Charm Loop Effects: Decoupling and Charmonium Gauss Centre for Supercomputing e.V.


Charm Loop Effects: Decoupling and Charmonium

Principal Investigator:
Francesco Knechtli

Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal (Germany)

Local Project ID:

HPC Platform used:

Date published:

Quantum Chromodynamics (QCD) is the theory proposed in the early 1970’s to explain the properties of the strong interactions. The latter are visible at two different scales of distance. In processes involving distances larger than 1 fm, strong interactions are (indirectly) responsible for binding protons and neutrons into the nuclei, which form the atoms we are made of. On the other hand, when dealing with short-distance processes (i.e. distances smaller than 0.8 fm), we know that they hold quarks together to form composite particles called hadrons, to which the proton and the neutron belong.

Quarks are elementary particles of spin ½ and represent, along with leptons, the smallest building blocks of matter, according to the Standard Model of Particle Physics (which also describes the electromagnetic and weak forces). The strong interactions are mediated by spin 1 particles, the so-called gluons, that can be considered the carriers of the strong force. One of the main features of QCD  is that quarks and gluons are never observed in isolation, but only within hadrons, that in turn are usually classified into mesons (composite particles made of a quark and an antiquark) and baryons (composite particles made of three quarks). The newly discovered states with a charmonium component could hint at the existence of exotic states such as tetra- or penta-quarks, but this is still under debate.

Quark confinement and hadron properties cannot be understood using perturbative methods and nowadays lattice QCD represents one of the most suitable tools to investigate QCD properties starting from first principles.  In this approach QCD is discretized on a Euclidean four-dimensional space-time and the quantities of interest, like masses and decay constants of hadrons, can be computed numerically via Monte Carlo methods. This kind of study requires a huge computational effort, especially when considering a theory with dynamical quarks, and the use of supercomputers is necessary if we want to achieve results that can be compared with experiments.

QCD encompasses six flavors of quarks (up, down, strange, charm, bottom, top). However, since quark masses cover a large range of values that can differ by several orders of magnitude, lattice QCD simulations often include the effects of only two, three or at most four flavors in the sea. In this project we want to estimate the effects of including a sea charm quark. In order to do that we consider QCD with just a single species of quarks, the charm quarks, and we compare the result obtained with this simplified model to a theory without dynamical quarks (often called quenched QCD). This gives the possibility to use moderately large lattice volumes and perform reliable extrapolations to zero lattice spacing.

In particular we focus on the study of charmonium states, which are composite particles made of a charm quark and a charm antiquark.  They are intensively studied in several experiments (Belle II, BESIII, LHCb, PANDA) and a lattice study of these particles can provide valuable inputs and information for future investigations. Our main result is a comparison of charmonium masses in the continuum limit. The masses of the particles of interest are extracted from the plateau average of the so-called effective masses, as shown in the figure below.

For the two lightest particles of the chamonium spectrum, called ηc and J/ψ, we find that charm quarks in the sea affect their mass difference, called hyperfine splitting, at a level of about 2%. For further details, we refer to our recent works below. We also have a follow-up project on SuperMUC which uses the data of this project generated on JUQUEEN and JUWELS to study the charm quark sea effects in the decay constants of charmonium and in the hyperfine splitting of Bc mesons.

Project Contributors

Salvatore Calì, Francesco Knechtli, Tomasz Korzec
Fakultät für Mathematik und Naturwissenschaften, Bergische Universität Wuppertal (Germany)

Jochen Heitger
Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster (Germany)

Björn Leder
Institut für Physik, Humboldt-Universität zu Berlin (Germany)

Graham Moir
Dept. of Mathematics, Hurstpierpoint College, College Lane, Hassocks (U. K.)


  1. S. Calì, F. Knechtli and T. Korzec, How much do charm sea quarks affect the charmonium spectrum?, Eur. Phys. J. C (2019) 79;
  2. S. Calì, F. Knechtli and T. Korzec, Comparison between models of QCD with and without dynamical charm quarks, in 36th International Symposium on Lattice Field Theory (Lattice 2018) East Lansing, MI, United States, July 22-28, 2018, 2018, 1811.05285;
  3. T. Korzec, F. Knechtli, S. Calì, B. Leder and G. Moir, Impact of dynamical charm quarks, PoS LATTICE2016 (2017) 126 [1612.07634].

Scientific Contact:

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

JSC project ID: hwu17

July 2019

Tags: Bergische Universität Wuppertal EPP