Tuesday, 26 June 2012

The Good and Bad Side of Finding the Higgs

In a previous post, I commented
Of course, in some respects it would be more interesting if those hints are wrong and there is no Standard Model Higgs ...
I thought I'd expand on this a bit.  You see, the LHC is a multi-billion dollar, multi-national enterprise.  Finding the Higgs would justify the whole endeavour, and should ensure funding for the next round of experiments, be it a linear collider, muon accelerator or whatever.  So why would I want there to be no Higgs?

The answer, obviously, is that there being no Higgs tells us something new.  This is, after all, how science advances: by being surprised.  But there is also the practical side, hinted at above: even if the LHC finding nothing would have profound physical implications, it would in all likelihood be the death knell for the field.  Finding nothing would be a public relations disaster.

The loophole is that finding the Higgs and finding nothing are not the only options.  If we find any new physics beyond the Standard Model, that would also satisfy the funding agencies (and likely win a Nobel prize).  So we basically have a table:

No Higgs
No BSM Physics
Field Dies
BSM Physics

The question then becomes: are we more likely to find new physics if we find a Higgs, or not?

The is actually a lot of reason to hope that we might find new physics if there is no Higgs.  The first is closely related to why we need a Higgs at all.  If we try to calculate the probability for two W-bosons1 to scatter as a function of energy, then without a Higgs the probability grows to become bigger than one at energies probed by the LHC.
The probability for Ws scattering off each other without a Higgs exceeds 1 at LHC energies.
What this means is that the theory must be corrected at or around this energy scale.  Adding a Higgs adds an extra contribution that turns out to keep the probability sensible.  If there is no Higgs, or anything Higgs-like, then instead what happens  is that the theory undergoes a phase transition, which is difficult to calculate but probably involves the Ws condensing into bound states.  In short, there must be something in this process that has not yet been found.

The LHC does not, of course, collide Ws; but they can be produced as higher-order quantum effects.  So the LHC does this experiment, and this process is an important one in Higgs searches.  Should there turn out not to be a Higgs, then we can continue to use the same methods to find whatever might be there.  The unfortunate downside is that in the worst case scenario, where the Ws form bound states, those bound states might just be too heavy to find with the LHC.  (It's hard to say with certainty because, as I mentioned, we can't calculate in this regime.)2

In summary, though, if there is no Higgs, we have a high probability (though not quite a certainty) to find something new.

What if we find the Higgs?  For the purposes of this consideration, I specifically mean a Higgs as hinted at in last years data: one that looks like a Standard Model Higgs, at least at first, with a mass of 125 GeV.3  How likely is is that we could find new physics?

There are two reasons to be sceptical that we will find anything.  The first is the tight indirect constraints from precision measurements of the interactions of the W and Z at LEP and the Tevatron.  These put generic models with LHC-accessible physics under very tight constraints.  While there are ways around those constraints, they require some effort.  Also, most of the models we have, we would expected to have found by now.  I wasn't active at the time, but I've heard that before LEP 2 ran, people said that it could rule out Supersymmetry (if it didn't find the Higgs).  That turned out to not strictly be true, but it serves as an example of my point.  (See also tomorrow's post.)

The second problem with the Higgs where it has been found is that it seems to be perfectly happy with nothing else until we reach the scale of quantum gravity.  To explain this, we need to consider something called the Higgs potential.  This is an energy that is associated with the Higgs taking a particular value.  It is generally assumed to look a bit like this:
Energy associated with different values of the Higgs field
The Higgs naturally wants to be at a low energy, in the same way that things in gravitational fields fall to the lowest points they can.  Here, the lowest energies are associated with non-zero values of the Higgs field, which is the key to the whole Higgs mechanism.

The precise form of the Higgs potential can be determined based on things already measured (the strength of the weak force, the top quark mass, etc.), the Higgs mass, and the scale at which non-Standard Model physics enters.  The last element is important because it determines how strongly the potential is corrected by quantum fluctuations.  In particular, strong quantum corrections can make the potential unstable so that the Higgs decays from the state we observe it in to a different one.

At first glance, this decay would be bad, and we can rule out models where it happens.  A little more thought shows that as long as the decay is sufficiently slow, so that it shouldn't have happened yet, its okay.  In either case, though, we can use a measurement of the Higgs mass to figure out the highest energy at which we must have new physics.  If that energy is below the scale of quantum gravity, then we know there must be something else.

Unfortunately, for a 125 GeV Higgs, it is not.

There have been a lot of papers on this point, especially since the results were announced last December.  I stole the following images from DeGrassi et al, which is pretty representative:
These plots show the Higgs mass on the horizontal axis and the top mass on the vertical axis.  Areas in green have no instability if there is no new physics up to the Planck scale; areas in yellow have a Higgs that will eventually decay, but are not ruled out; and areas in red must have new stuff before quantum gravity.  As can be seen, a 125 GeV Higgs lies firmly in the yellow region.

In summary, there is no inconsistency with finding the Higgs at 125 GeV and nothing else.  Sure, there are some reasons why we might hope to find more, including dark matter, flavour, and the strong CP problem, but they could all be solved at some very high energy scale.  If we find the Higgs, the probability of finding anything else is lower than if we don't.

At least, that's how I see it.

1. Remember that Ws are the carriers of the weak force.
2. There are reasons to think that his situation is disfavoured based on indirect constraints.  However, that would be too much of a digression.
3. Technically that's the rest mass energy, but I'm following common convention in particle physics to set the speed of light equal to one, so E = m.

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