# Next Generation Lattice QCD Simulations of the First Two Quark Generations at the Physical Point

An international team of scientists leverages the computing power of supercomputers for a very ambitious project which is embedded in the area of elementary particle interactions and in particular the strong interaction of quarks and gluons which is described theoretically by quantum chromodynamics (QCD), a relativistic quantum field theory. QCD is supposed to explain several peculiar observations we make in nature and which are essential to establish the world as we see it today: we cannot detect single quarks and gluons (confinement), the pions are much lighter than other mesons with a similar quark content (spontaneous chiral symmetry breaking (SχSB) and the particular η' meson is heavier than other, comparable mesons (topology). All these established phenomena, confinement, SχSB, and topology are of fully non-perturbative nature and cannot be studied with analytical methods such as perturbation theory.

Therefore, the major tool employed in this project to address questions of the strong interaction are numerical simulations within the framework of lattice QCD. In this approach, the theory is formulated on a 4-dimensional euclidean space-time grid which in turn allows to implement the theory on a supercomputer and perform large scale simulations using Markov chain Monte Carlo methods based on importance sampling. The goal of the project has been to compute the meson spectrum using QCD alone and see whether the observed spectrum indeed emerges from the simulations, establishing thus that QCD is a correct description of the strong interaction.

The great challenge of the project was that the computation ought to be done at the physical values of the pion, the Kaon and the D-meson masses, necessitating to include active light up and down quarks as well as heavier strange and charm quarks. Our European Twisted Mass Collaboration, which consists of about 40 physicists from seven European countries, has pioneered such calculations and has been the first to carry through simulations in this fully physical setup, producing very promising results (see below).

The operation of supercomputers in this project has been indispensable. First of all, the problem by itself is already 4-dimensional and the typical system sizes are V = 48^{3}·96 lattice points with 12 internal degrees of freedom per lattice site. The basic numerical problem is then the solution of a linear set of equations with a coeffcient matrix, although being sparse of size (12·V)⊗(12·V). In fact, such a solution is required millions of times. Second, the computing time increases with decreasing pion mass and even previous computations, where the pion mass has been 2-3 times larger than the physical one, needed leading edge supercomputer architectures to carry through the required simulations. As described above, this project made an effort to work now directly at the physical value of the pion mass and hence the supercomputing time had become extremely demanding. Without state-of-the-art supercomputers the project would not haven been possible.

However, the physical results of the project were very rewarding as can be seen in fig. 1. Here the ratio of various physical quantities compared to experimentally measured counterparts, taken from the particle data booklet, are plotted. As the graph shows, a full agreement between our ab-initio QCD calculations and experiment is found. This provides a very strong evidence that QCD can indeed explain the peculiar meson spectrum with the underlying fundamental and non-perturbative properties of QCD.

Source: Deutsches Elektronen-Synchrotron (DESY)

*FIG. 1: A comparison of experimentally observed meson masses and decay constants, Q*

_{phys}(taken from the particle data booklet) and the corresponding quantities calculated in this project within our lattice QCD approach, Q_{lat}, is shown.The project was made possible through the Partnership for Advanced Computing in Europe, PRACE. GCS HPC systems JUQUEEN of Jülich Supercomputing Centre and SuperMUC of LRZ Garching/Munich serve as computing platform for this project. Additional computing time for this project is provided by HPC system FERMI of the Italian supercomputing centre CINECA.

**Institutions and research team members:**

Karl Jansen (Principal Investigator)

*DESY, Platanenallee 6, 15738 Zeuthen, Germany*

C. Alexandrou

*Department of Physics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus, and Computation-based Science & The Cyprus Institute, P.O. Box 27456, 1645 Nicosia, Cyprus*

M. Constandinou

*Department of Physics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus*

G. Koutsou, M. Petschlies

*Computation-based Science and Technology Research Center, The Cyprus Institute, 20 Kavafi Str., 2121 Nicosia, Cyprus*

M. Brinet

*Laboratoire de Physique Subatomique et Cosmologie, Grenoble-Alpes/CNRS/IN2P3, 53 avenue des Martyrs, 38026 Grenoble, France*

P. Dimopoulos

*Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi, Compendio del Viminale, Piazza del Viminale 1 I-00184 Rome, Italy*

R. Frezzotti, G.C. Rossi

*Dip. di Fisica, Universita di Roma Tor Vergata and INFN, Sez. di Roma Tor Vergata, Via della Ricerca Scientica, I-00133 Roma, Italy*

B. Benoit, P. Boucaud, O. Pene

*Laboratoire de Physique Theorique (Bât. 210), Universite de Paris XI, CNRS-UMR8627, Centre d'Orsay, 91405 Orsay-Cedex, France*

K. Chichy, V. Drach, E. Garcia Ramos, B. Kostrzewa, A. Nube, C. Wiese

*DESY, Platanenallee 6, 15738 Zeuthen, Germany*

V.Lubicz, C. Tarantoni, S. Simula

*Dip. di Fisica, Universita di Roma Tre and INFN, Sez. di Roma III, Via della Vasca Navale, 84, I-00146 Roma, Italy*

C. Michael

*Theoretical Physics Division, Dept. of Mathematical Sciences, University of Liverpool, Liverpool, L69 7ZL, UK*

E. Pallante

*Centre for Theoretical Physics, University of Groningen, Nijenborgh 4, 9747 AG Groningen, The Netherlands*

K. Ottnad, C. Urbach, F. Zimmermann

*Helmholtz Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, 53515 Bonn, Germany*

F. Burger, G. Hotzel

*Institut für Physik, Humboldt Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany*

M. Kalinowski, D. Palao, M. Wagner

*Goethe-Universität Frankfurt am Main, Institut für Theoretische Physik, Max-von-Laue-Straße 1, 60438 Frankfurt am Main, Germany*

A. Shindler

*CERN, Physics Department, 1211 Geneva 23, Switzerland*

Karl Jansen

Deutsches Elektronen-Synchrotron (DESY)

Platanenallee 6, D-15738 Zeuthen/Germany

e-mail: Karl.Jansen@desy.de