- Lattice QCD calculations in the low-energy regime

Lattice QCD currently provides the only ab initio method for performing QCD calculations in the low-energy regime, and for acquiring a quantitative description of the physics of hadrons and nuclear forces with controlled systematic errors. To reliably connect hadron physics with QCD, extreme computing resources are required.

To make efficient use of the current investment in supercomputers, and to further advance high performance computing in Europe, a unified programming environment and the pooling of resources, both human and computational, are needed.

*Description of work and role of partners*

The proposed upgraded LEANNIS network will concentrate on hot topics in low-energy antikaon interactions with nucleons and nuclei to be studied in theory and experiment. It will take advantage of the basis created in the running LEANNIS network-project and of its outcome. Six main topics have been identified and are discussed in the following.

The participation of the subgroups is detailed below.

We briefly describe areas that we believe will be strongly impacted by the proposed project.

- Applied mathematics and machine issues. Future large-scale computations need dedicated research on domain decomposition and deflation techniques, as well as on new approaches for effective preconditioning of the Dirac operator.
- Stochastic noise techniques. The evaluation of quark-line disconnected contributions requires extreme computational resources. This demand can be further reduced by implementing noise reduction techniques, which can be applied to a wide range of problems.
- Constraining effective field theory. Effective field theories (EFTs) provide a bridge between QCD and low-energy phenomena. EFTs, constrained by Lattice QCD calculations, can be used to study processes not yet calculable with Lattice QCD, such as inelastic ones.
- Spectrum and properties of unstable particles. The main focus will be on meson and baryon resonances, and on exotic mesons, such as tetraquarks. The extension of Lüscher’s method to treat inelastic resonances is still a challenge. There is an intense experimental activity. New results from the BELLE collaboration hint at the existence of tetraquark states.
- Flavour-singlet mesons. Calculations of the hadron spectrum will extend to systems with the annihilation of an initial-state quark with an initial-state antiquark and mixing with gluonic degrees of freedom (glueballs).
- Renormalisation and improvement. Most hadron observables derive from matrix elements of local operators, which need to be renormalised and O(a) improved. Renormalisation constants and improvement coefficients will be computed for a wide class of operators.
- High-order stochastic perturbation theory. Numerical stochastic perturbation theory has advanced to the point that calculations of simple quantities in the pure gauge theory, up to more than 20 loops, are feasible. The calculations will be extended to include quark loops.
- How QCD makes a proton: flavour-singlet sea-quark and gluon contributions. In order to compute the flavour separated contributions of quarks and gluons to hadron matrix elements, improved estimators for quark and gluon operators need to be developed.
- Higher moments of structure functions. Lattice QCD can only produce moments of nucleon structure functions and generalised parton distributons (GPDs), and it is important to calculate as many moments as possible.
- Present techniques only permit calculations of the 3 lowest moments; new techniques for the calculation of higher moments are necessary.
- Form factors at high Q2. The direct calculation of nucleon elastic as well as N → N* and N → Δ transition form factors at large momentum transfer will enable to explore the onset of asymptotic scaling behaviours
- Operator product expansion and higher twist. A crucial role in the phenomenology of hadron structure and weak decays is plaid by the operator product expansion (OPE). Of particular interest are contributions of higher twist, which bear information about the onset of confinement at lower virtualities. In a pilot study it has been demonstrated that an entirely non-perturbative evaluation of the OPE is feasible.
- Heavy quark physics. Lattice QCD calculations are important tools for heavy quark physics. It is possible to generate background field configurations to simulate the charm quark directly. Newly discovered narrow resonances above the DD threshold have revived the interest in charm spectroscopy. The decays of bottom quarks can be described by distribution amplitudes (DAs), encoding the structure of bottom mesons and baryons at small distances.
- Fundamental symmetries. Various symmetries of Nature can be broken at small levels, with far reaching implications. A well known example is CP violation. A way of searching for this effect is a direct Lattice QCD calculation of the neutron electric dipole moment (EDM).
- Physics beyond the Standard Model? The muon (g-2). The muon (g-2) experiment at Brookhaven is a stringent test of the Standard Model and an excellent tool to look for new physics. The new experimental results differ from theory calculations by ≈ 3 standard deviations. While the QED and electroweak contributions are well under control, it is an open question the size of the hadronic contribution to (g-2)μ.
- QCD phase diagram. The study of the phase diagram of QCD guides our understanding of the strong interactions at extreme conditions. The upcoming experiments at LHC, RHIC and GSI will provide new insights into this problem. A quantitative determination of the phase boundaries in the light and strange quark mass plane is to be reached. An important theoretical question is which symmetries drive the various transitions of the phase diagram.
- Equation of State. The equation of state (EoS), at zero and non-zero baryon density, is important for hydrodynamical modelling of heavy ion collisions. The continuum limit has to be further approached. At temperatures of 300 MeV and higher the contribution of the charmed quark to the EoS cannot be neglected anymore. Simulations with 2+1+1 dynamical quarks will be performed at cut-offs much larger than the charmed quark mass.
- Universal aspects. The QCD phase transitions are characterised by deconfinement and chiral symmetry restoration. The determination of the universality classes of these phase transitions and the establishment of universal behaviour close to the phase boundaries has far reaching consequences to increase the predictive power significantly.
- Screening phenomena. Gluonic and fermionic screening masses give access to interaction scales in the QCD plasma at high temperature. It is our aim to bring the lattice results to a state of precision such that contact to
- (resummed) high-temperature perturbation theory and dimensionally reduced QCD can be established.
- Spectral properties. Changes of the particle spectrum have been advocated as probes for in-medium properties of the plasma. Ones should extract appropriate spectral densities, which detect bound states and identify their masses, and provide additional information on dilepton and photon rates in the light quark sector. Charm quarks will be accessible directly, while for bottom quarks effective theories are being developed and tested also at finite temperature.
- Quantum number fluctuations and correlations. Fluctuations of baryon number, isospin, charge and strangeness are an important tool to analyse heavy ion collisions experimentally. Present lattice calculations should be improved by going to smaller quark and towards the continuum limit. The noise of the numerical signal is dominated by quark-line disconnected terms; the computations will be improved by stochastic estimators and deflation techniques.
- The QCD vacuum. At the QCD phase transition(s) the properties of the vacuum change dramatically. The role of the temperature and density dependence of the non-perturbative topological structures of the QCD vacuum in triggering the phase transitions has to be studied.
- Chiral aspects of QCD thermodynamics. Chiral fermion have so far been too costly to simulate. With the advent of new computers and improved technology, it is becoming feasible to study QCD thermodynamics with chiral fermions.