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Computational Aspects of Lattice QCD
2003
Monte Carlo simulations applied to the lattice formulation of quantum chromodynamics (QCD) enable a study of the theory from first principles, in a nonperturbative way. After over two decades of developments in the methodology for this study and with present-day computers in the teraflops range, lattice-QCD simulations are now able to provide quantitative predictions with errors of a few percent. This means that these simulations will soon become the main source of theoretical results for comparison with experiments in physics of the strong interactions. It is therefore an important moment for the beginning of Brazilian participation in the field.
Introduction to the Standard Model, QCD and the Lattice
Progress of Theoretical Physics Supplement, 2003
A brief introduction to Quantum Chromodynamics (QCD) and its relation to the Standard Model (SM) of particle phyics is given. QCD is that part of the Standard Model relevant to the strong interactions. Strongly interacting matter makes up almost the entire mass of the tangible universe, from the protons and neutrons in the nuclei of atoms to the stars themselves. In the low-energy region of most interest, QCD is a strongly interacting theory and not soluble by any analytic means. The first principles, tool-of-choice for studying QCD in the interesting low-energy regime is lattice QCD, which puts space-time on a 4-dimensional lattice or grid. It requires the world's fastest supercomputers to attack this challenging problem.
1998
These notes aim to provide a pedagogical introduction to Lattice QCD. The topics covered include the scope of LQCD calculations, lattice discretization of gauge and fermion (naive, Wilson, and staggered) actions, doubling problem, improved gauge and Dirac actions, confinement and strong coupling expansions, phase transitions in the lattice theory, lattice operators, a general discussion of statistical and systematic errors in simulations of LQCD, the analyses of the hadron spectrum, glueball masses, the strong coupling constant, and the quark masses.
Simulation of the Lattice QCD and Technological Trends in Computation
2008
In this study, we focus on assessing the efficiency and the performance expected for the Lattice QCD problem on representative architectures and we project the expected improvement on these architectures and their impact on performance for Lattice QCD. We additionally try to pinpoint the limiting factors for performance on these architectures.
Palaiseau Automated Code Generation for Lattice QCD Simulation
2013
Quantum Chromodynamics (QCD) is the theory of strong nuclear force, responsible of the interactions between sub-nuclear particles. QCD simulations are typically performed through the lattice gauge theory approach, which provides a discrete analytical formalism called LQCD (Lattice Quantum Chromodynamics). LQCD simulations usually involve generating and then processing data on petabyte scale which demands multiple teraflop-years on supercomputers. Large parts of both, generation and analysis, can be reduced to the inversion of an extremely large matrix, the so-called Wilson-Dirac operator. For this purpose, and because this matrix is always sparse and structured, iterative methods are definitely considered. Therefore, the procedure of the application of this operator, resulting in a vector-matrix product, appears as a critical computation kernel that should be optimized as much as possible. Evaluating the Wilson-Dirac operator involves symmetric stencil calculations where each node h...
Lattice QCD thermodynamics on the Grid
Computer Physics Communications, 2010
We describe how we have used simultaneously O(10 3) nodes of the EGEE Grid, accumulating ca. 300 CPU-years in 2-3 months, to determine an important property of Quantum Chromodynamics. We explain how Grid resources were exploited eciently and with ease, using userlevel overlay based on Ganga and DIANE tools above standard Grid software stack. Application-specic scheduling and resource selection based on simple but powerful heuristics allowed to improve eciency of the processing to obtain desired scientic results by a specied deadline. This is also a demonstration of combined use of supercomputers, to calculate the initial state of the QCD system, and Grids, to perform the subsequent massively distributed simulations. The QCD simulation was performed on a 16 3 × 4 lattice. Keeping the strange quark mass at its physical value, we reduced the masses of the up and down quarks until, under an increase of temperature, the system underwent a second-order phase transition to a quark-gluon plasma. Then we measured the response of this system to an increase in the quark density. We nd that the transition is smoothened rather than sharpened. If conrmed on a ner lattice, this nding makes it unlikely for ongoing experimental searches to nd a QCD critical point at small chemical potential.
Lattice QCD Study for Confinement and Hadrons
Using SU(3) lattice QCD, we perform the detailed studies of the three-quark and the multi-quark potentials. From the accurate calculation for more than 300 different patterns of 3Q systems, the static ground-state 3Q potential Vrm3Qrmg.s.V_{\rm 3Q}^{\rm g.s.}Vrm3Qrmg.s. is found to be well described by the Coulomb plus Y-type linear potential (Y-Ansatz) within 1%-level deviation. As a clear evidence for Y-Ansatz, Y-type flux-tube formation is actually observed on the lattice in maximally-Abelian projected QCD. For about 100 patterns of 3Q systems, we perform the accurate calculation for the 1st excited-state 3Q potential Vrm3Qrme.s.V_{\rm 3Q}^{\rm e.s.}Vrm3Qrme.s. by diagonalizing the QCD Hamiltonian in the presence of three quarks, and find a large gluonic-excitation energy DeltaErm3QequivVrm3Qrme.s.−Vrm3Qrmg.s.\Delta E_{\rm 3Q} \equiv V_{\rm 3Q}^{\rm e.s.}-V_{\rm 3Q}^{\rm g.s.}DeltaErm3QequivVrm3Qrme.s.−Vrm3Qrmg.s. of about 1 GeV, which gives a physical reason of the success of the quark model. DeltaErm3Q\Delta E_{\rm 3Q}DeltaErm3Q is found to be reproduced by the ``inverse Mercedes Ansatz'', which ind...
Recent Progress in Lattice QCD
International Journal of Modern Physics A, 2009
In recent years, realistic unquenched QCD simulations have been carried out with various lattice actions. In this report, I explain the progress in theory and algorithms and some of the physics results.