Author: Matt Strassler

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.

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.