Dark matter’s hideout just got smaller, thanks to supercomputers.

Lattice QCD. Artist’s impression.

Physicists know they are missing something. Evidence that something’s wrong has piled up for decades: Galaxies and galaxy clusters don’t behave like Einstein’s theory of general relativity predicts. The observed discrepancies can be explained either by modifying general relativity, or by the gravitational pull of some, so-far unknown type of “dark matter.”

Theoretical physicists have proposed many particles which could make up dark matter. The most popular candidates are a class called “Weakly Interacting Massive Particles” or WIMPs. They are popular because they appear in supersymmetric extensions of the standard model, and also because they have a mass and interaction strength in just the right ballpark for dark matter. There have been many experiments, however, trying to detect the elusive WIMPs, and one after the other reported negative results.

The second popular dark matter candidate is a particle called the “axion,” and the worse the situation looks for WIMPs the more popular axions are becoming. Like WIMPs, axions weren’t originally invented as dark matter candidates.

The strong nuclear force, described by Quantum ChromoDynamics (QCD), could violate a symmetry called “CP symmetry,” but it doesn’t. An interaction term that could give rise to this symmetry-violation therefore has a pre-factor – the “theta-parameter” (θ) – that is either zero or at least very, very small. That nobody knows just why the theta-parameter should be so small is known as the “strong CP problem.” It can be solved by promoting the theta-parameter to a field which relaxes to the minimum of a potential, thereby setting the coupling to the troublesome term to zero, an idea that dates back to Peccei and Quinn in 1977.

Much like the Higgs-field, the theta-field is then accompanied by a particle – the axion – as was pointed out by Steven Weinberg and Frank Wilczek in 1978.

The original axion was ruled out within a few years after being proposed. But theoretical physicists quickly put forward more complicated models for what they called the “hidden axion.” It’s a variant of the original axion that is more weakly interacting and hence more difficult to detect. Indeed it hasn’t been detected. But it also hasn’t been ruled out as a dark matter candidate.

Normally models with axions have two free parameters: one is the mass of the axion, the other one is called the axion decay constant (usually denoted f_a). But these two parameters aren’t actually independent of each other. The axion gets its mass by the breaking of a postulated new symmetry. A potential, generated by non-perturbative QCD effects, then determines the value of the mass.

If that sounds complicated, all you need to know about it to understand the following is that it’s indeed complicated. Non-perturbative QCD is hideously difficult. Consequently, nobody can calculate what the relation is between the axion mass and the decay constant. At least so far.

The potential which determines the particle’s mass depends on the temperature of the surrounding medium. This is generally the case, not only for the axion, it’s just a complication often omitted in the discussion of mass-generation by symmetry breaking. Using the potential, it can be shown that the mass of the axion is inversely proportional to the decay constant. The whole difficulty then lies in calculating the factor of proportionality, which is a complicated, temperature-dependent function, known as the topological susceptibility of the gluon field. So, if you could calculate the topological susceptibility, you’d know the relation between the axion mass and the coupling.

This isn’t a calculation anybody presently knows how to do analytically because the strong interaction at low temperatures is, well, strong. The best chance is to do it numerically by putting the quarks on a simulated lattice and then sending the job to a supercomputer.

And even that wasn’t possible until now because the problem was too computationally intensive. But in a new paper, recently published in Nature, a group of researchers reports they have come up with a new method of simplifying the numerical calculation. This way, they succeeded in calculating the relation between the axion mass and the coupling constant.

Calculation of the axion mass based on high-temperature lattice quantum chromodynamics
S. Borsanyi et al
Nature 539, 69–71 (2016)

(If you don’t have journal access, it’s not the exact same paper as this but pretty close).

This result is a great step forward in understanding the physics of the early universe. It’s a new relation which can now be included in cosmological models. As a consequence, I expect that the parameter-space in which the axion can hide will be much reduced in the coming months.

I also have to admit, however, that for a pen-on-paper physicist like me this work has a bittersweet aftertaste. It’s a remarkable achievement which wouldn’t have been possible without a clever formulation of the problem. But in the end, it’s progress fueled by technological power, by bigger and better computers. And maybe that’s where the future of our field lies, in finding better ways to feed problems to supercomputers.