arXiv subjects

Shoji Hashimoto

Publications and source records attributed to Shoji Hashimoto.

At least 19 recordsLinked to original sources

arXiv2026

Smeared spectral functions from lattice QCD: opportunities and challenges

A broad class of physical observables can be expressed in terms of smeared spectral functions. Important examples include the hadronic vacuum polarization contribution to the muon $g-2$, hadronic $\tau$ decays, inclusive semileptonic $B$ and $D$ decays, and amplitudes for rare processes such as $B\to K^{(*)}\ell^+\ell^-$. In recent years, a variety of methods have been proposed to reconstruct or constrain such spectral functions from Euclidean correlators and related inputs. However, the inverse problem is intrinsically ill-posed, making it difficult to obtain fully reliable, model-independent results with controlled uncertainties. In this contribution, I summarize recent developments, discuss the opportunities offered by smeared spectral observables, and highlight the main challenges that remain.

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arXiv2026

The QCD phase diagram for three-flavor M\"obius domain-wall fermions

We investigate the phase transition of Quantum Chromodynamics (QCD) with three degenerate quark flavors at zero baryon chemical potential. Using M\"{o}bius domain-wall fermions as the lattice fermion formulation, we ensure excellent chiral symmetry preservation. Our simulations are performed at three different temporal lattice extents, $N_{t}=6, 8, 12$, with a fixed lattice spacing $a=0.1361(20)$ fm, corresponding to temperatures of 242(4), 181(3), and 121(2) MeV, respectively. We explore a range of quark masses and spatial volumes with aspect ratios $N_{s}/N_{t}$ spanning from 2 to 4. By analyzing the mass and volume dependencies of the plaquette, plaquette susceptibility, chiral condensate, chiral susceptibilities, and Binder cumulant, we identify the pseudocritical transition quark masses from our largest lattice volumes. For $N_t=6$, this is 184(10) MeV (determined from the plaquette susceptibility). For $N_t=8$ and 12, the transition points vary slightly depending on whether the total or disconnected chiral susceptibility is used, yielding ranges of 36(1)-39.1(9) MeV and 3.5(3)-3.7(2) MeV, respectively, in the $\overline{\text{MS}}$ scheme at a scale of $\mu=2$ GeV. The negligible volume dependence at $N_t=6$ and 8, combined with finite-size scaling analysis at $N_t=12$ revealing volume growth significantly weaker than expected for a first- or second-order phase transition, points to a continuous crossover at these specific quark mass points. Additionally, we study the effects of residual chiral symmetry breaking on the chiral condensate and chiral susceptibilities using two different values of $L_s$.

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arXiv2026

Spectral reconstruction from Euclidean lattice correlators through singular value decomposition

Reconstructing spectral densities from Euclidean lattice correlators requires an inverse Laplace transform, which is inherently ill-conditioned when applied to numerical data with statistical uncertainties. The maximum amount of information that can be extracted from the imaginary-time dependence of correlators can be characterized by the singular value decomposition (SVD) of the kernel function $\exp(-\omega t)$ defined on discrete sets of imaginary times $t$ and energies $\omega$. The SVD provides orthogonal basis functions in both the $t$- and $\omega$-spaces, while the singular values determine the magnitude of their contributions to the correlators. By retaining only the components associated with the largest singular values, for which the correlator data remain statistically significant, one can reconstruct smeared spectral functions with controlled uncertainties. The systematic error arising from the truncation can also be bounded under reasonable assumptions. In the limit where the ranges of $t$ and $\omega$ become infinitely large and continuous, the SVD basis approaches the Mellin transform, allowing a representation of the smeared spectrum that is independent of the details of the lattice parameters.

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arXiv2026

Study on the systematic effects on $b \to c$ inclusive semileptonic decays

We discuss the calculation of the inclusive semileptonic decay for the process $B_s \to X_c \, l \nu_l$ using lattice QCD. This calculation could be decisive in understanding the long-standing tension between inclusive and exclusive determinations of the CKM matrix element, $|V_{cb}|$. In this talk, we investigate the main sources of systematic uncertainty in these decays, including the impact of Jacobi smearing at the source and sink, variations in source-sink separation, and the intrinsic uncertainties of the inclusive reconstruction method itself. In addition, we explain how we can restrict the reconstruction of the inclusive decay rate to just the excited-state contributions. This is achieved by treating the ground-state contributions as an exclusive decay with well-controlled conventional techniques. Systematic effects from the reconstruction then only affect excited-state contributions. Where these are sub-dominant, a suppression of systematic effects is expected. We show results based on Chebyshev reconstruction, which are part of a larger effort towards a first phenomenologically relevant computation of the inclusive decay rate in the continuum and infinite-volume limits.

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arXiv2026

Inclusive semileptonic $D_s\to X_s\ell\bar\nu$ decays from lattice QCD: continuum and chiral extrapolation

We present results for the inclusive semileptonic $D_s \to X_s \ell\bar\nu$ decay rate from lattice QCD. Chiral and continuum extrapolations are performed using gauge ensembles generated with 2+1 flavours of M\"obius domain-wall fermions. Systematic errors are fully addressed including those from the integral over all possible final states. Our results are in agreement with currently available experimental data, with an error at the few-percent level.

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arXiv2026

Quark Number Susceptibilities and Conserved Charge Fluctuations in $(2+1)$-flavor QCD with M\"obius domain-wall fermions (MDWF)

We calculate second- and selected fourth-order conserved-charge fluctuations in $(2+1)$-flavor QCD using M\"obius domain-wall fermions (MDWF) along a line of constant physics. Gauge ensembles were generated for two light-to-strange quark-mass ratios, $m_l/m_s=1/10$ and $1/27.4$, corresponding to heavier-than-physical and physical pion masses, respectively. For $m_l/m_s=1/10$, calculations were carried out on lattices with temporal extents $N_\tau=12$ and $16$, enabling an assessment of lattice-spacing effects at heavier pion mass. For $m_l/m_s=1/27.4$, calculations were performed at $N_\tau=12$, allowing us to study the light-quark-mass dependence down to the physical point. Below the pseudocritical temperature, second-order electric-charge, strangeness, and off-diagonal conserved-charge fluctuations are consistent with QMHRG2020 hadron resonance gas calculations. Across the crossover region, these observables rise rapidly and tend toward their Stefan--Boltzmann limits. Selected fourth-order cumulants were also computed at the physical pion mass. Although these observables are statistically more demanding, several channels with controlled uncertainties permit a first comparison with hadron resonance gas calculations.

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arXiv2026

Real radiative decays of heavy pseudoscalar mesons

We report our ongoing lattice QCD study of radiative leptonic decays of the charged pseudoscalar mesons $D$, $D_s$, $B$, and $B_c \to \ell \nu_\ell \gamma$. We carry out our analysis on a single JLQCD ensemble with lattice spacing $a=0.044~\text{fm}$. This work is a step towards a complete QCD+QED lattice calculation of these modes, aimed at reducing theoretical uncertainties in the extraction of $|V_{cd}|$ and $|V_{cs}|$ and providing first-principles estimates of the corresponding form factors in the $B$ sector.

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arXiv2026

Inclusive and exclusive semileptonic decays of heavy mesons on the lattice

We report the recent progress from our group in extracting observables of both inclusive and exclusive semileptonic heavy-meson decays directly from lattice QCD four-point correlators. On the inclusive side, we illustrate how to estimate the systematic uncertainties from omitted higher-order terms and non-zero smearing of the kernel approximation, building on two important features of the Chebyshev expansion. On the exclusive side, we perform BCL parameterizations of the pseudoscalar to pseudoscalar form factors and compare the fitted coefficients with those from earlier results by HPQCD. We also perform a HQET-based parameterization of the P-wave form factors to shed new light on the 1/2-vs-3/2 puzzle. This work constitutes a step toward a unified lattice treatment of inclusive and exclusive semileptonic decays, relevant for the Vcb puzzle. In this study, we use lattice ensembles from the RBC/UKQCD collaboration for numerical investigations. Future developments from our group will focus on the control of other systematic effects for inclusive decays and investigations of other techniques with reduced statistical errors to extract exclusive contributions from lattice four-point correlators.

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arXiv2025

Unbiased Krylov subspace method for the extraction of ground state from lattice correlators

Ground-state energy and matrix element are reconstructed from correlators in lattice QCD by diagonalizing transfer matrix $\hat{T}$ within the Krylov subspace spanned by $\hat{T}^n|\chi\rangle$, where $|\chi\rangle$ is a state generated by an interpolating field on the lattice. In numerical applications, this strategy is spoiled by statistical noise. To circumvent the problem, we introduce a low-rank approximation based on a singular-value decomposition of a matrix made of the correlators. The associated bias is eliminated by an extrapolation to the limit of vanishing variance of energy eigenvalue. The strategy is tested using a set of mock data as well as real data of $K$ and $D_s$ meson correlators.

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arXiv2025

Inclusive semileptonic decays from lattice QCD: analysis of systematic effects

Lattice QCD calculations of inclusive semileptonic decay rates involve new types of systematic effects, such as truncation errors in the estimation of energy integrals, or finite-volume effects for multi-body final states. We investigate them for the lattice data of $D_s \to X_s \ell\nu$ decays, obtained using M\"obius domain-wall fermions. Separating the ground-state and excited-state contributions results in better control over these systematic effects. With the Chebyshev polynomial approximation, the truncation error is under control, while the finite-volume effects are estimated using a model to describe two-body final states.

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arXiv2025

Inclusive processes from lattice QCD: problems and opportunities

A strategy to compute inclusive hadronic processes in lattice QCD is discussed. The key idea is to view the inclusive decay or scattering rate as a smeared spectrum. The Euclidean time dependence of correlators obtained on the lattice can be used to approximate them. The method induces its own systematic errors in addition to the standard discretization effects and so on. It is crucial to estimate them in a rigorous manner to achieve first-principles calculations of this important new class of quantities.

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arXiv2025

Study on the $P$-wave form factors contributing to $ B_s $ to $D_s$ inclusive semileptonic decays from lattice simulations

We present a pilot study on extracting the form factors of the semileptonic decay of a $ B_s $ meson to the $P$-wave $ D_s^{**} $ states from $B_s$ four-point correlators. With their inclusive nature, four-point correlators include contributions from all possible final states. From the extracted $ P $-wave form factors, we obtain numerical results for the corresponding Isgur-Wise form factors. The results suggest significant contributions from radial excitations to the Uraltsev sum rule at zero-recoil. In this pilot study, a coarse lattice of $ 24^3\times 64 $ with lattice spacing of $0.11\,\mathrm{fm}$ is used for the analysis.

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arXiv2025

Three flavor QCD phase transition with M\"obius domain wall fermions

We present an updated study of the $N_f=3$ QCD phase transition using M\"{o}bius domain wall fermions. Simulations were performed on $N_t=12$ lattices with aspect ratios ranging from 2 to 4 for various quark masses, at a lattice spacing of $a=0.1361(20)$ fm, corresponding to a temperature of 121(2) MeV. To clarify the nature of the phase transition, a large-volume lattice, $48^3 \times 12\times 16$, was added to analyze the volume dependence of disconnected chiral susceptibility. By examining the chiral condensate, disconnected chiral susceptibility, and Binder cumulant, and incorporating results from $24^3 \times 12 \times 16$ and $36^3 \times 12 \times 16$ lattices reported in earlier studies, we observe that the transition is consistent with a crossover at a quark mass of approximately $m_f^{\mathrm{\overline {MS}}}(2\, \mathrm{GeV}) \sim 4$ MeV at this temperature. Furthermore, we discuss the effects of residual chiral symmetry breaking on the chiral condensate and disconnected chiral susceptibility for different sizes in the 5th direction.

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arXiv2025

Symmetry of screening masses of mesons in two-flavor lattice QCD at high temperatures

We investigate spatial two-point correlation functions of mesonic operators in two-flavor lattice QCD at high temperatures. The simulated temperatures over the range $T \in [147, 330]$ MeV, where the critical temperature is estimated around 165 MeV. To ensure a good control of the chiral symmetry we employ the M\"obius domain-wall fermion action for two degenerate flavors of quarks. With a lattice cut off $a^{-1}\sim 2.6$ GeV, the residual mass is reduced to 0.14 MeV. With the energy spectrum obtained from the screening mass at incremental values of the temperature range, we examine the $SU(2)_L\times SU(2)_R$ chiral symmetry, the anomalous axial $U(1)$ as well as an enhanced symmetry which exchanges the spin degrees of freedom. We also study how the data approaches the perturbative prediction given by twice the Matsubara frequency of free quarks.

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arXiv2025

Quark number susceptibility and conserved charge fluctuation for (2+1)-flavor QCD with M\"obius domain wall fermions

We present quark number susceptibilities and conserved charge fluctuations for (2+1)-flavor QCD using M\"obius Domain Wall fermions with a pion mass of $135~\rm{MeV}$. Our results are compared with hadron resonance gas models below the QCD transition temperature and with $\mathcal{O}(g^2)$ perturbation theory at high temperatures. Additionally, we compare our findings with results from staggered fermion discretizations. Furthermore, we also present results of leading order Kurtosis of electric charge and strangeness fluctuations.

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arXiv2024

Study of symmetries in finite temperature $N_f=2$ QCD with M\"obius Domain Wall Fermions

We report on the ongoing study of symmetry of $N_f=2$ QCD around the critical temperature. Our simulations of $N_f = 2$ QCD employ the M\"obius domain-wall fermion action with residual mass $\sim 1\mbox{MeV}$ or less, maintaining a good chiral symmetry. Using the screening masses from the two point spatial correlators we compare the mass difference between channels connected through various symmetry transformations. Our analysis focuses on restoration of the $SU(2)_L\times SU(2)_R$ as well as anomalously broken axial $U(1)_A$. We also present additional study of a potential $SU(2)_{CS}$ symmetry which may emerge at sufficiently high temperatures.

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arXiv2024

Systematic effects in the lattice calculation of inclusive semileptonic decays

We report on the calculation of the inclusive semileptonic decay of the $D_s$ meson on the lattice. We simulate the $D_s \rightarrow X_s\ell\nu_\ell$ process with M\"obius domain-wall charm and strange quarks, whose masses are approximately tuned to their physical values. Our simulations cover the whole kinematical region. The focus of this work is to present updates on our strategies towards estimating the systematic uncertainties in the determination of the inclusive decay rate. We specifically focus on the systematic errors due to the choice of our approximation strategy and finite-volume effects.

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arXiv2024

Anatomy of finite-volume effect on hadronic vacuum polarization contribution to muon g-2

Low-energy spectrum relevant to the lattice calculation of hadronic vacuum polarization contribution to muon anomalous magnetic moment a_\mu is dominantly given by two-pion states satisfying L\"uscher's finite-volume quantization condition. Finite-volume effects from those states may exhibit power-law dependence on the volume, contrary to an exponential suppression as suggested by chiral effective theory. Employing the finite-volume state decomposition of Euclidean correlators, we systematically investigate the volume dependence and identify the different volume scalings depending on the region. Using phenomenological inputs for \pi \pi phase shift and time-like pion form factor, we obtain an estimate for the finite-volume effects on a_\mu, which is consistent with previous works. Numerical results are given for the ``window'' observables of a_\mu.

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