A new theory SMASHes problems

Most of my school nightmares are history exams. But I also have physics nightmares, mostly about not being able to recall Newton’s laws. Really, I didn’t like physics in school. The way we were taught the subject, it was mostly dead people’s ideas. On the rare occasion our teacher spoke about contemporary research, I took a mental note every time I heard “nobody knows.” Unsolved problems were what fascinated me, not laws I knew had long been replaced by better ones.

Today, mental noting is no longer necessary – Wikipedia helpfully lists the unsolved problems in physics. And indeed, in my field pretty much every paper starts with a motivation that names at least one of these problems, preferably several.

A recent paper which excels on this count is that of Guillermo Ballesteros and collaborators, who propose a new phenomenological model named SM*A*S*H.

Unifying inflation with the axion, dark matter, baryogenesis and the seesaw mechanism
Guillermo Ballesteros, Javier Redondo, Andreas Ringwald, Carlos Tamarit
arXiv:1608.05414 [hep-ph]

A phenomenological model in high energy particle physics is an extension of the Standard Model by additional particles (or fields, respectively) for which observable, and potentially testable, consequences can be derived. There are infinitely many such models, so to grab the reader’s attention, you need a good motivation why your model in particular is worth the attention. Ballesteros et al do this by tackling not one but five different problems! The name SM*A*S*H stands for Standard Model*Axion*Seesaw*Higgs portal inflation.

First, there are the neutrino oscillations. Neutrinos can oscillate into each other if at least two of them have small but nonzero masses. But neutrinos are fermions and fermions usually acquire masses by a coupling between left-handed and right-handed versions of the particle. Trouble is, nobody has ever seen a right-handed neutrino. We have measured only left-handed neutrinos (or right-handed anti-neutrinos).

So to explain neutrino oscillations, there either must be right-handed neutrinos so heavy we haven’t yet seen them. Or the neutrinos differ from the other fermions – they could be so-called Majorana neutrinos, which can couple to themselves and that way create masses. Nobody knows which is the right explanation.

Ballesteros et al in their paper assume heavy right-handed neutrinos. These create small masses for the left-handed neutrinos by a process called see-saw. This is an old idea, but the authors then try to use these heavy neutrinos also for other purposes.

The second problem they take on is the baryon asymmetry, or the question why matter was left over from the Big Bang but no anti-matter. If matter and anti-matter had existed in equal amounts – as the symmetry between them would suggest – then they would have annihilated to radiation. Or, if some of the stuff failed to annihilate, the leftovers should be equal amounts of both matter and anti-matter. We have not, however, seen any large amounts of anti-matter in the universe. These would be surrounded by tell-tale signs of matter-antimatter annihilation, and none have been observed. So, presently, nobody knows what tilted the balance in the early universe.

In the SM*A*S*H model, the right-handed neutrinos give rise to the baryon asymmetry by a process called thermal leptogenesis. This works basically because the most general way to add right-handed neutrinos to the standard model already offers an option to violate this symmetry. One just has to get the parameters right. That too isn’t a new idea. What’s interesting is that Ballesteros et al point out it’s possible to choose the parameters so that the neutrinos also solve a third problem.

The third problem is dark matter. The universe seems to contain more matter than we can see at any wavelength we have looked at. The known particles of the standard model do not fit the data – they either interact too strongly or don’t form structures efficiently enough. Nobody knows what dark matter is made of. (If it is made of something. Alternatively, it could be a modification of gravity. Regardless of what xkcd says.)

In the model proposed by Ballesteros, the right-handed neutrinos could make up the dark matter. That too is an old idea and it’s not working very well: The more massive of the right-handed neutrinos can decay into lighter ones by emitting a photon and this hasn’t been seen. The problem here is getting the mass range of the neutrinos to both work for dark matter and the baryon asymmetry. Ballesteros et al solve this problem by making up dark matter mostly from something else, a particle called the axion. This particle has the benefit of also being good to solve a fourth problem.

Fourth, the strong CP problem. The standard model is lacking a possible interaction term which would cause the strong nuclear force to violate CP symmetry. We know this term is either absent or very tiny because otherwise the neutron would have an electric dipole moment, which hasn’t been observed.

This problem can be fixed by promoting the constant in front of this term (the theta parameter) to a field. The field then will move towards the minimum of the potential, explaining the smallness of the parameter. The field however is accompanied by a particle (dubbed the “axion” by Frank Wilczek) which hasn’t been observed. Nobody knows whether the axion exists.

In the SMASH model, the axion gives rise to dark matter by leaving behind a condensate and particles that are created in the early universe from the decay of topological defects (strings and domain walls). The axion gets its mass from an additional quark-like field (denoted with Q in the paper), and also solves the strong CP problem.

Fifth, inflation, the phase of rapid expansion in the early universe. Inflation was invented to explain several observational puzzles, notably why the temperature of the cosmic microwave background seems to be almost the same in every direction we look (up to small fluctuations). That’s surprising because in a universe without inflation the different parts of the hot plasma in the early universe which created this radiation had never been in contact before. They thus had no chance to exchange energy and come to a common temperature. Inflation solves this problem by blowing up an initially small patch to gigantic size. Nobody knows, however, what causes inflation. It’s normally assumed to be some scalar field. But where that field came from or what happened to it is unclear.

Ballesteros and his collaborators assume that the scalar field which gives rise to inflation is the Higgs – the only fundamental scalar which we have so far observed. This too is an old idea, and one that works badly. To make Higgs inflation works, one needs to introduce an unconventional coupling of the Higgs field to gravity, and this leads to a breakdown of the theory (loss of unitarity) in ranges where one needs it to work (ie the breakdown can’t be blamed on quantum gravity).

The SM*A*S*H model contains an additional scalar field which gives rise to a more complicated coupling and the authors claim that in this case the breakdown doesn’t happen until at the Planck scale (where it can be blamed on quantum gravity).

So, in summary, we have three right-handed neutrinos with their masses and mixing matrix, a new quark-like field and its mass, the axion field, a scalar field, the coupling between the scalar and the Higgs, the self-coupling of the scalar, the coupling of the quark to the scalar, the axion decay constant, the coupling of the Higgs to gravity, and the coupling of the new scalar to gravity. Though I might have missed something.

In case you just scrolled down to see if I think this model might be correct. The answer is almost certainly no. It’s a great model according to the current quality standard in the field. But when you combine several speculative ideas without observational evidence, you don’t get a model that is less speculative and has more evidence speaking for it.