Agostino Patella

A bstract: Electromagnetic corrections to hadronic vacuum polarization contribute significantly to the uncertainty of the Standard Model prediction of the muon anomaly, which poses conceptual and numerical challenges for ab initio lattice determinations. In this study, we compute the non-singlet contribution from intermediate Euclidean current separations in quantum chromo- and electrodynamics (QCD+QED) using C ^⋆ boundary conditions in two ways: either non-perturbatively by sampling the joint probability distribution directly or by perturbatively expanding from an isospin-symmetric theory. This allows us to compare the predictions and their uncertainties at a fixed lattice spacing and volume, including fully the sea quarks effects in both cases. Treating carefully the uncertainty due to tuning to the same renormalized theory with N _f = 1 + 2 + 1 quarks, albeit with unphysical masses, we find it advantageous to simulate the full QCD+QED distribution given a fixed number of samples. This study lays the ground-work for further applications of C ^⋆ boundary conditions to study QCD+QED at the physical point, essential for the next generation of precision tests of the Standard Model.

A bstract: In this work we provide a non-perturbative solution to the theoretical problem of extracting scattering amplitudes from Euclidean correlators in infinite volume. We work within the solid axiomatic framework of the Haag-Ruelle scattering theory and derive formulae which can be used to approximate scattering amplitudes arbitrarily well in terms of linear combinations of Euclidean correlators at discrete time separations. Our result generalizes and extends the range of applicability of a result previously obtained by Barata and Fredenhagen [1]. We provide a concrete procedure to construct such approximations, making our formulae ready to be used in numerical calculations of non-perturbative QCD scattering amplitudes. A detailed numerical investigation is needed to assess whether the proposed strategy can lead to the calculation of scattering amplitudes with phenomenologically satisfactory precision with presently available lattice QCD data. This will be the subject of future work. Nevertheless, the numerical accuracy and precision of lattice simulations is systematically improvable, and we have little doubts that our approach will become useful in the future.

Accounting for isospin-breaking corrections is critical for achieving subpercent precision in lattice computations of hadronic observables. A way to include QED and strong-isospin-breaking corrections in lattice QCD calculations is to impose C^⋆ boundary conditions in space. Here, we demonstrate the computation of a selection of meson and baryon masses on two QCD and five QCD+QED gauge ensembles in this setup, which preserves locality, gauge and translational invariance all through the calculation. The generation of the gauge ensembles is performed for two volumes, and three different values of the renormalized fine-structure constant at the U-symmetric point, corresponding to the SU(3)-symmetric QCD in the two ensembles where the electromagnetic coupling is turned off. We also present our tuning strategy and, to the extent possible, a cost analysis of the simulations with C^⋆ boundary conditions.

This work employs the spectral reconstruction approach of ref. [1] to determine an inclusive rate in the 1 + 1 dimensional O(3) non-linear σ-model, analogous to the QCD part of e⁺e⁻ → hadrons. The Euclidean two-point correlation function of the conserved current j is computed using Monte Carlo lattice field theory simulations for a variety of spacetime volumes and lattice spacings. The spectral density of this correlator is related to the inclusive rate for j → X in which all final states produced by the external current are summed. The ill-posed inverse problem of determining the spectral density from the correlation function is made tractable through the determination of smeared spectral densities in which the desired density is convolved with a set of known smearing kernels of finite width ϵ. The smooth energy dependence of the underlying spectral density enables a controlled ϵ → 0 extrapolation in the inelastic region, yielding the real-time inclusive rate without reference to individual finite-volume energies or matrix elements. Systematic uncertainties due to cutoff effects and residual finite-volume effects are estimated and taken into account in the final error budget. After taking the continuum limit, the results are consistent with the known analytic rate to within the combined statistical and systematic errors. Above energies where 20-particle states contribute, the overall precision is sufficient to discern the four-particle contribution to the spectral density.

We present the results of testing a new technique for stochastic noise reduction in the calculation of propagators by implementing it in OpenQ*D for two ensembles with O(a) improved Wilson fermion action, with periodic boundary conditions and pion masses of 437 MeV and 331 MeV, for the connected vector and pseudoscalar correlators. We find that the technique yields no speedup compared to traditional methods, owning to the failure of its underlying assumption that the spectra of the spatial Laplacian and Dirac operators are sufficiently similar for the technique’s purposes.

We present the results of testing a new technique for stochastic noise reduction in the calculation of propagators by implementing it in OpenQ*D for two ensembles with O(a) improved Wilson fermion action, with periodic boundary conditions and pion masses of 437 MeV and 331 MeV, for the connected vector and pseudoscalar correlators. We find that the technique yields no speedup compared to traditional methods, owning to the failure of its underlying assumption that the spectra of the spatial Laplacian and Dirac operators are sufficiently similar for the technique's purposes.