arXiv subjects

Thomas Blum

Publications and source records attributed to Thomas Blum.

At least 19 recordsLinked to original sources

arXiv2026

Calculation of neutron electric dipole moment from Lattice QCD

Experimental constraints on the neutron electric dipole moment (nEDM) may imply strong-CP problem in QCD, or unnatural smallness of the QCD theta angle. In this work, we present a novel determination of the neutron electric dipole moment (nEDM) $d_n$ sensitivity to theta term from nonperturbative QCD on a lattice with background electric field. Using Feynman-Hellmann theorem, we compute nEDM from the matrix element of local topological charge density between nucleon ground states spatially polarized by an electric field. These states have mixed spatial parity, and we construct them using variational analysis. We obtain statistically significant signal for the theta induced nEDM from lattices with 2+1 dynamical domain wall fermions corresponding to pion masses of 340, 420, and 576 MeV and lattice spacing $a\approx 0.11~\text{fm}$. After extrapolating to the physical point, we obtain $d_n=-0.0050(4)(8)\bar{\theta}$ e$\cdot$fm. Comparison with the current experimental bound on nEDM implies constraint $|\bar{\theta}|\lesssim 10^{-11}$, which confirms existence of the strong-CP problem in QCD. Our pioneering work demonstrates that neutron EDM can be reliably determined from the local density of topological charge with robust control of systematic effects, and can be directly extended to other CP-violating interactions.

hep-lat↗

arXiv2026

The Neutron Electric Dipole Moment from Lattice QCD using a Background Electric Field

We present the calculation of the neutron electric dipole moment (nEDM) $d_n$ using 2+1 flavor domain wall fermion ensembles with fixed lattice spacing $a\approx 0.11\,\text{fm}$ and pion masses of 340, 420, and 576 MeV. We show that the neutron electric dipole moment can be extracted from the energy shift induced by a static uniform external background electric field in the presence of the CP-violating QCD theta-term, $\bar\theta Q_{top}$. Motivated by the Feynman-Hellmann theorem, we employ sampling of the topological charge $q_\text{top}(t)$ on a single time-slice rather than the global topological charge $Q_\text{top}=\int q_\text{top}(t) \, dt$, which dramatically improves the statistical precision of the $\theta$-induced nEDM. Key to our method is to calculate the forward matrix element of the topological charge density in the nucleon deformed by a background electric field. We find that calculation with the traditional positive parity-projected nucleon operator is subject to large excited-state contamination. To remove the contamination, we construct the ground state of the deformed nucleon by solving a non-Hermitian generalized eigenvalue problem. With this approach, we find consistent values for the nEDM when using different nucleon interpolating operators, regardless of whether they are covariant or non-covariant under chiral transformations. Finally, after extrapolating to the physical point, we obtain $d_n=-0.0050(4)^\text{stat}(8)^\text{sys}\bar{\theta}$ $e$ fm, where the systematic uncertainty includes excited-state effects estimated as variation with the Euclidean-time fits and the dependence on the strength of the electric field applied to the neutron. Conventional systematic errors like discretization, finite-volume, and chiral extrapolation effects will be addressed in future work.

hep-lat↗

arXiv2026

Domain wall fermions

We introduce the formulation of domain wall fermions in the context of lattice QCD. We prove the recovery of exact chiral symmetry in the limit of an infinite fifth direction, and derive the effective four-dimensional operator satisfying the Ginsparg-Wilson relation obtained in this limit. We discuss the residual breaking of chiral symmetry for finite extent of the fifth direction, and how it is affected by spectral features of the Wilson kernel. We also discuss various improvements of domain wall fermions including notably M\"obius fermions. These notes are a chapter contributed to the on-line book ``Lattice QCD at 50 years'' (LQCD@50).

hep-lat↗

arXiv2026

The Light Quark Connected Hadronic Vacuum Polarization Contribution to the muon anomaly via Sparsened Meson Fields

We present an update on our determination of the light-quark connected contribution to the hadronic vacuum polarization (HVP) of the muon anomalous magnetic moment, $a_\mu$, on a finer lattice with 2+1+1 highly-improved staggered quark (HISQ) ensemble from the MILC collaboration with physical pion mass, 0.042 fm lattice spacing, and size $144^3 \times 288$ sites. Within the low-mode averaging (LMA) framework, the HVP correlator is decomposed into low-low (LL), high-low (HL), low-high (LH) and high-high (HH) components. Since the LL part dominates the total statistical uncertainty but is also the most computationally expensive to evaluate, we implement a sparsening strategy to construct the meson fields efficiently. This approach significantly reduces the computational cost while preserving signal quality. By combining the sparsened LL contribution with HL, LH and HH components, we achieve an improved determination of the light-quark connected HVP contribution to $a_\mu$.

hep-lat↗

arXiv2026

Progress on computing the hadronic vacuum polarization contribution to the muon anomalous magnetic moment with staggered fermions

We give an update of our calculation of the light-quark, connected, hadronic vacuum polarization contribution to the muon anomalous magnetic moment, or muon $g-2$. The update includes preliminary results on a $2 + 1 + 1$ highly-improved staggered quark (HISQ) ensemble from the MILC collaboration with physical pion mass, $0.042$ fm lattice spacing, and volume $144^3 \times 288$. We discuss code and algorithm improvements for these calculations to compute the vector-vector correlation function more efficiently.

hep-lat↗

arXiv2025

Machine-learning techniques as noise reduction strategies in lattice calculations of the muon $g-2$

Lattice calculations of the hadronic contributions to the muon anomalous magnetic moment are numerically highly demanding due to the necessity of reaching total errors at the sub-percent level. Noise-reduction techniques such as low-mode averaging have been applied successfully to determine the vector-vector correlator with high statistical precision in the long-distance regime, but display an unfavourable scaling in terms of numerical cost. This is particularly true for the mixed contribution in which one of the two quark propagators is described in terms of low modes. Here we report on an ongoing project aimed at investigating the potential of machine learning as a cost-effective tool to produce approximate estimates of the mixed contribution, which are then bias-corrected to produce an exact result. A second example concerns the determination of electromagnetic isospin-breaking corrections by combining the predictions from a trained model with a bias correction.

hep-lat↗

arXiv2024

Toward inclusive observables with staggered quarks: the smeared $R$~ratio

Inclusive hadronic observables are ubiquitous in particle and nuclear physics. Computation of these observables using lattice QCD is challenging due the presence of a difficult inverse problem. As a stepping stone to more complicated observables, we report on progress to compute the smeared $R$~ratio with staggered quarks using the spectral reconstruction algorithm of Hansen, Lupo, and Tantalo. We compare staggered-quark results on two ensembles to domain-wall results on a single ensemble and to the Bernecker-Meyer parameterization. This work utilizes two ensembles generated by the MILC collaboration using highly improved staggered quarks and one ensemble generated by the RBC/UKQCD collaboration using domain-wall quarks. Possible strategies for controlling opposite-parity effects associated with staggered quarks are discussed.

hep-lat↗

arXiv2023

$\Delta I = 3/2$ and $\Delta I = 1/2$ channels of $K\to\pi\pi$ decay at the physical point with periodic boundary conditions

We present a lattice calculation of the $K\to\pi\pi$ matrix elements and amplitudes with both the $\Delta I = 3/2$ and 1/2 channels and $\varepsilon'$, the measure of direct $CP$ violation. We use periodic boundary conditions (PBC), where the correct kinematics of $K\to\pi\pi$ can be achieved via an excited two-pion final state. To overcome the difficulty associated with the extraction of excited states, our previous work \cite{Bai:2015nea,RBC:2020kdj} successfully employed G-parity boundary conditions, where pions are forced to have non-zero momentum enabling the $I=0$ two-pion ground state to express the on-shell kinematics of the $K\to\pi\pi$ decay. Here instead we overcome the problem using the variational method which allows us to resolve the two-pion spectrum and matrix elements up to the relevant energy where the decay amplitude is on-shell. In this paper we report an exploratory calculation of $K\to\pi\pi$ decay amplitudes and $\varepsilon'$ using PBC on a coarser lattice size of $24^3\times64$ with inverse lattice spacing $a^{-1}=1.023$ GeV and the physical pion and kaon masses. The results are promising enough to motivate us to continue our measurements on finer lattice ensembles in order to improve the precision in the near future.

hep-lat↗

arXiv2023

Isospin 0 and 2 two-pion scattering at physical pion mass using all-to-all propagators with periodic boundary conditions in lattice QCD

A study of two-pion scattering for the isospin channels, $I=0$ and $I=2$, using lattice QCD is presented. Möbius domain wall fermions on top of the Iwasaki-DSDR gauge action for gluons with periodic boundary conditions are used for the lattice computations which are carried out on two ensembles of gauge field configurations generated by the RBC and UKQCD collaborations with physical masses, inverse lattice spacings of 1.023 and 1.378 GeV, and spatial extents of $L=4.63$ and 4.58 fm, respectively. The all-to-all propagator method is employed to compute a matrix of correlation functions of two-pion operators. The generalized eigenvalue problem (GEVP) is solved for a matrix of correlation functions to extract phase shifts with multiple states, two pions with a non-zero relative momentum as well as two pions at rest. Our results for phase shifts for both $I=0$ and $I=2$ channels are consistent with and the Roy Equation and chiral perturbation theory, though at this preliminary stage our errors for $I=0$ are large. An important outcome of this work is that we are successful in extracting two-pion excited states, which are useful for studying $K\toππ$ decay, on physical-mass ensembles using GEVP.

hep-lat↗

arXiv2023

Hadronic light-by-light contribution to the muon anomaly from lattice QCD with infinite volume QED at physical pion mass

The hadronic light-by-light scattering contribution to the muon anomalous magnetic moment, $(g-2$)/2, is computed in the infinite volume QED framework with lattice QCD. We report $a_\mu^\text{HLbL}=12.47(1.15)(0.95) \times 10^{-10}$ where the first error is statistical and the second systematic. The result is mainly based on the 2+1 flavor M\"obius domain wall fermion ensemble with inverse lattice spacing $a^{-1} = 1.73~\mathrm{GeV}$, lattice size $L=5.5~\mathrm{fm}$, and $m_\pi = 139~\mathrm{MeV}$, generated by the RBC-UKQCD collaborations. The leading systematic error of this result comes from the lattice discretization. This result is consistent with previous determinations.

hep-lat↗

arXiv2022

The muon anomalous magnetic moment: is the lattice spacing small enough?

We present new results for the light-quark connected part of the leading order hadronic-vacuum-polarization (HVP) contribution to the muon anomalous magnetic moment, using $2+1+1$ staggered fermions. We have collected more statistics on previous ensembles, and we added two new ensembles. This allows us to reduce statistical errors on the HVP contribution and related window quantities significantly. We also calculated the current-current correlator to next-to-next-to-leading order (NNLO) in staggered chiralperturbation theory, so that we can correct to NNLO for finite-volume, pion-mass mistuning and taste-breaking effects. We discuss the applicability of NNLO chiral perturbation theory, emphasizing that it provides a systematic EFT approach to the HVP contribution, but not to short- or intermediate-distance window quantities. This makes it difficult to assess systematic errors on the standard intermediate-distance window quantity that is now widely considered in the literature. In view of this, we investigate a longer-distance window, for which EFT methods should be more reliable. Our most important conclusion is that new high-statistics computations at lattice spacings significantly smaller than 0.06 fm are indispensable. The ensembles we use have been generously provided by MILC and CalLat.

hep-lat↗

arXiv2022

Lattice QCD and Particle Physics

Contribution from the USQCD Collaboration to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021).

hep-lat↗

arXiv2022

Report of the Snowmass 2021 Topical Group on Lattice Gauge Theory

Lattice gauge theory continues to be a powerful theoretical and computational approach to simulating strongly interacting quantum field theories, whose applications permeate almost all disciplines of modern-day research in High-Energy Physics. Whether it is to enable precision quark- and lepton-flavor physics, to uncover signals of new physics in nucleons and nuclei, to elucidate hadron structure and spectrum, to serve as a numerical laboratory to reach beyond the Standard Model, or to invent and improve state-of-the-art computational paradigms, the lattice-gauge-theory program is in a prime position to impact the course of developments and enhance discovery potential of a vibrant experimental program in High-Energy Physics over the coming decade. This projection is based on abundant successful results that have emerged using lattice gauge theory over the years: on continued improvement in theoretical frameworks and algorithmic suits; on the forthcoming transition into the exascale era of high-performance computing; and on a skillful, dedicated, and organized community of lattice gauge theorists in the U.S. and worldwide. The prospects of this effort in pushing the frontiers of research in High-Energy Physics have recently been studied within the U.S. decadal Particle Physics Planning Exercise (Snowmass 2021), and the conclusions are summarized in this Topical Report.

hep-lat↗

arXiv2022

The muon anomalous magnetic moment with staggered fermions: is the lattice spacing small enough?

We extend our previous work on the light-quark connected part, $a_μ^{\rm HVP,lqc}$, of the leading order hadronic-vacuum-polarization (HVP) contribution to the muon anomalous magnetic moment $a_μ$, using staggered fermions, in several directions. We have collected more statistics on ensembles with lattice spacings of $0.06$, $0.09$ and $0.12$ fm, and we added two new ensembles, both with lattice spacing $0.15$ fm, but with different volumes. The increased statistics allow us to reduce statistical errors on $a_μ^{\rm HVP,lqc}$ and related window quantities significantly. We also calculate the current-current correlator from which $a_μ^{\rm HVP,lqc}$ is obtained to next-to-next-to-leading order (NNLO) in staggered chiral perturbation theory, so that we can correct lattice values for $a_μ^{\rm HVP,lqc}$ to NNLO for finite-volume, pion-mass mistuning and taste-breaking effects. We discuss the applicability of NNLO chiral perturbation theory to $a_μ^{\rm HVP,lqc}$ and to the window quantities, emphasizing that it provides a systematic EFT approach to $a_μ^{\rm HVP,lqc}$, but not to short- or intermediate-distance window quantities. This makes it difficult to assess systematic errors on the standard intermediate-distance window quantity that is now widely considered in the literature. In view of this, we investigate a longer-distance window, for which EFT methods should be more reliable. Our most important conclusion is that, especially for staggered fermions, new high-statistics computations at lattice spacings smaller than $0.06$ fm are indispensable.

hep-lat↗

arXiv2022

Electric dipole moments and the search for new physics

Static electric dipole moments of nondegenerate systems probe mass scales for physics beyond the Standard Model well beyond those reached directly at high energy colliders. Discrimination between different physics models, however, requires complementary searches in atomic-molecular-and-optical, nuclear and particle physics. In this report, we discuss the current status and prospects in the near future for a compelling suite of such experiments, along with developments needed in the encompassing theoretical framework.

hep-ph↗

arXiv2022

Discovering new physics in rare kaon decays

The decays and mixing of $K$ mesons are remarkably sensitive to the weak interactions of quarks and leptons at high energies. They provide important tests of the standard model at both first and second order in the Fermi constant $G_F$ and offer a window into possible new phenomena at energies as high as 1,000 TeV. These possibilities become even more compelling as the growing capabilities of lattice QCD make high-precision standard model predictions possible. Here we discuss and attempt to forecast some of these capabilities.

hep-lat↗

arXiv2022

$K\toππ$ decay matrix elements at the physical point with periodic boundary conditions

We calculate $K\toππ$ matrix elements using periodic boundary conditions as an independent calculation from our previous study with G-parity boundary conditions. We present our preliminary results for $K\toππ$ three-point functions and matrix elements on a $24^3, a^{-1} = 1$~GeV, $2+1$-flavor Möbius DWF ensemble at physical pion and kaon masses generated by the RBC and UKQCD collaborations and discuss the prospect for high-precision computation of $\varepsilon'$ with periodic boundary conditions.

hep-lat↗

arXiv2021

The muon $g-2$ with four flavors of staggered quarks

We present updated results for the light-quark connected part of the leading hadronic contribution to the muon $g-2$ from configurations with 2+1+1 flavors of HISQ quarks using the time-momentum representation of the electromagnetic current correlator. We have added statistics on two ensembles as well as a fourth lattice spacing using configurations that have been generated by the MILC collaboration at the physical pion mass. Additionally we account for the leading finite-volume and taste-breaking effects using Staggered Chiral Perturbation Theory at NNLO.

hep-lat↗