at them and figure out what their properties should be, compare those properties to what you actually see. This is so important that there is literally an entire experiment at the Large Hadron Collider devoted to looking at B mesons in different ways. It’s called, cleverly enough, LHC B, B for bottom quark.

0:17:24.0 SC: This particular experiment, at any one experiment, you look for many, many different kinds of things, the thing that we’re looking for in the example that is relevant today is the decay of a B meson into electrons and muons, I should say electrons or muons, a neutral B meson, so that would be a bottom quark with, let’s say, an anti-down quark, okay, that’ll be electrically neutral. That can decay into a pair of electrons, that is to say not to electrons, but an electron and a positron, an electron and an anti-electron, so the net charge remains zero; or the B meson can decay into a muon in an anti-muon.

0:18:03.2 SC: So we make a prediction, we hire our best theorists, we set the graduate students to work here, we do Feynman diagrams, we do particle physics, and we make a prediction for the rate at which a certain kind of B meson should decay into electrons or into muons. And it turns out in the standard model, the relevant processes by which such a decay can happen treat electrons and muons basically alike, okay. There’s enough energy there that the mass scales are above the masses of the electrons and the muons, so you should just be able to decay into electrons and muons equally. That’s the theoretical prediction: The ratio of decays into electrons to the ratio of decays into muons should be about 1.

0:18:47.3 SC: What in fact you see at the LHC B experiment seems to be that there’s only about 85% as many muons being produced as electrons. 85% is not 100%; that was the theoretical prediction. Now, both the experimental result and the theoretical prediction have error bars, okay. The theoretical prediction has error bars because the way that we make calculations in particle physics makes a lot of approximations, you have to get those approximations under control, but there’s going to be some slop there, okay. That leads to an error bar, some uncertainty in the prediction. And of course, every experiment in the world has uncertainty in what it sees, you only collect a finite amount of data, you don’t completely understand your detector, all that stuff. But still, the difference between 85% and 100% is pretty noticeable.

0:19:38.5 SC: In mathematical terms, the way that particle physicists like to think about it is in terms of sigma, so if you imagine that your prediction is a gaussian, that is the fancy term for a Bell Curve, then the number of standard deviations away from the prediction is the number of sigma. So this particular example of the B mesons decaying into electrons and melons has a 3.5 sigma statistical significance, 3.5 standard deviation difference between the experimental result in the theoretical prediction. You can convert 3.5 sigma into a confidence level, this is to say 99.98% confidence. Now, that doesn’t mean that it’s 99.98% chance of being new physics, we’ll talk about that later, but it gives you a rough idea that this seems to be a big difference between the theoretical prediction and the experimental outcome, 3.5 sigma.

0:20:37.9 SC: Now, as many of you know, particle physicists are very, very persnickety about what counts as a discovery, that would really get you into the record books, particle physics-wise. They made up the standard that 3 sigma is what you call evidence for something, so we’re allowed to say that the LHC B has found evidence for a difference between the number of electrons and muons produced in the decays of B mesons. You don’t get to call it a discovery until you get 5 sigma, which is a much higher confidence level, so we’re at the evidence for level, not yet at the discovery level.

0:21:19.3 SC: The other anomaly that came a couple of weeks later is again an old one that has been verified apparently by this new experiment, and this is g-2 of the muon. G-2 is a way of characterizing how strong the muon is as a magnet. The muon is a charged particle, and it is spinning, and when you take electric charge and you move it, including spinning it, you create a magnetic field. This is a result of Maxwell’s equations back in the 1800s, okay. So a spinning charge particle like a muon is a little magnet, has a little magnetic field, and guess what, the standard model of particle physics predicts precisely how strong of a magnet it is.

0:22:04.9 SC: Classically, it’s not exactly right, but roughly speaking, if it weren’t for quantum mechanical corrections, the g, which is how we measure, we relate the amount of magnetic field to the amount of spin, g would equal 2. If there were no such thing as quantum mechanical corrections, there’s a number called g for a muon or for an electron, etcetera, different ones for every different kind of particle. For the muon, the classical value would be 2, that’s the ratio, roughly speaking, of the magnetic field to the spin of the particle. And there are quantum corrections in the world, and so you can predict those, and they’re very, very tiny. So rather than giving the actual value of g, We give g-2, so we separate out the classical part, which is the 2, and we just look at the difference.

0:22:49.8 SC: So the standard model predicts that for a muon g should be 2.002331841, plus some extra digits that are lost in the experimental error, 2.002331841, so you can see why you would subtract off the 2. And then you go out and measure it, you do the experiment that is done at Fermilab, and what you measure is 2.002331836, you got that? So if I subtract off the 2 for you, the g-2 prediction is 23318411, the measurement is 2331836, the difference between the 41 and the 36 in the last two digits there, and then there’s more digits after that, like I said. Okay, so that’s a difference.

0:23:39.4 SC: The magnetic field of the muon seems to be a tiny, tiny bit smaller than the standard model would predict. Now, you don’t measure the magnetic field directly, what you actually measure is you take a bunch of muons, you put them in a storage ring, okay, so it’s much like the Large Hadron Collider or any other particle physics experiment, you have a ring, you put some muons in there and you accelerate them and guide them with magnetic fields, and then you try to measure their properties. But as I said, muons don’t last forever, they decay, so it’s hard to do physics with muons, they keep the decaying on you, but if you really speed them up, very much, right, near the speed of light, then they’ll last long enough for you to do interesting physics on them.

0:24:21.1 SC: What you’re actually measuring is not the magnetic fields directly, but how the muons decay into electrons. The precise energy of the electrons they decay into and the precise angle at which they’re spat out, that depends on the spin and the magnetic field of the muon in predictable ways. So what we have is a difference once again between the prediction of the standard model and what we’ve measured at the straightforward, let’s just plug in and cross our fingers level. This is a 4.2 sigma result, a little more than 4 standard deviations between the standard model prediction and the actual experimental measurement. That equates to 99.9987% confidence. That’s a lot of confidence, but it’s not quite 5 sigma yet.

0:25:11.3 SC: Now, as I said, this is a result from Fermilab outside Chicago, you can go visit Fermilab, I don’t know, we’re still in the middle of a global pandemic, but if you have a chance, visiting Fermilab is a fun thing to do, it’s a very beautiful site. And what they’ve done is something extraordinarily clever and impressive. There was a previous measurement, like I said, there was a previous version of this experiment done at Brookhaven National Laboratory, which is on Long Island in New York, okay, so Brookhaven had this big storage ring, they did this measurement, they got an anomaly, they got about a 3 sigma difference between the standard model prediction and the experimental result.

0:25:52.0 SC: Now, the thing is, that Brookhaven, even though it’s a fantastic particle physics laboratory, it just doesn’t have the oomph that Fermilab does, it doesn’t have the ability to generate as many muons at the energies that Fermilab does. But it did have this beautiful storage ring for storing the muons once you made them, right, so people are wondering, and this is like almost 20 years ago, people were saying like, what should we do? Should we build a new storage ring at Fermilab so we have better muons or what’s the alternative to doing that. And they costed it out, it would cost a certain number of millions of dollars to build a new storage ring at Fermilab. It was about 10% of that price to literally pack up the storage ring at Brookhaven, put it on a boat, sail the boat around Florida through the Gulf of Mexico, up through the Mississippi River on a barge, unload the storage ring onto a big flatbed truck. We’re talking about… I should have looked this up, but the storage ring is a couple of tens of meters across, so it’s on a big truck and it extends across a three-lane highway. That’s roughly how big it is.

0:26:54.7 SC: I very much encourage you to go look up the images of this journey that the storage ring took from Brookhaven to Fermilab. Drive it across the State of Illinois in the middle of the night when there’s not a lot of traffic, unload it at Fermilab, put it together, build a new laboratory around it. That’s what they did. They actually did this a few years ago, the journey of the muon g-2 ring from Long Island to Illinois is one of the great triumphant stories in the history of particle physics. It’s well worth looking up.

0:27:25.8 SC: Okay, as I said on Twitter once, there’s a lot of hard hat work that goes into modern high energy particle physics, building things, moving them, putting them together, it’s really very, very impressive. And what we’re left with at the end of the day is a little bit of news from Europe, a little bit of news from the Midwestern United States, telling us that there are these experimental results with muons that are slightly at odds with the standard model of particle physics, neither one of them quite yet rises to the level of being 5 Sigma. In fact, I quoted the muon g-2 result as 4.2 sigma. I think it’s true, this is sometimes hard to dig out of things, but I think where that comes from is, the Brookhaven result by itself was 3 point some sigma, and then Fermilab with its data by itself was another 3 point some Sigma and they combined them, right.

0:28:21.0 SC: You’re allowed to do that. If you think that you’re both right, you’re allowed to combine them together to get a 4.2 sigma deviation. To be fair, they’re using the same storage ring, maybe that’s something to keep in mind. Anyway, you have these two results, both with muons, what does it mean? Well, it’s a difference between the prediction of the standard model of particle physics and what you observed, therefore, if it’s true, which we’ll talk about in a second, it is the sign that the standard model is not complete, that you need to invoke new physics of some sort.

0:28:52.9 SC: Now, as I said in the intro, nothing’s been upended, it’s not overthrowing the standard model. I talked about this a little bit on a radio program outside Chicago, and actually the radio host came up with the right analogy here, it’s adding on a new addition to your house, not demolishing your house and building another one, okay. All of the existing pieces of the standard model are 100% in place. If these results are correct, if they’re pointing to new physics, there are other particles, either bosons or fermions or some combination that’s kind of tricky, right, but there are new particles and fields that are not part of the standard model, that are gently influencing the particles that are in the standard model. But the particles that are in the standard model are still there. Nothing has changed about them, their interactions are the same, the underlying philosophy of dealing with these is still quantum field theory, etcetera.

0:29:45.2 SC: As a personal note, I have to be very, very specific because I am on the record as telling people that the physics, the laws of physics underlying our everyday lives are completely known, are well understood, and I know perfectly well when I say that out loud that people are going to misunderstand me, and I know exactly the ways in which they’re going to misunderstand me, and I try really hard, I bend over backwards to be impossible to be misunderstood, and yet it happens. So I got several people saying, so does this mean you were wrong when you said the laws of physics are completely well-understood. So I was certainly never saying that the laws of physics are completely understood, there are obviously physical phenomena that are not well-understood.

0:30:31.7 SC: Even within the realm, perfectly speaking, just of particle physics and quantum field theory, we don’t understand dark energy, we don’t understand the matter-antimatter asymmetry, we don’t understand dark matter, etcetera. Okay, lots of things we don’t understand. Very, very high confidence. There are new laws out there to be understood. My point was the stuff that makes up you and me and the environment around us, the everyday life part of that sentence, that part is understood. It is very, very, very, very probable that we will discover new physics that we don’t yet understand. My argument has always been, whatever those discoveries are, they will not affect how we think about the physics of everyday life, what is going on in your body and in the body of the floor beneath you, etcetera, okay.

0:31:14.2 SC: And guess what? These new results, even if they’re 100% true, leave that claim completely fine, completely unaltered. Because remember, the difference between, let’s say in the muon g-2, we’re talking about a difference in the magnetic moment of a muon between 2.002331841 and 2.002331836. That’s not the kind of difference that’s going to make a difference in your everyday life, especially ’cause you don’t have any muons inside you. Muons decay away very, very quickly. In both of these cases, what we’re finding is incredibly tiny changes between the predictions of the standard model and the experimental results, such that they will have no impact whatsoever on what is going on inside you biologically.

0:32:06.3 SC: To see these differences at work, you need to build a particle accelerator and you do extraordinarily careful measurements. I’s not going to help explain consciousness or anything like that, okay. Had to get off that off my chest. Thanks for indulging me there.

0:32:21.4 SC: Okay. Let’s go. Let’s be more serious. What could be going on? What is going on? When you say new physics, that could cover a lot of ground, what kind of new physics are we talking about here? Okay, well, again, the answer is actually pretty straightforward, it doesn’t require great new leaps of faith. These are results that would be fairly straightforward to explain. You have to be careful that when you explain it, you don’t introduce new anomalies elsewhere, but these are results that are the bread and butter of particle physics trying to explain.

0:32:53.2 SC: So here’s the basic story. You’ve heard of Feynman diagrams. Okay, this is Richard Feynman’s great calculational tool. A Feynman diagram is a way of thinking about how processes of interacting particles happen as described by quantum field theory. So a Feynman diagram has a bunch of particles coming in, indicated by lines, straight lines or wiggly lines or dashed lines or whatever, and then they interact with each other, they trade other particles back and forth in some complicated way or some simple way, then they go off in a new set of particles leaving, so they’re incoming particles, they’re interactions, and the particle lines that are entirely inside the diagram, that is to say neither coming from the beginning nor going out to the end, neither incoming nor outgoing particles, the inside particles are called virtual particles.

0:33:43.8 SC: So we say there are incoming particles, they exchange virtual particles and they convert into the outgoing particles. And these Feynman diagrams, these cartoons that we draw, they not only represent what can happen, they also are calculational tools. Every single cartoon Feynman diagram you draw represents a number, there’s an algorithm for converting each diagram into a number, and that number is the contribution of that diagram to the quantum mechanical amplitude corresponding to that process. So if you, let’s say, have two electrons coming together and they scatter off each other, what’s happening? Well, you draw two lines for two electrons, electrons coupled to photons, for example, so you would draw a diagram where two electrons come in, they exchange a photon, a little wiggly line, a virtual photon and then the two electrons go off, okay.

0:34:36.9 SC: So you have a way of converting that diagram into a number that’s a contribution to the amplitude for two electrons to scatter into two electrons. There’s another contribution coming from a diagram where you draw the two electrons come in, they exchange a virtual photon and then they exchange another virtual photon and then they scatter off, okay, so a two photon exchange. And guess what, you can exchange three photons or four photons, etcetera, every different diagram you draw makes a contribution to that final answer. Then you can draw diagrams that, for example, have two electrons come in, a photon leaves one, but rather than just being absorbed by the other one, this photon splits into an electron-positron pair, which hangs out for a little while and then gets reconverted into a photon and that photon gets absorbed by the other electron.

0:35:29.3 SC: So that has a contribution that you need to include. There are an infinite number of Feynman diagrams containing all the different particles of the standard model for any process that you want to imagine, in principle. This doesn’t seem very helpful by itself, how can I calculate an infinite number of diagrams? Well, the answer is, as the diagrams get more complicated, their contributions get smaller, at least when nature is being nice to us. This is what is called the perturbative regime in particle physics. The strong nuclear force is not perturbative, and therefore it’s a harder, kind of messy thing, as we’ll talk about in a second, but for things like electromagnetism where the weak force or exchanging Higgs bosons, all of these are perturbative, they have the property that the more complicated the Feynman diagram is, the tinier its contribution is to the ultimate answer.

0:36:23.1 SC: What that means is, if you look at just the simplest Feynman diagrams, you get a good approximation to the specific process that you’re looking at. And that’s why, as I alluded to before, your theoretical prediction comes with error bars. It is not a precise prediction, it is an approximation, because you’re ignoring the very complicated Feynman diagrams. When you’re doing work like this, when you’re doing these particular kinds of experiments where very, very high precision counts, you’ve still got to include quite a number of very, very complicated-looking Feynman diagrams. And there’s a lot of computational numerical work that goes into this, but still, you can not only calculate an answer which should be approximately right, you can predict approximately how right it is, you have an idea of what the errors are because you can approximate the even more complicated Feynman diagrams that you’re not actually computing, okay. So the theory gives you not only a prediction, but error bars on what the prediction is, so that’s very nice.

0:37:24.1 SC: That’s the kind of theory work that goes into predicting either the rate at which a B meson decays into electrons or muons, or the magnetic moment of the muon, which is measured in the muon g-2 experiment. The magnetic moment, why does that matter? All these Feynman diagrams? Well, because the magnetic moment is essentially an interaction between the particle and an external magnetic field, the magnetic field that is literally in the magnets in the ring. But to a particle physicist, a magnetic field is just a bunch of photons.

0:37:57.9 SC: So you can think of the interaction between the muon and the magnetic field it’s in as an interaction between a photon and the muon, and there will be many such interactions. One is direct, that’s the 2 in g-2, that’s a 2 you’re subtracting off, the photo just hits the muon, okay, and it has a little magnetic field, but then that muon can also spit off a photon which converts into an electron-positron pair, and maybe either the electron or the positron couples to the external magnetic field. So the way to think about it is, what you think of ordinarily as just a single particle, a single line moving through empty space all by itself, quantum mechanics tells us that, in fact, this particle is being renormalized.

0:38:42.8 SC: What does that mean? That means that there are quantum processes which you can think of in Feynman diagram language as particles being spit out and re-absorbed by that muon all the time. So what you should really think of as a little cloud around the muon of these virtual particles, so these virtual photons and electrons and heavier things, all of them contribute to the way in which the muon interacts with the magnetic field around it. It’s not just the magnetic field is fueling a little tiny point particle called the muon, the magnetic field is affecting a little cloud of all the particles in the standard model of particle physics with different contributions, which the standard model lets you predict, okay.

0:39:27.7 SC: So that’s all of the contributions to the g-2, other than the 2, these are all the virtual particles, and in fact, the first contribution to the g-2 was worked out by Julian Schwinger, the first contribution beyond the 2. Julian Schwinger, sort of a contemporary and rival of Richard Feynman, one of the other people who won the Nobel Prize for showing how to renormalize quantum electrodynamics, Schwinger was the first to calculate the quantum corrections to the magnetic moment, and he was so impressed by his own calculation, the result that he got is engraved on his tombstone, okay, so this is an important thing. I think he was calculating the magnetic moment, the anomalous magnetic moment, as we call it, of the electron, but once you get the electron, you can do it for the muon just as well, okay.

0:40:14.5 SC: So that’s what exists in the standard model, and the story for the decay of the B mesons is, well, the B meson is going to spit out some particle, a W boson or a Z boson, which will then decay into the electrons or to the muons, and you can calculate that too. It’s the same kind of thing, you do a bunch of Feynman diagrams, the more complicated ones or tinier, you add them up and you get the answer. So if you find that you do that, you’ve added up all these Feynman diagrams, you’ve gotten the answer in the standard model of particle physics, you make your prediction and it disagrees with the experimental result. What’s going on?

0:40:53.5 SC: It is not that hard to imagine there’s another particle that you didn’t know about because it’s not in the standard model of particle physics, and maybe it interacts directly with muons or maybe it interacts indirectly because it interacts with W bosons or with gluons even, or something like that. This is the game you start to play. Once you’ve been told, there’s this particular disagreement between the standard model prediction and what you actually see in the experiment, you can say, well, if I invent a new quantum field representing a new kind of particle, and I give it different interactions with muons and electrons and neutrinos and the whole shebang, then I can plug that new theory into the Feynman diagram machinery, make a new prediction and explain this anomaly.

0:41:39.9 SC: And what we’re not going to go into here are all the different possibilities, okay, that’s what you mean by these possibilities, the possibilities that particle physicists are considering are what are the new particles we could introduce into this game that would reproduce correctly the experimental results from LHC B and from the muon g-2 experiment. But nevertheless, there are some general principles that we can mention. Let me mention one very, very important general principle, which is that as the new particle you’re inventing becomes heavier and heavier, so one of the features of the new particle you’re inventing will be it has a mass, right.

0:42:15.5 SC: It’s not massless, or otherwise we’d have seen it a long time ago. Massless or low mass particles are easy to make. Heavy particles are hard to make, E equals MC squared, so you need more energy to make a heavy particle. What you’re imagining here, because we haven’t seen these particles directly, so we’ve done experiments, like at the Large Hadron Collider we made the Higgs boson by smashing protons together and seeing the decay products that would be representative of a Higgs boson decaying, and we declared victory, Nobel prizes, champagne bottles, the whole shebang. Even earlier than that, at what was called LEP, the Large Electron Positron collider, we made a whole bunch of Z bosons and we let them decay, and we saw everything that came out of the decay of the Z boson, and roughly speaking, that’s the best limit that we have on new physics up to a certain mass scale, because if the particle is lighter than the Z boson, the Z boson should have decayed into it, and that would have affected the probability of the Z decaying and therefore its lifetime, and we didn’t see anything.

0:43:20.0 SC: So we have pretty good evidence that any particles that are lighter than the Z boson or lighter than half the Z boson, if you want it to decay into a particle and an anti-particle pair, any particles lighter than the Z boson either don’t exist, or they’re so very, very weakly coupled to the Z boson that they just didn’t ever get produced. So for example, axions are hypothetical particles that would be much lighter than a Z boson, but just don’t decouple to the Z boson and therefore they’re just not produced in the width.

0:43:51.9 SC: In order for these particles, these hypothetical particles that we’re inventing to explain our muon anomalies, in order for them to be relevant, they need to couple to muons, obviously, and muons couple to Z bosons. So we expect that if you couple to muons you couple to Z bosons and therefore you already have a lower limit on what the mass of this new particle can be. So between the fact that the Z boson didn’t decay into it, and the fact that we didn’t, haven’t yet seen it directly at the Large Hadron Collider, we know that any new particles you’re going to invent are going to be fairly heavy, but they can’t be too heavy.

0:44:31.9 SC: That’s another feature of Feynman diagrams. What you’re imagining is that you have these virtual particles, these virtual quantum contributions to what you’re actually measuring. And one of the things that is part of the rule book of Feynman diagrams is the more massive a particle is, the less important its virtual particles are to whatever thing you’re looking at, in the limit as a new particle becomes heavier and heavier and heavier, its contribution to Feynman diagrams in the form of virtual particles gets less and less, goes to zero. So on the one hand, we have a lower limit on how massive these particles can be; on the other hand, there’s kind of an upper limit, not a very hard and fast upper limit, but they can’t be too heavy, otherwise they wouldn’t have any effect at all.

0:45:18.9 SC: So in both cases, very, very roughly speaking, the energy scales for these new particles have to be at approximately Large Hadron Collider energies, hundreds of times the mass of the proton. The Higgs boson is, I think, around 125 billion electron volts, that’s the unit people use. The proton is roughly 1 billion electron volts, so in my brain, ’cause I’m not very precise about these things, I convert mass of proton to billion electron volts, GeV, giga electron volts, billion electron volts. So the Higgs is about 125 GeV. The top quark is about 174 GeV. Those are the heaviest particles we’ve ever made.

0:46:01.5 SC: In order to explain these particular kinds of anomalies, we’re talking about particles with hundreds or maybe thousands of GeV, and that’s enough to give a little tiny nudge to the predictive effects in the muons that we’re measuring, and may be enough to actually make it at the LHC. That’s the hopeful thing, and I should say, to be perfectly fair, to give credit here, a lot of the specific numbers that I’m quoting to you I got from the Resonaances blog. Resonaances is a blog that you should follow if you’re a fan of real particle physics. Adam Falkowski, aka Jester online, is a working particle businesses who follow these anomalies and tells you what to think about them in great detail, so that’s where I’m getting these particular numbers from.

0:46:50.1 SC: But you could have guessed. Honestly, I’m trying to be accurate ’cause there’s always sneaky things in particle physics that you might miss, but your guess would have been that that was about the right energy scale for new physics to be there, because if it were lighter than that, we would have seen it; if it were heavier than that, we wouldn’t be able to see it. The current state of the art for looking for new kinds of physics is hundreds or thousands, hundreds or thousands of billion electron volts, that’s where these new particles might be. So that’s what the kind of thing we’re going to want.

0:47:23.3 SC: Now, there are many different candidates for making this, right? Grand unification gives us new particles, supersymmetry gives us new particles, extra dimensional models, either large extra dimensions or warped extra dimensions. There’s many, many different kinds of specific models. That’s exactly what I’m not going to be talking about in any detail, ’cause I don’t know which one is right, and I’m pretty sure no one knows what is right, there were literally 50 papers that appeared on the archive the day after the muon g-2 result came out, because everyone had their favorite model ready to go, they knew the experiment would be telling us its results, they plugged in the numbers and submitted their paper. Okay, there’s a lot of different possibilities out there.

0:48:07.0 SC: I do want to say just a couple of things about why the specific experiments are so good, why muons, rights? Is it… Should we be thinking that because both the LHC B result and Fermilab muon g-2 result came from muons, does that indicate that there’s something special about muons? No, it doesn’t, it doesn’t either directly or even maybe. It’s always possible, but it would be a coincidence. The energy scales implied by these two different results are slightly different from each other, so there’s no sort of plug and play single particle that explains both of them at once. Maybe you can be clever. Again, it’s always hard when the theories haven’t settled down yet to make statements about, no one will come up with a theory that does this, ’cause particle physicists are very clever at coming up with theories that do things, so maybe there’s a single particle that explains both, but more likely than not, you’re going to need two different kinds of particles.

0:49:09.9 SC: The point of the muons is just that they’re a good place to look, it’s looking under the lamp post, okay. Muon are about 200 times heavier than electrons, which makes them more sensitive to new physics. Muons couple more strongly to the Higgs boson, for example, and more than that, they just have a little bit more oomph to make virtual particles and to be affected by them. Like I said, they’re unstable, but they live long enough to put them in a storage ring and search for the different effects. In the case of the LHC B decays, you’re literally comparing the electrons as a decay product to something else, so you want to compare them to something that are electron-like, but not too much heavier: The muon is just the perfect thing to look at.

0:49:52.4 SC: So it’s probably just a fact that the muons are a good tool for looking for new physics rather than we’re learning something specific about muons, okay. That’s one point I wanted to make. The other point I wanted to make is, is it right? Should we believe these results, right, what confidence should we have that these results are actually giving us new physics. So let’s talk a little bit about the sigmas, the actual confidence intervals we’re being quoted here, 3 point something, 4 point something sigma, so more than evidence for, less than discovery.

0:50:30.9 SC: What should you think when you are told by particle physicists that they have a 3.5 sigma result, for example, just to pick a number. So 3.5 sigma converts into a 1 in 5000 chance, and sometimes people will say kind of casually there’s a 1 in 5000 chance of seeing this result if it weren’t new physics, and what they’re trying to tell you is it’s probably new physics, but that’s clearly wrong. And most everyone knows this, I’m just making explicit what everyone knows, I’m not saying anything especially profound. The fact that something is a 3.5 sigma deviation between prediction and observation does not mean there’s only 1 in 5000 chance that it’s new physics, what it means is there is only a 1 in 5000 chance that it would be a statistical fluctuation if you got both your theory and your experiment correct.

0:51:30.1 SC: So in other words, like we said, your theory has error bars, your theory is not making a perfect prediction, there are some error bars in your theoretical confidence that you’re making the right prediction, and the experiment, every experiment has error bars also, as anyone who’s done a physics lab in college can attest. So the correct thing to say is that there’s a 1 in 5000 chance of a 3.5 sigma result being a statistical fluctuation, if you have exactly correctly characterized the error bars on both your theory and your experiment.

0:52:06.7 SC: Now, particle physicists have made up these thresholds, like I said, 3 sigma is evidence for, 5 sigma is discovery. That’s completely made up, okay. The reality is 3 sigma results happen all the time, and in fact, 5 sigma results happen pretty convincingly and then go away pretty commonly, I should say, and then go away, because we don’t understand the theory or the experiment exactly all the time. So the question is, once you have a 4 sigma result, even if it’s not technically what particle physicists have invented as a threshold to call it a discovery, it’s really unlikely to be a statistical fluctuation.

0:52:47.0 SC: The reason why, you might say, look, once I’m at 1 in 1000, I think it’s pretty unlikely to be a statistical fluctuation, that’s probably not right, because you’re looking at many, many different effects. The point is, you can do a thousand different measurements of a thousand different quantities in particle physics, no problem, and if you really did understand both your theory and your experiment, you’d still expect to see at least one 1 in 1000 chance, right? There’s an effect you have to be very careful about, let’s say you’re looking for the Higgs boson and you don’t know what the mass is, we know what it is now, but before we found it, we didn’t know, so you’re separately asking yourself the question, have I seen the Higgs boson at 110 GeV, have I seen it at 111 GeV, have I seen it 112 GeV?

0:53:31.0 SC: All the different possible measurement outcomes you could get, and so if you’re doing a lot of measurements, the chances of getting as a statistical fluctuation go up, that is one effect to keep in mind. The much bigger thing to worry about is that you’ve goofed, either on the theory side or the experiment side. So let’s think about that. For the LHC, where they made the B mesons and they decayed slightly less often into means than we predicted, could we be making up a mistake either theoretically or experimentally.

0:54:03.6 SC: Theoretically, we’re on solid ground for this particular experiment, and the biggest reason why, there’s sort of a natural explanation for that. What you’re predicting is the ratio of the percentage of time the B meson decays into muons versus decaying into electrons. If you make either one of those predictions, the rate at which it decays into electrons or the rate at which it decays into muons, it’s easy to make mistakes, because there’s a lot going on in these Feynman diagrams, there are processes you don’t completely understand, you might have some mistakes in there, but we think, we have good theoretical reason to think you should be making the same mistakes in both cases.

0:54:44.0 SC: So if for example, let’s say there’s a contribution of, I don’t know, the top quark to the rate of this particular decay, and maybe that’s hard to predict, ’cause it’s hard to make top quarks, hard to study them, etcetera, fine, but it should be whatever it is the same uncertainty in your prediction for the muon decays and the electron decays. So our theory predictions for the decay rates of the B mesons are under pretty good control, we think. However, the experiment is very hard to do, okay. The experiment is actually measuring, as we might guess, the number of electrons that are produced and the number of muons that are produced.

0:55:27.7 SC: The ways in which you detect electrons and muons are different. And you have… And this is where it gets into the nitty-gritty of doing experiments, there are detector efficiencies, you know you’re not going to see every electron or every muon being made, so you have to model what those efficiencies are, and they’re going to be a little bit different for muons and for electrons, if only because there are holes in your detector, right, there’s a beam pipe where the beam comes in before things smash together and you make new particles. You don’t have 2π steradians coverage in your detector, and there’s other more subtle things going on, but the point is, you need to do a little experimental artistry to exactly characterize what you expect in terms of the number of electrons and the number of muons, and obviously there are thousands of people working on this.

0:56:18.7 SC: They’ve worked very hard. They’re the best in the world at what they do. We have every reason to believe that what they have done is as good as can be done. It doesn’t mean it’s right, it’s still possible to make mistakes. The good news is there is another experiment called the Belle II experiment, Belle, in Japan, which should be doing the same kind of experiment in a few years from now, so we’ll be checking it, okay, so there is an anomaly, it’s checkable. Wait a few years, we’ll see what happens.

0:56:47.7 SC: That’s the story for the B decays. What about for the muons’ magnetic moment, the g-2? Well, we did do the experiment twice, we did it at Brookhaven, we did it at Fermilab, but it uses the same storage ring. That shouldn’t be a problem, that’s not really where your errors bars come from. There is again going to be a follow-up experiment, there is an experiment at J-PARC, again in Japan, just like Belle is, which will be separately using a completely different method measuring g-2 for the muon, so that should give us some very honest check on the Fermilab results.

0:57:25.8 SC: But we think once again, that in this case, we actually have the experimental facility pretty well figured out, we’re not trying to distinguish between electrons and muons, we’re just measuring the properties of the electrons where the muons create them. We have to very, very well understand the magnetic field that the muons are in, but we think that’s doable. So it’s a very, very, very slight discrepancy between theory and experiment, but we think that the experiment is under control.

0:57:56.3 SC: The theory in the case of the muon g-2 is much harder, because you’re not comparing muons to electrons, you’re just trying to directly calculate the property of muons. So what are you trying to calculate? You’re doing all these Feynman diagram calculations, the muon spits off virtual particles, they can spit off more virtual particles, you have to go for five different spittings off and reabsorptions before you get to the level of accuracy you need to compare with the data. That’s very hard to do, and it’s not just that it’s work, I already alluded earlier to the fact that this whole Feynman diagram story doesn’t really work very naturally with the strong interactions, with quantum chromodynamics, the strong nuclear force.

0:58:44.0 SC: For the strong nuclear force, simple diagrams are not necessarily more important than complicated diagrams, so you can’t just do the first few simple ones and then stop. So you might say, well, then it’s just hopeless. How are we even calculating this at all? It turns out there are two different things you can do, okay. What do you need to do is understand how the strongly interacting particles, quarks and gluons, how they indirectly interact with muons.

0:59:12.9 SC: So what you can do is just measure that separately, so separately from measuring the muons’ magnetic moment, you can do other experiments, at the LHC and Fermilab and elsewhere, which give you phenomenological data, as we say, so data directly from the experiment about what the coupling is between muons and strongly interacting particles in different regimes. So then rather than calculating a bunch of Feynman diagrams, you can just measure the relative contributions of these strongly interacting particles to what it is you’re trying to figure out. That’s a thing you can do, and that is what was done. That is where we got the result of the standard model prediction, which is off by 4 sigma from what Fermilab actually measured.

1:00:00.0 SC: But there’s another way to do it, there’s another way to figure out what the contributions are from the strong interactions, which is to try to calculate them directly, so not use experimental data, to try to calculate them, but rather than using Feynman diagrams, using what is called lattice quantum chronodynamics. So basically, a lattice is just a big computer simulation where you sort of put all of the gluons and the quarks onto this computer and you say, alright, tell me, just do all these non-peturbative calculations, tell me what the answer is, tell me how strongly the strongly interacting particles affect the properties of the muons.

1:00:37.4 SC: And that has been done also, this is an ongoing project, and here’s the punchline, I really should have led with this, but many of you already know it, a result was released or was actually published, it was released earlier, but it was published the same day that Fermilab’s muon g-2 result came out, and these lattice calculations claim that the theory fits the data fine, that there isn’t really any discrepancy, or more like there’s less than a 2 sigma discrepancy between the theoretical predictions and the experimental result.

1:01:12.7 SC: In other words, these lattice people are claiming that with their technique of making the standard model prediction, there’s nothing to be explained, it fits the measurement that Fermilab has come up with. Now the theorists at Fermilab and elsewhere who made the prediction that didn’t agree, they know that, we all talk to each other in particle physics, we all publish papers, we read each other’s papers, we go to the same conferences, okay. These are two different methods for calculating the same result, and they don’t quite agree. I mean, they’re sort of 2 sigma away from each other, and then the lattice thing is another 2 sigma away from the experiment, so it’s 4 sigma total, and that’s very, very rough, don’t quote me on that, but that’s the basic idea.

1:01:57.1 SC: So the people at Fermilab and in that experiment thought about it, and they said, look, we can’t on this time scale, verify the experiments, the claims that are being made, they’re not experiments, the theoretical claims, computational results of the lattice simulations, so we’re not going to include it. We can check and verify and try to understand these phenomenological measurements that we have under control, so that’s what we’re going to go with.

1:02:21.8 SC: So of course, future work is required, so that, it’s always the end of these ambiguous stories, not only do we need future work in the form of better experiments, but we need to figure out this theoretical disagreement between different ways of including the contributions of strongly interacting particles to the magnetic moment of the muon, two different ways, give you different results. Maybe one of them is right. Maybe both of them are right. No, they can’t both be right. They’re in disagreement. Maybe they’re both wrong, that’s always possible, but it’s answerable, is the point, this is a theoretical calculation, you don’t need to build a bigger particle accelerator to do it.

1:03:03.2 SC: You might need to build a bigger computer to get more accurate lattice QCD. By the way, lattice QCD is very hard. Lattice quantum chromodynamics, it’s a notoriously difficult thing to do, so even though it agrees with the experiment, we shouldn’t jump right to saying, well, that one’s probably right. We should just be honest and sort of suspend our judgment. Maybe there’s a real anomaly here, maybe it’s not. The theorists will try to get it right.

1:03:29.4 SC: And it’s important to try to get it right, because even if at the end of the day, you say, well, I do have an anomaly here, it’s just one number, it’s the magnetic moment of the muon, there are a number of different particle physics scenarios that could ultimately account for it, and therefore it’s enormously strong motivation to build the next generation of colliders. Before you even do that, I should, of course, say, this goes without saying, it’s enormous motivation just to keep looking for things at the Large Hadron Collider.

1:04:00.7 SC: The LHC found the Higgs boson, but they didn’t turn it off. It’s still going, it’s still supposed to be going for years into the future, and so when you give the experimenters a target to look for, that helps them in their searches, so it’s completely possible that over the next, let’s say, five years, the Large Hadron Collider discovers new particles directly that were not in the standard model of particle physics. Many of us, myself included, hoped and expected that that would have happened by now, and sort of it’s been frustrating that it hasn’t. But that doesn’t mean it won’t happen. The low-hanging fruit has been picked, the LHC looked in the obvious places, but now, alright, there’s higher up there on the tree, there could be more fruit up there, it’s still worth looking for that, and if we have a target to shoot for, it becomes much more motivated.

1:04:48.5 SC: But still, there’s also a scenario in which the LHC goes for another five or 10 years and doesn’t find anything. Then it gives very, very strong motivation for building an even more powerful particle physics experiment. You know, in a sense, I can’t help it say it makes us even more heartbroken that we didn’t build the superconducting super collider here in the United States. In the 1990s, before the Large Hadron Collider got off the ground, the US had this plan. They even started, they started building the tunnel underneath Waxahachie, Texas to build a superconducting super collider, and the SSC, as it was called, would have been finished before the LHC and it would have been higher energy, noticeably higher energy.

1:05:32.3 SC: So these questions we’re asking about could the LHC some day see other particle that is being hinted at by these new anomalies. Well, if the LHC will eventually be able to find it, the SSC would have found it by now, but we decided collectively through our decision-making process as a nation that it wasn’t worth the money to us here in the United States. Here, now, the United States is no longer in the running for building the next generation high energy particle physics accelerator, we’re not trying, we’re not putting forward plausible plans to do it. These things are so expensive, you need multinational cooperation to do it.

1:06:12.1 SC: The United States, infamously, is not very good at multinational cooperation, and we just don’t have the national gumption right now to do it by ourselves, so it might happen in Europe, it might happen in Asia, in China or Japan or somewhere else. Hopefully it happens, ’cause I do think that discovering new particles is important. So let’s end on that note, ’cause I think that that is an optimistic place to end. Discovering new particles is important. Why? Not because of the particles, you’ve discovered another particle, big whoop in some sense, okay. You have a lot of particles already, what are you going to do with the new one?

1:06:46.0 SC: Well, the point is that the new particle implies new ideas, it implies new physics, as we like to say. It’s not going to help us build better smartphones or vaccines for the next global pandemic, it helps us better understand the laws of nature. What we’re hoping for is not just one more particle to add to the zoo, what we’re hoping is that that particle gives us evidence for some new principles, whether that principle is there are extra dimensions of space or there is supersymmetry, or there’s grand unification, or there are new laws, new forces that might be related to dark matter somehow, there’s many different possibilities, right? New dynamics, who knows?

1:07:27.0 SC: But that’s what’s exciting, not finding a new particle, it’s finding new kinds of physics entirely. Will that necessarily happen if these anomalies turned out to be true? Well, I don’t know, we don’t know. I can’t say that. But if we don’t follow them up, then we don’t find these things, that we can say, right. And it is a feature of particle physics that you can do these clever experiments like the muon g-2 and find a new phenomena, the magnetic moment of the muon is a little bit different, but you can’t study them in detail. You got that one number, it’s very, very hard to go beyond that.

1:08:04.7 SC: To do detailed experimentation of what is out there, what properties it has, how the new particles and fields interact with each other, you need to build a giant particle accelerator that can reach really, really high energies. That’s the only way we know how to do it. So I’m hopeful. Like, look, I try to be level-headed about this, I was disappointed when the LHC didn’t find anything right away, and so it’s easy to become a little bit jaded and cynical saying, yeah, this is just an anomaly, it’ll go away like all the other anomalies, and maybe that’s true, but maybe not.

1:08:38.5 SC: We’re allowed to be a little bit hopeful to say, maybe this is it, maybe this is the time that we go beyond the standard model, the first truly new surprising result that was completely unexpected in a particle physics experiment since the 1970s, a particle physics experiment here on Earth. We had neutrino masses and things like that, but those were a little bit expected also, so this is something different. If it’s true. Maybe it’s true, maybe it’s not, that kind of epistemic uncertainty, that’s where we’ve got to live, that’s where the excitement comes. Enjoy it, revel in it, let’s see what happens next.

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