Towards a new determination of the QCD Lambda parameter from running couplings in the three-flavour theory

We review our new strategy and current status towards a high precision computation of the Lambda parameter from three-flavour simulations in QCD. To reach this goal we combine specific advantages of the Schr\"odinger functional and gradient flow couplings.Comment: 7 pages, 3 figures; Proceedings of the 32nd International Symposium on Lattice Field Theory; 23-28 June, 2014, Columbia University, New Yor

Determination of the Δ(1232)\Delta(1232) axial and pseudoscalar form factors from lattice QCD

We present a lattice QCD calculation of the $\Delta(1232)$ matrix elements of the axial-vector and pseudoscalar currents. The decomposition of these matrix elements into the appropriate Lorentz invariant form factors is carried out and the techniques to calculate the form factors are developed and tested using quenched configurations. Results are obtained for 2+1 domain wall fermions and within a hybrid scheme with domain wall valence and staggered sea quarks. Two Goldberger-Treiman type relations connecting the axial to the pseudoscalar effective couplings are derived. These and further relations based on the pion-pole dominance hypothesis are examined using the lattice QCD results, finding support for their validity. Utilizing lattice QCD results on the axial charges of the nucleon and the $\Delta$, as well as the nucleon-to-$\Delta$ transition coupling constant, we perform a combined chiral fit to all three quantities and study their pion mass dependence as the chiral limit is approached

Schwinger-Dyson equations in large-N quantum field theories and nonlinear random processes

We propose a stochastic method for solving Schwinger-Dyson equations in large-N quantum field theories. Expectation values of single-trace operators are sampled by stationary probability distributions of the so-called nonlinear random processes. The set of all histories of such processes corresponds to the set of all planar diagrams in the perturbative expansions of the expectation values of singlet operators. We illustrate the method on the examples of the matrix-valued scalar field theory and the Weingarten model of random planar surfaces on the lattice. For theories with compact field variables, such as sigma-models or non-Abelian lattice gauge theories, the method does not converge in the physically most interesting weak-coupling limit. In this case one can absorb the divergences into a self-consistent redefinition of expansion parameters. Stochastic solution of the self-consistency conditions can be implemented as a "memory" of the random process, so that some parameters of the process are estimated from its previous history. We illustrate this idea on the example of two-dimensional O(N) sigma-model. Extension to non-Abelian lattice gauge theories is discussed.Comment: 16 pages RevTeX, 14 figures; v2: Algorithm for the Weingarten model corrected; v3: published versio

The electromagnetic form factors of the Omega in lattice QCD

We present results on the Omega baryon electromagnetic form factors using $N_f=2+1$ domain-wall fermion configurations for three pion masses in the range of about 350 to 300 MeV. We compare results obtained using domain wall fermions with those of a mixed-action (hybrid) approach, which combine domain wall valence quarks on staggered sea quarks, for a pion mass of about 350 MeV. We pay particular attention in the evaluation of the subdominant electric quadrupole form factor to sufficient accuracy to exclude a zero value, by constructing a sequential source that isolates it from the dominant form factors. The $\Omega^-$ magnetic moment, $\mu_{\Omega^{-}}$, the electric charge and magnetic radius, $\langle r^{2}_{E0/M1} \rangle$, are extracted for these pion masses. The electric quadrupole moment is determined for the first time using dynamical quarks.Comment: 13 pages, 10 Figure

Power corrections from decoupling of the charm quark

Decoupling of heavy quarks at low energies can be described by means of an effective theory as shown by S. Weinberg in Ref. [1]. We study the decoupling of the charm quark by lattice simulations. We simulate a model, QCD with two degenerate charm quarks. In this case the leading order term in the effective theory is a pure gauge theory. The higher order terms are proportional to inverse powers of the charm quark mass $M$ starting at $M^{-2}$. Ratios of hadronic scales are equal to their value in the pure gauge theory up to power corrections. We show, by precise measurements of ratios of scales defined from the Wilson flow, that these corrections are very small and that they can be described by a term proportional to $M^{-2}$ down to masses in the region of the charm quark mass

Delta electromagnetic form factors and quark transverse charge densities from lattice QCD

We discuss the techniques to extract the electromagnetic Delta form factors in Lattice QCD. We evaluate these form factors using dynamical fermions with smallest pion mass of about 350 MeV. We pay particular attention to the extraction of the electric quadrupole form factor that signals a deformation of the Delta. The magnetic moment of the $\Delta$ is extrapolated using a chiral effective field theory. Using the form factors we evaluate the transverse density distributions in the infinite momentum frame showing deformation in the Delta.Comment: 9 pages, 6 figures, Invited Talk at the 6th International Workshop on Chiral Dynamics, CD09, July 6-10, 2009, Bern, Switzerlan