arXiv subjects

Erik Lundstrum

Publications and source records attributed to Erik Lundstrum.

3 recordsLinked to original sources

arXiv2026

Isospin breaking corrections to a lattice QCD calculation of $\varepsilon'$

Because of the $ΔI = 1/2$ rule, the effects of electromagnetism and the isospin-breaking light quark mass difference on the direct CP violation parameter $\varepsilon'$ may be as large as 25\% and are consequently of immediate interest. In a lattice QCD calculation the effects of isospin breaking on the various features of kaon decay can be clearly distinguished and those effects enhanced by the $ΔI=1/2$ rule on $\varepsilon'$ explicitly identified. We show that all such enhanced effects can be captured in a QCD + QED lattice calculation in which the exchanged photon has an energy in an accessible, intermediate range between 0.5-2.0 GeV. Short-distance effects ($2.0 \mathrm{\ GeV} \lesssim E_γ$), usually treated in QCD and electroweak perturbation theory, are not enhanced by the $ΔI=1/2$ rule, beyond the well-understood contribution of the two electroweak penguin operators. Infrared photons do not contribute to $\varepsilon'$ while low-energy photons ($E_γ\lesssim 0.5$ GeV) are not $ΔI=1/2$ rule enhanced or are suppressed by one order in chiral perturbation theory (ChPT). An explicit ChPT estimate of this low-energy-photon contribution, a contribution that is difficult to determine in a finite-volume lattice calculation, suggests that the effect on $\varepsilon'$ is on the order of 0.5\%.

hep-lat↗

arXiv2025

Extended framework for the hybrid Monte Carlo in lattice gauge theory

We develop an extended framework for the hybrid Monte Carlo (HMC) algorithm in lattice gauge theory by embedding the $SU(N)$ group into the space of general complex matrices,$M_N(\mathbb{C})$. 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 $W \in M_N(\mathbb{C})$ as the dynamical variables without group theoretic constraints. The framework enables us to introduce non-separable Hamiltonians for the HMC in lattice gauge theory exactly, whose immediate application includes the Riemannian manifold HMC.

hep-lat↗

arXiv2025

Generalized HMC using Nambu mechanics for lattice QCD

I describe a generalization of the hybrid Monte Carlo (HMC) algorithm in which the molecular dynamics (MD) steps utilize Nambu generalized Hamiltonian dynamics. Characterized by multiple Hamiltonian functions, this formalism allows me to include forces from non-local objects in the MD evolution while preserving the target probability distribution. In this way, the changes proposed by the MD at one location can be made using instantaneous knowledge of the long-distance behavior of the gauge field to a degree beyond that usually provided by the fermion determinant. This represents a promising method for reducing critical slowing down in lattice QCD simulations.

hep-lat↗