Lattice QCD Study of Charmonium-like States

In the recent years a number of exciting non-conventional charmonium-like states were experimentally discovered. Many of them, in particular the charged ones, cannot have the conventional quark-antiquark structure. These states lie near the strong-decay thresholds or they are resonances above the threshold. None of these states has been properly studied using the non-perturbative first-principle tool Quantum Chromodynamics (QCD) on the lattice, i.e., taking into account the threshold effects and coupling to open strong decay channels. Only the masses of the states that lie well below strong decay threshold have been reliably calculated. We propose to study the interesting charmonium and charmonium-like states near or above threshold using lattice QCD and including such coupling to intermediate meson-meson channels. We use Monte-Carlo integration for the quantization of QCD and will consider several scattering channels. The states will be created/annihilated using a number of quark-antiquark and meson-meson interpolators. New efficient methods will be employed, among them stochastic distillation and variational analysis. The scattering phase shifts will be extracted from the obtained energy levels. These will allow the extraction of masses and the decay widths for various hadronic resonances. Many of the interesting states discovered in experiment (for example X(3872), (3770), c0 (2P), Z+(4430)) appear in the scattering of DD, DD*, D*D 1 in S-wave or P-wave. So we will analyze those scattering channels and extract the corresponding scattering phase shifts. Possible shallow bound-states will be identified by careful study of possible extra energy levels. The result for DD* scattering in S-wave will be of particular interest, since the exciting narrow resonance X(3872) was observed in many experiments close to D 0 D0 * threshold. We will simulate separately I=0, I=1 and mixed isospin, which should help to clarify its nature. A study of DD scattering in P-wave is crucial for near-threshold (3770), which comes out too heavy in previous lattice simulations. The D*D 1 scattering in S-wave will shed light on the controversial Z+(4430). We believe that we will be able to deliver original physics results, that do not yet exist in the literature. These would be very valuable for the interpretation of the recently observed charmonium and charmonium-like states.

We computed masses and decay properties of elementary particles based on Quantum Chromodynamics (QCD). QCD is supposedly the fundamental quantum field theory of quarks and gluons that make up 99,98% of observed matter. The theory describes the strong interaction, which binds quarks and gluons in the atomic core particles proton and neutron. These are but two out of many more hadrons that have been observed in experiments in the recent decades. Of particular interest are the recently discovered hadrons that are built from light quarks (up, down, strange) as well as heavy quarks (charm, bottom). The formulation of QCD on a space-time grid allows us to compute these hadrons in first principles calculations and confirm their measured properties or even predict them. Until recently the computations disregarded an important aspect: most of the particles are not stable, as assumed for simplification, but they are resonances and decay in a finite (short) life time into lighter hadrons. In particular charmonium-like hadrons, where charm quarks are bound to charm antiquarks, are puzzling. On one hand methods used until recently cannot describe them correctly; on the other hand some of them are candidates for tetraquarks, built from a pair of quarks and a pair of antiquarks. In our project we developed new methods and considered for the first time for several quantum channels the hadronic decays and the influence on the particle properties. In some cases we could find agreement of the theory with the experimental results and in some cases we could even predict particles not yet observed in experiments. This kind of computations is demanding. In our case we needed more than a million CPUhours, which were available on compute-clusters. The necessary storage amounted to several dozen terabytes. Our group was international. Project partner Sasa Prelovsek works at the University of Ljubljana (Slovenija), an external partner Daniel Mohler was at FermiLab (FNAL near Chicago, USA) and in Graz the Indian nationality researcher Padmanath Madanagopalan and I collaborated. Thanks to modern communication tools this collaboration was very successful. Our results were published in internationally reputed journals and presented at several conferences.