Hadron Physics from Lattice QCD (DFG SFB TRR55)

Low energy phenomena in Quantum Chromodynamics (QCD) are not accessible to perturbative methods. A suitable non-perturbative approach is lattice QCD which in the last two decades was developed into a reliable quantitative tool. The goal of the SFB TRR55 is to study hadron physics using lattice QCD methods and to further develop lattice techniques. Project A1, `The QCD phase diagram and the critical point`, will focus on the analysis of various aspects of the QCD phase diagram such as non-vanishing magnetic field, QCD at finite baryon density, and QCD with hypothetical quark masses and numbers of flavors. In particular it is also planned to develop new techniques for the analysis of the QCD phase diagram. The subprojects Graz is responsible for concern the development of new approaches to QCD at finite density and the study of the QCD phase diagram. The QCD phase diagram is currently an important focus of research, both experimentally and in theoretical work. Abinitio results from lattice QCD at finite density would be very much welcome, but the notorious fermion sign problem/complex action problem at finite density has painfully slowed down any progress. It could well be that completely new approaches will be necessary for a proper treatment of finite density lattice QCD. The Graz-subprojects of A1 (Subproject 3 and Subproject 5) are devoted to exploring such new strategies. Taylor expansion has been used as a tool for studying the region of small chemical potential in the vicinity of the deconfinement crossover, but several questions remain open, in particular convergence issues. Building on our previous work, in Subproject 3,`Fugacity expansion for QCD at non-vanishing chemical potential`, we will explore fugacity expansion as an alternative approach, which, since it has a different structure (Taylor versus Laurent series) could have better convergence properties. The physics goal is to better delimit the position of a possible critical endpoint. Dramatic improvement in the simulation of lattice field theories at finite density was achieved in recent years by using alternative representations (dual variables), in particular in terms of fluxes and surfaces. In Subproject 5,`Dual variables in QCD and effective theories`, we will develop our previous studies with dual variables further towards more realistic effective theories of QCD, and ideally also the full QCD case. We explore the potential for alternative representations of QCD and effective theories, in particular representations in terms of loops and surfaces. New algorithmic ideas based on the Svistunov Prokof`ev worm algorithm will be developed. In addition to the two subprojects of A1 Graz is responsible for, we will also significantly contribute as Co- investigators in Project A12, `Phenomenological aspects of the QCD crossover region`, and parts of that project were formulated by C. Gattringer.

The project Hadron Physics with Lattice QCD which is supported by the DFG as SFB TRR55 and where the Graz group is financed by the FWF via the DACH agreement, studies ab-initio calculations in QCD. QCD (Quantum Chromodynamics) is the fundamental theory of quarks and gluons which constitute nuclear matter. The basic equations of QCD are known for more than 50 years, but the computation of observables is still a considerable challenge. The reason is the non-linearity of the QCD equations of motion, which spoils a perturbative analysis for processes at low energies. In the collaborative research project Hadron Physics with Lattice QCD a modern approach is used where QCD is formulated on a space-time lattice. In this formulation numerical methods from statistical mechanics can be applied, so called Monte Carlo simulations. In the last 20 years this approach was developed into a powerful quantitative tool. The goal of the project is to address several related questions in hadron physics. Hadrons are the bound states of QCD with the building blocks of nuclei, proton and neutron, as the most prominent representatives. The Graz group is contributing in two subprojects. A1: The QCD phase diagram and the critical point and A12: Phenomenological aspects of the QCD crossover region. Both subprojects analyze QCD at very high temperatures and densities, which are relevant for the physics shortly after the big bang. In particular the calculations at finite density pose numerical as well as conceptional challenges, since the above mentioned Monte Carlo simulations cannot be applied directly because the Boltzmann factors become complex and do not have a probabilistic interpretation (complex action problem). The Graz group has focused on the development of new approaches to overcome the complex action problem. In particular three different approaches were studied: Fugacity expansion, density of states methods and the dual approach. In the fugacity expansion the theory is expanded around the case of vanishing density. In the density of states approach one first determines an auxiliary quantity, the density of states, which in a second step then is used to evaluate observables. In the dual approach the theory is reformulated in terms of new variables, so-called worldlines, such that the complex action problem is circumvented completely. All three methods were successfully tested in simple systems and are now being developed further towards full QCD calculations in a follow-up project that has already been granted.