High Energy Physics Lattice

Using recent results on higher order cumulants of conserved charge fluctuations from lattice QCD, we construct mean, variance, skewness, kurtosis, hyper-skewness and hyper-kurtosis of net-baryon number distributions for small baryon chemical potentialsμB. For the strangeness neutral case (μS=0) at fixed ratio of electric charge to baryon number density (nQnB=0.4), which is appropriate for a comparison with heavy ion collisions, we present results forκBσ2B,SBσ3B/MB,κHBσ4BandSHBσ5B/MBon the crossover line for the chiral transition,Tpc(μB). Continuum extrapolations for this pseudo-critical transition line have recently been reported by HotQCD up to baryon chemical potentialsμB≃300MeV [arXiv:1812.08235]. These cumulant ratios are of direct relevance for comparisons with corresponding ratios measured by STAR in the BES-I and II runs at beam energiessNN−−−−√≥20GeV. In particular, we point out that recent high statistics results on skewness and kurtosis of net-baryon number distributions obtained by STAR atsNN−−−−√=54.4GeV put strong constraints on freeze-out parameters and are consistent with predictions from thermal QCD.

We compute boundary correlation functions for scalar fields on tessellations of two- and three-dimensional hyperbolic geometries. We present evidence that the continuum relation between the scalar bulk mass and the scaling dimension associated with boundary-to-boundary correlation functions survives the truncation of approximating the continuum hyperbolic space with a lattice.

We compute hybrid static potentials in SU(2) lattice gauge theory using a multilevel algorithm and three different small lattice spacings. The resulting static potentials, which are valid for quark-antiquark separations as small as 0.05 fm, are important e.g. when computing masses of heavy hybrid mesons in the Born-Oppenheimer approximation. We also discuss and exclude possible systematic errors from topological freezing, the finite lattice volume and glueball decays.

We present a lattice-QCD determination of the elastic isospin-1/2S-wave andP-waveKπscattering amplitudes as a function of the center-of-mass energy using Lüscher's method. We perform global fits ofK-matrix parametrizations to the finite-volume energy spectra for all irreducible representations with total momenta up to3–√2πL; this includes irreps that mix theS- andP-waves. Several different parametrizations for the energy dependence of theK-matrix are considered. We also determine the positions of the nearest poles in the scattering amplitudes, which correspond to the broadκresonance in theS-wave and the narrowK∗(892)resonance in theP-wave. Our calculations are performed with2+1dynamical clover fermions for two different pion masses of317.2(2.2)and175.9(1.8)MeV. Our preferredS-wave parametrization is based on a conformal map and includes an Adler zero; for theP-wave we use a standard pole parametrization including Blatt-Weisskopf barrier factors. TheS-waveκ-resonance pole positions are found to be[0.86(12)−0.309(50)i]GeVat the heavier pion mass and[0.499(55)−0.379(66)i]GeVat the lighter pion mass. TheP-waveK∗-resonance pole positions are found to be[0.8951(64)−0.00250(21)i]GeVat the heavier pion mass and[0.8718(82)−0.0130(11)i]GeVat the lighter pion mass, which corresponds to couplings ofgK∗Kπ=5.02(26)andgK∗Kπ=4.99(22), respectively.

We analyze the spectrum of two- and three-pion states of maximal isospin obtained recently for isosymmetric QCD with pion massM≈200MeV in Ref. [1]. Using the relativistic three-particle quantization condition, we find∼2σevidence for a nonzero value for the contact part of the three-π+(I=3) scattering amplitude. We also compare our results to leading-order chiral perturbation theory. We find good agreement at threshold, and some tension in the energy dependent part of the three-π+scattering amplitude. We also find that the two-π+(I=2) spectrum is fit well by ans-wave phase shift that incorporates the expected Adler zero.

We show that the nature of the topological fluctuations inSU(3)gauge theory changes drastically at the finite temperature phase transition. Starting from temperatures right above the phase transition topological fluctuations come in well separated lumps of unit charge that form a non-interacting ideal gas. Our analysis is based on a novel method to count not only the net topological charge, but also separately the number of positively and negatively charged lumps in lattice configurations using the spectrum of the overlap Dirac operator. This enables us to determine the joint distribution of the number of positively and negatively charged topological objects, and we find this distribution to be consistent with that of an ideal gas of unit charged topological objects.

In recent years, the existence of a hadronically stableb¯b¯udtetraquark with quantum numbersI(JP)=0(1+)was confirmed by first principles lattice QCD computations. In this work we use lattice QCD to compare two frequently discussed competing structures for this tetraquark by considering meson-meson as well as diquark-antidiquark creation operators. We use the static-light approximation, where the twob¯quarks are assumed to be infinitely heavy with frozen positions, while the lightuanddquarks are fully relativistic. By minimizing effective energies and by solving generalized eigenvalue problems we determine the importance of the meson-meson and the diquark-antidiquark creation operators with respect to the ground state. It turns out, that the diquark-antidiquark structure dominates forb¯b¯separationsr<0.25fm, whereas it becomes increasingly more irrelevant for larger separations, where theI(JP)=0(1+)tetraquark is mostly a meson-meson state. We also estimate the meson-meson to diquark-antidiquark ratio of this tetraquark and find around60%/40%.

In a previous paper \cite{Jahn:2018dke} we presented a methodology for computing the topological susceptibility of QCD at temperatures where it is small and standard methods fail. Here we improve on this methodology by removing two barriers to the reweighting method's moving between topological sectors. We present high-statistics, continuum-extrapolated results for the susceptibility of pure-glue QCD up to7Tc. We show that the susceptibility varies with temperature asT−6.7±0.3betweenT=2.5TcandT=7Tc, in good agreement with expectations based on the dilute instanton gas approximation.

The CKM matrix elementsVcbandVubcan be obtained by combining data from the experiments with lattice QCD results for the semi-leptonic form factors for theB¯→D∗ℓν¯andB¯→πℓν¯decays. It is highly desirable to use the Oktay-Kronfeld (OK) action for the form factor calculation on the lattice, since the OK action is designed to reduce the heavy quark discretization error down to theO(λ4)level in the power counting rules of the heavy quark effective theory (HQET). Here, we present a matching calculation to improve heavy-heavy and heavy-light currents up to theλ3order in HQET, the same level of improvement as the OK action. Our final results for the improved currents are being used in a lattice QCD calculation of the semi-leptonic form factors for theB¯→D∗ℓν¯andB¯→Dℓν¯decays.

Nonlocal quark bilinear operators connected by link paths are used for studying parton distribution functions (PDFs) and transverse momentum-dependent PDFs of hadrons using lattice QCD. The nonlocality makes it difficult to understand the renormalization and improvement of these operators using standard methods. In previous work, we showed that by introducing an auxiliary field on the lattice, one can understand an on-axis Wilson-line operator as the product of two local operators in an extended theory. In this paper, we provide details about the calculation in perturbation theory of the factor for conversion from our lattice-suitable renormalization scheme to the MS-bar scheme. Extending our work, we study Symanzik improvement of the extended theory to understand the pattern of discretization effects linear in the lattice spacing,a, which are present even if the lattice fermion action exactly preserves chiral symmetry. This provides a prospect for an eventualO(a)improvement of lattice calculations of PDFs. We also generalize our approach to apply to Wilson lines along lattice diagonals and to piecewise-straight link paths.