High Energy Physics Lattice

Lattice QCD allows us to probe the low-lying hadron spectrum in finite-volume using a basis of single- and multi-hadron interpolating operators. Here we examine the effect of including tetraquark operators on the spectrum in the scalar meson sectors containing theK∗0(700)(κ) and thea0(980)inNf=2+1QCD, withmπ≈230MeV. Preliminary results of additional finite-volume states found using tetraquark operators are shown, and possible implications of these states are discussed.

We develop a method to compute inclusive semi-leptonic decay rate of hadrons fully non-perturbatively using lattice QCD simulations. The sum over all possible final states is achieved by a calculation of the forward-scattering matrix elements on the lattice, and the phase-space integral is evaluated using their dependence on the time separation between two inserted currents. We perform a pilot lattice computation for the B_s -> X_c l nu decay with an unphysical bottom quark mass and compare the results with the corresponding OPE calculation. The method to treat the inclusive processes on the lattice can be applied to other processes, such as the lepton-nucleon inelastic scattering.

O(N)-symmetric lattice scalar fields are considered, coupled to a chemical potential and source terms. At the example of N=2, it is shown that such systems can even in (0+1) dimensions produce infinite-range correlations and a non-zero vacuum expectation value whenever the chemical potential assumes certain discrete values. Different mechanisms for how the latter phenomena are produced are discussed, depending on whether source terms are set to zero or non-zero values. In the conclusion, the relation of these findings to the Mermin-Wagner theorem is addressed.

In this paper we consider the influence of relativistic rotation on the confinement/deconfinement transition in gluodynamics within lattice simulation. We perform the simulation in the reference frame which rotates with the system under investigation, where rotation is reduced to external gravitational field. To study the confinement/deconfinement transition the Polyakov loop and its susceptibility are calculated for various lattice parameters and the values of angular velocities which are characteristic for heavy-ion collision experiments. Different types of boundary conditions (open, periodic, Dirichlet) are imposed in directions, orthogonal to rotation axis. Our data for the critical temperature are well described by a simple quadratic functionTc(Ω)/Tc(0)=1+C2Ω2withC2>0for all boundary conditions and all lattice parameters used in the simulations. From this we conclude that the critical temperature of the confinement/deconfinement transition in gluodynamics increases with increasing angular velocity. This conclusion does not depend on the boundary conditions used in our study and we believe that this is universal property of gluodynamics.

We explore the thermodynamics of the 1+1-dimensional Gross-Neveu (GN) model at finite number of fermion flavorsNf, finite temperature and finite chemical potential using lattice field theory. In the limitNf→∞the model has been solved analytically in the continuum. In this limit three phases exist: a massive phase, in which a homogeneous chiral condensate breaks chiral symmetry spontaneously, a massless symmetric phase with vanishing condensate and most interestingly an inhomogeneous phase with a condensate, which oscillates in the spatial direction. In the present work we use chiral lattice fermions (naive fermions and SLAC fermions) to simulate the GN model with 2, 8 and 16 flavors. The results obtained with both discretizations are in agreement. Similarly as forNf→∞we find three distinct regimes in the phase diagram, characterized by a qualitatively different behavior of the two-point function of the condensate field. ForNf=8we map out the phase diagram in detail and obtain an inhomogeneous region smaller as in the limitNf→∞, where quantum fluctuations are suppressed. We also comment on the existence or absence of Goldstone bosons related to the breaking of translation invariance in 1+1 dimensions.

We investigate the interaction between a heavy quark-antiquark pair in color octet configuration in gluon plasma. We calculate nonperturbatively an effective thermal potential for such a pair through the study of the correlation function of a hybrid state withQQ¯octet and an adjoint gluon source in the static limit. We discuss the extraction of an octet potential, and present results for the effective thermal potential between octetQQ¯pair in gluon plasma for moderately high temperatures≲2Tc. The implications of our result are discussed.

This notebook tutorial demonstrates a method for sampling Boltzmann distributions of lattice field theories using a class of machine learning models known as normalizing flows. The ideas and approaches proposed in arXiv:1904.12072, arXiv:2002.02428, and arXiv:2003.06413 are reviewed and a concrete implementation of the framework is presented. We apply this framework to a lattice scalar field theory and to U(1) gauge theory, explicitly encoding gauge symmetries in the flow-based approach to the latter. This presentation is intended to be interactive and working with the attached Jupyter notebook is recommended.

We search for possibly existent bound states in the heavy-light tetraquark channels with quark contentb¯b¯ud,b¯b¯usandb¯c¯udusing lattice QCD. We carry out calculations on several gauge link ensembles withNf=2+1flavours of domain-wall fermions and consider a basis of local and non-local interpolators. Besides extracting the energy spectrum from the correlation matrices, we also perform a Lüscher analysis to extrapolate our results to infinite volume.

We studyθdependence of the vacuum energy for the 4d SU(2) pure Yang-Mills theory by lattice numerical simulations. The response of topological excitations to the smearing procedure is investigated in detail, in order to extract topological information from smeared gauge configurations. We determine the first two coefficients in theθexpansion of the vacuum energy, the topological susceptibilityχand the first dimensionless coefficientb2, in the continuum limit. We find consistency of the SU(2) results with the largeNscaling. By analytic continuing the number of colors,N, to non-integer values, we infer the phase diagram of the vacuum structure of SU(N) gauge theory as a function ofNandθ. Based on the numerical results, we provide quantitative evidence that 4d SU(2) Yang-Mills theory atθ=πis gapped with spontaneous breaking of the CP symmetry.

We show the equivalence of the 2D Ising model to standard free Euclidean lattice fermions of the Wilson Majorana type. The equality of the loop representations for the partition functions of both systems is established exactly for finite lattices with well-defined boundary conditions. The honeycomb lattice is particularly simple in this context and therefore discussed first and only then followed by the more familiar square lattice case.