Tag Archives: naturalness

At the Naturalness 2014 Conference

Greetings from the last day of the conference “Naturalness 2014“, where theorists and experimentalists involved with the Large Hadron Collider [LHC] are discussing one of the most widely-discussed questions in high-energy physics: are the laws of nature in our universe “natural” (= “generic”), and if not, why not? It’s so widely discussed that one of my concerns coming in to the conference was whether anyone would have anything new to say that hadn’t already been said many times.

What makes the Standard Model’s equations (which are the equations governing the known particles, including the simplest possible Higgs particle) so “unnatural” (i.e. “non-generic”) is that when one combines the Standard Model with, say, Einstein’s gravity equations. or indeed with any other equations involving additional particles and fields, one finds that the parameters in the equations (such as the strength of the electromagnetic force or the interaction of the electron with the Higgs field) must be chosen so that certain effects almost perfectly cancel, to one part in a gazillion* (something like 10³²). If this cancellation fails, the universe described by these equations looks nothing like the one we know. I’ve discussed this non-genericity in some detail here.

*A gazillion, as defined on this website, is a number so big that it even makes particle physicists and cosmologists flinch. [From Old English, gajillion.]

Most theorists who have tried to address the naturalness problem have tried adding new principles, and consequently new particles, to the Standard Model’s equations, so that this extreme cancellation is no longer necessary, or so that the cancellation is automatic, or something to this effect. Their suggestions have included supersymmetry, warped extra dimensions, little Higgs, etc…. but importantly, these examples are only natural if the lightest of the new particles that they predict have masses that are around or below 1 TeV/c², and must therefore be directly observable at the LHC (with a few very interesting exceptions, which I’ll talk about some other time). The details are far too complex to go into here, but the constraints from what was not discovered at LHC in 2011-2012 implies that most of these examples don’t work perfectly. Some partial non-automatic cancellation, not at one part in a gazillion but at one part in 100, seems to be necessary for almost all of the suggestions made up to now.

So what are we to think of this? Continue reading

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”.

Did the LHC Just Rule Out String Theory?!

Over the weekend, someone said to me, breathlessly, that they’d read that “Results from the Large Hadron Collider [LHC] have blown string theory out of the water.”

Good Heavens! I replied. Who fed you that line of rubbish?!

Well, I’m not sure how this silliness got started, but it’s completely wrong. Just in case some of you or your friends have heard the same thing, let me explain why it’s wrong.

First, a distinction — one that is rarely made, especially by the more rabid bloggers, both those who are string lovers and those that are string haters. [Both types mystify me.] String theory has several applications, and you need to keep them straight. Let me mention two.

  1. Application number 1: this is the one you’ve heard about. String theory is a candidate (and only a candidate) for a “theory of everything” — a silly term, if you ask me, for what it really means is “a theory of all of nature’s particles, forces and space-time”. It’s not a theory of genetics or a theory of cooking or a theory of how to write a good blog post. But it’s still a pretty cool thing. This is the theory (i.e. a set of consistent equations and methods that describes relativistic quantum strings) that’s supposed to explain quantum gravity and all of particle physics, and if it succeeded, that would be fantastic.
  2. Application number 2: String theory can serve as a tool. You can use its mathematics, and/or the physical insights that you can gain by thinking about and calculating how strings behave, to solve or partially solve problems in other subjects. (Here’s an example.) These subjects include quantum field theory and advanced mathematics, and if you work in these areas, you may really not care much about application number 1. Even if application number 1 were ruled out by data, we’d still continue to use string theory as a tool. Consider this: if you grew up learning that a hammer was a religious idol to be worshipped, and later you decided you didn’t believe that anymore, would you throw out all your hammers? No. They’re still useful even if you don’t worship them.

BUT: today we are talking about Application Number 1: string theory as a candidate theory of all particles, etc. Continue reading

SEARCH day 1

The first day of the SEARCH workshop was focused on current and future measurements of the new Higgs particle discovered in 2012. A lot of the issues I’ve written about before (for instance here and here) and most of the updates were rather technical, so I won’t cover them today. But I thought it useful to take a look at what was said by Raman Sundrum and separately by Nima Arkani-Hamed, whom you’ve heard about many times (for instance, here and here), on the subject of the hierarchy problem and “naturalness”.

First, let me remind you of the issue. The hierarchy problem can be phrased in many ways. Here’s one. Here’s another: for a Standard Model Higgs (the simplest possible type of Higgs particle) to show up, without any other new particles or forces at the Large Hadron Collider, is … well, let’s say it’s completely shocking, with a caveat. Why?

  • Because every spin-zero particle (or particle-like object) that has ever been observed, in particle physics and in similar contexts within solids and fluids, has been accompanied by new phenomena at an energy scale comparable to the scalar’s mass-energy (E=mc2 energy).
  • And although we cannot calculate the mass of the Higgs particle using the Standard Model (the equations we use to predict the behavior of the known particles and forces) — the Higgs particle’s mass is something we put in to the equations, which is why we didn’t know, before the LHC, what it would be — there are many speculative theories that go beyond the Standard Model where the Higgs particle’s mass can be computed, or at least estimated. And in all of these cases, the Higgs particle is accompanied by other particles and forces that show up at scales comparable to the Higgs particle’s mass-energy.

This fact — that spin-zero particles like the Higgs are accompanied by other particles and forces at a similar energy range — isn’t a mystery. Particle physicists (and others who use quantum field theory, the type of math used in the Standard Model) understand why this should be true, and have for several decades. The jargon is that it is “natural” (not meaning “from nature”, but rather meaning “generically true”) for spin-zero particles to have other particles and forces around at comparable energy scales. (I’ll explain the argument another time.)

So to discover the Higgs particle at a mass-energy of 125 GeV, and no other new particles or phenomena below, say, 1000-2000 GeV or so, would fly in the face of what we’ve seen again and again in physics, both in past data and in calculations within speculative theories. In this sense, finding nothing except a Standard Model Higgs at the LHC would be shocking. (I say “would be” rather than “is” because the LHC is still young, and no overarching conclusions can yet be drawn from its current data.)

But — here’s the caveat — how bad is this shock? After all, somewhat surprising things do happen in nature all the time. Only astonishingly, spectacularly surprising things are very rare. Yes, it would be a very big shock if new particles and forces associated with the Higgs have a mass-energy a trillion trillion times higher than that of the Higgs. But what if they’re just a few times higher than would be natural, let’s say at 10,000 GeV — which would be out of reach of the LHC? Maybe that is a small enough shock that we shouldn’t pay it much attention.  Unfortunately, this is a judgment call; there’s no sharp answer to this question.

Raman Sundrum and his three options.

Raman Sundrum and his three options.

As Sundrum put it, there are (crudely) three logically distinct possibilities for what lies ahead:

  • No shock: The hierarchy problem is resolved naturally; the associated new particles will soon be seen at the LHC.
  • Mild shock: The hierarchy problem is resolved in a roughly natural way; most of the associated new particles will be a bit beyond the reach of the LHC, but perhaps one or more will be lightweight enough to be discovered during the lifetime of the LHC.
  • Severe shock: The hierarchy problem is not resolved naturally; any associated particles may lie far out of reach, though of course other particles (associated, say, with dark matter) might still show up at the LHC.

Arkani-Hamed made a similar distinction, but addressed the third case in more detail, breaking it up into two sub-cases.

  • The solution to the hierarchy problem is that it results from a bias (= selection effect = a form of the “anthropic principle”) ; the universe is huge, complex and diverse, with particles and forces that differ from place to place [sometimes called a “multiverse”], and most of that universe is inhospitable to life of any sort; the reason we live in an unusual part of that universe, with a lightweight unaccompanied scalar particle, is because this happens to be the only place (or one of very few places) that life could have evolved. A key test of this argument is to show that if the particles and forces of nature were much different from what we find them in our part of the universe, then our environment would become completely inhospitable — perhaps there would be no atoms, or no stars. It is controversial whether this test has been passed; good arguments can be made on both sides.
  • The solution to the hierarchy problem involves a completely novel mechanism.   Easy to say — but got any ideas?  Arkani-Hamed gave us two examples of mechanisms which he had studied that he couldn’t make work — but perhaps someone else can do better.  One is based on trying to apply notions related to self-organized criticality, but he was never able to make much progress.  Another is based on an idea of Ed Witten’s that perhaps our world is best understood as one that
    1. has two dimensions of space (not the obvious three)
    2. is supersymmetric (which seems impossible, but in three dimensions supersymmetry and gravity together imply that particles and their superpartner particles need not have equal masses)
    3. has extremely strong forces

    All of this seems completely contradictory with what we observe in our world. But! One of the important conceptual lessons from string theory [this is yet another example of something important that would not have been learned if people hadn’t actually been studying string theory] is that when forces become very strong, making the physics extremely complicated to describe, it is possible that a better description of that world becomes available — and that in some special cases, this better description has one additional dimension of space and weaker forces. In short, Witten’s idea is that our way of understanding our world, with three spatial dimensions, no apparent superymmetry and no extremely strong forces, might actually be simply an alternative and simpler description of a supersymmetric world with only two spatial dimensions with an extremely strong force. Arkani-Hamed, trying to apply this to the hierarchy problem, noticed this idea makes a prediction, but he showed that the prediction is false in the Standard Model, and it seems impossible to add any collection of particles that would make it true.

    Nima Arkani-Hamed, waving his hands.

    A well-dressed Nima Arkani-Hamed, waving his hands.