arXiv subjects
Publications and source records attributed to Marc Wagner.
We discuss the non-perturbative computation and interpretation of a colour adjoint static potential based on Wilson loops with generator insertions. Numerical lattice results for SU(2) gauge theory are presented and compared to corresponding perturbative results.
We review the status of an ongoing long-term lattice investigation of the spectrum and structure of tetraquark candidates. We focus on the light scalar meson $a_0(980)$. First steps regarding the study of a possibly existing $c c \bar{c} \bar{c}$ tetraquark are also outlined.
We present results of a 2+1+1 flavor twisted mass lattice QCD computation of the spectrum of $D$ mesons and $D_s$ mesons and of charmonium. Particular focus is put on the positive parity $D$ states (so-called $D^{\ast \ast}$ mesons) with quantum numbers $J^P = 0^+$, $1^+$ and $2^+$. Besides computing their masses we are also separating and classifying the two $J^P = 1^+$ states according to the angular momentum/spin of their light degrees of freedom (light quarks and gluons) $j =1/2, 3/2$.
At small lattice spacing QCD simulations are expected to become stuck in a single topological sector. Observables evaluated in a fixed topological sector differ from their counterparts in full QCD, i.e. at unfixed topology, by volume dependent corrections. We investigate these corrections in the two-flavor Schwinger model, which is in several aspects similar to QCD, using Wilson fermions. We also try to remove these corrections by suitable extrapolations to infinite volume.
The intention of these lecture notes is to outline the basics of lattice hadron spectroscopy to students from other fields of physics, e.g. from experimental particle physics, who do not necessarily have a background in quantum field theory. After a brief motivation and discussion of QCD, it is explained, how QCD can in principle be solved numerically using lattice QCD. The main part of these lecture notes is concerned with quantum numbers of hadrons, corresponding hadron creation operators, and how the mass of a hadron can be determined from a temporal correlation function of such operators. Finally, three recent lattice hadron spectroscopy examples from the literature are discussed on an elementary level.
We present lattice results for the a_0(980) state using a variational approach with a variety of creation operators: quark-antiquark, mesonic molecule, diquark-antidiquark as well as two-meson type. Focus is put on recent technical advances, in particular the computation of singly disconnected diagrams.
We explore and compare three mixed action setups with Wilson twisted mass sea quarks and different valence quark actions: (1) Wilson twisted mass, (2) Wilson twisted mass + clover and (3) Wilson + clover. Our main goal is to reduce lattice discretization errors in mesonic spectral quantities, in particular to reduce twisted mass parity and isospin breaking.
Utilizing lattice QCD results for the potential of two static antiquarks and two dynamical quarks as well as quark model techniques for the dynamics of two heavy antiquarks in a cloud of two light quarks, we are provided with an accurate framework for the study of possibly existing heavy-heavy-light-light tetraquarks. Among the possible quantum numbers of such a system, we find binding in only one channel, the scalar isosinglet. Solving the Schroedinger equation for the displacement of the heavy antiquarks and taking systematic errors into account, we find an antibottom-antibottom-light-light bound state with a confidence level of around 1.8 sigma ... 3.0 sigma and binding energy of approximately 30 MeV ... 57 MeV.
We study possibilities to define a static quark anti-quark pair in a colour-adjoint orientation based on Wilson loops with generator insertions, using both lattice QCD and leading order perturbation theory in various gauges. Non-perturbatively, the only way to obtain non-zero results while maintaining positivity of the Hamiltonian is by some form of temporal gauge. In this case the correlator is equivalent to a gauge invariant correlation function of a static quark anti-quark pair and a static adjoint quark, the resulting three-point potential is attractive. Saturating open colour indices with colour magnetic fields instead also leads to a gauge invariant correlator. However this object is found to couple to the singlet sector only. There appears to be no lattice observable that reproduces the repulsive adjoint potential predicted by perturbation theory in Lorenz or Coulomb gauges.
We present preliminary results of an ongoing lattice QCD computation of the spectrum of $D$ mesons and $D_s$ mesons and of charmonium using 2+1+1 flavors of twisted mass sea and valence quarks.
We study light scalar mesons with particular focus on the a_0(980) using lattice QCD with 2+1+1 dynamical quark flavors. To investigate the structure of these scalar mesons and to identify, whether a sizeable tetraquark component is present, we use a large set of operators, including diquark-antidiquark, mesonic molecule and two-meson operators. We find that the low-lying states overlap essentially exclusively with two-meson states. This indicates that in the channels investigated no tightly bound four-quark states of either molecular or diquark-antidiquark type exist.
We study a model of dyons for SU(2) Yang-Mills theory at finite temperature T < T_c, in particular its ability to generate a confining force between a static quark antiquark pair. The interaction between dyons corresponds to a long-range 1/r potential, which in naive treatments with a finite number of dyons typically gives rise to severe finite volume effects. To avoid such effects we apply the so-called Ewald method, which has its origin in solid state physics. The basic idea of Ewald's method is to consider a finite number of dyons inside a finite cubic volume and enforce periodicity of this volume. We explain the technicalities of Ewald's method and outline how the method can be applied to a wider class of 1/r^p long-range potentials.
We study the light scalar mesons a_0(980) and kappa using N_f = 2+1+1 flavor lattice QCD. In order to probe the internal structure of these scalar mesons, and in particular to identify, whether a sizeable tetraquark component is present, we use a large set of operators, including diquark-antidiquark, mesonic molecule and two-meson operators. The inclusion of disconnected diagrams, which are technically rather challenging, but which would allow us to extend our work to e.g. the f_0(980) meson, is introduced and discussed.
We carry out an exploratory study of the isospin one a0(980) and the isospin one-half kappa scalar mesons using Nf=2+1+1 Wilson twisted mass fermions at one lattice spacing. The valence strange quark is included as an Osterwalder-Seiler fermion with mass tuned so that the kaon mass matches the corresponding mass in the unitary Nf=2+1+1 theory. We investigate the internal structure of these mesons by using a basis of four-quark interpolating fields. We construct diquark-diquark and molecular-typecinterpolating fields and analyse the resulting correlation matrices keeping only connected contributions. For both channels, the low-lying spectrum is found to be consistent with two-particle scattering states. Therefore, our analysis shows no evidence for an additional state that can be interpreted as either a tetraquark or a tightly-bound molecular state.
We present first results of a 2+1+1 flavor twisted mass lattice QCD computation of strange and charm meson masses. We focus on D and D_s mesons with spin J = 0,1 and parity P = -,+.
It is a long discussed issue whether light scalar mesons have sizeable four-quark components. We present an exploratory study of this question using N_f=2+1+1 twisted mass lattice QCD. A mixed action approach ignoring disconnected contributions is used to calculate correlator matrices consisting of mesonic molecule, diquark-antidiquark and two-meson interpolating operators with quantum numbers of the scalar mesons a0(980) (1(0^++)) and kappa (1/2(0+)). The correlation matrices are analyzed by solving the generalized eigenvalue problem. The theoretically expected free two-particle scattering states are identified, while no additional low lying states are observed. We do not observe indications for bound four-quark states in the channels investigated.
We discuss possibilities and problems to non-perturbatively define and compute a static color triplet potential in SU(2) gauge theory. Numerical lattice results are presented and compared to analytical perturbative results.
As an approach to describe the long-range properties of non-Abelian gauge theories at non-zero temperature T < T_c, we consider a non-interacting ensemble of dyons (magnetic monopoles) with non-trivial holonomy. We show analytically, that the quark-antiquark free energy from the Polyakov loop correlator grows linearly with the distance, and how the string tension scales with the dyon density. In numerical treatments, the long-range tails of the dyon fields cause severe finite-volume effects. Therefore, we demonstrate the application of Ewald's summation method to this system. Finite-volume effects are shown to be under control, which is a crucial requirement for numerical studies of interacting dyon ensembles.