High Energy Physics Lattice

Excited state contributions represent a formidable challenge for hadron structure calculations in lattice QCD. For physical systems that exhibit an exponential signal-to-noise problem they often hinder the extraction of ground state matrix elements, introducing a major source of systematic error in lattice calculations of such quantities. The development of methods to treat the contribution of excited states and the current status of related lattice studies are reviewed with focus on nucleon structure calculations that are notoriously affected by excited state contamination.

We present the first calculation within lattice QCD of excited light meson resonances withJPC=1−−,2−−and3−−. Working with an exact SU(3) flavor symmetry, for the singlet representation of pseudoscalar-vector scattering, we find two1−−resonances, a lighter broad state and a heavier narrow state, a broad2−−resonance decaying in bothP- andF-waves, and a narrow3−−state. We present connections to experimentalω⋆J,ϕ⋆Jresonances decaying intoπρ,KK¯∗,ηωand other final states.

We investigate the phase structure of a four dimensional SO(4) invariant lattice Higgs-Yukawa model comprising four reduced staggered fermions interacting with a real scalar field. The fermions belong to the fundamental representation of the symmetry group while the three scalar field components transform in the self-dual representation of SO(4). We explore the phase diagram and find evidence of a continuous transition between a phase where the fermions are massless to one where the fermions acquire mass. This transition is not associated with symmetry breaking and there is no obvious local order parameter.

We continue our study of spectroscopy data for the SU(3) gauge theory with eight fundamental fermions, motivated by the effective field theory framework of dilaton chiral perturbation theory (dChPT). At leading order dChPT predicts a constant mass anomalous dimensionγm, consistent with the assumed proximity of an infrared fixed point. For the relatively large fermion masses simulated by the LatKMI collaboration, the influence of the infrared fixed point diminishes, and our fits suggest thatγmstarts running. Since a complete higher-order analysis is not feasible with presently available data, we adopt a more phenomenological approach. We propose a partial extension to higher orders, which incorporates the running ofγminto the tree-level lagrangian. We find that this extension successfully describes the full fermion-mass range of the LatKMI data, including the pion taste splittings which arise from using staggered fermions in the lattice simulations. We also investigate a more general class of dilaton potentials proposed in the literature, using both the LSD and LatKMI data sets, concluding that these data favor the form predicted by dChPT.

Based on our analysis of the contributions from the connected and disconnected contraction diagrams to the pion-kaon scattering amplitude, we provide the first determination of the low-energy constantLr0in SU(4|1)Partially-Quenched Chiral Perturbation Theory from data of the Extended Twisted Mass Collaboration,Lr0=0.51(26)??10??atμ=1GeV.

We report the results of a lattice quantum chromodynamics calculation ofFK/Fπusing Möbius domain-wall fermions computed on gradient-flowedNf=2+1+1highly-improved staggered quark (HISQ) ensembles. The calculation is performed with five values of the pion mass ranging from130≲mπ≲400MeV, four lattice spacings ofa∼0.15,0.12,0.09and0.06fm and multiple values of the lattice volume. The interpolation/extrapolation to the physical pion and kaon mass point, the continuum, and infinite volume limits are performed with a variety of different extrapolation functions utilizing both the relevant mixed-action effective field theory expressions as well as discretization-enhanced continuum chiral perturbation theory formulas. We find that thea∼0.06fm ensemble is helpful, but not necessary to achieve a subpercent determination ofFK/Fπ. We also include an estimate of the strong isospin breaking corrections and arrive at a final result ofFK±/Fπ±=1.1942(45)with all sources of statistical and systematic uncertainty included. This is consistent with the Flavour Lattice Averaging Group average value, providing an important benchmark for our lattice action. Combining our result with experimental measurements of the pion and kaon leptonic decays leads to a determination of|Vus|/|Vud|=0.2311(10).

Since the pioneering work of Lüscher in the 1980s it is well known that considering quantum systems in finite volume, specifically, finite periodic boxes, can be used as a powerful computational tool to extract physical observables. While this formalism has been worked out in great detail in the two-body sector, much effort is currently being invested into deriving analogous relations for systems with more constituents. This work is relevant not only for nuclear physics, where lattice methods are now able to calculate few- and many-nucleon states, but also for other fields such as simulations of cold atoms. This article discusses recent progress regarding the extraction of few-body bound-state and resonance properties from finite-volume calculations of systems with an arbitrary number of constituents.

Two field-sparsening methods, namely the sparse-grid method and the random field selection method, are used in this paper for the construction of the 2-point and 3-point correlation functions in lattice QCD. We argue that, due to the high correlation among the lattice correlators at different field points associated with source, current, and sink locations, one can save a lot of computational time by performing the summation over a subset of the lattice sites. Furthermore, with this strategy, one only needs to store a small fraction of the full quark propagators. It is found that the number of field points can be reduced by a factor of∼100 for the point-source operator and a factor of∼1000 for the Gaussian-smeared operator, while the uncertainties of the correlators only increase by∼15\%. Therefore, with a modest cost of the computational resources, one can approach the precision of the all-to-all correlators using the field-sparsening methods.

In the absence of a genuine solution to the sign problem, lattice studies at imaginary quark chemical potential are an important tool to constrain the QCD phase diagram. We calculate the values of the tricritical quark masses in the Roberge-Weiss plane,μ=ıπT/3, which separate mass regions with chiral and deconfinement phase transitions from the intermediate region, for QCD withNf=2unimproved staggered quarks onNτ=6lattices. A quantitative measure for the quality of finite size scaling plots is developed, which significantly reduces the subjective judgement required for fitting. We observe that larger aspect ratios are necessary to unambiguously determine the order of the transition than atμ=0. Comparing with previous results fromNτ=4we find a∼50% reduction in the light tricritical pion mass. The heavy tricritical pion mass stays roughly the same, but is too heavy to be resolved onNτ=6lattices and thus equally afflicted with cut-off effects. Further comparison with other discretizations suggests that current cut-off effects on the light critical masses are likely to be larger than∼100%, implying a drastic shrinking of the chiral first-order region to possibly zero.

We discuss recent progress in studying Quantum Chromodynamics at finite temperature usingNf=2+1+1Wilson twisted mass fermions. Particular interest is in QCD symmetries and their breaking and restoration. First, we discuss the behaviour of theη′meson at finite temperature, which is tightly connected to the axial and chiral symmetries. The results suggest a small decrease of theη′mass in the pseudo-critical region coming close to the non-anomalous contribution and subsequent growth at large temperatures. Second, we present the first results of lattice simulations of Quantum Chromodynamics withNf=2+1+1twisted mass Wilson fermions at physical pion, strange and charm masses. We estimate the chiral pseudo-critical temperatures for different observables. Our preliminary results are consistent with a second order transition in the chiral limit, however other scenarios are not excluded.