# Hadron Scattering and Resonance Properties from Lattice QCD

**Principal Investigator:** Carsten Urbach, Helmholtz Institut für Strahlen und Kernphysik (Theorie), Rheinische Friedrich-Wilhelms-Universität Bonn (Germany)

**HPC Platform:** JUQUEEN of JSC and Hazel Hen of HLRS

**Date published: **Februray 2018

**Project-ID @ JSC:** hbn28, **@ HLRS:** GCS_hsrp

It is a long lasting dream in nuclear physics to study nuclei like, for instance, carbon directly from Quantum Chromodynamics (QCD), the underlying fundamental theory of strong interactions. Such a theoretical investigation from first principles is difficult for several reasons: first, QCD describes a strong interaction which cannot be solved approximately. Therefore, lattice QCD as a non-perturbative method is required, for which the space-time is discretised with finite lattice spacing. Second, the degrees of freedom in QCD are so-called quarks and gluons, while nuclei can be described reasonably well as bound states of protons and neutrons. Protons and neutrons consist of three quarks each. The computational complexity in lattice QCD is proportional to the factorial of the number of involved quarks. Thus, a nucleus with more than five protons and neutrons, i.e. more than 15 quarks represents a major challenge. This challenge requires the usage of most modern supercomputer resources available for instance at the Jülich Supercomputing Centre (JSC) or the High Performance Computing Center Stuttgart (HLRS). Third, bound states like nuclei can be studied in lattice QCD only indirectly. This indirect approach is named Lüscher method and can be understood as follows: imaging two, for simplicity fully equal particles in a box with finite edge length L. If the edge length L is much larger than the typical interaction range of the two particles one expects little interaction between the two particles. Any measurement of the two particle system will, hence, yield twice what one measures for a single particle. As soon as L becomes close to the interaction range one expects, however, modifications. And these modifications are directly related to the interaction properties of the two particles.

In order to tackle this challenge, scientists of the Rheinische Friedrich-Wilhelms-Universität Bonn together with scientists from Peking University have started to investigate two meson systems first. Two meson systems involve four quarks (and anti-quarks) in total. Still, in order to study many different two meson systems, large scale computer resources are required. With the resources provided to us by the computer centres in Jülich and Stuttgart we were able to study two pion systems with various isospins, pion-kaon and kaon-kaon.

One of the results is shown in the figure. It represents today's most precise determination of the so-called scattering length of the pion-pion system with isospin two. Results for three values of the lattice spacing and different pion mass over pion decay constant values are shown. In nature we measure the pion mass over pion decay value roughly equal to one, to which we extrapolate.

Copyright: Universität Bonn, HISKP

**References: **

[1] C. Helmes et al., JHEP 1509 (2015) 109

[2] L. Liu et al., Phys. Rev. D 96 (2017) no.5, 054516

[3] C. Helmes et al., Phys. Rev. D 96 (2017) no.3, 034510

**Scientific Contact:**

Prof. Dr. Carsten Urbach

Rheinische Friedrich-Wilhelms-Universität Bonn

Helmholtz Institut für Strahlen und Kernphysik (Theorie)

Nussallee 14-16, D-53115 Bonn (Germany)

e-mail: urbach [@] hiskp.uni-bonn.de

*May 2018*