Ok, everyone; by now you’ve all learned that the ATLAS experiment at the Large Hadron Collider [LHC] announced recently their measurement of the mass of the Higgs particle, in its decay to two photons, is at 126.6±0.3±0.7 GeV/c²; and meanwhile they measure the mass for apparently the same particle, in its decay to two lepton/anti-lepton pairs, to be 123.5±0.9+0.4-0.2 GeV/c², about 3 GeV/c² lower. “So bizarre”, wrote Michael Moyer at Scientific American, bandying about the idea that there are two Higgs-like bosons in this data (though, having pointed out the ambulance to you, and neglecting also to mention CMS’s data from November that directly disfavors this interpretation of the ATLAS data, he tells you later that some physics bloggers say you shouldn’t chase it…)
Well. How bizarre is this 2.7 standard deviation discrepancy really?
At the end of this post are 20 plots showing randomly generated data, in amounts comparable to those used in the current measurement of Higgs decaying to two lepton/anti-lepton pairs (often called “four leptons” for short). [Warning: This certainly hasn’t been done with the level of care needed to match the ATLAS measurement in any precise way; I’ll say a bit more below about the caveats.]
In some of the plots, there’s just a random flat background of about 40 events, similar (though not identical) to what arises in the four-lepton Higgs measurement.
In some of the plots, there’s a Higgs-like peak of about 20 events — a very sharp peak with a perfect detector, but one which is smoothed out a bit by the inevitable imperfections in a real particle detector.
In each plot with a peak, the mass of the Higgs has been chosen to lie somewhere between 122 GeV/c² and 127 GeV/c² [not equally populated].
So:
Can you tell which plots have a Higgs-like signal, and which ones don’t?
In each plot where there is a signal, can you estimate the Higgs mass? Again, in each plot, it lies somewhere between 122 and 127 GeV/c². You’re not going to get it exactly right — that’s impossible — but do your best, and let’s see what happens.
A couple of additional comments to help you:
The resolution on the measurement (i.e., the effect of imperfections in the measurement) is such that with infinite amounts of data, the peak that you’d observe would be a bump whose width, at half the bump’s maximum height, would be about 4 GeV/c².
The bins in each plot are 1 GeV/c² wide; the bin just to the right of the number 2 in “125” runs from 125 to 126, the next from 126 to 127, and so forth.
Lastly, a caveat: in the real ATLAS or CMS measurement, the mass of the Higgs is not measured simply by fitting a Gaussian peak over a flat background. So don’t take this exercise too seriously! It’s just a useful learning experience, and nothing more. What the experiments actually do is far more sophisticated, accounting for the properties of each event separately!!
Here we go: Good Hunting! (If your browser has trouble with the figure, try clicking on it.)
Twenty sets of simulated data, showing number of events versus the “mass” of a putative particle, in GeV/c2. Each contains about 40 events of a non-Higgs-like background that is flat in mass. Some but not all plots contain a signal which is in the form of a peak, comparable to the current size of the expected Higgs particle signal (about 20 events). In each case the mass of the Higgs is chosen between 122 and 127 GeV/c2. Experimental imperfections make the full-width of the signal peak at half its maximum about 4 GeV/c2 wide.
Yes, it was funny, as I hope you enjoyed in my post from Saturday; but really, when we step back and look at it, something is dreadfully wrong and quite sad. Somehow TIME magazine, fairly reputable on the whole, in the process of reporting the nomination of a particle (the Higgs Boson; here’s my FAQ about it and here’s my layperson’s explanation of why it is important) as a Person (?) of the Year, explained the nature of this particle with a disastrous paragraph of five astoundingly erroneous sentences. Treating this as a “teaching moment” (yes, always the professor — can’t help myself) I want to go through those sentences carefully and fix them, not to string up or further embarrass the journalist but to be useful to my readers. So that’s coming in a moment.
But first, a lament.
Who’s at fault here, and how did this happen? There’s plenty of blame to go around; some lies with the journalist, who would have been wise to run his prose past a science journalist buddy; some lies with the editors, who didn’t do basic fact checking, even of the non-science issues; some lies with a public that (broadly) doesn’t generally care enough about science for editors to make it a priority to have accurate reporting on the subject. But there’s a history here. How did it happen that we ended up a technological society, relying heavily on the discoveries of modern physics and other sciences over the last century, and yet we have a public that is at once confused by, suspicious of, bored by, and unfamiliar with science? I think a lot of the blame also lies with scientists, who collectively over generations have failed to communicate both what we do and why it’s important — and why it’s important for journalists not to misrepresent it. (more…)
After a hiatus for a hurricane and a trip to a conference in Asia, I am adding one more article to my series on How the Higgs Field Works, following my series of articles on Fields and Particles. (These sets of articles require a little math and physics background, the sort you’d get in your first few months of a beginning university or pre-university physics class. I’m still thinking about how to structure a similar set of articles that require no math or physics; that’s much harder, of course!)
This article contains the most elaborate equations and concepts that I’ve had to introduce to my readers, so it won’t be suitable for everyone (though it still only requires some first-year physics/math.) But on the other hand, it seems necessary for me to write it, since it’s the only place that I’ve explained not only why the Higgs field can give mass to the known particles, but why it (or something very much like it) must do so.
(Note that in these articles I’m mainly concentrating on the simplest type of Higgs, the Standard Model Higgs field and particle. However, most of the basic concepts in these articles apply even for more complicated cases.)
Last week, I promised you I’d fill in the details of my statement that the recent measurement (of the rare process in which a Bs meson decays to a muon and an anti-muon — read here for the physics behind this process) by the LHCb experiment at the Large Hadron Collider [LHC] had virtually no effect on the constraints on any speculative theories, including supersymmetry, contrary to the statements in the press and by a certain LHCb member. Today I’m providing you with some sources for this statement.
A number of my colleagues have tasked themselves with keeping track of how measurements at the Large Hadron Collider and elsewhere are affecting certain subclasses of variants of the supersymmetry. They call themselves the “Mastercode Project”; here’s their website. They’re not the only ones looking at this, but among them is Professor Gino Isidori, whom I was talking to last week, so I’ve gotten this information from him. I quote from the MasterCode website regarding last week’s result from LHCb: “The new measurement provides a valuable new constraint on the supersymmetric parameter space, but the observation of a Standard Model-like branching fraction for the Bs→μ+μ– decay is quite consistent with supersymmetry. In fact, a Standard Model-like branching fraction of this decay was expected in constrained supersymmetric models like the CMSSM or NUHM1 (see, e.g., the recent MasterCode results for further details). As a result, the favoured regions in the parameter space of these models do not change significantly after the inclusion of the new constraint. ”
Now before I explain what this means, it’s important to have some terminology, running from most general to most specific.
Supersymmetry: the general theory that space and time are more subtle than they appear to be, and as a result, for every known particle in nature there is a corresponding superpartner particle with the property that either the particle is a boson and its superpartner a fermion, or vice versa. (Read more about supersymmetry here, and more about fermions and bosons here and here.)
CMSSM (Constrained MSSM): a much smaller subclass of variants of the MSSM in which the masses of the superpartners are assumed to be related to each other in particular ways (the details are technical and not essential, so I’ll skip them.)
NUHM1 (Non-Uniform Higgs Mass variant of the MSSM): another small subclass of the MSSM variants, slightly more general than the CMSSM.
Keep in mind that
ruling out the CMSSM or NUHM1 does not mean that the MSSM is ruled out;
ruling out the MSSM does not mean that supersymmetry at the TeV scale is ruled out;
ruling out supersymmetry at the TeV scale does not mean that supersymmetry is ruled out.
Among the many goals of the LHC is to find or rule out supersymmetry at the TeV scale. (It cannot hope to rule out supersymmetry altogether; that would presumably require a vastly more powerful collider that won’t likely be built for centuries, if ever.) It’s not enough to rule out the CMSSM, or the NUMH1, or even the MSSM. Similar statements apply for other speculative ideas that propose as yet unknown particles and forces; it’s not enough for the LHC to rule out just the simplest variants of these ideas.
Now if it turns out that supersymmetry is part of nature, rather few of my colleagues expect the variant we find to be contained within the CMSSM or NUHM1; and personally (though I’m probably in the minority) I have long doubted that it would be contained within the MSSM. Nevertheless, it is instructive to look at how LHC data is impacting the CMSSM and the NUHM1 subclasses of supersymmetry variants. One just must be careful not to over-interpret; the exclusion of most variants in the CMSSM is not an indication that most variants of TeV-scale supersymmetry as a whole are excluded.
Now in this context, let’s see how the new measurement that was announced last week affects the CMSSM and the NUHM1. In Figure 1 is a plot showing the allowed variants of the CMSSM and the NUMH1, as a function of two quantities: on the horizontal axis, MA, which if large is (approximately but essentially) the mass of four of the five Higgs particles in the MSSM, and on the vertical axis, tan β, the ratio of the values of the two non-zero Higgs fields that are required in the MSSM. In solid red and solid blue are the one-standard-deviation and two-standard-deviation allowed regions after the new LHCb measurement is accounted for; any variant of the theory not sitting inside the blue region is excluded by the data. The dashed bands show the same thing before the new LHCb measurement. Since the dashed and solid blue bands are right on top of each other, you see there’s almost no effect at all. That’s what was behind my claim last Friday.
Fig. 1: Constraints on the CMSSM (left) and NUHM1 (right) subclasses of supersymmetric theories, before and after the HCP conference of last week. The quantities on the horizontal and vertical axes are explained in the text. In both plots: solid red (blue) give the constraints at one (two) standard deviations; variants outside the blue curve are excluded. Dashed red (blue) are the same limits before the new LHCb measurement. Notice there is almost no change.
But please, don’t misinterpret what I’m saying (or my colleagues) as suggesting that the LHC’s data has had no impact on the list of possible variants of supersymmetry! Far from it! Many variants are excluded, and many popular (but not necessarily more likely) subclasses of variants of supersymmetry have been pushed into regions that many would consider corners. The only statement in Figure 1 is that the new LHCb measurement didn’t make these corners smaller. But to see how things have changed since before the LHC began, look at Figure 2, which shows how the LHC as a whole — all the measurements from LHCb, ATLAS and CMS taken together — have affected the CMSSM and NUMH1 since 2009. (The CMSSM and NUHM1 also make assumptions about where dark matter comes from, so even effects of the dark matter measurements from the XENON100 experiment are included here.)
Fig. 2: as in Figure 1, except that the dashed lines give the constraints on the CMSSM and NUHM1 before the LHC began taking data, and the solid line gives the constraints after the data taken through early summer 2011 was analyzed. Notice the scale on the horizontal axis is different from that of Figure 1.
Figure 2 is a similar plot to Figure 1 — but this time, solid blue and red indicate the impact of LHC data as of summer 2011, and the dashed blue and red indicate the situation before the LHC started. Now compare the dashed blue line in Figure 2 (before the LHC) with the solid blue line in Figure 1 (now); note the scale on the horizontal axis is different!. You’ll see that in the CMSSM it was possible before the LHC to have MA as low as 350 GeV/c², but now it has to be over 900 GeV/c², which many would consider a rather high value. In the NUHM1 there’s been a similar shift from 150 to about 300 GeV/c², not yet so high but still a significant increase. And meanwhile, while almost any value of tan β from 2 up to 60 was allowed before the LHC, this number is now limited to a smaller range. For example, if MA were below 900 GeV/c², then the CMSSM would be excluded and the NUHM1 would be allowed only for tan β < 30 or so. This upper limit on tan β is mainly caused by the similar LHCb measurement presented back in March (and mentioned by me on Friday), and by similar ones from the CMS, CDF and ATLAS experiments.
But clearly there are plenty of variants within the NUHM1 that remain viable. And the NUHM1 is not representative of the full range of possibilities within the MSSM, so even if the NUHM1 were excluded, we’d still have a long way to go to exclude the MSSM, much less all of TeV-scale supersymmetry. In short, it’s neither all nor nothing.Yes, a lot of progress has been made; LHC data (and data from other sources) have ruled out a lot of variants of TeV-scale supersymmetry. But no, we’re not yet close to ruling out the full range of variants.
Please note that I’m not telling you this because I’m some devotee of supersymmetry who believes deeply in his heart that we’ll someday find it, and is trying to persuade you not to give up. I’m just laying out for you the facts on the ground. Do you imagine that I’m happy that a long, painful slog lies ahead, during which particle physicists — theorists and experimentalists — will painstakingly cover all the possible variants of supersymmetry, and slowly but surely determine whether or not supersymmetry is absent at the TeV scale? Don’t you think my life and that of my colleagues would be a lot easier if we could snap our fingers and with one or two quick measurements settle the question of whether supersymmetry is a fact of nature or not? Unfortunately, things don’t work that way. You should simply ignore the irresponsible grand statements you will see in the press and on various blogs; indeed, sweeping remarks are a sign of careless thinking, and you should beware. The truth is that only through very hard work — by the experts who make the measurements, by those who advise them on which measurements to make, and by those who do the calculations that are the ingredients for studies like the MasterCode Project — can we hope to settle profound questions about nature.
I’m always amused at how very reasonable remarks so often generate attacks from unreasonable people. I wrote a perfectly ordinary post about what one does and doesn’t learn from LHCb’s important new measurement at the Large Hadron Collider [LHC] (and in fact I overstated the significance of the result — more on that later), and somehow I touched off a mini-firestorm. Well, that just indicates how essential it is to have calm people expressing sensible points of view. When people become so politicized that they can’t distinguish propaganda from science, that’s not good.
Forget supersymmetry — because none of my remarks have anything to do with this theory in particular, and the theory doesn’t deserve the excessive attention it’s getting. Take any theory: call it Theory X. Extra dimensions; compositeness of quarks and leptons; non-commutative spacetime; grand unification; your-theory-here. The idea behind theory X may be very clever, but as always, there are many variants of theory X, because an idea is almost never precise enough to permit a unique realization. Each variant makes definite predictions, but keep in mind that detailed experimental predictions may very well differ greatly from variant to variant.
Now, here is a logical fact: one of two options is true.
Option A: One variant of theory X is “correct” (its predictions agree with nature) while all other variants are “wrong” (disagree with nature)
Option B: All variants of theory X are wrong.
Nature is what it is; there are no other options (and this is not the place for a discussion about this basic scientific assumption, so pace, please, philosophers.). [More precisely about option A: the space of variants is continuous, so the correct statement is that an arbitrary small region in this space is correct; you can put in the correct calculus vocabulary as you like. I’ll stick with the imprecise language for brevity.]
For either option, as more and more data is collected, more and more variants of theory X will become “dead” — excluded because of a disagreement with data. Therefore — obviously! — a reduction in the number of live (i.e. unexcluded) models always takes place over time. And this has absolutely no bearing on whether, at the end, all variants of X will be dead, or one (or perhaps several very similar ones) are still alive.
And thus it makes absolutely no sense to describe, as a “blow to theory X” — in particular, to the idea behind theory X — a measurement that excludes (“kills”) even a big fraction, but not virtually all, of the variants of theory X. It’s certainly a blow to those variants; in fact, it is a fatal blow for them. But it does nothing to distinguish between Option A and Option B. It only tells us that if Option A is true, the variant of X that will be alive at the end is not among the ones that have just been killed.
This isn’t rocket science, folks. It’s logic. [Well – As a commenter points out, it’s not “logic” in the strictest sense; but it is basic scientific reasoning.] And if we take theory X to be the Standard Model itself, I’ve just described its history. (more…)
The measurement is of how often B_s mesons (hadrons containing a bottom quark and a strange anti-quark, or vice versa, along with many quark/anti-quark pairs and gluons) decay to a muon and an anti-muon. This process (which I described last year — only about one in 300,000,000 B_s mesons decays this way) has three nice features:
The worst thing about the BBC article is the headline, “Supersymmetry theory dealt a blow” (though that’s presumably the editor’s fault, as much as or more than the author’s) and the ensuing prose, “The finding deals a significant blow to the theory of physics known as supersymmetry.” What’s wrong with it? It’s certainly true that the measurement means that many variants of supersymmetry (of which there are a vast number) are now inconsistent with what we know about nature. But what does it mean to say a theory has suffered a blow? and why supersymmetry?
First of all, whatever this new measurement means, there’s rather little scientific reason to single out supersymmetry. The rough consistency of the measurement with the prediction of the Standard Model is a “blow” (see below) against a wide variety of speculative ideas that introduce new particles and forces. It would be better simply to say that it is a blow for the Standard Model — the model to beat — and not against any speculative idea in particular. Supersymmetry is by no means the only idea that is now more constrained than before. The only reason to single it out is sociological — there are an especially large number of zealots who love supersymmetry and an equal number of zealots who hate it.
Now about the word “blow”. New measurements usually don’t deal blows to ideas, or to a general theory like supersymmetry. That’s just not what they do. They might deal blows to individual physicists who might have a very particular idea of exactly which variant of the general idea might be present in nature; certain individuals are surely more disappointed than they were before yesterday. But typically, great ideas are relatively flexible. (There are exceptions — the discovery of a Higgs particle was a huge blow to the idea behind “technicolor” — but in my career I’ve seen very few.) It is better to think of each new measurement as part of a process of cornering a great idea, not striking and injuring it — the way a person looking for treasure might gradually rule out possibilities for where it might be located.
Then there’s the LHCb scientist who is quoted as saying that “Supersymmetry may not be dead but these latest results have certainly put it into hospital”; well… Aside from the fact that this isn’t accurate scientifically (as John Ellis points out at the end of the article), it’s just not a meaningful or helpful way to think about what’s going on at the LHC. (more…)
Robert Garisto sent me a reply to my previous post; here it is. [A “vev” is shorthand for a non-zero value in the vacuum of space, what I call a “non-zero average value”.]
—
Matt – Thanks for your extensive reply to my comment! Of course I agree that a scalar field without a vev can have a hard mass term. And I do agree that how the Higgs boson gets mass is at least somewhat different than how the W does.
Let’s agree to define a Higgs as a scalar field with a vev. Then I think you agree that the mass of the excitation about the vev, the Higgs boson, is not a hard mass term, one obtains it by finding the minimum of the potential as you did above. Now if there are other scalars with vevs, the mass of the Higgs boson we are concentrating on can depend on those too. But isn’t it correct to say that the mass of such a Higgs boson goes to zero in the limit that all of those vevs go to zero? If so, I would say that the Higgs boson mass is provided by the Higgs fields (all scalars with nonzero vevs).
Anyway, the main reason I made the comment is that for the purposes of explaining to the public electroweak symmetry breaking, I think it makes sense to say that the Higgs boson mass comes from the Higgs field, because it is, in the SM, proportional to the vev. It’s also kind of neat, I think.
—
We disagree, that’s all there is to it. What Garisto says about the Standard Model is a simple consequence of dimensional analysis, not a fundamental relation that applies widely. And no, it is not correct to say that the mass of a Higgs boson always goes to zero in the limit that all vevs go to zero; there can be first order phase transitions in which, as the parameters change, the Higgs field’s vev jumps from non-zero to zero abruptly, and the mass of the Higgs particle is never zero. So I think to tell the public that the Higgs particle gets its mass from the Higgs field is to confuse them into thinking that the Higgs particle gets its mass the same way the other known particles do — which is false.
But in any case, we agree it’s not that big a deal. The thing which is important for the public to understand is that the Higgs field does not give mass to all massive objects — such as atomic nuclei and black holes. And the thing which it is important for particle physics students to understand is that the Higgs mass is not generically proportional to the vev of the Higgs field.
When I wrote my article last week about the relation between the Higgs and gravity, emphasizing that there really was no relation at all, I said that the Higgs field is not the universal giver of mass. I cited four reasons:
The Higgs field does not give an atomic nucleus all of its mass, and since the nucleus is the vast majority of the mass of an atom, that means it does not provide all of the mass of ordinary matter.
Black holes appear at the centers of galaxies, and they appear to be crucial to galaxy formation; but the Higgs field does not provide all of a black hole’s mass. In fact the Higgs field’s contribution to a black hole’s mass can even be zero, because black holes can in principle be formed from massless objects, such as photons.
There is no reason to think that dark matter, which appears to make up the majority of the masses of galaxies and indeed of all matter in the universe, is made from particles that get all of their mass from the Higgs field.
The Higgs field, though it provides the mass for all other known particles with masses, does not provide the Higgs particle with its mass.
Although it doesn’t matter too much to the main point of the Higgs-and-gravity article (since the first three points are not in question), the editor of a leading physics journal, Robert Garisto, took issue with the fourth point, arguing that I was making a statement that really wasn’t right, or at least is too strong. His argument has some merit, though in the end, I stick with my statement. I think it’s worth describing what he had in mind (as best I understand it) and why I feel strongly that one should think about it differently. There are some semantic aspects to the disagreement, but there are also some interesting and important subtle scientific points. I don’t want to suggest that this discussion is really that big a deal — the very fact that we can argue about whether the Higgs field does or doesn’t provide the Higgs particle with its mass distinguishes the Higgs particle from, say, the W particle, whose mass indisputably arises from the Higgs field. But there’s something to learn here about quantum field theory and how the Higgs mechanism works. (more…)
With my series of articles on Fields and Particles complete, I’m continuing my series of articles on How the Higgs Field Works. (These sets of articles require a little math and physics background, the sort you’d get in your first few months of a beginning university or pre-university physics class.)
The first article in the new series was an overview of The Basic Idea behind how the Higgs field works. (In these articles I’m mainly concentrating on the simplest type of Higgs, the Standard Model Higgs field and particle.) Then came an article about why and how the Higgs field becomes non-zero. And the newest article explains how the Higgs particle arises as the quantum of waves that oscillate around the non-zero value of the Higgs field, and how its mass is determined by the equation of motion of the Higgs field.
This Wednesday I was visiting the University of Massachusetts, in the currently colorful town of Amherst, where I gave a colloquium(an hour-long talk aimed at a physics department’s undergraduate majors, graduate students and faculty who are not themselves experts in particle physics) entitled The Quest for the Higgs Boson. It’s similar to the one I gave two weeks ago at the University of Toronto, which is available on-line now. There’s audio and there are slides, but no video, so I’m afraid you’ll have to figure out on your own how the slides and audio fit together; but I think it should be fairly obvious.
If, however, you’re not a physicist or physics student, but you have been following particle physics a little bit, perhaps by reading this blog or Scientific American articles or books for laypeople by, say, Brian Greene or Lisa Randall, then you might instead want to try listening to this lecture I gave recently, which is also in the form of an audio feed plus slides. It makes far fewer assumptions about what audience members are familiar with. And of course there’s always my [in]famous video clips from my March 2011 public lecture on the Large Hadron Collider; a bit out of date since they were made before the new Higgs-like particle was found, but still basically covering what you need to know.
Please note these presentations are under copyright.
