Are Axions Dark Matter? (Script) (Patreon)

What does the strong nuclear force, the fundamental symmetries of nature, and a laundry detergent have in common? They’re all important parts of the tale of the axion - a tale whose end may take us beyond the standard model and solve one of the most vexing mysteries in astrophysics. The mystery of dark matter. 

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The story of the axion is a classic physics tale: intrepid scientists delve deep into trackless mathematics in search of answers to a mystery. And there, against all expectations, they find the hint of a completely new and unexpected denizen of the natural world. In this case the mystery was a subtle inconsistency in the behavior of the fundamental forces. And the unexpected discovery? A brand new particle - the axion - which, while not proven to exist, may explain a much more famous conundrum. The axion may explain dark matter. 

To understand the origins of the axion we need to go back and look at one of the most powerful concepts in physics: symmetry. We expect the laws of physics to be symmetric with respect to certain properties of the universe. If the equations describing a given physical process do not change when you transform a particular property, we say that process is symmetric to that transformation. For example, most of physics is symmetric to mirror reflections - the world mostly works the same when you flip the sign of the x, y, and z axes. Another example is flipping the charges of particles - positive to negative and vice versa - most of the equations of physics hold under that flip. But not all. In a previous episode we talked about how the weak nuclear force is NOT symmetric under combined charge and mirror inversion and  - or in physics-speak, the weak force is not CP symmetric - its behavior changes if you flip charges and do a mirror or parity reflection. 

Okay, so what has all this got to do with axions? Hold on, we’ll get there. Given CP violation in the weak force it’s natural to ask if it happens in the strong nuclear force also. The strong force is the fundamental force that binds quarks together into protons and neutrons, and is mediated by the gluon particle. 

Our best theoretical description of the strong force is quantum chromodynamics - QCD. That’s a deep and rich subject that will get its own episode before long. For now it’s enough to know that the equations of motion of the strong force, derived with QCD, actually allow violation of CP symmetry. In fact they almost demand it - and yet no such violation has ever been observed. 

Here’s one example - if this the strong force is CP violating, it’s predicted that the neutron should exhibit an electric field like you’d get from a pair of positive and negative charges - an electric dipole field. Our very sensitive measurements have found that no such field exists- or if there is then it’s more than a trillion times weaker than predicted by a CP-violating QCD. This discrepancy between theory and experiment is known as the strong CP problem and is currently unsolved.

It’s a proposed solution to the strong CP problem that’s going to give us the axion. But before we can see how that happens, we need to understand why quantum chromodynamics predicts a CP violation in the first place. Compared to  quantum electrodynamics, which describes electromagnetism, QCD is complicated to say the least. 

For one thing, the vacuum in QCD is full of weird structure. You might ask how can a vacuum, aka “nothing” have structure? Well, in quantum field theories, the vacuum isn’t really nothing. “Vacuum” is the word we use to describe the lowest energy state of a field - which is what you’ll find when there are no actual particles around, and as we saw in previous episodes, it’s a very lively place! Particularly in QCD, where there isn’t just one lowest energy state - there are infinite lowest energy states. 

The vacuum can hop between these different states. But because they all have the same energy, quantum weirdness allows the QCD vacuum sort of simultaneously occupy all of them at once. This bizarre structure for the vacuum alters the equations of QCD, adding new terms to its equations of motion that are governed by a new fundamental constant - theta. It’s tricky to describe what theta actually signifies - in fact there are different physical interpretations - but one way to describe it is that it’s a phase offset picked up by the quantum field as it moves between the different possible minimum energy states of the vacuum. 

And it’s these new terms - the ones added by the weird vacuum - that appear to violate CP symmetry. That means the strong force should show CP violation. So why doesn’t it? One possible explanation is that this theta value - the constant covering the CP violating terms - is just equal to zero. That would cause those terms to vanish. But there’s no good reason why theta should be zero - at least not within the standard model of particle physics. This fundamental constant may have ended up very close to zero just by chance, but physicists hate using random chance to explain the precise refinement of a value - what they call fine tuning. In 1977 Roberto Peccei and Helen Quinn proposed another solution: what if theta isn’t a constant, but can change in value, both over space and over time. In other words, make theta a new type of field - a dynamic field rather than a fundamental constant. Theta will then naturally fall to zero - because that reduces the overall energy of the vacuum, and the universe always seeks the lowest energy configuration. 

By the way, there is actually another solution to the strong CP problem which states that if any of the quarks are massless, its CP symmetry is automatically violated. However, as far as we can tell, none of the quarks are massless and so this solution is not generally accepted - turning theta into a quantum field is the most promising solution.

So you might recall that in quantum field theory a particle is just an oscillation in a quantum field. So with a new field - this theta field - we have the potential for new particles. Theta can oscillate very slightly around its value of zero - and that oscillation gives us the axion.  It was actually that of two titans of physics - Frank Wilczek and Steven Weinberg - who first  realised that this new field could be quantised to give rise to a new particle. Wilczeck sheepishly notes that this meant they got to name the particle. He named it after axion detergent as it seemed to ‘clean up’ the CP problem quite well. This hypothetical axion particle would have no electric charge, no quantum spin, be extremely light - a tiny fraction of the mass of the already tiny electron. It would interact very weakly via the strong and weak nuclear forces, and via gravity.

So how might we detect such elusive particles? Well, even though axions have no electric charge, they can still interact with the electromagnetic field and produce photons via the strong force. They would do this by generating pairs of virtual quarks which then decay into photons - the so-called Primakoff effect. This would look like an axion turning into a photon - typically in the presence of a strong magnetic field. And photons can turn into axions in a similar way.

This actually gives us an experiment. It should be possible to shine a light through a solid, opaque wall. It goes like this: a light is passed through a strong magnetic field and then blocked by a metal wall. But some photons get converted to axions in the field, and so pass directly through the wall before turning into photons again, where they can be detected. At least in theory - so far several experiments have not confirmed axions this way, at least so far.

One issue may be that we just can’t make sufficiently strong artificial magnetic fields. So why not let nature do at least half of the heavy lifting? This is precisely what the CERN Axion Solar Telescope (CAST) in Switzerland does. If axions exist then they should be produced in reasonable quantities in the core of the sun. There, X-rays are constantly bouncing off electrons and protons in the presence of strong electromagnetic fields. Perfect conditions for  producing axions, among other things. So the Sun’s core may spew out countless axions. CAST forms the detector part of the apparatus and uses strong magnetic fields of its own to try to turn those axions back into detectable photons. No luck yet, but the range of possible properties of axions is being narrowed down.

There are other spacey tests for axions. Magnetars - highly magnetic pulsars - and quasars may convert some of their own gamma ray output into axions - and that dip in gamma ray output may be measurable. In a separate phenomenon, there does seem to be a slight overabundance of gamma rays from very distant astrophysical sources like blazars. A lot of those gamma rays should be absorbed traveling through the vast, non-quite-empty tracks of intergalactic space on their way to us. It appears that too few are absorbed, and so some astrophysicists have hypothesized that some gamma rays get converted back and forth between axions and photons by the magnetic fields of entire galaxies. That makes them invisible for part of their journey, so less likely to be blocked.

Experiments thus far have not given a reliable positive result, but it may be that axions are just lighter or more weakly interacting than we think and so not detectable by current experiments. But new experiments and upgrades of existing experiments will whittle away the parameter space of possible axion properties - and eventually we’ll either spot it or decide it’s a lost cause.

This all seems like a lot of work for a hypothetical particle predicted from speculative math. But there’s a good reason for all this effort: axions may be ... dark matter. They have the right properties - no direction interaction with light, and only weak interactions via the other forces. And although these particles are extremely light, axions, if they exist, are likely to have been produced in prodigious numbers in the Big Bang. That means there could be enough of them to explain the invisible source of gravity that seems to dominate the universe - what we call dark matter. If axions do turn out to be real may clean up two of the most vexing problems in modern physics - the strong CP problem AND the nature of dark matter. Not bad for one of the tiniest and most elusive potential particles in all of spacetime.