Category Archives: Higgs

Higgs Experts: A Small But Important Correction to a Previous Post

I have to admit that this post is really only important for experimentalists interested in searching for non-Standard Model decays of the Higgs particle.  I try to keep these technical posts very rare, but this time I do need to slightly amend a technical point that I made in an article a few weeks ago. Continue reading

What if the Large Hadron Collider Finds Nothing Else?

In my last post, I expressed the view that a particle accelerator with proton-proton collisions of (roughly) 100 TeV of energy, significantly more powerful than the currently operational Large Hadron Collider [LHC] that helped scientists discover the Higgs particle, is an obvious and important next steps in our process of learning about the elementary workings of nature. And I described how we don’t yet know whether it will be an exploratory machine or a machine with a clear scientific target; it will depend on what the LHC does or does not discover over the coming few years.

What will it mean, for the 100 TeV collider project and more generally, if the LHC, having made possible the discovery of the Higgs particle, provides us with no more clues?  Specifically, over the next few years, hundreds of tests of the Standard Model (the equations that govern the known particles and forces) will be carried out in measurements made by the ATLAS, CMS and LHCb experiments at the LHC. Suppose that, as it has so far, the Standard Model passes every test that the experiments carry out? In particular, suppose the Higgs particle discovered in 2012 appears, after a few more years of intensive study, to be, as far the LHC can reveal, a Standard Model Higgs — the simplest possible type of Higgs particle?

Before we go any further, let’s keep in mind that we already know that the Standard Model isn’t all there is to nature. The Standard Model does not provide a consistent theory of gravity, nor does it explain neutrino masses, dark matter or “dark energy” (also known as the cosmological constant). Moreover, many of its features are just things we have to accept without explanation, such as the strengths of the forces, the existence of “three generations” (i.e., that there are two heavier cousins of the electron, two for the up quark and two for the down quark), the values of the masses of the various particles, etc. However, even though the Standard Model has its limitations, it is possible that everything that can actually be measured at the LHC — which cannot measure neutrino masses or directly observe dark matter or dark energy — will be well-described by the Standard Model. What if this is the case?

Michelson and Morley, and What They Discovered

In science, giving strong evidence that something isn’t there can be as important as discovering something that is there — and it’s often harder to do, because you have to thoroughly exclude all possibilities. [It’s very hard to show that your lost keys are nowhere in the house — you have to convince yourself that you looked everywhere.] A famous example is the case of Albert Michelson, in his two experiments (one in 1881, a second with Edward Morley in 1887) trying to detect the “ether wind”.

Light had been shown to be a wave in the 1800s; and like all waves known at the time, it was assumed to be a wave in something material, just as sound waves are waves in air, and ocean waves are waves in water. This material was termed the “luminiferous ether”. As we can detect our motion through air or through water in various ways, it seemed that it should be possible to detect our motion through the ether, specifically by looking for the possibility that light traveling in different directions travels at slightly different speeds.  This is what Michelson and Morley were trying to do: detect the movement of the Earth through the luminiferous ether.

Both of Michelson’s measurements failed to detect any ether wind, and did so expertly and convincingly. And for the convincing method that he invented — an experimental device called an interferometer, which had many other uses too — Michelson won the Nobel Prize in 1907. Meanwhile the failure to detect the ether drove both FitzGerald and Lorentz to consider radical new ideas about how matter might be deformed as it moves through the ether. Although these ideas weren’t right, they were important steps that Einstein was able to re-purpose, even more radically, in his 1905 equations of special relativity.

In Michelson’s case, the failure to discover the ether was itself a discovery, recognized only in retrospect: a discovery that the ether did not exist. (Or, if you’d like to say that it does exist, which some people do, then what was discovered is that the ether is utterly unlike any normal material substance in which waves are observed; no matter how fast or in what direction you are moving relative to me, both of us are at rest relative to the ether.) So one must not be too quick to assume that a lack of discovery is actually a step backwards; it may actually be a huge step forward.

Epicycles or a Revolution?

There were various attempts to make sense of Michelson and Morley’s experiment.   Some interpretations involved  tweaks of the notion of the ether.  Tweaks of this type, in which some original idea (here, the ether) is retained, but adjusted somehow to explain the data, are often referred to as “epicycles” by scientists.   (This is analogous to the way an epicycle was used by Ptolemy to explain the complex motions of the planets in the sky, in order to retain an earth-centered universe; the sun-centered solar system requires no such epicycles.) A tweak of this sort could have been the right direction to explain Michelson and Morley’s data, but as it turned out, it was not. Instead, the non-detection of the ether wind required something more dramatic — for it turned out that waves of light, though at first glance very similar to other types of waves, were in fact extraordinarily different. There simply was no ether wind for Michelson and Morley to detect.

If the LHC discovers nothing beyond the Standard Model, we will face what I see as a similar mystery.  As I explained here, the Standard Model, with no other particles added to it, is a consistent but extraordinarily “unnatural” (i.e. extremely non-generic) example of a quantum field theory.  This is a big deal. Just as nineteenth-century physicists deeply understood both the theory of waves and many specific examples of waves in nature  and had excellent reasons to expect a detectable ether, twenty-first century physicists understand quantum field theory and naturalness both from the theoretical point of view and from many examples in nature, and have very good reasons to expect particle physics to be described by a natural theory.  (Our examples come both from condensed matter physics [e.g. metals, magnets, fluids, etc.] and from particle physics [e.g. the physics of hadrons].) Extremely unnatural systems — that is, physical systems described by quantum field theories that are highly non-generic — simply have not previously turned up in nature… which is just as we would expect from our theoretical understanding.

[Experts: As I emphasized in my Santa Barbara talk last week, appealing to anthropic arguments about the hierarchy between gravity and the other forces does not allow you to escape from the naturalness problem.]

So what might it mean if an unnatural quantum field theory describes all of the measurements at the LHC? It may mean that our understanding of particle physics requires an epicyclic change — a tweak.  The implications of a tweak would potentially be minor. A tweak might only require us to keep doing what we’re doing, exploring in the same direction but a little further, working a little harder — i.e. to keep colliding protons together, but go up in collision energy a bit more, from the LHC to the 100 TeV collider. For instance, perhaps the Standard Model is supplemented by additional particles that, rather than having masses that put them within reach of the LHC, as would inevitably be the case in a natural extension of the Standard Model (here’s an example), are just a little bit heavier than expected. In this case the world would be somewhat unnatural, but not too much, perhaps through some relatively minor accident of nature; and a 100 TeV collider would have enough energy per collision to discover and reveal the nature of these particles.

Or perhaps a tweak is entirely the wrong idea, and instead our understanding is fundamentally amiss. Perhaps another Einstein will be needed to radically reshape the way we think about what we know.  A dramatic rethink is both more exciting and more disturbing. It was an intellectual challenge for 19th century physicists to imagine, from the result of the Michelson-Morley experiment, that key clues to its explanation would be found in seeking violations of Newton’s equations for how energy and momentum depend on velocity. (The first experiments on this issue were carried out in 1901, but definitive experiments took another 15 years.) It was an even greater challenge to envision that the already-known unexplained shift in the orbit of Mercury would also be related to the Michelson-Morley (non)-discovery, as Einstein, in trying to adjust Newton’s gravity to make it consistent with the theory of special relativity, showed in 1913.

My point is that the experiments that were needed to properly interpret Michelson-Morley’s result

  • did not involve trying to detect motion through the ether,
  • did not involve building even more powerful and accurate interferometers,
  • and were not immediately obvious to the practitioners in 1888.

This should give us pause. We might, if we continue as we are, be heading in the wrong direction.

Difficult as it is to do, we have to take seriously the possibility that if (and remember this is still a very big “if”) the LHC finds only what is predicted by the Standard Model, the reason may involve a significant reorganization of our knowledge, perhaps even as great as relativity’s re-making of our concepts of space and time. Were that the case, it is possible that higher-energy colliders would tell us nothing, and give us no clues at all. An exploratory 100 TeV collider is not guaranteed to reveal secrets of nature, any more than a better version of Michelson-Morley’s interferometer would have been guaranteed to do so. It may be that a completely different direction of exploration, including directions that currently would seem silly or pointless, will be necessary.

This is not to say that a 100 TeV collider isn’t needed!  It might be that all we need is a tweak of our current understanding, and then such a machine is exactly what we need, and will be the only way to resolve the current mysteries.  Or it might be that the 100 TeV machine is just what we need to learn something revolutionary.  But we also need to be looking for other lines of investigation, perhaps ones that today would sound unrelated to particle physics, or even unrelated to any known fundamental question about nature.

Let me provide one example from recent history — one which did not lead to a discovery, but still illustrates that this is not all about 19th century history.

An Example

One of the great contributions to science of Nima Arkani-Hamed, Savas Dimopoulos and Gia Dvali was to observe (in a 1998 paper I’ll refer to as ADD, after the authors’ initials) that no one had ever excluded the possibility that we, and all the particles from which we’re made, can move around freely in three spatial dimensions, but are stuck (as it were) as though to the corner edge of a thin rod — a rod as much as one millimeter wide, into which only gravitational fields (but not, for example, electric fields or magnetic fields) may penetrate.  Moreover, they emphasized that the presence of these extra dimensions might explain why gravity is so much weaker than the other known forces.

Fig. 1: ADD's paper pointed out that no experiment as of 1998 could yet rule out the possibility that our familiar three dimensional world is a corner of a five-dimensional world, where the two extra dimensions are finite but perhaps as large as a millimeter.

Fig. 1: ADD’s paper pointed out that no experiment as of 1998 could yet rule out the possibility that our familiar three-dimensional world is a corner of a five-dimensional world, where the two extra dimensions are finite but perhaps as large as a millimeter.

Given the incredible number of experiments over the past two centuries that have probed distances vastly smaller than a millimeter, the claim that there could exist millimeter-sized unknown dimensions was amazing, and came as a tremendous shock — certainly to me. At first, I simply didn’t believe that the ADD paper could be right.  But it was.

One of the most important immediate effects of the ADD paper was to generate a strong motivation for a new class of experiments that could be done, rather inexpensively, on the top of a table. If the world were as they imagined it might be, then Newton’s (and Einstein’s) law for gravity, which states that the force between two stationary objects depends on the distance r between them as 1/r², would increase faster than this at distances shorter than the width of the rod in Figure 1.  This is illustrated in Figure 2.

Fig. 2: If the world were as sketched in Figure 1, then Newton/Einstein's law of gravity would be violated at distances shorter than the width of the rod in Figure 1.  The blue line shows Newton/Einstein's prediction; the red line shows what a universe like that in Figure 1 would predict instead.  Experiments done in the last few years agree with the blue curve down to a small fraction of a millimeter.

Fig. 2: If the world were as sketched in Figure 1, then Newton/Einstein’s law of gravity would be violated at distances shorter than the width of the rod in Figure 1. The blue line shows Newton/Einstein’s prediction; the red line shows what a universe like that in Figure 1 would predict instead. Experiments done in the last few years agree with the blue curve down to a small fraction of a millimeter.

These experiments are not easy — gravity is very, very weak compared to electrical forces, and lots of electrical effects can show up at very short distances and have to be cleverly avoided. But some of the best experimentalists in the world figured out how to do it (see here and here). After the experiments were done, Newton/Einstein’s law was verified down to a few hundredths of a millimeter.  If we live on the corner of a rod, as in Figure 1, it’s much, much smaller than a millimeter in width.

But it could have been true. And if it had, it might not have been discovered by a huge particle accelerator. It might have been discovered in these small inexpensive experiments that could have been performed years earlier. The experiments weren’t carried out earlier mainly because no one had pointed out quite how important they could be.

Ok Fine; What Other Experiments Should We Do?

So what are the non-obvious experiments we should be doing now or in the near future?  Well, if I had a really good suggestion for a new class of experiments, I would tell you — or rather, I would write about it in a scientific paper. (Actually, I do know of an important class of measurements, and I have written a scientific paper about them; but these are measurements to be done at the LHC, and don’t involve a entirely new experiment.)  Although I’m thinking about these things, I do not yet have any good ideas.  Until I do, or someone else does, this is all just talk — and talk does not impress physicists.

Indeed, you might object that my remarks in this post have been almost without content, and possibly without merit.  I agree with that objection.

Still, I have some reasons for making these points. In part, I want to highlight, for a wide audience, the possible historic importance of what might now be happening in particle physics. And I especially want to draw the attention of young people. There have been experts in my field who have written that non-discoveries at the LHC constitute a “nightmare scenario” for particle physics… that there might be nothing for particle physicists to do for a long time. But I want to point out that on the contrary, not only may it not be a nightmare, it might actually represent an extraordinary opportunity. Not discovering the ether opened people’s minds, and eventually opened the door for Einstein to walk through. And if the LHC shows us that particle physics is not described by a natural quantum field theory, it may, similarly, open the door for a young person to show us that our understanding of quantum field theory and naturalness, while as intelligent and sensible and precise as the 19th century understanding of waves, does not apply unaltered to particle physics, and must be significantly revised.

Of course the LHC is still a young machine, and it may still permit additional major discoveries, rendering everything I’ve said here moot. But young people entering the field, or soon to enter it, should not assume that the experts necessarily understand where the field’s future lies. Like FitzGerald and Lorentz, even the most brilliant and creative among us might be suffering from our own hard-won and well-established assumptions, and we might soon need the vision of a brilliant young genius — perhaps a theorist with a clever set of equations, or perhaps an experimentalist with a clever new question and a clever measurement to answer it — to set us straight, and put us onto the right path.

A 100 TeV Proton-Proton Collider?

During the gap between the first run of the Large Hadron Collider [LHC], which ended in 2012 and included the discovery of the Higgs particle (and the exclusion of quite a few other things), and its second run, which starts a year from now, there’s been a lot of talk about the future direction for particle physics. By far the most prominent option, both in China and in Europe, involves the long-term possibility of a (roughly) 100 TeV proton-proton collider — that is, a particle accelerator like the LHC, but with 5 to 15 times more energy per collision.

Do we need such a machine? Continue reading

Could the Higgs Decay to New Z-like Particles?

Today I’m continuing with my series, begun last Tuesday (click here for more details on the project), on the possibility that the Higgs particle discovered 18 months ago might decay in unexpected ways.

I’ve finished an article describing how we can, with current and with future Large Hadron Collider [LHC] data, look for a Higgs particle decaying to two new spin one particles, somewhat similar to the Z particle, but with smaller mass and much weaker interactions with ordinary matter.  [For decays to spin zero particles, click here.] Just using existing published plots on LHC events with two lepton/anti-lepton pairs, my colleagues and I, in our recent paper, were able to put strong limits on this scenario: for certain masses, decays to the new particles can occur in at most one in a few thousand Higgs particles.  The ATLAS and CMS experiments could certainly do better, perhaps even to the point of making a discovery with existing data, if this process is occurring in nature.

The Higgs could decay to two new spin-one particles, here labelled ZD, which in turn could each produce a lepton/anti-lepton pair.  The resulting signature would be spectacular, but neither ATLAS nor CMS has done a optimizal search for this signal covering the full allowed ZD mass range.

The Higgs could decay to two new spin-one particles, here labelled ZD, which in turn could each produce a lepton/anti-lepton pair (e = electron, μ = muon). The resulting signature would be spectacular, but neither ATLAS nor CMS has yet published an optimal search for this signal across the full allowed ZD mass range.

You might wonder how particle physicists could have missed a particle with a mass lower than that of the Z particle; wouldn’t we already have observed it? A clue as to how this can occur: it took much longer to discover the muon neutrino than the muon, even though the neutrino has a much lower mass. Similarly, it took much longer to discover the Higgs particle than the top quark, even though the Higgs has a lower mass. Why did this happen?

It happened because muon neutrinos interact much more weakly with ordinary matter than do muons, and are therefore much harder to produce, measure and study than are muons. Something similar is true of the Higgs particle compared to the top quark; although the top quark is nearly 50% heavier than the Higgs, the Large Hadron Collider [LHC] produces 20 times as many top quarks and anti-quarks as Higgs particles, and the signature of a top quark is usually more distinctive. So new low-mass particles to which the Higgs particle can perhaps decay could easily have been missed, if they interact much more weakly with ordinary matter than do the Z particle, top quark, bottom quark, muon, etc.

The muon neutrino was discovered not because these neutrinos were directly produced in collisions of ordinary matter but rather because muons were first produced, and these then decayed to muon neutrinos (plus an electron and an electron anti-neutrino).  Similarly, new particles may be discovered not because we produce them directly in ordinary matter collisions, but because, as in the above figure, we first produce a Higgs particle in proton-proton collisions at the LHC, and the Higgs may then in turn decay to them.

I should emphasize that direct searches for these types of new particles are taking place, using both old and new data from a variety of particle physics machines (here’s one example.) But it is often the case that these direct searches are not powerful enough to find the new particles, at least not soon, and therefore they may first show up in unexpected exotic decays of the Higgs… especially since the LHC has already produced a million Higgs particles, most of them at the ATLAS and CMS experiments, with a smaller fraction at LHCb.

I hope that some ATLAS and CMS experimenters are looking for this signal… and that we’ll hear results at the upcoming Moriond conference.

More Examples of Possible Unexpected Higgs Decays

As I explained on Tuesday, I’m currently writing articles for this website that summarize the results of a study, on which I’m one of thirteen co-authors, of various types of decays that the newly-discovered Higgs particle might exhibit, with a focus on measurements that could be done now with 2011-2012 Large Hadron Collider [LHC] data, or very soon with 2015-2018 data.  See Tuesday’s post for an explanation of what this is all about.

On Tuesday I told you I’d created a page summarizing what we know about possible Higgs decays to two new spin-zero particles, which in turn decay to quark pairs or lepton pairs according to our general expectation that heavier particles are preferred in spin-zero-particle decays. A number of theories (including models with more Higgs particles, certain non-minimal supersymmetric models, some Little Higgs models, and various dark matter models) predict this possibility.

Today I’ve added to that page (starting below figure 4) to include possible Higgs decays to two new spin-zero particles which in turn decay to gluon or photon pairs, according to our general expectation that, if the new spin-zero particles don’t interact very strongly with quarks or leptons, then they will typically decay to the force particles, with a rate roughly related to the strengths of the corresponding forces.  While fewer known theories directly predict this possibility compared to the one in the previous paragraph, the ease of looking for Higgs particles decaying to four photons motivates an attempt to do so in current data.

I have a few other classes of Higgs particle exotic decays to cover, so more articles on this subject will follow shortly!

Unexpected Decays of the Higgs Particle: What We Found

A few weeks ago, I reported on the completion of a large project, with which I’ve been personally involved, to investigate how particle physicists at the Large Hadron Collider [LHC] could be searching, not only in the future but even right now, for possible “Exotic Decays” of the newly-discovered Higgs particle .

By the term “exotic decays” (also called “non-Standard-Model [non-SM] Decays”), we mean “decays of this particle that are not expected to occur unless there’s something missing from the Standard Model (the set of equations we use to describe the known elementary particles and forces and the simplest possible type of Higgs field and its particle).”  I’ve written extensively on this website about this possibility (see herehere,  hereherehereherehere and here), though mostly in general terms. In our recent paper on Exotic Decays, we have gone into nitty-gritty detail… the sort of detail only an expert could love.  This week I’m splitting the difference, providing a detailed and semi-technical overview of the results of our work.  This includes organized lists of some of the decays we’re most likely to run across, and suggestions regarding the ones most promising to look for (which aren’t always the most common ones.)

Before I begin, let me again mention the twelve young physicists who were co-authors on this work, all of whom are pre-tenure and several of whom are still not professors yet.  [ When New Scientist reported on our work, they unfortunately didn’t even mention, much less list, my co-authors.] They are (in alphabetical order): David Curtin, Rouven Essig, Stefania Gori, Prerit Jaiswal, Andrey Katz, Tao Liu, Zhen Liu, David McKeen, Jessie Shelton, Ze’ev Surujon, Brock Tweedie, and Yi-Ming Zhong. Continue reading

Our Survey of Exotic Decays of the Higgs is Done

After many months gestation and a difficult labor, a behemoth is born!  Yes, it’s done, finally: our 200 page tome entitled “Exotic Decays of the 125 GeV Higgs Boson“.  Written by thirteen hard-working theoretical particle physicists, this is a paper that examines a wide class of possible decays that our newly found Higgs particle might exhibit, but that would not occur if the Standard Model of particle physics (the equations we use to describe the known elementary particles and forces plus the simplest possible type of Higgs particle) were all there was to see at the Large Hadron Collider [LHC], the giant proton-proton collider outside of Geneva, Switzerland.  

[Non-experts; sorry, but this paper was written for experts, and probably has a minimum of two words of jargon per sentence. I promise you a summary soon.]

Why is looking for unusual and unexpected decays of the Higgs particle so important?  [I’ve written about the possibility of these “exotic” decays before on this website (see herehere,  hereherehereherehere and here).]  Because Higgs particles are sensitive creatures, easily altered, possibly in subtle ways, by interactions with new types of particles that we wouldn’t yet know about from the LHC or our other experiments. (This sensitivity of the Higgs was noted as far back to the early 1980s, though its generality was perhaps only emphasized in the last decade.)  The Higgs particle is very interesting not only on its own, for what it might reveal about the Higgs field (on which our very existence depends), but also as a potential opportunity for the discovery of currently unknown, lightweight particles, to which it might decay.  Such particles might be the keys to unlocking secrets of nature, such as what dark matter is, or maybe even (extreme speculation alert) the naturalness puzzle — very roughly, the puzzle of why the mass of the Higgs particle can be so small compared to the masses of the smallest possible black holes.

The goal of our paper, which is extensive in its coverage (though still not comprehensive — this is a very big subject) is to help our experimental colleagues at ATLAS and CMS, the general purpose experiments at the LHC, decide what to search for in their current (2011-2012) and future (2015-) data, and perhaps assist in their decisions on triggering strategies for the data collecting run that will begin in 2015.  (Sorry, LHCb folks, we haven’t yet looked at decays where you’d have an advantage.) And we hope it will guide theorists too, by highlighting important unanswered questions about how to look for certain types of exotic decays.  Of course the paper has to go through peer review before it is published, but we hope it will be useful to our colleagues immediately. Time is short; 2015 is not very far away.

Although our paper contains some review of the literature, a number of its results are entirely new.  I’ll tell you more about them after I’ve recovered, and probably after most people are back from break in January.  (Maybe for now, as a teaser, I’ll just say that one of the strongest limits we obtained, as an estimate based on reinterpreting published ATLAS and CMS data, is that no more than a few × 10-4 of Higgs particles decay to a pair of neutral spin-one particles with mass in the 20 – 62 GeV/c2 range… and the experimentalists themselves, by re-analyzing their data, could surely do better than we did!)  But for the moment, I’d simply like to encourage my fellow experts, both from the theory side and the experimental side, to take a look… comments are welcome.

Finally, I’d like to congratulate and thank my young colleagues, all of whom are pre-tenure and several of whom are still not professors yet, on their excellent work… it has been a pleasure to collaborate with them.  They led the way, not me.  They are (in alphabetical order): David Curtin, Rouven Essig, Stefania Gori, Prerit Jaiswal, Andrey Katz, Tao Liu, Zhen Liu, David McKeen, Jessie Shelton, Ze’ev Surujon, Brock Tweedie, and Yi-Ming Zhong. They hail from around the world, but they’ve worked together like family… a great example of how our international effort to understand nature’s deep mysteries brings unity of purpose from a diversity of origins.

Visiting the University of Maryland

Along with two senior postdocs (Andrey Katz of Harvard and Nathaniel Craig of Rutgers) I’ve been visiting the University of Maryland all week, taking advantage of end-of-academic-term slowdowns to spend a few days just thinking hard, with some very bright and creative colleagues, about the implications of what we have discovered (a Higgs particle of mass 125-126 GeV/c²) and have not discovered (any other new particles or unexpected high-energy phenomena) so far at the Large Hadron Collider [LHC].

The basic questions that face us most squarely are:

Is the naturalness puzzle

  1. resolved by a clever mechanism that adds new particles and forces to the ones we know?
  2. resolved by properly interpreting the history of the universe?
  3. nonexistent due to our somehow misreading the lessons of quantum field theory?
  4. altered dramatically by modifying the rules of quantum field theory and gravity altogether?

If (1) is true, it’s possible that a clever new “mechanism” is required.  (Old mechanisms that remove or ameliorate the naturalness puzzle include supersymmetry, little Higgs, warped extra dimensions, etc.; all of these are still possible, but if one of them is right, it’s mildly surprising we’ve seen no sign of it yet.)  Since the Maryland faculty I’m talking to (Raman Sundrum, Zakaria Chacko and Kaustubh Agashe) have all been involved in inventing clever new mechanisms in the past (with names like Randall-Sundrum [i.e. warped extra dimensions], Twin Higgs, Folded Supersymmetry, and various forms of Composite Higgs), it’s a good place to be thinking about this possibility.  There’s good reason to focus on mechanisms that, unlike most of the known ones, do not lead to new particles that are affected by the strong nuclear force. (The Twin Higgs idea that Chacko invented with Hock-Seng Goh and Roni Harnik is an example.)  The particles predicted by such scenarios could easily have escaped notice so far, and be hiding in LHC data.

Sundrum (some days anyway) thinks the most likely situation is that, just by chance, the universe has turned out to be a little bit unnatural — not a lot, but enough that the solution to the naturalness puzzle may lie at higher energies outside LHC reach.  That would be unfortunate for particle physicists who are impatient to know the answer… unless we’re lucky and a remnant from that higher-energy phenomenon accidentally has ended up at low-energy, low enough that the LHC can reach it.

But perhaps we just haven’t been creative enough yet to guess the right mechanism, or alter the ones we know of to fit the bill… and perhaps the clues are already in the LHC’s data, waiting for us to ask the right question.

I view option (2) as deeply problematic.  On the one hand, there’s a good argument that the universe might be immense, far larger than the part we can see, with different regions having very different laws of particle physics — and that the part we live in might appear very “unnatural” just because that very same unnatural appearance is required for stars, planets, and life to exist.  To be over-simplistic: if, in the parts of the universe that have no Higgs particle with mass below 700 GeV/c², the physical consequences prevent complex molecules from forming, then it’s not surprising we live in a place with a Higgs particle below that mass.   [It’s not so different from saying that the earth is a very unusual place from some points of view — rocks near stars make up a very small fraction of the universe — but that doesn’t mean it’s surprising that we find ourselves in such an unusual location, because a planet is one of the few places that life could evolve.]

Such an argument is compelling for the cosmological constant problem.  But it’s really hard to come up with an argument that a Higgs particle with a very low mass (and corresponding low non-zero masses for the other known particles) is required for life to exist.  Specifically, the mechanism of “technicolor” (in which the Higgs field is generated as a composite object through a new, strong force) seems to allow for a habitable universe, but with no naturalness puzzle — so why don’t we find ourselves in a part of the universe where it’s technicolor, not a Standard Model-like Higgs, that shows up at the LHC?  Sundrum, formerly a technicolor expert, has thought about this point (with David E. Kaplan), and he agrees this is a significant problem with option (2).

By the way, option (2) is sometimes called the “anthropic principle”.  But it’s neither a principle nor “anthro-” (human-) related… it’s simply a bias (not in the negative sense of the word, but simply in the sense of something that affects your view of a situation) from the fact that, heck, life can only evolve in places where life can evolve.

(3) is really hard for me to believe.  The naturalness argument boils down to this:

  • Quantum fields fluctuate;
  • Fluctuations carry energy, called “zero-point energy”, which can be calculated and is very large;
  • The energy of the fluctuations of a field depends on the corresponding particle’s mass;
  • The particle’s mass, for the known particles, depends on the Higgs field;
  • Therefore the energy of empty space depends strongly on the Higgs field

Unless one of these five statements is wrong (good luck finding a mistake — every one of them involves completely basic issues in quantum theory and in the Higgs mechanism for giving masses) then there’s a naturalness puzzle.  The solution may be simple from a certain point of view, but it won’t come from just waving the problem away.

(4) I’d love for this to be the real answer, and maybe it is.  If our understanding of quantum field theory and Einstein’s gravity leads us to a naturalness problem whose solution should presumably reveal itself at the LHC, and yet nature refuses to show us a solution, then maybe it’s a naive use of field theory and gravity that’s at fault. But it may take a very big leap of faith, and insight, to see how to jump off this cliff and yet land on one’s feet.  Sundrum is well-known as one of the most creative and fearless individuals in our field, especially when it comes to this kind of thing. I’ve been discussing some radical notions with him, but mostly I’ve been enjoying hearing his many past insights and ideas… and about the equations that go with them.   Anyone can speculate, but it’s the equations (and the predictions, testable at least in principle if not in practice, that you can derive from them) that transform pure speculations into something that deserves the name “theoretical physics”.