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Charm Loop Effects: Decoupling and Charmonium

Principal Investigator: Francesco Knechtli, Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal (Germany)

The strong interactions are described by quantum chromodynamics (QCD). The elementary particles that feel the strong force are quarks and gluons. They cannot be seen in isolation but they make up composite particles that are called hadrons (proton, neutron, pions, kaons, etc.). The mechanism responsible for the formation of hadrons is confinement. In order to study it, QCD is discretized on a Euclidean four-dimensional space-time, called the lattice. QCD on the lattice can be studied using Monte Carlo simulations on supercomputers.

There are 6 species of quarks called the up (u), down (d), strange (s), charm (c), bottom (b) and top (t) quarks. Up, down and strange are the light quarks. Most of the matter we are made of can be explained using the up and down quarks and their strong interactions. In fact the proton and the neutron are 3-quark states made of uud and udd quarks respectively. Other particles, like the kaons, contain the strange quark and can be produced by colliding particles, for examples protons in the LHC accelerator at CERN.

Charm, bottom and top are the heavy quarks. States containing the charm and bottom quarks can be produced at particle accelerators. Examples are the charmonium states, made of a charm quark and its anti-particle, like the eta_c and J/psi particles, and the bottomonium states, made of a bottom quark and its anti-particle. The top quark decays very fast into a bottom quark and cannot form bound states.

Heavy quarks also contribute to the energy of particles through the so-called “vacuum polarization effects”. Quantum mechanics and the theory of relativity allow the formation of a quark and anti-quark pair out of the vacuum for a short time before it is annihilated. This has measurable effects. For instance, a doubling of the charm quark's mass would lead to a proton mass that is increased by 5%. In the project “Charm loop effects: decoupling and charmonium” the researchers compute the vacuum polarization effects due to the charm quark in a model close to QCD.

An enormous computational effort is made by various collaborations to simulate up, down and strange quarks. It is important to estimate the effects of including a charm quark. This can be done by simulating a toy model which is QCD with just a single species of quarks, the charm quarks. A comparison with simulations of only gluons allows to precisely extract the information needed. Since the charm quark is heavier than a proton and it is 12 times heavier than the strange quark, finer lattices than they are presently simulated with the light quarks are required to control the extrapolation to zero lattice spacing.

Charm Loop Effects: Decoupling and CharmoniumCopyright: Bergische Universität Wuppertal

The figure above demonstrates the extraction of the mass of states made of a quark and an antiquark, both with the mass of the charm quark on our finest lattice. They have pseudo-scalar (black circles) and vector (blue diamonds) quantum numbers. The mass is obtained from the plateau average of the effective masses which are plotted. The simulation of such large lattices require considerable computational resources which have been granted to the researchers on HPC system JUQUEEN of JSC (for the generation of the large lattices and their analysis) and on JURECA (for the analysis of the smaller lattices).


This work is part of the ALPHA collaboration. The researchers involved are:
Salvatore Calì (Bergische Universität Wuppertal and University of Cyprus)
Jochen Heitger (Westfälische Wilhelms-Universität Münster)
Francesco Knechtli (PI, Bergische Universität Wuppertal)
Tomasz Korzec (Bergische Universität Wuppertal)
Björn Leder (Humboldt-Universität zu Berlin)
Graham Moir (University of Cambridge, UK)

The study of decoupling was initiated by
Rainer Sommer (NIC, DESY, Zeuthen and Humboldt-Universität zu Berlin)

Scientific Contact:
Prof. Dr. F. Knechtli
Bergische Universität Wuppertal
Fakultät für Mathematik und Naturwissenschaften
Gaußstraße 20, D-42119 Wuppertal (Germany)
e-mail: knechtli [at]

September 2016

JSC Project ID: hwu17