Professors at research universities engage in many different activities, and one which is little known to the public involves teaching at short and focused “schools” for graduate students. These schools, which generally last one to four weeks, and are usually (but not always) held outside the main academic year in winter or summer, allow these students to learn advanced topics in short courses that their universities wouldn’t be able to offer.
For instance, at most universities in the United States, a course focused on the theory of quarks and gluons (the set of equations known as “QCD”) would be attended by just a few students. And many universities don’t even have a professor who is truly expert on this subject. But when interested students from many universities are brought together at one of these specially organized schools, a world’s expert on QCD can teach a group of students as large as fifty or more. Not only is there economy of scale in this arrangement, it also helps to foster a future community among the students who attend. I myself went to one such school when I was a graduate student, and the faculty and students I met there include a number who are my professional peers today.
Usually, professors are not paid to teach at these schools, even though preparing a course is often a huge amount of work. There are two inducements, other than the satisfaction derived from the teaching itself. The first is that travel and lodging are free for the teacher; they are paid for by the organizers of the school, who in turn get the required funds from their university and/or government organizations. The latter (wisely, in my opinion) see such schools as having national value, in that they help assure a strong national research community in the future. The second is that the schools are often held in places where a person would not regret spending a week. The schools at which I have taught over the years have occurred in Boulder, Colorado (USA); Vancouver, British Columbia (Canada); Fermilab National Lab in Aurora, Illinois (USA); Cambridge, England; Kyoto, Japan; and Varna, Bulgaria. I’ve also taught in Italy, previously in the towns of Trieste and Erice, and this month in Florence (i.e. Firenze). For the next ten days or so, I’ll be at the Galileo Galilei Institute for Theoretical Physics (GGI), which is named, of course, after Florence’s most famous scientist.
(Several of my previous short courses are available in written or video form, and most are still sufficiently up-to-date to be useful to future experts. All of them assume, at least in large part, that a student has had a beginning course in quantum field theory. I can provide some links later this week if there is interest, though most of them easily show up in a web search.)
This is my first visit to the GGI, which is associated with the University of Florence, and is located on a hill a couple of miles from downtown Florence, not very far from where Galileo himself lived for some years. It was founded around 2006 to host focused research workshops, as well as brief schools. The theoretical particle physics graduate students at this school have already learned about dark matter from Tomer Volansky (a collaborator of mine on a trigger-related project), and about supersymmetry from David Shih (a former colleague at Rutgers and a recent collaborator on a supersymmetry/LHC project.) They’ll also be learning about the Higgs phenomenon and its generalizations from Raman Sundrum (who’s been mentioned many times on this blog, and whom I visited last month); about the physics of “flavor” — including the issue of how the six different types quarks transition from one to another via the weak nuclear force — from Gino Isidori; and about the physics of quarks and gluons from one of the world’s great experts, Stefano Catani. (You may not recognize these names, as none of them have written books for the public or developed a popular website or blog; but any expert in the theoretical particle physics knows them very well.) And last and perhaps least, they’ll be learning various bits of particle physics that one ought to know in the context of particle colliders, and particularly of the Large Hadron Collider [LHC], from me.
One corollary of this news is that I’ll be pretty busy for the next ten days, so I’m not sure how active the blog will really be. But I can promise you at least one post on string theory!
Today, Wednesday December 4th, at 8 pm Eastern/5 pm Pacific time, Sean Carroll and I will be interviewed again by Alan Boyle on “Virtually Speaking Science”. The link where you can listen in (in real time or at your leisure) is
What is “Virtually Speaking Science“? It is an online radio program that presents, according to its website:
Informal conversations hosted by science writers Alan Boyle, Tom Levenson and Jennifer Ouellette, who explore the explore the often-volatile landscape of science, politics and policy, the history and economics of science, science deniers and its relationship to democracy, and the role of women in the sciences.
[This is the seventh post in a series that begins here.]
In the last post in this series, I pointed out that there’s a lot about quantum field theory [the general case] that we don’t understand. In particular there are many specific quantum field theories whose behavior we cannot calculate, and others whose existence we’re only partly sure of, since we can’t even write down equations for them. And I concluded with the remark that part of the reason we know about this last case is due to “supersymmetry”.
What’s the role of supersymmetry here? Most of the time you read about supersymmetry in the press, and on this website, it’s about the possible role of supersymmetry in addressing the naturalness problem of the Standard Model [which overlaps with and is almost identical to the hierarchy problem.] But actually (and I speak from personal experience here) one of the most powerful uses of supersymmetry has nothing to do with the naturalness problem at all.
The point is that quantum field theories that have supersymmetry are mathematically simpler than those that don’t. For certain physical questions — not all questions, by any means, but for some of the most interesting ones — it is sometimes possible to solve their equations exactly. And this makes it possible to learn far more about these quantum field theories than about their non-supersymmetric cousins.
Who cares? you might ask. Since supersymmetry isn’t part of the real world in our experiments, it seems of no use to study supersymmetric quantum field theories.
But that view would be deeply naive. It’s naive for three reasons. (more…)
I have two very different presentations to give this week, on two very similar topics. First I’m going to the LHC Physics Center [LPC], located at the Fermilab National Accelerator Laboratory, host of the now-defunct Tevatron accelerator, the predecessor to the Large Hadron Collider [LHC]. The LPC is the local hub for the United States wing of the CMS experiment, one of the two general-purpose experiments at the LHC. [CMS, along with ATLAS, is where the Higgs particle was discovered.] The meeting I’m attending is about supersymmetry, although that’s just its title, really; many of the talks will have implications that go well beyond that specific subject, exploring more generally what we have and still could search for in the LHC’s existing and future data. I’ll be giving a talk for experts on what we do and don’t know currently about one class of supersymmetry variants, and what we should be perhaps be trying to do next to cover cases that aren’t yet well-explored.
Second, I’ll be going to Argonne National Laboratory, to give a talk for the scientists there, most of whom are not particle physicists, about what we have learned so far about nature from the LHC’s current data, and what the big puzzles and challenges are for the future. So that will be a talk for non-expert scientists, which requires a completely different approach.
Both presentations are more-or-less new and will require quite a bit of work on my part, so don’t be surprised if posts and replies to comments are a little short on details this week…
For Non-Experts Who've Read a Bit About Particle Physics
I spent yesterday, and am spending today, at Princeton University, participating in a workshop that brings together a group of experts from the CMS experiment, one of the two general purpose experiments at the Large Hadron Collider (where the Higgs particle was discovered.) They’ve invited me, along with a few other theoretical physicists, to speak to them about additional strategies they might use in searching for phenomena that are not expected to occur within the Standard Model (the equations we use to describe the known elementary particles and forces.) This sort of “consulting” is one of the roles of theorists like me. It involves combining a broad knowledge of the surprises nature might have in store for us with a comprehensive understanding of what CMS and its competitor ATLAS (as well as other experiments at and outside the LHC) have and have not searched for already.
Yesterday afternoon’s back-and-forth between the theorists and the experimentalists was focused on signals that are very hard to detect directly, such as (still hypothetical) dark matter particles. These could perhaps be produced in the LHC’s proton-proton collisions, but could then go undetected, because (like neutrinos) they pass without hitting anything inside of CMS. But even though we can’t detect these particles directly, we can sometimes tell indirectly that they’re present, if the collision simultaneously makes something else that recoils sharply away from them. That sometime else could be a photon (i.e. a particle of light) or a jet (the spray of particles that tells you that a high-energy gluon or quark was produced) or perhaps something else. There was a lot of interesting discussion about the various possible approaches to searching for such signals more effectively, and about how the trigger strategy might need to be adjusted in 2015, when the LHC starts taking data again at higher energy per collision, so that CMS remains maximally sensitive to their presence. Clearly there is much more work to do on this problem.
Since the mainstream news media, in their reporting on the new result from the LUX experiment I wrote about Wednesday, insists on confusing the public with their articles and headlines, I thought I’d better write a short post reminding my readers what we do and don’t know about dark matter.
Do we know dark matter exists?
Scientists are, collectively, pretty darn sure, though not 100% certain. Certainly something is out there that acts a lot like a dark form of matter (i.e. something that gravitates and clumps, but doesn’t shine, either in visible light or in any other form of electromagnetic waves). There have been some proposals that try to get around dark matter, by modifying gravity, but these haven’t worked that well. Meanwhile the evidence that there really is dark stuff out there that really behaves like matter continues to grow year by year, and every claim that it actually isn’t there (such as this one I wrote about — see the second half of the article) has turned out to be wrong. Dark matter is needed to explain features of the cosmic microwave background, to explain how galaxies form, to explain why we see certain types of gravitational lensing, etc. etc. No one alternative can explain all of these things. And dark matter easily arises in many particle physics theories, so it’s not hard to imagine it might be created in the early universe and be a dominant player today.
Do we know dark matter is made from particles (i.e. ultra-microscopic objects with uniform properties)?
No, that’s not certain. Particles would do the job, but that’s not a proof it is made from particles.
If dark matter is made from particles, do we know these are Weakly Interacting Massive Particles (WIMPs) — to be precise, particles that interact with the Standard Model via the weak nuclear force or the Higgs force or something else we already know about?
No. Dark matter could be WIMPs. Or dark matter could be made from a very different type of particle called “axions”. Or dark matter could be made from particles that aren’t of either of these types. This could include particles that only interact with ordinary matter through the force of gravity, which could make them very, very hard to detect.
Do most scientists believe dark matter is made from WIMPs? (This was claimed to be true in several news articles.)
As far as I can tell, most experts do not know what to think; some have a bias toward one idea or another, but when pressed admit there’s no way to know. Many scientists think WIMPs are a good candidate, but I’ve never heard anyone say they are the only one.
So why are so many experiments (there’s a partial list here) looking for WIMPs?
Partly because they can. Sometimes science involves looking under the lamppost for your keys. You look where you can because you can look there, and you may get lucky — it has happened many times before in history. That’s fine as long as you remember that’s what you are doing.
Not that WIMPs are the only things that people are looking for. They can also look for axions, and there are experiments doing that search too. Looking for other types of dark matter particles directly is sometimes very difficult. Some of these other types of particles could be found by the experiments at the Large Hadron Collider [LHC] (and people are looking.) Others could be found by experiments such as FERMI and AMS, through the effect of dark matter annihilation to known particles (and people are looking; there’s even a hint, not yet shown to be wrong). Still other possible types of dark matter particles are completely inaccessible to modern experiments, and may remain so for a long time to come.
If we don’t know dark matter is particles, or that those particles are WIMPs, then why do the headlines say “dark matter search in final phase” in reference to the new result from LUX, even though LUX is mainly only looking for WIMPs?
Don’t ask me. Ask the editors at CBS and the BBC why their headlines about science are so often inaccurate.
The search for dark matter will end when some type of dark matter is found (or somehow shown convincingly not to exist), not before. The former could happen any day; the latter will not happen anytime soon. The only thing that is currently approaching its end is the search for WIMPs as the dark matter (and even that search will not, unfortunately, end as soon or as conclusively as we would like.) If WIMPs aren’t found, that just probably means that dark matter is something else on the list I gave you above: some other type of particle, or some other type of thing that isn’t a particle. Or it could mean that dark matter forms clumps, rather than being smoothly distributed through our galaxy, and that we’re unlucky enough to be in an empty zone. Certainly, if LUX and XENON1T and the other current experiments don’t find anything, we will not be able conclude that dark matter doesn’t exist. Only those who don’t understand the science will attempt to draw that conclusion.
So why is the LUX experiment’s result so important?
Well, it’s important, but not amazingly important, because indeed, (a) they didn’t find anything, and (b) it’s not like they ruled out a whole class of possibilities (e.g. WIMPs) all at once. But still, (i) they did rule out a possibility that several other experiments were hinting at, and that’s important, because it settles an outstanding scientific issue, and (ii) their experiment works very, very well, which is also important, because it means they have a better chance at a discovery in their next round of measurements than they would have otherwise. In short: they deserve and will get a lot of praise and admiration for their work… but their result, unlike the discover of the Higgs particle by the LHC experiments, isn’t Nobel Prize-worthy. And indeed, it’s not getting a front-page spread in the New York Times, for good reason.
is 12 times stronger than the previous one. While this is still a billion times larger than what is expected in the Standard Model of particle physics (the equations used for the known elementary particles and forces), there are various types of as-yet unknown particles and forces that could easily produce a much larger electron EDM, through new violations of T symmetry (or, almost equivalently, CP symmetry). These effects could have been large enough to have been discovered by this experiment, so those types of possible phenomena are now more constrained than before. Fortunately, there’s more to look forward to; the method these folks are using can eventually be improved by another factor of 10 or so, meaning that a discovery using this technique is still possible.
This morning the LUX dark matter experiment reported new results, and knocked everyone’s socks off. They have understood their backgrounds from radioactivity much better and more quickly than most of us expected, using new calibration methods and a much better characterization of their backgrounds than has previously been possible. Although they have a detector only a bit larger than XENON100 and have only run the detector underground for three months, compared to the year or so that XENON100 ran previously, their limits on the rate for a dark matter particle to hit a Xenon nucleus beats XENON100’s results by a factor of 2 for a dark matter particle of mass 1000 GeV/c², increasing to about a factor of 3 for a dark matter particle in the 100 GeV/c² mass range, and soaring to a factor of 20 for a dark matter particle in the 10 GeV/c² mass range. Consequently, LUX pretty definitively rules out the possibility, hinted at by several dark matter experiments (as discussed in the second half of the article I wrote about this in April), of a dark matter particle in the 5 – 20 GeV/c² mass range. (See the figure below.) While XENON100 seemed to contradict this possibility already, it didn’t do so by a huge factor, so there were questions raised as to whether their result was convincing. But the sort of ~10 GeV/c² dark matter that people were talking about is ruled out by LUX by such a large factor that finding ways around their result seems nigh impossible. And again, there’s more to look forward to; by 2015 their results should improve by another factor of 5 or so… so they get another shot at a discovery, as will XENON1T, the successor to XENON100.
Congratulations to both groups for their spectacular achievements!
Results from the LUX paper, showing excluded regions as a function of dark-matter particle mass (horizontal axis) and dark-matter/nucleus collision rate (vertical axis), with labels added (hopefully correctly) by me. The shaded blue area is the range that LUX expected to reach, and the blue line their actual limit, which considerably exceeds the XENON100 result (red line) at all masses. The left plot shows the mass range 3 – 4000 GeV/c^2; the right plot is an inset showing details of the 5 – 12 GeV/c^2 mass region, along with the hints of signals from DAMA/LIBRA, COGENT, CMDS and CRESST, all of which now appear entirely implausible.
A week at CERN, the laboratory that hosts the Large Hadron Collider [LHC] (where the Higgs particle was discovered), is always extremely packed, and this one was no exception. It’s very typical that on a given day I’ll have four or five intense one-on-one scientific meetings with colleagues, both theorists and experimenters, and will attend a couple of presentations on hot topics — or perhaps ten, if there’s a conference going on (which is almost always.) Work starts at 9 am and typically ends at 7 pm. And of course I have my own work to do — papers to finish, for instance — so after a break for dinner, I keep working til midnight. Squeezing in time for writing blog posts can be tough under these conditions! But at least it is for very good reasons.
Just this morning I’ve just attended two talks related to a future particle physics collider that people are starting to think seriously about… a collider (currently called T-LEP) that would be built in an 80 kilometer-long [50 mile-long] circular tunnel, and in which electrons and positrons [positron = anti-electron] would be smashed together. The physics program of such a machine would be quite broad, including intensive studies of the four heaviest known particles in nature: the Z particle, the W particle, the Higgs particle and the top quark. Any one of them might reveal secrets when investigated in detail. In fact, T-LEP’s extremely precise measurements, made in the 100-500 GeV = 0.1-0.5 TeV energy range, would be used to check the equations that explain how the Higgs field gives elementary particles their masses to one part in a thousand, and to potentially be indirectly sensitive to effects of unknown particles and forces all the way up to 10-30 TeV energy scales.
After that I had a typical meeting with an experimentalist at the CMS experiment, discussing the many ways that one might still make discoveries using the existing 2011-2012 LHC data. The big concern here is that the LHC experimenters are so busy getting ready for the 2015 run of the LHC that they may not fully exploit the data that they already have.
In sports, as in science, there are two very different types of heroes. There are the giants who lead the their teams and their sport, winning championships and accolades, for years, and whose fame lives on for decades: the Michael Jordans, the Peles, the Lou Gherigs, the Joe Montanas. And then there are the unlikely heroes, the ones who just happen to have a really good day at a really opportune time; the substitute player who comes on the field for an injured teammate and scores the winning goal in a championship; the fellow who never hits a home run except on the day it counts; the mediocre receiver who turns a short pass into a long touchdown during the Super Bowl. We celebrate both types, in awe of the great ones, and in amused pleasure at the inspiring stories of the unlikely ones.
In science we have giants like Newton, Darwin, Boyle, Galileo… The last few decades of particle physics brought us a few, such as Richard Feynman and Ken Wilson, and others we’ll meet today. Many of these giants received Nobel Prizes. But then we have the gentlemen behind what is commonly known as the Higgs particle — the little ripple in the Higgs field, a special field whose presence and properties assure that many of the elementary particles of nature have mass, and without which ordinary matter, and we ourselves, could not exist. Following discovery of this particle last year, and confirmation that it is indeed a Higgs particle, two of them, Francois Englert and Peter Higgs, have been awarded the 2013 Nobel Prize in physics. Had he lived to see the day, Robert Brout would have been the third.
The paper written by Brout and Englert; the two papers written by Higgs; the paper written by Gerald Guralnik, Tom Kibble and Carl Hagen; these tiny little documents, a grand total of five and one half printed pages — these were game-winning singles in the bottom of the 9th, soft goals scored with a minute to play, Hail-Mary passes by backup quarterbacks — crucial turning-point papers written by people you would not necessarily have expected to find at the center of things. Brout, Englert, Higgs, Guralnik, Kibble and Hagen are (or rather, in Brout’s case, sadly, were) very fine scientists, intelligent and creative and clever, and their papers, written in 1964 when they were young men, are imperfect but pretty gems. They were lucky: very smart but not extraordinary physicists who just happened to write the right paper at the right time. In each case, they did so
…not by studying the real world but by studying simplified, imaginary worlds, in which it was easier to learn the general lessons they wanted to extract…
…and with no suspicion that their results would instead be applied to a different real-world question: the possibility that the weak nuclear force is associated with photon-like particles, called W and Z, that have a mass.[A photon is a particle of light, has spin=1, and, unlike the W and Z particles, has no mass.]
History in general, and history of science in particular, is always vastly more complex than the simple stories we tell ourselves and our descendants. Making history understandable in a few pages always requires erasing complexities and subtleties that are crucial for making sense of the past. Today, all across the press, there are articles explaining incorrectly what Higgs and the others did and why they did it and what it meant at the time and what it means now. I am afraid I have a few over-simplified articles of my own. But today I’d like to give you a little sense of the complexities, to the extent that I, who wasn’t even alive at the time, can understand them. And also, I want to convey a few important lessons that I think the Hi(gg)story can teach both experts and non-experts. Here are a couple to think about as you read:
1. It is important for theoretical physicists, and others who make mathematical equations that might describe the world, to study and learn from imaginary worlds, especially simple ones. That is because
1a. one can often infer general lessons more easily from simple worlds than from the (often more complicated) real one, and
1b. sometimes an aspect of an imaginary world will turn out to be more real than you expected!
2. One must not assume that research motivated by a particular goal depends upon the achievement of that goal; even if the original goal proves illusory, the results of the research may prove useful or even essential in a completely different arena.
My summary today is based on a reading of the papers themselves, on comments by John Iliopoulos, and on a conversation with Englert, and on reading and hearing Higgs’ own description of the episode.
The story is incompletely but perhaps usefully illustrated in the figure below, which shows a cartoon of how four important scientific stories of the late 1950s and early 1960s came together. They are:
How do superconductors (materials that carry electricity without generating heat) really work?
How does the proton get its mass, and why are pions (the lightest hadrons) so much lighter than protons?
Why do hadrons behave the way they do; specifically, as suggested by J.J. Sakurai(who died rather young, and after whom a famous prize is named), why are there photon-like hadrons, called rho mesons, that have mass?
How does the weak nuclear force work? Specifically, as suggested by Schwinger and developed further by his student Glashow, might it involve photon-like particles (now called W and Z) with mass?
These four questions converged on a question of principle: “how can mass be given to particles?”, and the first, third and fourth were all related to the specific question of “how can mass be given to photon-like particles?’’ This is where the story really begins. [Almost everyone in the story is a giant with a Nobel Prize, indicated with a parenthetic (NPyear).]
My best attempt at a cartoon history…
In 1962, Philip Anderson (NP1977), an expert on (among other things) superconductors, responded to suggestions and questions of Julian Schwinger (NP1965) on the topic of photon-like particles with mass, pointing out that a photon actually gets a mass inside a superconductor, due to what we today would identify as a sort of “Higgs-type’’ field made from pairs of electrons. And he speculated, without showing it mathematically, that very similar ideas could apply to empty space, where Einstein’s relativity principles hold true, and that this could allow elementary photon-like particles in empty space to have mass, if in fact there were a kind of Higgs-type field in empty space.
In all its essential elements, he had the right idea. But since he didn’t put math behind his speculation, not everyone believed him. In fact, in 1964 Walter Gilbert (NP1980 for chemistry, due to work relevant in molecular biology — how’s that for a twist?) even gave a proof that Anderson’s idea couldn’t work in empty space!
But Higgs immediately responded, arguing that Gilbert’s proof had an important loophole, and that photon-like particles could indeed get a mass in empty space.
Meanwhile, about a month earlier than Higgs, and not specifically responding to Anderson and Gilbert, Brout and Englert wrote a paper showing how to get mass for photon-like particles in empty space. They showed this in several types of imaginary worlds, using techniques that were different from Higgs’ and were correct though perhaps not entirely complete.
A second paper by Higgs, written before he was aware of Brout and Englert’s work, gave a simple example, again in an imaginary world, that made all of this much easier to understand… though his example wasn’t perhaps entirely convincing, because he didn’t show much detail. His paper was followed by important theoretical clarifications from Guralnik, Hagen and Kibble that assured that the Brout-Englert and Higgs papers were actually right. The combination of these papers settled the issue, from our modern perspective.
And in the middle of this, as an afterthought added to his second paper only after it was rejected by a journal, Higgs was the first person to mention something that was, for him and the others, almost beside the point — that in the Anderson-Brout-Englert-Higgs-Guralnik-Hagen-Kibble story for how photon-like particles get a mass, there will also generally be a spin-zero particle with a mass: a ripple in the Higgs-type field, which today we call a Higgs-type particle. Not that he said very much! He noted that spin-one (i.e. photon-like) and spin-zero particles would come in unusual combinations. (You have to be an expert to even figure out why that counts as predicting a Higgs-type particle!) Also he wrote the equation that describes how and why the Higgs-type particle arises, and noted how to calculate the particle’s mass from other quantities. But that was it. There was nothing about how the particle would behave, or how to discover it in the imaginary worlds that he was considering; direct application to experiment, even in an imaginary world, wasn’t his priority in these papers.
In his second paper, Higgs considers a simple imaginary world with just a photon-like particle and a Higgs-type field. Equation 2b is the first place the Higgs-type particle explicitly appears in the context of giving photon-like particles a mass (equation 2c). From Physical Review Letters, Volume 13, page 508
About the “Higgs-type” particle, Anderson says nothing; Brout and Englert say nothing; Guralnik et al. say something very brief that’s irrelevant in any imaginable real-world application. Why the silence? Perhaps because it was too obvious to be worth mentioning? When what you’re doing is pointing out something really “important’’ — that photon-like particles can have a mass after all — the spin-zero particle’s existence is so obvious but so irrelevant to your goal that it hardly deserves comment. And that’s indeed why Higgs added it only as an afterthought, to make the paper a bit less abstract and a bit easier for a journal to publish. None of them could have imagined the hoopla and public excitement that, five decades later, would surround the attempt to discover a particle of this type, whose specific form in the real world none of them wrote down.
In the minds of these authors, any near-term application of their ideas would probably be to hadrons, perhaps specifically Sakurai’s theory of hadrons, which in 1960 predicted the “rho mesons”, which are photon-like hadrons with mass, and had been discovered in 1961. Anderson, Brout-Englert and Higgs specifically mention hadrons at certain moments. But none of them actually considered the real hadrons of nature, as they were just trying to make points of principle; and in any case, the ideas that they developed did not apply to hadrons at all. (Well, actually, that’s not quite true, but the connection is too roundabout to discuss here.) Sakurai’s ideas had an element of truth, but fundamentally led to a dead end. The rho mesons get their mass in another way.
Meanwhile, none of these people wrote down anything resembling the Higgs field which we know today — the one that is crucial for our very existence — so they certainly didn’t directly predict the Higgs particle that was discovered in 2012. It was Steven Weinberg (NP1979) in 1967, and Abdus Salam (NP1979) in 1968, who did that. (And it was Weinberg who stuck Higgs’ name on the field and particle, so that everyone else was forgotten.) These giants combined
the ideas of Higgs and the others about how to give mass to photon-like particles using a Higgs-type field, with its Higgs-type particle as a consequence…
…with the 1960 work of Sheldon Glashow (NP1979), Schwinger’s student, who like Schwinger proposed the weak nuclear force was due to photon-like particles with mass,…
…and with the 1960-1961 work of Murray Gell-Man (NP1969) and Maurice Levy and of Yoichiro Nambu (NP2008) and Giovanni Jona-Lasinio, who showed how proton-like or electron-like particles could get mass from what we’d now call Higgs-type fields.
The Hi(gg)story is populated with giants. I’m afraid my attempt to tell the story has giant holes to match. But as far as the Higgs particle that was discovered last year at the Large Hadron Collider, the unlikely heroes of the story are the relatively ordinary scientists who slipped in between the giants and actually scored the goals.
[This is the third post in a series; here’s #1 and #2.]
The quantum field theory that we use to describe the known particles and forces is called the “Standard Model”, whose structure is shown schematically in Figure 1. It involves an interweaving of three quantum field theories — one for the electromagnetic force, one for the weak nuclear force, and one for the strong nuclear force — into a single more complex quantum field theory.
We particle physicists are extremely fortunate that this particular quantum field theory is just one step more complicated than the very simplest quantum field theories. If this hadn’t been the case, we might still be trying to figure out how it works, and we wouldn’t be able to make detailed and precise predictions for how the known elementary particles will behave in our experiments, such as those at the Large Hadron Collider [LHC].
In order to make predictions for processes that we can measure at the LHC, using the equations of the Standard Model, we employ a method of successive approximation (with the jargon name “method of perturbations”, or “perturbation `theory’ ”). It’s a very common method in math and science, in which
we make an initial rough estimate,
and then correct the estimate,
and then correct the correction,
etc.,
until we have a prediction that is precise enough for our needs.
What are those needs? Well, the precision of any measurement, in any context, is always limited by having
a finite amount of data (so small statistical flukes are common)
imperfect equipment (so small mistakes are inevitable).
What we need, for each measurement, is a prediction a little more precise than the measurement will be, but not much more so. In the difficult environment of the LHC, where measurements are really hard, we often need only the first correction to the original estimate; sometimes we need the second (see Figure 2).
Fig. 2: Top quark/anti-quark pair production rate as a function of the energy of the LHC collisions, as measured by the LHC experiments ATLAS and CMS, and compared with the prediction within the Standard Model. The measurements are the colored points, with bars indicating their uncertainties. The prediction is given by the colored bands — purple for the initial estimate, red after the first correction, grey after the second correction — whose widths indicate how uncertain the prediction is at each stage. The grey band is precise enough to be useful, because its uncertainties are comparable to those of the data. And the data and Standard Model prediction agree!
Until recently the calculations were done by starting with Feynman’s famous diagrams, but the diagrams are not as efficient as one would like, and new techniques have made them mostly obsolete for really hard calculations.
The method of successive approximation works as long as all the forces involved are rather “weak”, in a technical sense. Now this notion of “weak” is complicated enough (and important enough) that I wrote a whole article on it, so those who really want to understand this should read that article. The brief summary suitable for today is this: suppose you took two particles that are attracted to each other by a force, and allowed them to glom together, like an electron and a proton, to form an atom-like object. Then if the relative velocity of the two particles is small compared to the speed of light, the force is weak. The stronger the force, the faster the particles will move around inside their “atom”. (For more details see this article. )
For a weak force, the method of successive approximation is very useful, because the correction to the initial estimate is small, and the correction to the correction is smaller, and the correction to the correction to the correction is even smaller. So for a weak force, the first or second correction is usually enough; one doesn’t have to calculate forever in order to get a sufficiently precise prediction. The “stronger” the force, in this technical sense, the harder you have to work to get a precise prediction, because the corrections to your estimate are larger.
If a force is truly strong, though, everything breaks down. In that case, the correction to the estimate is as big as the estimate, and the next correction is again just as big, so no method of successive approximation will get you close to the answer. In short, for truly strong forces,you need a completely different approach if you are to make predictions.
In the Standard Model, the electromagnetic force and the weak nuclear force are “weak” in all contexts. However, the strong nuclear force is (technically) “strong” for any processes that involve distances comparable to or larger than a proton‘s size (about 100,000 times smaller than an atom) or energies comparable to or smaller than a proton’s mass-energy (about 1 GeV). For such processes, successive approximation does not work at all; it can’t be used to calculate a proton’s size or mass or internal structure. In fact the first step in that method would estimate that quarks and anti-quarks and gluons are free to roam independently and the proton should not exist at all… which is so obviously completely wrong that no method of correcting it will ever give the right answer. I’ll get back to how we show protons are predicted by these equations, using big computers, in a later post.
But there’s a remarkable fact about the strong nuclear force. As I said, at distances the size of a proton or larger, the strong nuclear force is so strong that successive approximation doesn’t work. Yet, at distances shorter than this, the force actually becomes “weak”, in the technical sense, and successive approximation does work there.
Let me make sure this is absolutely clear, because the difference between what we think of colloquially as “weak” is different from “weak” in the sense I’m using it here. Suppose you put two quarks very close together, at a distance r closer together than the radius R of a proton. In Figure 3 I’ve plotted how big the strong nuclear force (purple) and the electromagnetic force (blue) would be between two quarks, as a function of the distance between them. Notice both forces are very strong (colloquially) at short distances (r << R), but (I assert) both forces are weak (technically) there. The electromagnetic force is much the weaker of the two, which is why its curve is lower in the plot.
Now if you move the two quarks apart a bit (increasing r, but still with r << R), both forces become smaller; in fact both decrease almost like 1/r², which would be your first, naive estimate, same as in your high school science class. If this naive estimate were correct, both forces would maintain the same strength (technically) at all distances r.
But this isn’t quite right. Since the 1950s, it was well-known that the correction to this estimate (using successive approximation methods) is to make the electromagnetic force decrease just a little faster than that; it becomes a tiny bit weaker (technically) at longer distances. In the 60s, that’s what most people thought any force described by quantum field theory would do. But they were wrong. In 1973, David Politzer, and David Gross and Frank Wilczek, showed that for the quantum field theory of quarks and gluons, the correction to the naive estimate goes the other direction; it makes the force decrease just a little more slowly than 1/r². [Gerard ‘t Hooft had also calculated this, but apparently without fully recognizing its importance…?] It is the small, accumulating excess above the naive estimate — the gradual deviation of the purple curve from its naive 1/r² form — that leads us to say that this force becomes technically “stronger” and “stronger” at larger distances. Once the distance r becomes comparable to a proton’s size R, the force becomes so “strong” that successive approximation methods fail. As shown in the figure, we have some evidence that the force becomes constant for r >> R, independent of distance. It is this effect that, as we’ll see next time, is responsible for the existence of protons and neutrons, and therefore of all ordinary matter.
Fig. 3: How the electromagnetic force (blue) and the strong nuclear force (purple) vary as a function of the distance r between two quarks. The horizontal axis shows r in units of the proton’s radius R; the vertical axis shows the force in units of the constant value that the strong nuclear force takes for r >> R. Both forces are “weak” at short distances, but the strong nuclear force becomes “strong” once r is comparable to, or larger than, R.
So: at very short distances and high energies, the strong nuclear force is a somewhat “weak” force, stronger still than the electromagnetic and weak nuclear forces, but similar to them. And therefore, successive approximation can tell you what happens when a quark inside one speeding proton hits a quark in a proton speeding the other direction, as long as the quarks collide with energy far more than 1 GeV. If this weren’t true, we could make scarcely any predictions at the LHC, and at similar proton-proton and proton-antiproton colliders! (We do also need to know about the proton’s structure, but we don’t calculate that: we simply measure it in other experiments.) In particular, we would never have been able to calculate how often we should be making top quarks, as in Figure 2. And we would not have been able to calculate what the Standard Model, or any other quantum field theory, predicts for the rate at which Higgs particles are produced, so we’d never have been sure that the LHC would either find or exclude the Standard Model Higgs particle. Fortunately, it is true, and that is why precise predictions can be made, for so many processes, at the LHC. And the success of those and other predictions underlies our confidence that the Standard Model correctly describes most of what we know about particle physics.
But still, the equations of the strong nuclear force have only quarks and anti-quarks and gluons in them — no protons, neutrons, or other hadrons. Our understanding of the real world would certainly be incomplete if we didn’t know why there are protons. Well, it turns out that if we want to know whether protons and neutrons and other hadrons are actually predicted by the strong nuclear force’s equations, we have to test this notion using big computers. And that’s tricky, even trickier than you might guess.
