The origin of mass. Or, the pion’s PR problem.

Diagram depicting pion exchange
between a proton and a neutron.
Image souce: Wikipedia.

When the discovery of the Higgs boson was confirmed by CERN, physicists cheered and the world cheered with them. Finally they knew what gave mass to matter, or so the headlines said. Except that most of the mass carried by matter doesn’t come courtesy of the Higgs. Rather, it’s a short-lived particle called the pion that generates it.

The pion is the most prevalent meson, composed of a quark and anti-quark, and the reason you missed the headlines announcing its discovery is that it took place already in 1947. But the mechanism by which pions give rise to mass still holds some mysteries, notably nobody really knows at which temperature it happens. In a recent PRL now researchers at RHIC in Brookhaven have taken a big step towards filling in this blank.

Observation of charge asymmetry dependence of pion elliptic flow and the possible chiral magnetic wave in heavy-ion collisions
STAR Collaboration
Phys. Rev. Lett. 114, 252302 (2015)
arXiv:1504.02175 [nucl-ex]

There are three variants of pions: one positively charged, one negatively charged, and one neutral. The mechanism of mass generation by pions is mathematically very similar to the Higgs mechanism, but it involves entirely different particles and symmetries, and an energy about one thousandth of that where the Higgs mechanism operates.

In contrast to the Higgs which gives masses to elementary particles, the pion is responsible for generating most of the masses of composite particles that are found in atomic nuclei, protons and neutrons, collectively called nucleons. If we would only add up the masses of the elementary particles – the up and down quarks – that they are made up of, we would get a badly wrong answer. Instead, much of the mass is in a background condensate, mathematically analogous to the Higgs field (vev).

The pion is the Goldstone boson of the “chiral symmetry” of the standard model, a symmetry that relates left-handed with right-handed particles. It is also one of the best examples for technical naturalness. The pion’s mass is suspiciously small, smaller than one would naively expect, and therefore technical naturalness tells us that we ought to find an additional symmetry when the mass is entirely zero. And indeed it is the chiral symmetry that is recovered when the pions’ masses all vanish. The pions aren’t exactly massless because chiral symmetry isn’t an exact symmetry, after all the Higgs does create masses for the quarks, even if they are only small ones.

Mathematically all this is well understood, but the devil is in the details. The breaking of chiral symmetry happens at an energy where the strong nuclear force is strong indeed. This is in contrast to the breaking of electro-weak symmetry that the Higgs participates in, which happens at much higher energies. The peculiar nature of the strong force has it that the interaction is “asymptotically free”, meaning it gets weaker at higher energies. When it’s weak, it is well understood. But at low energies, such as close by chiral symmetry breaking, little can be calculated from first principles. Instead, one works on the level of effective models, such as that based on pions and nucleons rather than quarks and gluons.

We know that quarks cannot float around freely but that they are always bound together to multiples that mostly neutralize the “color charge” that makes quarks attract each other. This requirement of quarks to form bound states at low energies is known as “confinement” and exactly how it comes about is one of the big open questions in theoretical physics. Particle physicists deal with their inability to calculate it by using tables and various models for how the quarks find and bind each other.

The breaking of chiral symmetry which gives mass to nucleons is believed to take place at a temperature close by the transition in which quarks stop being confined. This deconfinement transition has been subject of much interest and lead to some stunning insights about the properties of the plasma that quarks form when no longer confined. In particular this plasma turned out to have much lower viscosity than originally believed, and the transition turned out to be much smoother than expected. Nature is always good for a surprise. But the chiral phase transition hasn’t attracted much attention, at least so far, though maybe this is about to change now.

These properties of nuclear matter cannot be studied in collisions of single highly energetic particles, like proton-proton collisions at the LHC. Instead, one needs to bring together as many quarks as possible, and for this reason one collides heavy nuclei, for example gold or lead nuclei. RHIC at Brookhaven is one of the places where these studies are done. The GSI in Darmstadt, Germany, another one. And the LHC also has a heavy ion program, another run of which is expected to take place later this year.

But how does one find out whether chiral symmetry is restored together with the deconfinement transition? It’s a tough question that I recall being discussed already when I was an undergraduate student. The idea that emerged over long debates was to make use of the coupling of chiral matter to magnetic fields.

The heavy ions that collide move at almost the speed of light and they are electrically charged. Since moving charges create magnetic fields, this generically causes very strong magnetic fields in the collision region. The charged pions that are produced in large amounts when the nuclei collide couple to the magnetic field. And their coupling depends on whether or not they have masses, ie it depends on whether chiral symmetry was restored or not. And so the idea is that one measures the distribution of charged pions that come out of the collision of the heavy nuclei, and from that one infers whether chiral symmetry was restored and, ideally, what was the transition temperature and the type of phase transition.

So much for the theory. In practice of course it isn’t that easy to find out exactly what gave rise to the measured distribution. And so the recent results have to be taken with a grain of salt: even the title of the paper carefully speaks of a “possible observation” rather than declaring it has been observed. It will certainly take more study to make sure they are really seeing chiral symmetry restoration and not something else. In any case though, I find this an interesting development because it demonstrates that the method works, and I think this will be a fruitful research direction about which we will hear more in the future.

For me chirality has always been the most puzzling aspect of the standard model. It’s just so uncalled for. That molecules come in left-handed and right-handed variants, and biology on Earth settled on mostly the left-handed, ones can be put down as a historical accident – one that might not even have repeated on other planets. But fundamentally, on the level of elementary particles, where would such a distinction come from?

The pion, I think, deserves a little bit more attention.