arXiv subjects

Taku Izubuchi

Publications and source records attributed to Taku Izubuchi.

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 $d_n=-0.0050(4)(8)\barθ$ e$\cdot$fm. Comparison with the current experimental bound on nEDM implies constraint $|\barθ|\lesssim 10^{-11}$, 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.

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arXiv2026

First Lattice QCD Determination of Lepton-Flavor-Universality Ratios in Light-Meson Leptonic Decays

The ratio of electronic to muonic leptonic decay widths, $R_{e/μ}$, for the light mesons $π$ and $K$, provides a clean test of lepton flavor universality (LFU) and a sensitive probe of physics beyond the Standard Model. Its Standard-Model prediction is exceptionally precise, with the leading uncertainty associated with the structure-dependent (SD) radiative correction of $O(0.1\%)$. As experiments such as PIONEER and NA62 aim for unprecedented precision, this SD correction has become an essential ingredient in precision experiment--theory comparisons. We present the first lattice QCD$+$QED calculation of this SD correction at the physical pion mass and in the continuum limit. We employ the infinite-volume reconstruction (IVR) method with Coulomb-gauge photons, significantly reducing both statistical errors and finite-volume effects. We obtain the Standard-Model predictions, $R_{e/μ}=1.23501(10)\times10^{-4}$ for $π$ and $R_{e/μ}=2.47653(34)\times10^{-5}$ for $K$. Our results reduce the hadronic uncertainty in $R_{e/μ}$, provide the most precise Standard-Model predictions to date, and establish first-principles benchmarks for future high-precision tests of LFU.

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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, $\barθQ_{top}$. 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 $θ$-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 $d_n=-0.0050(4)^\text{stat}(8)^\text{sys}\barθ$ $e$ 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.

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arXiv2026

Isospin-breaking effects in inclusive hadronic $τ$ data for the muon $(g-2)$ from first principles

The knowledge of isospin-breaking effects in hadronic $τ$ decays is required for a high-precision determination of the Hadronic-Vacuum-Polarization contribution to $(g-2)_μ$ from experimental $τ$ data. In this work we present a strategy for their calculation in a fully inclusive setup from first-principles Lattice QCD+QED simulations. We separate radiative corrections in three infrared safe classes, which we study individually. We provide analytic expressions for their effects in the initial state and propose a strategy for final-state corrections directly in Euclidean space. We also examine the non-factorizable contributions and highlight the challenges associated with their analytic continuation from Euclidean to Minkowski space. By studying short-distance corrections in the context of momentum schemes, we provide a prescription for the renormalization of the individual terms at first order in the ispospin-breaking parameters.

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arXiv2026

Lattice Calculation of Short-Range Contributions to Neutrinoless Double-Beta Decay $π^-\toπ^+ ee$ at Physical Pion Mass

Neutrinoless double-beta ($0νββ$) decays provide an excellent probe for determining whether neutrinos are Dirac or Majorana fermions. The short-range matrix elements associated with the $π^- \to π^+ ee$ process contribute at leading order in the $0νββ$ decay channel $nn \to ppee$ through pion exchange between nucleons. However, current lattice calculations show notable discrepancies in predicting these short-range contributions. To address this issue, we perform a lattice QCD calculation of the $π^- \to π^+ ee$ matrix elements using domain wall fermion ensembles at the physical pion mass generated by the RBC and UKQCD Collaborations. To mitigate contamination from around-the-world effects, we develop a new method to reconstruct and subtract them directly from lattice data. We then perform a nonperturbative renormalization using the RI/SMOM scheme. Compared with previous studies, this work reduces the uncertainties in the matrix elements and provides an independent cross-check that helps to reconcile the discrepancies among previous lattice calculations.

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arXiv2026

Lattice Calculation of Light Meson Radiative Leptonic Decays

In this work, we perform a lattice QCD calculation of the branching ratios and the form factors of radiative leptonic decays $P \to \ell ν_\ell γ$ ($P = π, K$) using $N_f=2+1$ domain wall fermion ensembles generated by the RBC and UKQCD collaborations at the physical pion mass. We adopt the infinite volume reconstruction (IVR) method, which extends lattice data to infinite volume and effectively controls the finite volume effects. This study represents a first step toward a complete calculation of radiative corrections to leptonic decays using the IVR method, including both real photon emissions and virtual photon loops. For decays involving a final state electron, collinear radiative corrections, enhanced by the large logarithmic factors such as $\ln(m_π^2/m_e^2)$ and $\ln(m_K^2/m_e^2)$, can reach the level of $O(10\%)$ and are essential at the current level of theoretical and experimental precision. After including these corrections, our result for $π\to eν_eγ$ agrees with the PIBETA measurement; for $K \to eν_eγ$, our results are consistent with the KLOE data and exhibit a $1.7σ$ tension with E36; and for $K \to μν_μγ$, where radiative corrections are negligible, our results confirm the previously observed discrepancies between lattice results and the ISTRA/OKA measurements at large photon energies, and with the E787 results at large muon photon angles.

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arXiv2025

Gluon Unpolarized, Polarized, and Transversity GPDs from Lattice QCD: Lorentz-Covariant Parametrization (Part I)

We identify the matrix elements necessary to determine the leading-twist gluon generalized parton distributions (GPDs) $H_g,~E_g,~\wt{H}_g,~\wt{E}_g,~H^T_g,~E^T_g, \wt{H}^T_g ,~\wt{E}^T_g$ in lattice QCD calculations. We present a method to achieve a Lorentz-covariant parameterization of the matrix elements in terms of a linearly independent basis of tensor structures. This parameterization is crucial for projecting lattice QCD matrix elements onto light cone distributions. For the first time, we determine the corresponding components that project onto the linear combinations of invariant amplitudes, which reduce to the different gluon GPDs in the light cone limit and enable their separation in a lattice QCD calculation for spin-$0$ and spin-$\frac{1}{2}$ hadrons. Hence, this work lays the foundation for the numerical determination of the gluon GPDs from first-principle lattice QCD calculations, directly advancing our understanding of the mass and spin structures and mechanical properties of the nucleon, as well as the physics underlying deeply virtual Compton scattering and deeply virtual meson production in a range of experimental processes.

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arXiv2025

Polarized and unpolarized gluon PDFs: generative machine learning applications for lattice QCD matrix elements at short distance and large momentum

Lattice quantum chromodynamics (QCD) calculations share a defining challenge by requiring a small finite range of spatial separation $z$ between quark/gluon bilinears for controllable power corrections in the perturbative QCD factorization, and a large hadron boost $p_z$ for a successful determination of collinear parton distribution functions (PDFs). However, these two requirements make the determination of PDFs from lattice data very challenging. We present the application of generative machine learning algorithms to estimate the polarized and unpolarized gluon correlation functions utilizing short-distance data and extending the correlation up to $zp_z \lesssim 14$, surpassing the current capabilities of lattice QCD calculations. We train physics-informed machine learning algorithms to learn from the short-distance correlation at $z\lesssim 0.36$ fm and take the limit, $p_z \to \infty$, thereby minimizing possible contamination from the higher-twist effects for a successful reconstruction of the polarized gluon PDF. We also expose the bias and problems with underestimating uncertainties associated with the use of model-dependent and overly constrained functional forms, such as $x^α(1-x)^β$ and its variants to extract PDFs from the lattice data. We propose the use of generative machine learning algorithms to mitigate these issues and present our determination of the polarized and unpolarized gluon PDFs in the nucleon.

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arXiv2025

Improvement in Autocorrelation Times Measured by the Master-Field Technique using Field Transformation HMC in 2+1 Domain Wall Fermion Simulations

The Field-Transformation Hybrid Monte-Carlo (FTHMC) algorithm potentially mitigates the issue of critical slowing down by combining the HMC with a field transformation, originally proposed by Lüscher and motivated as trivializing the theory. For the transformation, we use a single invertible discrete smearing step inspired by the Wilson flow but which resembles a Jacobian-computable generalisation of the stout smearing step. This is applied to a system with Iwasaki gauge fields and 2+1 Domain-Wall fermions. We have studied the effect of different smearing parameter values on autocorrelation times of Wilson-flowed energies with different flow time. We have found a reduction of exponential autocorrelation times for infra-red observables such as Wilson flowed energy densities and topological charge densities when a larger value of the smearing parameter is used. The autocorrelation times of local observables are computed using an approach akin to the master-field technique, allowing us to estimate the effect of the field transformation with different parameters based on a small number of configurations.

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arXiv2024

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 $a_μ^\text{HLbL}=12.47(1.15)(0.95) \times 10^{-10}$ where the first error is statistical and the second systematic. The result is mainly based on the 2+1 flavor Möbius domain wall fermion ensemble with inverse lattice spacing $a^{-1} = 1.73~\mathrm{GeV}$, lattice size $L=5.5~\mathrm{fm}$, and $m_π= 139~\mathrm{MeV}$, 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.

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arXiv2024

$ΔI = 3/2$ and $ΔI = 1/2$ channels of $K\toππ$ decay at the physical point with periodic boundary conditions

We present a lattice calculation of the $K\toππ$ matrix elements and amplitudes with both the $ΔI = 3/2$ and 1/2 channels and $\varepsilon'$, the measure of direct $CP$ violation. We use periodic boundary conditions (PBC), where the correct kinematics of $K\toππ$ 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 $K\toππ$ 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 $K\toππ$ 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.

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arXiv2023

Decimation map in 2D for accelerating HMC

To accelerate the HMC with field transformation, we consider a variant of the trivializing map, the decimation map, which can be regarded as a coarse-graining transformation. Using the 2D $U(1)$ pure gauge model, combined with the guided Monte Carlo algorithm, we show that the integrated autocorrelation time of the topological charge can be exponentially improved in the wall clock time. Our study indicates that incorporating renormalization group picture is a powerful and essential ingredient to accelerate the HMC at large $β$.

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arXiv2023

The calculations of Nucleon Electric Dipole Moment using background field on Lattice QCD

Measurements of nucleon and nuclei Electric Dipole Moments (EDMs) play an important role in probing CP violation and exploring physics beyond the Standard Model. We extract the neutron EDM by measuring the energy shift of the nucleon two-point correlation function in the presence of a background field. The UV divergence of the topological charge density operator is mitigated using gradient flow, and the diffusion effect induced by the gradient flow process is included into the fit ansatz. Our calculations were carried out on two 2+1 DWF fermion, Iwasaki, gauge field ensembles generated by the RBC/UKQCD collaborations with inverse lattice spacing 1.73 GeV and pion masses of about 340 and 420 MeV.

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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.

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arXiv2023

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

The two pion channel in Lattice QCD has long been a primary testing ground for studying multiparticle scattering in finite volume QCD. With the development of sophisticated techniques such as distillation, it is possible to carefully study two-pion scattering in order to constrain associated low-energy constants. In this work, correlation functions with multiparticle interpolating operators are constructed to compute pion scattering phase shifts and scattering lengths in the isospin 0 and 2 channels with both sea and valence quarks at physical mass. Contamination from vacuum and thermal contributions are explicitly quantified with dedicated calculations and the results obtained after subtracting these nuisance terms are compared with the traditional correlator time series subtraction method. Two physical point ensembles with different lattice actions are used, and our finest ensemble gives results for scattering lengths and phase shifts consistent with phenomenology to within the reported statistical uncertainty.

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arXiv2022

Use of Schwinger-Dyson equation in constructing an approximate trivializing map

We construct an approximate trivializing map by using a Schwinger-Dyson equation. The advantage of this method is that: (1) The basis for the flow kernel can be chosen arbitrarily by hand. (2) It can be applied to the general action of interest. (3) The coefficients in the kernel are determined by lattice estimates of the observables, which does not require analytic calculations beforehand. We perform the HMC with the effective action obtained by the Schwinger-Dyson method, and show that we can have better control of the effective action than the known $t$-expansion construction. However, the algorithmic overhead is still large and overwhelming the gain though faster decorrelation is observed for long-range observables in some cases. This contribution reports the preliminary results of this attempt.

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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).

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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.

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