No abstract

A method for computing electromagnetic properties of hadrons in lattice QCD is described and preliminary numerical results are presented. The electromagnetic field is introduced dynamically, using a noncompact formulation. Employing enhanced electric charges, the dependence of the pseudoscalar meson mass on the (anti)quark charges and masses can be accurately calculated. At $\beta=5.7$ with Wilson action, the $\pi^+-\pi^0$ splitting is found to be $4.9(3)$ MeV. Using the measured $K^0-K^+$ splitting, we also find $m_u/m_d = .512(6)$. Systematic errors are discussed

Approximate Markov chain Monte Carlo (MCMC) offers the promise of more rapid sampling at the cost of more biased inference. Since standard MCMC diagnostics fail to detect these biases, researchers have developed computable Stein discrepancy measures that provably determine the convergence of a sample to its target distribution. This approach was recently combined with the theory of reproducing kernels to define a closed-form kernel Stein discrepancy (KSD) computable by summing kernel evaluations across pairs of sample points. We develop a theory of weak convergence for KSDs based on Stein's method, demonstrate that commonly used KSDs fail to detect non-convergence even for Gaussian targets, and show that kernels with slowly decaying tails provably determine convergence for a large class of target distributions. The resulting convergence-determining KSDs are suitable for comparing biased, exact, and deterministic sample sequences and simpler to compute and parallelize than alternative Stein discrepancies. We use our tools to compare biased samplers, select sampler hyperparameters, and improve upon existing KSD approaches to one-sample hypothesis testing and sample quality improvement.

We relate the energy-momentum-tensor trace anomaly in spin-1/2 quantum electrodynamics to the functions P(a), &(a) defined through the Callan-Symanzik equations, and prove finiteness of B,, when the anomaly is taken into account.

The scalar, isovector meson propagator is analyzed in quenched QCD, using the MQA pole-shifting ansatz to study the chiral limit. In addition to the expected short-range exponential falloff characteristic of a heavy scalar meson, the propagator also exhibits a longer-range, negative metric contribution which becomes pronounced for smaller quark masses. We show that this is a quenched chiral loop effect associated with the anomalous structure of the η ′ propagator in quenched QCD. Both the time dependence and the quark mass dependence of this effect are well-described by a chiral loop diagram corresponding to an η ′ -π intermediate state, which is light and effectively of negative norm in the quenched approximation. The relevant parameters of the effective Lagrangian describing the scalar sector of the quenched theory are determined.