The form factor that yields the light-by-light scattering contribution to the muon anomalous magnetic moment is computed in lattice QCD+QED and QED. A non-perturbative treatment of QED is used and is checked against perturbation theory. The hadronic
contribution is calculated for unphysical quark and muon masses, and only the diagram with a single quark loop is computed. Statistically significant signals are obtained. Initial results appear promising, and the prospect for a complete calculation with physical masses and controlled errors is discussed.
We present a new class of statistical error reduction techniques for Monte-Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in
the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation functions and masses of the pion, nucleon, and vector meson in $N_f=2+1$ lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte-Carlo calculations over conventional methods for the same cost.
We demonstrate the new class of variance reduction techniques for hadron propagator and nucleon isovector form factor in the realistic lattice of $N_f=2+1$ domain-wall fermion. All-mode averaging (AMA) is one of the powerful tools to reduce the stati
stical noise effectively for wider varieties of observables compared to existing techniques such as low-mode averaging (LMA). We adopt this technique to hadron two-point functions and three-point functions, and compare with LMA and traditional source-shift method in the same ensembles. We observe AMA is much more cost effective in reducing statistical error for these observables.
At stronger gauge-field couplings, the domain wall fermion (DWF) residual mass, a measure of chiral symmetry breaking, grows rapidly. This measure is largely due to near zero fermion eigenmodes of logarithm of the 4D transfer matrix along the fifth d
imension, and these eigenmodes increase rapidly at strong coupling. To suppress these eigenmodes, we have added to the DWF path integral a multiplicative weighting factor consisting of a ratio of determinants of Wilson-Dirac fermions having a chirally twisted mass with a large negative real component and a small imaginary chiral component. Numerical results show that this weighting factor with an appropriate choice of twisted masses significantly suppresses the residual mass while allowing adequate topological tunneling.
