Lattice Gauge Theory and the Origin of Mass

Abstract

Most of the mass of everyday objects resides in atomic nuclei; the total of the electrons' mass adds up to less than one part in a thousand. The nuclei are composed of nucleons-protons and neutrons-whose nuclear binding energy, though tremendous on a human scale, is small compared to their rest energy. The nucleons are, in turn, composites of massless gluons and nearly massless quarks. It is the energy of these confined objects, via M = E/c 2 , that is responsible for everyday mass. This article discusses the physics of this mechanism and the role of lattice gauge theory in establishing its connection to quantum chromodynamics.

Melting Hadrons, Boiling Quarks

“…A test of bag models ideas is the computation of the hadron mass spectrum and demonstration that the mass of hadrons is not determined by the mass of quarks bound inside. Indeed, this has been shown [186,187]; the confining vacuum structure contributes as much as 96% of the mass of the matter, the Higgs field the remaining few-%.…”

“…In fact, many textbooks argue that this has already been settled 20 years ago in accelerator experiments, so a counter question could be, why bother to do lattice-QCD to prove QCD? One can present as example of a new insight the argument that the mass of matter is not due to the Higgs field [186,187].…”

Gravitational waves from chiral phase transition in a conformally extended standard model

“…The other one is the dynamical scale symmetry breaking by strong dynamics in nonabelian gauge theories, e.g., Quantum Chromodynamics (QCD). We recall that about 99 % of the energy portion of the ordinary matter in the Universe -baryon -is generated by the nonperturbative effect in QCD [11], dynamical chiral symmetry breaking [12][13][14]. Several realistic models using the strong dynamics have been suggested in [15][16][17][18][19][20]: It has been found that not only the Higgs mass term, but also the dark matter mass [15][16][17][19][20][21][22], contributing to 27 % of the total energy of the Universe [23], as well as the Planck mass [24] can be generated by dynamical scale symmetry breaking.…”

“…At finite temperature the real QCD does not undergo a phase transition (PT), rather a continuous change of crossover type [25]. However, for sufficiently small current quark masses, the system a mayumi@hep.s.kanazawa-u.ac.jp b jikubo4@gmail.com arXiv:1910.05025v1 [hep-ph] 11 Oct 2019 can undergo a first-order PT [26][27][28][29], and such a situation can be realized in hidden sector models [17,30,31] (see also [32] and references therein), in which dynamical breaking of scale symmetry takes place at energies higher than the SM scale. If the coupling of the hidden sector to the SM is very small, a chief signal from the hidden sector is the gravitational wave (GW) background produced at a first-order PT in a certain epoch of the Universe [33], see e.g.…”

Dynamical emergence of the Universe into the false vacuum

“…Others will argue that confinement is a low energy phenomenon unrelated to short distance scales. For nucleons one finds [26] m B ≃ m QCD and thus there could be little if any relation to Higgs, with light quarks having a few percent influence on baryon masses m 2 B − m 2 QCD ∝ m 2 q . Fortunately, as we will argue, this ignorance about what controls baryon mass plays a small role in our considerations.…”