# Study of Strong Decays and Resonances at the Physical Pion Mass in Lattice QCD

**Principal Investigator:** Prof. Dr. Gunnar Bali, Institut für Theoretische Physik, Universität Regensburg (Germany)

**HPC Platform:** SuperMUC of LRZ

**Date published: **March 2018

**Project-ID @ LRZ:** pr94ni

Quarks and gluons do not appear as free particles in nature but are only found within bound states, the so-called mesons (containing as many quarks as antiquarks) and baryons (containing 3 more quarks than antiquarks). This phenomenon is known as "confinement." The theory governing the strong interactions between quarks and gluons is called QCD (Quantum Chromodynamics) and this constitutes, along with the electroweak interactions, the standard model of elementary particle physics. QCD bound state problems cannot be solved analytically; at present, they need to be simulated on supercomputers within the framework of Lattice QCD.

Only a few mesonic and baryonic resonances, such as the pion and the proton, are stable against strong interaction, while the vast majority of QCD excitations are so-called resonances that undergo strong decays. These resonances can be characterized by a real part (roughly corresponding to the mass) and an imaginary part (roughly corresponding to the decay width or inverse lifetime) of a point on a so-called complex Riemann-sheet. Properties of such resonances can be explored in lattice simulations by varying the momentum and the simulation volume and the formalism for doing this has been worked out some time ago. However, it remained a great challenge to obtain meaningful results at realistically small quark masses. In this project, using cutting-edge numerical methods and algorithms, this has been achieved for the first time.

*Figure 1: The p-wave scattering phase shift of π-π and π-K systems as a function of the centre of mass energy, corresponding to the ρ and K ^{*} resonances*. (c) Universität Regensburg

Two systems have been investigated. The standard example is the decay of the ρ-resonance into two pions [1]. For the first time the scattering phase shift was extracted at nearly physical quark masses (see figure 1), where noise to signal problems become severe. Subsequently, a long standing problem was approached: Back in 2003 the BaBar collaboration discovered a scalar Ds meson (composed of a charm quark and a strange antiquark). Directly afterwards this was confirmed by the CLEO collaboration who reported an additional, similar axialvector state. The masses of these states were much lower than what had been suggested theoretically before discovery and both are close (but below) strong decay thresholds, which made them prime candidates for novel tetraquark (or molecular) states. With several unusual charmonium resonances discovered recently, tetraquarks are a hot topic. Studying such systems on the lattice, including the thresholds, requires realistically light sea quark masses. In this case we were not only able to extract the resonance parameters [2] but also for the first time electroweak decay constants [2,3] have been computed, see figure 2. There are some indications from this simulation that the lower lying state indeed has a more complicated internal structure than the naive quark model would have suggested for a quark-antiquark state.

*Figure 2: Vector and scalar decay constants of the scalar D ^{*}_{s0}(2317) resonance for two pion masses, as a function of the spatial lattice size. The vector decay constant is relevant for (so-far unobserved) leptonic decay channels.* (c) Universität Regensburg

**References: **

[1] ρ and K^{∗} resonances on the lattice at nearly physical quark masses and Nf=2, Gunnar S. Bali, Sara Collins, Antonio Cox, Gordon Donald, Meinulf Göckeler, Christian B. Lang, Andreas Schäfer, Phys.Rev. D93, 054509 (2016).

[2] Masses and decay constants of the D^{*}_{s0}(2317) and D_{s1}(2460) from Nf=2 lattice QCD close to the physical point, Gunnar S. Bali, Sara Collins, Antonio Cox, Andreas Schäfer, Phys. Rev. D96, 074501 (2017).

[3] Decay constants of scalar and axialvector Ds mesons, Gunnar S. Bali, Sara Collins, Antonio Cox, Andreas Schäfer, in preparation.

**Scientific Contact:**

Prof. Dr. Gunnar Bali

Institut für Theoretische Physik

Universität Regensburg

Universitätsstr. 31, D-93053 Regensburg (Germany)

E-mail: gunnar.bali[@]ur.de