We numerically investigate the transition of the static quark-antiquark string into a static-light mesonantimeson system. Improving noise reduction techniques, we are able to resolve the signature of string breaking dynamics for n f 2 lattice QCD at zero temperature. This result can be related to properties of quarkonium systems. We also study short-distance interactions between two static-light mesons.

We demonstrate the utility of a spectral approximation to fermion loop operators using low-lying eigenmodes of the hermitian Dirac-Wilson matrix, Q = γ5M . The investigation is based on a total of 400 full QCD vacuum configurations, with two degenerate flavors of dynamical Wilson fermions at β = 5.6, at two different sea quark masses. The spectral approach is highly competitive for accessing both topological charge and disconnected diagrams, on large lattices and small quark masses. We propose suitable partial summation techniques that provide sufficient saturation for estimating Tr Q −1 , which is related to the topological charge. In the effective mass plot of the η ′ meson we achieved a consistent early plateau formation, by ground state projecting the connected piece of its propagator. PACS: 11.15.Ha, 12.38.Gc 2 We employ the Arnoldi method as provided by the parallel Arnoldi Package PARPACK [23] from Rice University. The Arnoldi method is designed for non-hermitian matrices, but it reduces, when applied to a hermitian matrix, to the Lanczos method.

We present a review of the properties of generalized domain wall Fermions, based on a (real) Möbius transformation on the Wilson overlap kernel, discussing their algorithmic efficiency, the degree of explicit chiral violations measured by the residual mass (m res ) and the Ward-Takahashi identities. The Möbius class interpolates between Shamir's domain wall operator and Boriçi's domain wall implementation of Neuberger's overlap operator without increasing the number of Dirac applications per conjugate gradient iteration. A new scaling parameter (α) reduces chiral violations at finite fifth dimension (L s ) but yields exactly the same overlap action in the limit L s → ∞. Through the use of 4d Red/Black preconditioning and optimal tuning for the scaling α(L s ), we show that chiral symmetry violations are typically reduced by an order of magnitude at fixed L s . At large L s we argue that the observed scaling for m res = O(1/L s ) for Shamir is replaced by m res = O(1/L 2 s ) for the properly tuned Möbius algorithm with α = O(L s ).

A new class of domain wall fermions is defined that interpolates between Shamir's and Boriçi's form without increasing the number of Dirac applications per CG iteration. This class represents a full (real) Möbius transformation of the Wilson kernel. Simulations on quenched Wilson lattices with β = 6.0 show that the number of lattice sites (L s ) in the fifth dimension can be reduced by a factor of 2 or more at fixed value of chiral symmetry violations measured by the residual mass (m res ).

The magnetic dipole, the electric quadrupole and the Coulomb quadrupole amplitudes for the transition γN → ∆ are calculated in quenched lattice QCD at β = 6.0 with Wilson fermions. Using a new method combining an optimal combination of interpolating fields for the ∆ and an overconstrained analysis, we obtain statistically accurate results for the dipole form factor and for the ratios of the electric and Coulomb quadrupole amplitudes to the magnetic dipole amplitude, REM and RSM , up to momentum transfer squared 1.5 GeV 2 . We show for the first time using lattice QCD that both REM and RSM are non-zero and negative, in qualitative agreement with experiment and indicating the presence of deformation in the N-∆ system. PACS numbers: 11.15.Ha, 12.38.Gc, 12.38.Aw, 14.70.Dj Deformation is an important and well studied phenomenon in atomic and nuclear physics, and it is desirable to understand whether it also arises in low-lying hadrons and if so, why. For classical and quantum systems with spins larger than 1/2, the one-body quadrupole operator provides a convenient characterization of deformation. Experimentally, however, in the excited spin 3/2 ∆, which can have a non-zero quadrupole moment, it is not practical to measure it, and the spin 1/2 nucleon, which is easily accessible to measurement, cannot have a spectroscopic quadrupole moment. Hence, the experiment of choice to reveal the presence of deformation in the low-lying baryons is measuring the N -∆ transition amplitude, and significant effort has been devoted to photoproduction experiments on the nucleon at Bates [1] and Jefferson Lab [2] in order to measure to high accuracy the ratios of the electric (E2) and Coulomb (C2) quadrupole amplitudes to the magnetic dipole (M1) amplitude. If both the nucleon and the ∆ are spherical, then E2 and C2 are expected to be zero. Although M1 is indeed the dominant amplitude, there is mounting experimental evidence over a range of momentum transfers that E2 and C2 are non-zero [3]. Similarly in lattice QCD, for hadrons with spins larger than 1/2, the deformation is determined by measuring their quadrupole moment knowing the hadron wave function, which can be obtained via density correlators [4,5]. Using these techniques, it was shown that the rho has a non-spherical spatial distribution with a nonzero quadrupole moment and that the ∆ acquires a small deformation as the quark mass decreases [4]. However, direct contact with experiment is established by calculating the N to ∆ transition form factors.In this work we calculate these form factors as a function of the momentum transfer in lattice QCD in the quenched approximation on a lattice of size 32 3 × 64 at β = 6.0. We obtain, for the first time, accurate results for the E2 and C2 moments for momentum transfer squared, q 2 , up to about 1.5 GeV 2 . Our results are sufficiently accurate to exclude a zero value. The two novel aspects, as applied to the N to ∆ matrix elements, that are crucial for obtaining this accuracy are: 1) An optimal combination of three-point function...