The fundamental constituents of the strong force are quarks and gluons, which themselves bind together to form the familiar building blocks of nuclear physics, protons and neutrons. The two most common forms of quarks are the up quark and the down quark. The electric charge of the up quark is +2/3, whereas the down quark carries charge -1/3. A proton is composed of two up quarks and one down quark, adding to a net charge of +1, whereas the neutron has two down and one up quark, producing a chargeneutral object. Lattice QCD simulations have reached a precision now, where isospin breaking effects become important. This has two sources, the mass difference of up and down quarks, and the electromagnetic interactions. Both effects are of the same order of magnitude, so a direct calculation from QCD and QED is necessary.
Most important for our understanding of the salient features of QCD, such as quark confinement and spontaneous chiral symmetry breaking, is the understanding of the properties of the vacuum. Simulations of QCD and QED allow us to study the effect of dynamical quarks on the vacuum. A snapshot of the vacuum fields is shown in Figure 1, in form of a three-dimensional slice of space-time. The topological charge density of the QCD fields is rendered with the magnetic field of QED. The positive topological charge lump at the lower left of the image is accompanied by large magnetic field strength, presenting an opportunity to observe the chiral magnetic effect which separates right- and left-handed quarks. It has been predicted theoretically, but never observed.
Isospin breaking effects are crucial for our existence. The Universe would not exist in the present form if the neutron — proton mass difference were only slightly — — different. If it would be larger than the binding energy of the deuteron, no fusion would take place. If it would be a little smaller, all hydrogen would have been burned to helium. Knowing the mass of neutron and proton and how it depends on the mass and charge of the individual quarks, we can express the allowed region in terms of the u and d quark masses and the electromagnetic coupling, as shown in the Figure 2. It turns out that both αEM and the ratio of light quark masses must be finely tuned.
Bibliography:
[1] R. Horsley, Y. Nakamura, H. Perlt, D. Pleiter, P.E.L. Rakow, G. Schierholz, A. Schiller, R. Stokes, H. Stüben, R.D. Young and J.M. Zanotti, J. Phys. G43 (2016) 10LT02.
[2] R. Horsley, Y. Nakamura, H. Perlt, D. Pleiter, P.E.L. Rakow, G. Schierholz, A. Schiller, R. Stokes, H. Stüben, R.D. Young and J.M. Zanotti, JHEP1604 (2016) 093
