Light baryons such as the familiar proton and neutron make up most of the matter in the visible universe. These baryons have constituents of three types of ‘flavour’ of quarks: up, down and strange or u, d and s. Particles group together in families or multiplets, the octet multiplet is shown on the left-hand side of the figure.
The mass splitting between the proton and neutron is a very delicately balanced quantity, partly caused by the mass difference between the u and d quarks, and partly by QED effects. Small changes in this mass difference would have profound effects on the way the universe looks today. The initial balance between hydrogen and helium, established in the first half-hour after the Big Bang, depends strongly on the neutron half-life, and so on the p-n mass splitting. Later, the production of carbon and oxygen in stars also depends strongly on the proton-neutron splitting.
The strong force binding the quarks together is described by quantum chromo-dynamics or QCD, which has to be numerically simulated (via lattice QCD). A compilation of recent lattice determinations of baryon mass splittings is given in the right panel of the figure. In particular there is also mass splitting between the particles at the centre of the octet the Sigma and Lambda. This is more complicated case as the states mix. We have now extended our previous results to include this case and determined the mixing angle and mass splitting. While the effects of mixing on the masses are very small (second order in the angle), it can be much larger for decay rates.
While the main force between the quarks and antiquarks comes from QCD there is also a contribution from the electromagnetic force, QED, which is usually left out of lattice calculations. We are also doing calculations with both forces included, to see how important the effects of QED are.