Christoph Lehner

We present a study using the distillation method to analyze the spectra of nucleon, nucleon-pion, and nucleon-pion-pion states in the positive-parity sector, as well as nucleon and nucleon-pion states in the negative-parity sector. The study uses seven domain-wall fermion ensembles with varying pion masses ( m π = 139 – 279 MeV ), lattice spacings ( a − 1 = 1.730 GeV and a − 1 = 2.359 GeV ) and volumes ( m π L = 3.8 – 7.5 ). To address the large number of contractions in this project, we implemented an algorithm to automate the contraction of nucleon-pion correlation functions that contain an arbitrary number of pions. In the positive-parity sector, we extrapolate the nucleon mass to the physical point. This study demonstrates the effectiveness of the distillation method for baryonic quantities with a focus on multihadronic states and establishes a foundation for future work.

The long-distance contribution of QED corrections to the hadronic vacuum polarization is particularly challenging to compute in lattice QCD + QED . Currently, it is one of the limiting factors toward matching the precision of the recent result by the Fermilab E989 experiment for the muon g − 2 . In this work, we present a method for obtaining high-precision results for this contribution by reconstructing exclusive finite-volume state contributions. We find relations between the pion-photon contributions of individual diagrams and demonstrate the reconstruction method with lattice QCD + QED data at a single lattice spacing of a − 1 ≈ 1.73 GeV and m π ≈ 275 MeV .

In previous work [D. Giusti, Methods for high-precision determinations of radiative-leptonic decay form factors using lattice QCD, ], we showed that form factors for radiative leptonic decays of pseudoscalar mesons can be determined efficiently and with high precision from lattice QCD using the “three-dimensional (3D) method,” in which three-point functions are computed for all values of the current insertion time and the time integral is performed at the data-analysis stage. Here, we demonstrate another benefit of the 3D method: the form factors can be extracted for any number of nonzero photon virtualities from the same three-point functions at no extra cost. We present results for the D s → ℓ ν γ * vector form factor as a function of photon energy and photon virtuality, for both positive and negative virtuality, for a single ensemble with 340 MeV pion mass and 0.11 fm lattice spacing. In our analysis, we separately consider the two different time orderings and the different quark flavors in the electromagnetic current. We discuss in detail the behavior of the unwanted exponentials contributing to the three-point functions, as well as the choice of fit models and fit ranges used to remove them for various values of the virtuality. While positive photon virtuality is relevant for decays to multiple charged leptons, negative photon virtuality suppresses soft contributions and is of interest in QCD-factorization studies of the form factors.

We develop an extended framework for the hybrid Monte Carlo (HMC) algorithm in lattice gauge theory by embedding the S U ( N ) group into the space of general complex matrices, M N ( C ) . Auxiliary directions will be completely factorized in the path integral, and the embedding does not alter the expectation values of the original theory. We perform the molecular dynamics updates by using the matrix elements of W ∈ M N ( C ) as the dynamical variables without group theoretic constraints. The framework enables us to introduce nonseparable Hamiltonians for the HMC in lattice gauge theory exactly, whose immediate application includes the Riemannian manifold HMC.

The separation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment into Euclidean windows allows for a tailored approach to address the different dominant challenges at short, intermediate, and long distances. We present a novel approach to compute the short-distance window without the need for using perturbative QCD. We combine a quenched continuum extrapolation using 18 lattice spacings ( 1.6 GeV ≲ a − 1 ≲ 6.1 GeV ) with a separate continuum extrapolation of the sea quark effects. This method allows for the computationally expensive sea quark effects to be estimated using only a smaller number of ensembles at coarser lattice spacings, while largely confining the logarithmic dependency of the continuum extrapolation to the quenched component.

We provide the first calculation of the Euclidean long-distance window of the isospin-symmetric light-quark connected contribution to the hadronic vacuum polarization for the muon g − 2 and find a μ LD , iso , conn , ud = 411.4 ( 4.3 ) ( 2.4 ) × 10 − 10 . We also provide the currently most precise calculation of the total isospin-symmetric light-quark connected contribution, a μ iso , conn , ud = 666.2 ( 4.3 ) ( 2.5 ) × 10 − 10 in the BMW20 world, which is more than 4 σ larger compared to the data-driven estimates of Boito [] and 1.7 σ larger compared to the lattice QCD result of BMW20.

The separation of the hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment into Euclidean windows allows for a tailored approach to address the different dominant challenges at short, intermediate, and long distances. We present a novel approach to compute the short-distance window without the need for using perturbative QCD. We combine a quenched continuum extrapolation using 18 lattice spacings ($1.6 \,\text{GeV} \lesssim a^{-1} \lesssim 6.1\,\text{GeV}$) with a separate continuum extrapolation of the sea-quark effects. This method allows for the computationally expensive sea-quark effects to be estimated using only a smaller number of ensembles at coarser lattice spacings, while largely confining the logarithmic dependency of the continuum extrapolation to the quenched component.