N_f = 4 × 1 Flavor Lattice QCD Calculations with Smeared Clover Fermions

**Principal Investigator:**

Kálmán Szabó

**Affiliation:**

Institute for Advanced Simulation at Jülich Supercomputing Centre

**Local Project ID:**

hjs00

**HPC Platform used:**

JUQUEEN of JSC

**Date published:**

The up and down quark masses, *m** _{u}*and

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 *δ**m *= *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

*δ**m *= *m*_{u}*− m** _{d}*=

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

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.

**Scientific Contact:**

Prof. Dr. Kálmán Szabó

Forschungszentrum Jülich GmbH

Institute for Advanced Simulation (IAS), Jülich Supercomputing Centre (JSC)

Wilhelm-Johnen-Straße, D-52425 Jülich (Germany)

e-mail: szaboka [@] general.elte.hu

*JSC Project ID: hjs00*

*October 2019*