ELEMENTARY PARTICLE PHYSICS

The fundamental constituents of the strong nuclear 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 quarks carry electric charges +2/3 (up) and −1/3 (down). A proton is composed of two up quarks and one down quark (it has charge +1), whereas the neutron has two down and one up quark (it is charge-neutral). The understanding of the strong nuclear force has now matured to the level where quantitative statements can be made about the role of electric charges on the quark-gluon structure of matter.

The elementary constituents of the strong nuclear force are quarks and gluons, which themselves bind together to form the familiar building blocks of nuclear physics, protons and neutrons. The interactions between the elementary quarks and gluons are described by the fundamental relativistic quantum field theory of Quantum Chromodynamics (QCD).

Electromagnetism is understood in terms of Quantum Electrodynamics (QED) which describes the interactions between electrically charged particles and photons. The frontiers of experimental measurement and theoretical calculation have successfully tested this theory to better than parts-per-billion accuracy.

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 and hence producing a chargeneutral object.

Owing to the difficulty of performing QCD calculations (neglecting electromagnetism), the strong force of QCD has not been tested to anywhere near the same degree as QED. Nevertheless, recent progress has seen the value for the proton mass from Lattice QCD agree with experiment at an unprecedented accuracy of 2%, i.e. Lattice QCD simulations have now reached a precision where electromagnetic corrections from QED become important.

In the present work, simulations in dynamically-coupled QCD+QED were performed. In addition to the up and down quarks the (next heavier) strange quark (with charge −1/3) was treated dynamically as well. Essential for the dynamics are the gluon and photon fields which are able to communicate through the dynamical sea quarks popping in and out of existence within the vacuum. Figure 1 shows an example of the interplay between the QED magnetic field and the QCD topological charge density of the vacuum from a simulation on a 24³×48 lattice. Note that it is not straightforward to visualise QCD because the gluon fields describe eight charges (and are represented in the computer by arrays of complex 3×3 matrices).

Isospin breaking effects (due to the differences between up and down quarks) are crucial for the existence of our Universe. Our Universe would not exist in the present form if the neutron-proton mass difference would only be 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. Hence, dynamically-coupled QCD+QED simulations were employed to conduct an investigation into the isospin splittings of the low-lying hadron spectrum, as shown in Figure 2. Given the long-range nature of QED (the photon is massless), it is expected that the lattice simulations will be affected by the fact that it is performed on a finite volume, hence in all cases, results are presented for independent simulations on two different volumes.

Taking the results from Figure 2, a total neutron-proton mass splitting of 1.27(75)(50)MeV was found, where the central value and statistical error are taken from the larger (48³×96) volume and the difference between the two volumes is taken as a systematic error. This is in excellent agreement with the experimentally observed mass splitting of 1.30MeV.

An important feature of these simulations is the clean separation of electromagnetic (QED) and strong (QCD) contributions to this splitting where it was found that the contribution from QED is −1.53(25)(50)MeV and the contribution from QCD is 2.79(67)(40)MeV.

Hence, it is observed that the stability of the universe is due to a finely tuned cancellation between the effects of the electromagnetic and strong forces of nature.