arXiv subjects

Kohei Sato

Publications and source records attributed to Kohei Sato.

16 recordsLinked to original sources

arXiv2026

An improvement of model-independent method for meson charge radius calculation

We propose a variant of the model-independent method for determining meson charge radii from spatial moments of correlation functions on the lattice. Traditional determinations based on fits to the momentum transfer squared dependence of form factors are subject to systematic uncertainties arising from the choice of fit ansatz. By contrast, model-independent methods based on spatial moments provide a useful framework for determining the slope of the form factor without assuming its functional form. Recently, Feng et al. proposed a model-independent method, which drastically suppresses the finite-volume effect in the charge radius coming from higher-order contributions of the expansion of the form factor with respect to the momentum transfer squared. In this work, we introduce an auxiliary function of the momentum transfer squared and reformulate the method in terms of its product with the form factor, rather than the form factor itself, thereby further suppressing higher-order contributions, notably in cases of small volume and large radius. In particular, we investigate quadratic and logarithmic forms as practical choices for this auxiliary function. Applying this method to mock data based on a monopole form factor, as well as to actual lattice QCD data using $N_f=2+1$ gauge ensembles at $m_\pi \simeq 0.5$ and $0.3$ GeV, we find that it reduces residual finite-volume effects and provides an effective framework for meson charge radius determinations.

hep-lat↗

arXiv2026

Resolutions and deformations of cyclic quotient surface singularities

In this paper, we investigate the relations among various results concerning the minimal resolution of cyclic quotient singularities of the form $\mathbb{C}^2/G$. We refer to these as "bamboo-type" singularities, since the dual graphs of the exceptional curves in their resolutions resemble the shape of bamboo. We present classical results on the minimal resolution of singularities, the $G$-Hilbert scheme, the generalized McKay correspondence, deformations of singularities, and quiver varieties. These results have been obtained independently in different contexts, and here we provide a unified exposition enriched with numerous examples, which we hope will serve as a useful guide to the study of two-dimensional cyclic singularities. Moreover, this survey aims to offer insights that may inspire generalizations to non-cyclic singularities and to higher-dimensional quotient singularities.

math.AG↗

arXiv2026

Recent update of nucleon axial-vector charge with the PACS10 superfine lattice

We update the results of the nucleon axial-vector charge with the third ensemble of the PACS10 gauge configurations, which are generated by the PACS Collaboration at the physical point with lattice volume larger than $(10\;{\rm fm})^4$ and three different lattice spacings, 0.085 fm (coarse), 0.063 fm (fine) and 0.041 fm (superfine). Although the results of the first two ensembles generated at the coarse and fine lattice spacings are published, our study using the third one generated at the superfine lattice spacing is still underway. In this work, the low-energy relations arising from the partially conserved axial-vector current (PCAC) relation are also examined in terms of the nucleon three-point functions to verify whether the lattice QCD data correctly reproduces the physics in the continuum within the statistical accuracy.

hep-lat↗

arXiv2026

Special vs Essential

We show a correspondence between the compact exceptional curves and divisors on $G-{\rm Hilb}(\mathbf{C}^3)$ and some non-trivial irreducible representations of $G \subset GL(n,C)$ which are special (or essential). Moreover, we provide an explicit construction of the small resolution of $G-{\rm Hilb}(\mathbf{C}^3)$ and, using this resolution, we construct a correspondence between special and essential representations. These results are an extension of ``Special McKay correspondence'' and ``Reid's recipe''.

math.AG↗

arXiv2025

Investigating the axial structure of the nucleon based on large-volume lattice QCD at the physical point

We present a short summary for the calculations of the nucleon $\textit{isovector}$ form factors, which are relevant to improving the accuracy of the current neutrino oscillation experiments. The calculations are carried out with two of three sets of the $2+1$ flavor lattice QCD configurations generated at the physical point in large spatial volumes by the PACS Collaboration. The two gauge configurations are generated with the six stout-smeared $O(a)$ improved Wilson quark action and Iwasaki gauge action at the lattice spacing of $0.09$ fm and $0.06$ fm. We summarize the results for three form factors as well as the nucleon axial-vector ($g_A$), induced pseudoscalar ($g_P^*$) and pion-nucleon ($g_{\pi NN}$) couplings. Although our couplings agree with the experimental data, a firm conclusion should be drawn only after a continuum limit extrapolation is taken. We investigate the partially conserved axial-vector current (PCAC) relation in the context of the nucleon correlation functions. The low-energy relations arising from the PCAC relation can be used to verify whether the lattice QCD data correctly reproduce the physics in the continuum within the statistical accuracy. It is demonstrated that our $\textit{new analysis}$ reduces the systematic uncertainty for the induced pseudoscalar and pseudoscalar form factors to a greater extent than the $\textit{traditional analysis}$, and the results offer a theoretical insight into the pion-pole dominance model. Finally, we examine the applicable $q^2$ region for the low-energy relations.

hep-lat↗

arXiv2025

Method for high-precision determination of the nucleon axial structure using lattice QCD: Removing $\pi N$-state contamination

We performed a precise calculation of physical quantities related to the axial structure of the nucleon using 2+1 flavor lattice QCD gauge configuration (PACS10 configuration) generated at the physical point with lattice volume larger than $(10\;{\mathrm{fm}})^4$ by the PACS Collaboration. The nucleon matrix element of the axial-vector current has two types of the nucleon form factors, the axial-vector ($F_A$) form factor and the induced pseudoscalar ($F_P$) form factor. Recently lattice QCD simulations have succeeded in reproducing the experimental value of the axial-vector coupling, $g_A$, determined from $F_A(q^2)$ at zero momentum transfer $q^2=0$, at a percent level of statistical accuracy. However, the $F_P$ form factor so far has not reproduced the experimental values well due to strong $\pi N$ excited-state contamination. Therefore, we proposed a simple subtraction method for removing the so-called leading $\pi N$-state contribution, and succeeded in reproducing the values obtained by two experiments of muon capture on the proton and pion electro-production for $F_P(q^2)$. The novel approach can also be applied to the nucleon pseudoscalar matrix element to determine the pseudoscalar ($G_P$) form factor with the help of the axial Ward-Takahashi identity. The resulting form factors, $F_P(q^2)$ and $G_P(q^2)$, are in good agreement with the prediction of the pion-pole dominance model. In the new analysis, the induced pseudoscalar coupling $g_P^\ast$ and the pion-nucleon coupling $g_{\pi NN}$ can be evaluated with a few percent accuracy including systematic uncertainties using existing data calculated at two lattice spacings.

hep-lat↗

arXiv2025

A proposal for removing $\pi N$-state contamination from the nucleon induced pseudoscalar form factor in lattice QCD

In the PACS10 project, the PACS collaboration has generated three sets of the PACS10 gauge configurations at the physical point with lattice volume larger than $(10\;{\rm fm})^4$ and three different lattice spacings. The isovector nucleon form factors had been already calculated by using two sets of the PACS10 gauge configurations. In our strategy, the smearing parameters of the nucleon interpolation operator were highly optimized to eliminate as much as possible the contribution of excited states in the nucleon two-point function. This strategy was quite successful in calculations of the electric ($G_E$), magnetic ($G_M$) and axial-vector ($F_A$) form factors, while the induced pseudoscalar ($F_P$) and pseudoscalar ($G_P$) form factors remained strongly affected by residual contamination of $\pi N$-state contribution. In this work, we propose a simple method to remove the $\pi N$-state contamination from the $F_P$ form factor, and then evaluate the induced pseudoscalar charge $g_P^\ast$ and the pion-nucleon coupling $g_{\pi NN}$ from existing data in a new analysis. Applying this method to the $G_P$ form factor is also considered with a help of the axial Ward-Takahashi identity.

hep-lat↗

arXiv2024

Calculation of meson charge radii using model-independent method in the PACS10 configuration

We report our preliminary results for the charge radii of $\pi^{+}$ and $K^{+}$ mesons with the PACS10 configuration generated at the physical point using the Iwasaki gauge action and $N_{f}=2+1$ stout-smeared nonperturbatively $\mathcal{O}(a)$ improved Wilson quark action, especially at $0.085$ fm corresponding lattice size $128^4$. The charge radii are obtained from a model-independent method that directly calculates the first-order differential coefficient of the electromagnetic form factor and also from a traditional method that analyzes the form factor using a fit ansatz. We compare our preliminary results obtained by these methods with previous lattice calculations and experiments.

hep-lat↗

arXiv2024

Studies of nucleon isovector structure with the PACS10 superfine lattice

We present the results for the nucleon axial-vector, induced pseudoscalar and pion-nucleon couplings obtained from 2+1 flavor lattice QCD at the physical point with a large spatial extent of about 10 fm. Our calculations are performed with the PACS10 gauge configurations generated by the PACS Collaboration with the six stout-smeared $O(a)$ improved Wilson-clover quark action and Iwasaki gauge action at $\beta$ = 1.82, 2.00 and 2.20 corresponding to lattice spacings of 0.09 fm (coarse), 0.06 fm (fine) and 0.04 fm (superfine), respectively. We first evaluate the value of the nucleon axial-vector coupling. In addition, the induced pseudoscalar and pion-nucleon couplings from the induced pseudoscalar form factor are also investigated. Combining the results obtained from the all of our coarse, fine and superfine lattices, we finally discuss the systematic uncertainties in our calculation based on the comparison with both of the experimental values and lattice QCD results provided by the other collaborations.

hep-lat↗

arXiv2023

Nucleon form factors in $N_f=2+1$ lattice QCD at the physical point : finite lattice spacing effect on the root-mean-square radii

We present results for the nucleon form factors: electric ($G_E$), magnetic ($G_M$), axial ($F_A$), induced pseudoscalar ($F_P$) and pseudoscalar ($G_P$) form factors, using the second PACS10 ensemble that is one of three sets of $2+1$ flavor lattice QCD configurations at physical quark masses in large spatial volumes (exceeding $(10\ \mathrm{fm})^3$). The second PACS10 gauge configurations are generated by the PACS Collaboration with the six stout-smeared $O(a)$ improved Wilson quark action and Iwasaki gauge action at the second gauge coupling $\beta=2.00$ corresponding to the lattice spacing of $a=0.063$ fm. We determine the isovector electric, magnetic and axial radii and magnetic moment from the corresponding form factors, as well as the axial-vector coupling $g_A$. Combining our previous results for the coarser lattice spacing [E. Shintani et al., Phys. Rev. D99 (2019) 014510; Phys. Rev. D102 (2020) 019902 (erattum)], the finite lattice spacing effects on the isovector radii, magnetic moment and axial-vector coupling are investigated using the difference between the two results. It was found that the effect on $g_A$ is kept smaller than the statistical error of 2% while the effect on the isovector radii was observed as a possible discretization error of about 10%, regardless of the channel. We also report the partially conserved axial vector current (PCAC) relation using a set of nucleon three-point correlation functions in order to verify the effect by $O(a)$-improvement of the axial-vector current.

hep-lat↗

arXiv2023

Comparison with model-independent and dependent analyses for pion charge radius

Traditionally, there has been a method to extract the charge radius of a hadron based on the fits of its form factor with some model assumptions. In contrast, a completely different method has been proposed, which does not depend on the models. In this report, we explore several improvements to this model-independent method for analyzing the pion charge radius. Furthermore, we compare the results of the pion charge radius obtained from $N_{f}=2+1$ lattice QCD data at $m_π=0.51$ GeV using the three different methods: the traditional model-dependent method, the original model-independent method, and our improved model-independent method. In this comparison, we take into account systematic errors estimated in each analysis.

hep-lat↗

arXiv2023

Ronkin/Zeta Correspondence

The Ronkin function was defined by Ronkin in the consideration of the zeros of almost periodic function. Recently, this function has been used in various research fields in mathematics, physics and so on. Especially in mathematics, it has a closed connections with tropical geometry, amoebas, Newton polytopes and dimer models. On the other hand, we have been investigated a new class of zeta functions for various kinds of walks including quantum walks by a series of our previous work on Zeta Correspondence. The quantum walk is a quantum counterpart of the random walk. In this paper, we present a new relation between the Ronkin function and our zeta function for random walks and quantum walks. Firstly we consider this relation in the case of one-dimensional random walks. Afterwards we deal with higher-dimensional random walks. For comparison with the case of the quantum walk, we also treat the case of one-dimensional quantum walks. Our results bridge between the Ronkin function and the zeta function via quantum walks for the first time.

math-ph↗

arXiv2022

Calculation of the pion charge radius from an improved model-independent method

We propose a new improved model-independent method for calculating the pion charge radius. In a recently-proposed model-independent method for the pion charge radius, we find it difficult to compute the pion charge radius for small pole mass $M_{\rm{pole}}^2$ and volume due to systematic errors coming from finite volume effect and higher-order contamination of the Taylor expansion of the form factor. We circumvent this difficulty by introducing a new appropriate function and propose a modified method that can calculate the pion charge radius with less systematic errors in the small $M_{\rm{pole}}^2$ and volume cases. As preliminary results, we check that our improved model-independent method works well on a mockup data and also an actual lattice QCD data at the pion mass of 0.51 GeV.

hep-lat↗

arXiv2022

Gas Adsorption and Diffusion Behaviors in Interfacial Systems Composed of a Polymer of Intrinsic Microporosity and Amorphous Silica: A Molecular Simulation Study

We investigate the adsorption and diffusion behaviors of CO2, CH4, and N2 in interfacial systems composed of a polymer of intrinsic microporosity (PIM-1) and amorphous silica using grand canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations. We build model systems of mixed matrix membranes (MMMs) with PIM-1 chains sandwiched between silica surfaces. Gas adsorption analysis using GCMC simulations shows that gas molecules are preferentially adsorbed in microcavities distributed near silica surfaces, resulting in an increase in the solubility coefficients of CO2, CH4, and N2 compared to bulk PIM-1. In contrast, diffusion coefficients obtained from MD simulations and then calibrated using the dual-mode sorption model show different tendencies depending on gas species: CO2 diffusivity decreases in MMMs compared to PIM-1, whereas CH4 and N2 diffusivities increase. These differences are attributed to competing effects of silica surfaces: the emergence of larger pores as a result of chain packing disruption, which enhances gas diffusion, and a quadrupole-dipole interaction between gas molecules and silica surface hydroxyl groups, which retards gas diffusion. The former has a greater impact on CH4 and N2 diffusivities, whereas the latter has a greater impact on CO2 diffusivity due to the strong quadrupole-dipole interaction between CO2 and surface hydroxyls. These findings add to our understanding of gas adsorption and diffusion behaviors in the vicinity of PIM-1/silica interfaces, which are unobtainable in experimental studies.

cond-mat.mtrl-sci↗

arXiv2021

Hilbert desingularizations for three dimensional canonical cyclic quotient singularities

In this paper, we shall discuss Hilbert property of ${\rm Hilb}^{G}(\mathbb{C}^{3})$, Fujiki-Oka resolutions and iterated Fujiki-Oka resolutions for three dimensional canonical cyclic quotient singularities by using the classification shown by Ishida and Iwashita\cite{II}. Finally, we shall prove that there exists a Hilbert desingularization for any three dimensional canonical cyclic quotient singularity.

math.AG↗

arXiv2020

Crepant Property of Fujiki-Oka Resolutions for Gorenstein Abelian Quotient Singularities

We show a sufficient condition for Fujiki-Oka resolutions of Gorenstein abelian quotient singularities to be crepant in all dimensions by using Ashikaga's continuous fractions. Moreover, we prove that all three dimensional Gorenstein abelian quotient singularities possess a crepant resolution as a corollary. This alternative proof of existence needs only simple computations comparing with the results ever known.

math.AG↗