How is the mass distributed in ordinary matter?

Question

How is the mass distributed in ordinary matter?

In the ordinary things around us, we know that most of the mass is in the cores of the atoms, the electrons around it contributing only a very small amount. If we then look inside the nucleons, the rest mass of the constituent quarks also is relatively small so that isn't dominant. The main contributions might then come from the kinetic energy of those quarks, or from other virtual quarks being present, or from the energy of the gluons.

Question 134160 and question 137127 seem to indicate that the first or the last of those latter three would dominate, but it isn't completely clear. Is there a summary somewhere of how those different terms contribute? Or can these contributions not unambiguously be separated?

Answer 1

It is correct that the current light quark masses contribute only about 1% of the nucleon mass, and the main contribution is coming from the strong interaction. How one decomposes this contribution to different sources is ambiguous. All of these decompositions are related to the energy-momentum tensor.

For instance in the decomposition introduced in https://arxiv.org/abs/hep-ph/9410274, the term describing the contribution of the quarks (and antiquarks) contains both the kinetic as well as the potential energies (due to the presence of the covariant derivative) (see around Eq. (28)). These are estimated to contribute about 1/3 of the nucleon mass and the energy of the gluons is also about 1/3 at the renormalization scale $\mu^2 = 1\, \rm{GeV}^2$ in the $\bar{MS}$ scheme. (The scale dependence of these two terms however cancels.)

State-of-the-art lattice results are also in agreement with these estimates (see the abstract of https://arxiv.org/abs/1808.08677).