Does most of the Universe's mass come from pions (or 'virtual' pions) rather than gluons and quarks?

Question

After the discovery of the Higgs boson, we were all told that most of a proton's or neutron's mass does not actually come from their three main ('valence') quarks and their interaction with the Higgs, but from non-valence 'virtual' quarks (condensate?), quark kinetic energies and gluons (perhaps something called, mysteriously, a 'trace anomaly', too).

Recently, though, Sabine Hossenfelder posted a video called, "You probably don't know why you have mass".

In it, she said that the real story is pions.

Is she right? Is there a detailed list of the various contributions to masses, no matter how technical?

P.S.: Does the mathematical term 'trace anomaly' mean they aren't sure about the amount of contributions from each source of mass??

Answer 1

The claim that pions or a "pion condensate" accounts for most of the mass of matter is wrong. There are several things getting mixed up here:

1. The exact computation of the masses of hadrons - which constitute most of the masses of nuclei - is a complicated topic because nuclei exist at ordinary everyday energies where QCD is strongly coupled and hence not amenable to perturbation. One computation (see also this answer of mine) attributes the hadron masses to four distinct channels of contribution:

   • Quark condensate: 9%
   • Quark energy: 32%
   • Gluon energy: 36%
   • Trace anomaly: 23%

   Note that neither of these is a "pion condensate", and there is a "quark condensate", but it doesn't make up the bulk of the mass.

2. There is a sense in which indeed the pion is more important for nuclei than gluons or quarks or the Higgs: It is the main force carrier in the effective theory of the nuclear force (or residual strong force), but also not the only one, see this answer by rob for more on the residual strong force.

   So on the level of the nucleus, the answer to "what binds the hadrons together" is indeed "mostly pions". But that doesn't mean the mass of a nucleus is mostly caused by pions, the mass of the nucleus is mostly the hadron mass (see point 1) modulated by binding energy effects (sometimes called the mass defect).

3. Now in this effective theory where the pions mediate the nuclear force, the pions can "condense" (acquire a vacuum expectation value) just like any other field in a field theory. This is a possible explanation for what happens at high densities of nuclei (see e.g. this answer by user200143), but it is not something that happens in ordinary matter.

Answer 2

Oof... lies to children. I'm not sure why I'm getting involved if you cannot listen through the lines... Anyway, it is a theological physics nomenclature issue.

Most of the video is sound and useful to, e.g. a high-school student; and a diplomatic critic might even call the pion jazz at the end of the video, min 5:00 et seq, sensible, provided the pion rhetoric is understood, by HEP physicists, to vaguely mean chiral symmetry breaking in QCD (χSB). But not, not pion condensation as she garbles in min 6:00!

She mumbles she has a background in nuclear physics, and, indeed, nuclear physics has been veering into "hadronics", a hybrid compromise between QCD and nuclear physics methods. I am not familiar with specific papers she might be alluding to, but there is lots of preaching on such things in YouTube videos...

In it, she said that the real story is pions... Is she right? Is there a detailed list of the various contributions to masses,... no matter how technical?

There is no "real story", beyond a technical understanding of χSB in QCD, a subtle story. Lattice gauge simulators of QCD provide technical lists of contributions, e.g., cf. this; and both HEP and nuclear physicists concoct models emphasizing the salient features of the picture... arm waving with math, with which physicists feel more comfortable.

In my favorite picture (cloudy bag models), in a small region near the confinement radius (the boundary of protons and neutrons), the sea quarks have condensed effecting dynamically broken chiral symmetry: thereby coupling to almost massless "pions" (pseudogoldstone bosons) and enhancing the masses of these quarks by a factor of 50-100 thus turning them into some type of "constituent quarks", three of which comprise the p and the n. Dodgy and flakey, ill met by moonlight.

Whether you can morph this quark condensate to a "pion condensate" in contiguous language is something you might not be that keenly intrigued by. Or shouldn't be. Conflating quark chiral condensation with pion condensation would roll eyes in most circles I work in.

P.S.: Does the mathematical term 'trace anomaly' mean they aren't sure about the amount of contributions from each source of mass??

No, this is a hyper-narrow technical term of the QCD coupling running with its strictly quantum (this is what is meant by "anomaly") β-function associating to the trace of the energy-momentum tensor dynamically breaking scale invariance. (Trace is the summation of repeated indices in that tensor...) "We" are pretty sure, provided we fully appreciate the meaning of the technical terms involved.

Answer 3

To understand this we need to take a step back and consider what we mean by a particle in quantum field theory.

To give a rather arm waving description, we consider particles to be states of a quantum field. That is, when we excite the quantum field by adding energy to it this creates a particle. Specifically the objects we consider particles are states of the quantum field with a well defined momentum i.e. infinite plane waves. But we only get these states for non-interacting particles i.e. an isolated particle travelling in a straight line.

So in quantum field theory a particle is only a particle when it's the only particle in the universe, though in practice we get a good approximation for any particle that isn't strongly interacting with another particle. By strongly interacting we usually mean the interaction energy is comparable to or greater than the particle's rest mass energy. So for example in a hydrogen atom the interaction energy of $13.6~\mathrm{eV}$ is much less than the electron rest mass of $511~\mathrm{keV}$ and it's an excellent approximation to treat the hydrogen atom as made up of one proton and one electron.

But in a hadron the quarks interact so strongly that the interaction energy is much, much larger that the rest masses of the valence quarks, and this means we cannot even approximately describe the quarks inside a hadron as particles. The hadron is a state of the quantum fields that cannot be simply described as a combination of particles, and in this sense the hadron does not contain particles at all.

The problem is we do not have a good understanding of the states of a quantum field ... well ... apart from the free particle states. When we do QFT calculations we are calculating scattering probabilities for two free particle states using perturbation theory - we are not directly calculating the field state. But we can argue that we can approximate the hadron state as a sum of many different free particle states, where each of the terms in the sum represents the things we call virtual particles. And when we do this we find our sum contains terms for three real particles, i.e. the three valence quarks, and an infinite number of other terms corresponding to the virtual particles.

But this is an in principle calculation that we can only approximate, and there are various ways we can approach the approximate calculation. The most accurate method we have is lattice QCD but this is hard to explain in simple terms. What Hossenfelder is saying is that a lot of the terms in our (hypothetical) calculation correspond to (virtual) pions and therefore we can argue that a lot of mass of a hadron comes from pions. I have no idea of how accurate this is, but given that we are doing a lot of arm waving I wouldn't be surprised if it were true.

I haven't really answered your question:

Is there a detailed list of the various contributions to masses

because I don't think there is a simple answer. This is an area we don't understand well, and in fact only a few months ago a calculation suggested we got the contribution from charm quarks in protons wrong, so this is an active area of research. But I hope this has helped you understand the issues involved and why Hossenfelder's claim is plausible once you decode exactly what she is claiming.