Search

The recently reported new measurement of the anomalous magnetic moment of the muon, aΜ, by the E989 collaboration at Fermilab has increased the tension with the Standard Model (SM) prediction to 4.2 standard deviations. In order to increase the sensitivity of SM tests, the precision of the theoretical prediction, which is limited by the strong interaction, must be further improved. In our project we employ lattice QCD to compute the leading hadronic contributions to aΜ and various other precision observables, such as the energy dependence (“running”) of the electromagnetic coupling, α, and the electroweak mixing angle, sin2 θW. Here we report on the performance of our simulation codes used for the generation of gauge ensembles at (near-)physical pion masses and fine lattice spacings. Furthermore, we present results for the hadronic running of α, the electroweak mixing angle, as well as the hadronic vacuum polarisation and light-by-light scattering contributions to aΜ. Results from an ancillary calculation of the spectrum in the isovector channel are crucial in order to further increase the precision of our determination of the hadronic vacuum polarisation contribution.

We review lattice results related to pion, kaon, D-meson, B-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor f+(0) arising in the semileptonic K→π transition at zero momentum transfer, as well as the decay constant ratio fK/fπ and its consequences for the CKM matrix elements Vus and Vud. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of SU(2)L×SU(2)R and SU(3)L×SU(3)R Chiral Perturbation Theory. We review the determination of the BK parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for mc and mb as well as those for D- and B-meson decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant αs. Finally, in this review we have added a new section reviewing results for nucleon matrix elements of the axial, scalar and tensor bilinears, both isovector and flavor diagonal.

We present results for the strange contribution to the electromagnetic form factors of the nucleon computed on the coordinated lattice simulation ensembles with Nf=2+1 flavors of O(a)-improved Wilson fermions and an O(a)-improved vector current. Several source-sink separations are investigated in order to estimate the excited-state contamination. We calculate the form factors on six ensembles with lattice spacings in the range of a=0.049–0.086 fm and pion masses in the range of mπ=200–360 MeV, which allows for a controlled chiral and continuum extrapolation. In the computation of the quark-disconnected contributions, we employ hierarchical probing as a variance-reduction technique.

We discuss the treatment of resonances and multi-particle states in lattice QCD. The Lüscher formalism in conjunction with the calculation of matrix correlators and solving a generalised eigenvalue problem represents a powerful technique to determine the pole position corresponding to resonance in the complex energy plane. We present preliminary results for the $\rho$-resonance and the conjectured H-dibaryon. We also discuss the relevance of the Lüscher formalism to constrain the iso-vector spectral function which has an important application in the lattice calculation of the hadronic vacuum polarisation contribution to the muon anomalous magnetic moment.

We present preliminary results on the axial form factor $G_A(Q^2)$ and the induced pseudoscalar form factor $G_P(Q^2)$ of the nucleon. A systematic analysis of the excited-state contributions to form factors is performed on the CLS ensemble `N6' with $m_\pi = 340 \ \text{MeV}$ and lattice spacing $a \sim 0.05 \ \text{fm}$. The relevant three-point functions were computed with source-sink separations ranging from $t_s \sim 0.6 \ \text{fm}$ to $t_s \sim \ 1.4 \ \text{fm}$. We observe that the form factors suffer from non-trivial excited-state contributions at the source-sink separations available to us. It is noted that naive plateau fits underestimate the excited-state contributions and that the method of summed operator insertions correctly accounts for these effects., Comment: 7 pages, 12 figures; talk presented at Lattice 2014 -- 32nd International Symposium on Lattice Field Theory, 23-28 June, 2014, Columbia University New York, NY

We compute the leading-order low-energy constants of the DeltaS=1 effective weak Hamiltonian in the quenched approximation of QCD with up, down, strange, and charm quarks degenerate and light. They are extracted by comparing the predictions of finite volume chiral perturbation theory with lattice QCD computations of suitable correlation functions carried out with quark masses ranging from a few MeV up to half of the physical strange mass. We observe a large DeltaI=1/2 enhancement in this corner of the parameter space of the theory. Although matching with the experimental result is not observed for the DeltaI=1/2 amplitude, our computation suggests large QCD contributions to the physical DeltaI=1/2 rule in the GIM limit, and represents the first step to quantify the role of the charm quark-mass in K-->pipi amplitudes.

We present our preliminary results for three-point correlation functions involving the operators entering the $\Delta{S}=1$ effective Hamiltonian with an active charm quark, obtained using overlap fermions in the quenched approximation. This is the first computation carried out for valence quark masses small enough so as to permit a matching to Quenched Chiral Perturbation Theory in the $\epsilon$-regime. The commonly observed large statistical fluctuations are tamed by means of low-mode averaging techniques, combined with restrictions to individual topological sectors. We also discuss the matching of the resulting hadronic matrix elements to the effective low-energy constants for $\Delta{S}=1$ transitions. This involves (a) finite-volume corrections which can be evaluated at NLO in Quenched Chiral Perturbation Theory, and (b) the short-distance renormalization of the relevant four-quark operators in discretizations based on the overlap operator. We discuss perturbative estimates for the renormalization factors and possible strategies for their non-perturbative evaluation. Our results can be used to isolate the long-distance contributions to the $\Delta I=1/2$ rule, coming from physics effects around the intrinsic QCD scale.

In lattice QCD it is possible, in principle, to determine the parameters in the effective chiral lagrangian (including weak interaction couplings) by performing numerical simulations in the $\epsilon$--regime, i.e. at quark masses where the physical extent of the lattice is much smaller than the Compton wave length of the pion. The use of a formulation of the lattice theory that preserves chiral symmetry is attractive in this context, but the numerical implementation of any such approach requires special care in this kinematical situation due to the presence of some very low eigenvalues of the Dirac operator. We discuss a set of techniques (low-mode preconditioning and adapted-precision algorithms in particular) that make such computations numerically safe and more efficient by a large factor., Comment: Plain TeX source, 32 pages, figures included

We investigate the efficiency of single timeslice stochastic sources for the calculation of light meson masses on the lattice as one varies the quark mass. Simulations are carried out with Nf = 2 flavours of non-perturbatively O(a) improved Wilson fermions for pion masses in the range of 450 - 760 MeV. Results for pseudoscalar and vector meson two-point correlation functions computed using stochastic as well as point sources are presented and compared. At fixed computational cost the stochastic approach reduces the variance considerably in the pseudoscalar channel for all simulated quark masses. The vector channel is more affected by the intrinsic stochastic noise. In order to obtain stable estimates of the statistical errors and a more pronounced plateau for the effective vector meson mass, a relatively large number of stochastic sources must be used., Comment: 18 pages, 6 figures

We report on our on-going project to compute mesonic and baryonic two- and three-point correlation functions in simulations using Nf=2 flavours of O(a) improved Wilson quarks and the Wilson plaquette action. We present performance figures for the DD-HMC algorithm on commodity cluster hardware and discuss the issue of critical slowing down, which is particularly pronounced for the topological charge. The effectiveness of stochastic noise sources and Jacobi smearing are investigated. Our preliminary results obtained at three quark masses on 96x48^3 at beta=5.5 imply that the lattice spacing is about 0.06 fm, while the smallest pion mass in the current runs is around 360 MeV, which corresponds to m_pi*L=5.3., 7 pages, 4 figures, presented at 27 International Symposium on Lattice Field Theory, July 26-31, 2009, Peking University, Beijing, China

We discuss a new method to determine the low-energy couplings of the $\Delta S=1$ weak Hamiltonian in the $\epsilon$-regime. It relies on a matching of the topological poles in $1/m^2$ of three-point functions of two pseudoscalar densities and a four-fermion operator computed in lattice QCD, to the same observables in the Chiral Effective Theory. We present the results of a NLO computation in chiral perturbation theory of these correlation functions together with some preliminary numerical results., Comment: 7 pages. Contribution to Lattice 2007

We present results for the non-perturbative renormalisation of four-fermion operators with two flavours of dynamical quarks. We consider both fully relativistic left current-left current operators, and a full basis for $\Delta B=2$ operators with static heavy quarks. The renormalisation group running of the operators to high energy scales is computed in the continuum limit for a family of Schroedinger Functional renormalisation schemes, via standard finite size scaling techniques. The total renormalisation factors relating renormalisation group invariant to bare operators are computed for a choice of lattice regularisations., Comment: 7 pages, 2 figures, Proceedings from the XXV International Symposium on Lattice Field Theory, Regensburg, Germany Typos corrected + typographic adjustments

We compute the leading-order low-energy constants of the DeltaS=1 effective weak Hamiltonian in the quenched approximation of QCD with up, down, strange, and charm quarks degenerate and light (GIM limit). The low-energy constants are extracted by comparing the predictions of finite volume chiral perturbation theory with lattice QCD computations of suitable correlation functions carried out with quark masses ranging from a few MeV up to half of the physical strange mass. We observe a large DeltaI=1/2 enhancement in this corner of the parameter space of the theory. Although matching with the experimental result is not observed for the DeltaI=1/2 amplitude, our computation suggests large QCD contributions to the physical DeltaI=1/2 rule in the GIM limit, and represents the first step to quantify the role of the charm quark-mass in K-->pipi amplitudes. We compute the leading-order low-energy constants of the DeltaS=1 effective weak Hamiltonian in the quenched approximation of QCD with up, down, strange, and charm quarks degenerate and light. They are extracted by comparing the predictions of finite volume chiral perturbation theory with lattice QCD computations of suitable correlation functions carried out with quark masses ranging from a few MeV up to half of the physical strange mass. We observe a large DeltaI=1/2 enhancement in this corner of the parameter space of the theory. Although matching with the experimental result is not observed for the DeltaI=1/2 amplitude, our computation suggests large QCD contributions to the physical DeltaI=1/2 rule in the GIM limit, and represents the first step to quantify the role of the charm quark-mass in K-->pipi amplitudes.

We discuss the renormalisation properties of parity-odd Delta B=2 operators with the heavy quark treated in the static approximation. Via twisted mass QCD (tmQCD), these operators provide the matrix elements relevant for the B0-B0bar mixing amplitude. The layout of a non-perturbative renormalisation programme for the operator basis, using Schroedinger Functional techniques, is described. Finally, we report our results for a one-loop perturbative study of various renormalisation schemes with Wilson-type lattice regularisations, which allows, in particular, to compute the NLO anomalous dimensions of the operators in the SF schemes of interest., 6 pages, 1 figure, parallel talk given at LATTICE 2005, Trinity College, Dublin, July 25-30, 2005 (heavy quarks)

We introduce the contributions to the proceedings of Working Group V. The main topics were: present and future experiments dedicated to charm physics, the interplay between high-precision measurements and better control over theoretical uncertainties, and searches for signals of new physics in the charm sector. The comparison of Lattice QCD calculations with precise measurements of charm semi-leptonic and leptonic decays can have a major impact on the determination of CKM matrix elements from measurements of B meson decays., Based on a summary talk by H.W. at the 2nd Workshop on the Unitarity Triangle, 5-9 April 2003, Durham, UK (eConf C0304052).6 pages LaTeX, no figures, uses ckm.cls

PUBLISHED, We present a comprehensive study of the masses of pseudoscalar and vector mesons, as well as octet and decuplet baryons computed in O(a)-improved quenched lattice QCD. Results have been obtained using the nonperturbative definition of the improvement coefficient csw , and also its estimate in tadpole improved perturbation theory. We investigate effects of improvement on the incidence of exceptional configurations, mass splittings, and the parameter J. By combining the results obtained using nonperturbative and tadpole improvement in a simultaneous continuum extrapolation, we can compare our spectral data to experiment. We confirm earlier findings by the CP-PACS Collaboration that the quenched light hadron spectrum agrees with experiment at the 10% level., This work was supported by the Particle Physics & Astronomy Research Council ~PPARC! through grants GR/L56336 and GR/L29927. We also acknowledge the support by EPSRC under grant GR/K41663. H.P.S. acknowledges the support of the Leverhulme foundation and the JSPS Research for the Future program. H.W. is grateful to Akira Ukawa for the hospitality at the Center of Computational Physics, University of Tsukuba, where part of this work was completed. D.G.R. and H.W. acknowledge the financial support of PPARC.

26 pp. (1993)., An exploratory numerical study of the influence of heavy fermion doublets on the mass of the Higgs boson is performed in the decoupling limit of a chiral SU(2)$_L$ ⊗ SU(2)$_R$ symmetric Yukawa model with mirror fermions. The behaviour of fermion and boson masses is investigated at infinite bare quartic coupling on 4$^3$·8, 6$^3$·12 and 8$^3$·16 lattices. A first estimate of the upper bound on the renormalized quartic coupling as a function of the renormalized Yukawa coupling is given. On the algorithmic side, several standard fermion matrix inversion methods were tried and tuned for better performance.

14 pp. (1993)., The vacuum stability lower bound on the mass of the Higgs boson is numerically investigated in an SU(2)L ⊗ SU(2)R symmetric Yukawa model, which describes two heavy degenerate fermion doublets in the limit of vanishing gauge couplings. The values for the lower bound are in good agreement with those obtained from an integration of the one-loop β-functions, although the couplings are strong. The upper bound on the fermion mass and renormalized Yukawa coupling is also determined in the part of bare parameter space where reflection positivity has been proven.