Most of the known visible mass in the universe (i.e., excluding dark matter) is made up of protons and neutrons. We know that protons and neutrons are themselves made up of yet smaller particles called quarks and gluons. The gluons are massless so you would think that most of the mass of the universe would be quark mass. But that is not the case. In fact, quark masses are a small fraction of the total mass of each proton and neutron. So where does the rest of the mass come from?
To understand this we need to look at the relationship between mass and energy, first formulated by Albert Einstein in the equation that is now famously written as E=mc2, though that is not how Einstein initially formulated it. This results in the mass of a composite object not being just the sum of the masses of its component objects, because other forms of energy can contribute to the mass too.
Take for example the deuteron, a composite nucleus that we know is made up of one proton and one neutron. The mass of a free proton is 938.272 MeV/c2 and the mass of a free neutron is 939.565 MeV/c2, but the mass of the deuteron is 1875.612 MeV/c2, which is less than 1877.837 MeV/c2, the sum of the two free masses. What happened to the missing mass of 2.225 MeV/c2? When the two particles were brought close together and became bound as one entity, some of the mass was released as energy. It is this that keeps the deuteron as a single unit. To separate the deuteron into its composite parts, we need to provide from outside an amount of energy equal to that difference.
In the case of the deuteron, it is possible to separate the two components and measure their masses individually. But in the case of the quarks and gluons within the proton and neutron, we can never free them and study their properties in isolation. They are permanently confined within the protons and neutrons and that makes directly measuring their masses impossible and we have to use various theoretical techniques to estimate them. The theory that is used is called Quantum Chromodynamics (QCD) that forms part of what is called the Standard Model of particle physics. The problem is that QCD is not easy to use to do the calculation. A new paper uses what is called lattice gauge theory to obtain a more accurate estimate of where the mass of the proton lies.
The researchers rely on a powerful method known as lattice QCD, which places quarks on the sites of a lattice and gluons on the links between them. This rigorous representation of QCD can be implemented numerically, and it is the only QCD-based method that can make quantitative predictions on length scales comparable to the proton or larger. (At these scales, the interactions between quarks and gluons are so strong, they cannot be handled with Feynman diagrams and other “perturbative” methods.) However, lattice QCD is an expensive technique. The discretization creates errors, and to remove them entails taking the lattice spacing, a, to zero. This step is achieved in practice by performing multiple calculations at different values of a, at a high numerical cost that scales as a-6. Nevertheless, lattice QCD has matured significantly in recent years, allowing for the most precise determination of the quark masses and many properties of light and heavy mesons, which are comprised of a quark and an antiquark.
The mass of the composite object (the proton) is larger than the masses of its constituents, the opposite of what we saw with the deuteron. The researchers find that the quark masses make up just 9% of the proton mass. The rest of the mass of the proton comes from the quark energy (~32%), the gluonic field strength energy (∼37%), and the anomalous gluonic contribution (∼23%) .
The smallest contribution, the quark condensate, is a mixture of the up and down quarks and a “sea” of virtual strange quarks, and it is the only one that would vanish if the quark masses were zero. The other three terms are all related to the dynamics of the quarks and gluons and their confinement within the proton. The quark energy and gluonic field strength equate to the kinetic energy of the confined quarks and confined gluons, respectively. The anomalous term is a purely quantum effect. It is associated with the QCD mass scale and consists of contributions from condensates of all quark flavors, including the strange, charm, bottom, and top quarks. The calculation by Yang and colleagues shows that, if the up, down, and strange quark masses were all zero, the proton would still have more than 90% of its experimental mass. In other words, nearly all the known mass in the Universe comes from the dynamics of quarks and gluons.
So to sum up, only about 9% the mass of the visible universe is made up of the masses of the quarks that we think are its most fundamental constituents. The rest comes from various forms of energies of the quarks and gluons within the protons and neutrons. In our current models, we think that the visible matter makes up just 5% of the total mass-energy of the universe, with 26% coming from dark matter and the remaining 69% from dark energy. Hence quark masses make up just 0.45% of the total mass-energy of the universe.