arXiv subjects

Patrick R. Oare

Publications and source records attributed to Patrick R. Oare.

4 recordsLinked to original sources

arXiv2025

Moment problems and bounds for matrix-valued smeared spectral functions

Numerical analytic continuation arises frequently in lattice field theory, particularly in spectroscopy problems. This work shows the equivalence of common spectroscopic problems to certain classes of moment problems that have been studied thoroughly in the mathematical literature. Mathematical results due to Kovalishina enable rigorous bounds on smeared matrix-valued spectral functions, which are implemented numerically for the first time. The required input is a positive-definite matrix of Euclidean-time correlation functions; such matrices are routinely computed in variational spectrum studies using lattice quantum chromodynamics. This work connects the moment-problem perspective to recent developments using the Rayleigh--Ritz method and Lanczos algorithm. Possible limitations due to finite numerical precision are discussed.

hep-lat↗

arXiv2023

Gravitational form factors of the pion from lattice QCD

The two gravitational form factors of the pion, $A^π(t)$ and $D^π(t)$, are computed as functions of the momentum transfer squared $t$ in the kinematic region $0\leq -t< 2~\text{GeV}^2$ on a lattice QCD ensemble with quark masses corresponding to a close-to-physical pion mass $m_π\approx 170~\text{MeV}$ and $N_f=2+1$ quark flavors. The flavor decomposition of these form factors into gluon, up/down light-quark, and strange-quark contributions is presented in the $\overline{\text{MS}}$ scheme at energy scale $μ=2~\text{GeV}$, with renormalization factors computed nonperturbatively via the RI-MOM scheme. Using monopole and $z$-expansion fits to the gravitational form factors, we obtain estimates for the pion momentum fraction and $D$-term that are consistent with the momentum fraction sum rule and the next-to-leading order chiral perturbation theory prediction for $D^π(0)$.

hep-lat↗

arXiv2023

Hadronic Structure, Conformal Maps, and Analytic Continuation

We present a method for analytic continuation of retarded Green functions, including Euclidean Green functions computed using lattice QCD. The method is based on conformal maps and construction of an interpolation function which is analytic in the upper half plane. A novel aspect of our method is rigorous bounding of systematic uncertainties, which are handled by constructing the full space of interpolating functions (at each point in the upper half-plane) consistent with the given Euclidean data and the constraints of analyticity. The resulting Green function in the upper half-plane has an appealing interpretation as a smeared spectral function.

hep-lat↗

arXiv2022

Neutrinoless Double Beta Decay from Lattice QCD: The Short-Distance $π^-\rightarrowπ^+ e^- e^-$ Amplitude

This work presents a determination of potential short-distance contributions to the unphysical $π^-\rightarrowπ^+ e^- e^-$ decay through lattice QCD calculations. The hadronic contributions to the transition amplitude are described by the pion matrix elements of five Standard Model Effective Field Theory operators, which are computed on five ensembles of domain-wall fermions with $N_f = 2 + 1$ quark flavors with a range of heavier-than-physical values of the light quark masses. The matrix elements are extrapolated to the continuum, physical light-quark mass, and infinite volume limit using a functional form derived in chiral Effective Field Theory ($χ\mathrm{EFT}$). This extrapolation also yields the relevant low-energy constants of $χ\mathrm{EFT}$, which are necessary input for $χ\mathrm{EFT}$ calculations of neutrinoless double beta decay of nuclei.

hep-lat↗