ELEMENTARY PARTICLE PHYSICS

The up and down quark masses, m_uand m_d, are two parameters of the Standard Model of Particle Physics. According to current understanding these numbers are fundamental, no commonly accepted principle is known, from which they can be derived. Knowing these numbers with a decent precision is important, since it might shed light on the origin of these parameters – e. g. for the discovery of the periodic table it was necessary to know the atomic weight of several chemical elements. Additionally, if the up mass was found zero, this would solve a long-standing puzzle of the theory of the strong interaction (aka. strong CP problem).

These masses cannot be directly determined through experiment because of the confinement of quarks within hadrons. Lattice quantum chromodynamics (QCD) provides an ab-initio approach to the non-perturbative calculation of QCD correlation functions. This method can be used to determine the light quark masses from the experimental values of hadron masses. The average of the up and down quark masses

has been studied by many lattice QCD research groups and nowadays it can be computed with percent level precision.

In this project we aimed for the computation of the light-quark mass difference δm = m_u− m_d. This quantity is much more difficult to obtain than m_ud. It has only a small effect on the hadron masses, of order percent, naively a larger precision is needed than for the determination of m_ud. Also one has to take into account the effects of the electromagnetic interaction, which are of the same size as δm. In most earlier lattice simulations all these effects have been neglected.

In our computations we implemented the electromagnetic interaction on the lattice. To reduce the costs we discarded all such photons, that could create quark–anti- quark pairs. Removing this restriction is an important task for the future. For the quark mass difference we obtained

δm = m_u− m_d= −2.41(6)(4)(9) MeV,

where we give separately statistical, systematic errors and also an estimate of the neglected electromagnetic effects. Furthermore using earlier results for the average quark mass m_ud  we could determine the individual quark masses and their ratios. The up quark mass

m_u = 2.27(6)(5)(4) MeV

implies that the m_u= 0 solution to the strong CP problem is very strongly ruled out. As one can see from these results, the neglected electromagnetic effects constitute a dominant source of the error. It is therefore desirable to eliminate this error with fully dynamical photons in the simulation. This is work-in-progress.

Figure 1 shows our extraction procedure for the quark mass difference. Two hadron mass differences, built from kaons and pions, are plotted against each other. The slope of the line can be related to δm by a simple relation. Each point is obtained with a simulation of the order of million core-hours.