# Excited State Artefacts in Calculations of Hadron 3-Point Functions

**Principal Investigator:** Andreas Schäfer, Institut für Theoretische Physik, Universität Regensburg (Germany)

**HPC Platform: **SuperMUC of LRZ

Lattice QCD (Quantum Chromodynamics) allows to calculate properties of states which are composed of quarks and gluons, called hadrons. The most important hadrons are proton and neutron, i.e. the nucleons, also because many high energy accelerators like the Large Hadron Collider (LHC in CERN, Geneva) are proton-proton colliders such that the reliable interpretation of the observed reactions requires a detailed knowledge of the proton structure.

To obtain this information from Lattice QCD one has to calculate what is called “3-point- functions”. One inserts at some point in simulation time a source for a hadronic state with the quantum numbers of, e.g., the proton and at another time a sink for these quantum numbers. A mathematical trick, called analytic continuation is used to project these states onto the real physical proton state for times between those of between source and sink. This being the exact physical infinitely-many particle state allows to calculate all matrix elements one is interested in. The reliability of the results depends among other things on how good this projection works. As all admixtures of higher energy states die out exponentially with the size of the simulated time range this projection was assumed to be under very good control, a believe which turned out recently to have been overly optimistic. However, with the large computer resources provided, e.g., by SuperMUC the research team was able to do this much more precisely. Also, the scientists were able to simulate for physical quark masses rather than having to rely on extrapolations from simulations with larger than physical quark masses.

The message of these results is mixed and not yet well understood. In this project the researchers have undertaken careful analyses of several benchmark properties to find evidence for the source of the remaining discrepancies.

Copyright: Universität Regensburg, Institut für Theoretische Physik

Copyright: Universität Regensburg, Institut für Theoretische Physik

An especially striking example is provided by the difference of the axial vector coupling constants of proton and neutron and the pion decay constant. The former is a key quantity characterizing the proton and neutron spin structure, which is relevant e.g. for W-boson production at LHC. The pion decay constant parameterizes the coupling of a pion to a quark and anti-quark state. While the data for both quantities fluctuate wildly and disagrees with the experimental value, their ration extrapolates smoothly in mass to the correct value, see Fig.1 and 2. Thus it can be concluded that whatever is the origin of the remaining discrepancies, it has to be the same for both observables and it has to factorize, which very strongly limits the possibilities. One of the few remaining possibilities are finite volume effects which are known to be potentially unusually large for pionic properties, because the pion is by far the lightest hadron with the correspondingly largest Debye wave length. This possibility is under debate. The final resolution will probably require simulations on still larger lattices.

**Scientific Contact:**

Prof. Dr. Andreas Schäfer

Institut für Theoretische Physik, Universität Regensburg

D-93040 Regensburg/Germany

e-mail: andreas.schaefer@physik.uni-r.de

*July 2014*