arXiv subjects

Toru Sato

Publications and source records attributed to Toru Sato.

At least 19 recordsLinked to original sources

arXiv2025

Contribution of Subthreshold States to the Residual Energy Distribution of $^{159}$Dy

We investigate the residual energy distribution in the electron capture (EC) process of $^{159}$Dy, emphasizing the role of subthreshold atomic states, which have typically been omitted in conventional spectral analyses. By incorporating these energetically forbidden hole states into the spectral function $P(E)$, we demonstrate a significant enhancement - over an order of magnitude - in the EC rate near the zero-momentum neutrino emission region. This enhancement increases further with larger $Q$ values, contrary to standard expectations. Our analysis shows that $P(E)$ can be experimentally determined, resolving ambiguities near the endpoint and enabling new approaches to 'ultra-low $Q$ value' EC reactions for neutrino mass studies.

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arXiv2025

Dynamical coupled-channel models for hadron dynamics

Dynamical coupled-channel (DCC) approaches parametrize the interactions and dynamics of two and more hadrons and their response to different electroweak probes. The inclusion of unitarity, three-body channels, and other properties from scattering theory allows for a reliable extraction of resonance spectra and their properties from data. We review the formalism and application of the ANL-Osaka, the Juelich-Bonn-Washington, and other DCC approaches in the context of light baryon resonances from meson, (virtual) photon, and neutrino-induced reactions, as well as production reactions, strange baryons, light mesons, heavy meson systems, exotics, and baryon-baryon interactions. Finally, we also provide a connection of the formalism to study finite-volume spectra obtained in Lattice QCD, and review applications involving modern statistical and machine learning tools.

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arXiv2025

Pole-Expansion of Two-Hadron Imaginary-Time Correlation Function -a new method of analysis for unstable states in lattice QCD-

We analyze the pole expansion of the two-hadron imaginary-time correlation function. We first explain the general idea that the imaginary-time correlation function is expressed as a sum of the pole terms, the Mittag-Leffler expansion, in terms of the uniformization variable, which makes the S-matrix single-valued. We then derive explicit expressions of the pole expansion for the single-channel ($\rho$ meson) and two-channel ($\Lambda(1405)$) examples and demonstrate that the pole expansion actually holds employing phenomenological models, the vector-dominance model for the $\rho$ meson and the chiral unitary model for $\Lambda(1405)$. From this observation we propose the pole expansion as a method to extract information of unstable states such as masses and widths from the two-hadron imaginary-time correlation functions obtained by lattice QCD simulations.

hep-lat↗

arXiv2023

Survival Probability of Unstable States in Coupled-Channels -- nonexponential decay of "threshold-cusp"

We investigate the survival probability of unstable states, the time-dependence of an initial state, in coupled channels. First, we extend the formulation of the survival probability from single channel to coupled channels (two channels). We derive an exact general expression of the two-channel survival probability using uniformization, a method which makes the coupled-channel S matrix single-valued, and the Mittag-Leffler expansion, i.e. a pole expansion. Second, we calculate the time dependence of the two-channel survival probability by employing the derived expression. It is the minimal distance between the pole and the physical region in the complex energy plane, not the imaginary part of the pole energy, which determines not only the energy spectrum of the Green's function but also the survival probability. The survival probability of the "threshold-cusp" caused by a pole on the unusual complex-energy Riemann sheet is shown to decay, not grow in time though the imaginary part of the pole energy is positive. We also show that the decay of the "threshold-cusp" is non-exponential. Thus, the "threshold-cusp" is shown to be a new type of unstable mode, which is found only in coupled channels.

hep-ph↗

arXiv2022

Neutrinoless Double Beta Decay and $<\eta>$ Mechanism in the Left-Right Symmetric Model

The neutrinoless double beta ($0\nu\beta\beta$) decay is studied in the framework of left-right symmetric model. The coexistence of left and right handed currents induces rather complicated interactions in the mixing of lepton and hadrons, called $<\lambda>$ mechanism and $<\eta>$ mechanism in addition to the conventional effective neutrino mass $ $ mechanism. In this letter we indicate the possible magnification of $<\eta>$ mechanism and importance to survey $0\nu\beta\beta$ decay of different nuclei for specifying New Physics beyond the Standard Model.

hep-ph↗

arXiv2022

Analytic Map of Three-Channel S Matrix -Generalized Uniformization and Mittag-Leffler Expansion-

We explore the analytic structure of the three-channel $S$ matrix by generalizing uniformization and making a single-valued map for the three-channel $S$ matrix. First, by means of the inverse Jacobi's elliptic function we construct a transformation from eight Riemann sheets of the center-of-mass energy squared complex plane onto a torus, on which the three-channel $S$ matrix is represented single-valued. Secondly, we show that the Mittag-Leffler expansion, a pole expansion, of the three-channel scattering amplitude includes not only topologically trivial but also nontrivial contributions and is given by the Weierstrass zeta function. Finally, we examine the obtained formula in the context of a simple three-channel model. Taking a simple non-relativistic effective field theory with contact interaction for the $S=-2$, $I=0$, $J^P = 0^+$, $\Lambda\Lambda-N\Xi-\Sigma\Sigma$ coupled-channel scattering, we demonstrate that the scattering amplitude as a function of the uniformization variable is, in fact, given by the Mittag-Leffler expansion with the Weierstrass zeta function and that it is dominated by contributions from neighboring poles.

hep-ph↗

arXiv2021

Near-threshold Spectrum from Uniformized Mittag-Leffler Expansion -Pole Structure of $Z(3900)$-

We demonstrate how S-matrix poles manifest themselves as the physical spectrum near the upper threshold in the context of the two-channel uniformized Mittag-Leffler expansion, an expression written as a sum of pole terms under an appropriate variable where the S-matrix is made single-valued (uniformization). We show that the transition of the spectrum is continuous as a S-matrix pole moves across the boundaries of the complex energy Riemann sheets and that the physical spectrum peaks at or near the upper threshold when the S-matrix pole is positioned sufficiently close to it on the uniformized plane. There is no essential difference on which sheet the pole is positioned. What is important is the existence of a pole near the upper threshold and the distance between the pole and the physical region, not on which complex energy sheet the pole is positioned. We also point out that when the pole is close to the upper threshold, the complex pole does not have the usual meaning of the resonance. Neither the real part represents the peak energy, nor the imaginary part represents the half width. Subsequently, we try to understand the current status of $Z(3900)$ from the viewpoint of the uniformized Mittag-Leffler expansion reflecting in particular, Phys.Rev.Lett.117, 242001 (2016) in which they concluded that $Z(3900)$ is not a conventional resonance but a threshold cusp. We point out that their results turn out to indicate the existence of S-matrix poles near the $\bar D D^*$ threshold, which is most likely the origin of the peak found in their calculation of the near-threshold spectrum. In order to support our argument, we set up a separable potential model which shares common behavior of poles near the $\bar D D^*$ threshold to the above-mentioned reference and show in our model that the structures near the $\bar D D^*$ threshold are indeed caused by these near-threshold poles.

hep-ph↗

arXiv2021

Classifying near-threshold enhancement using deep neural network

One of the main issues in hadron spectroscopy is to identify the origin of threshold or near-threshold enhancement. Prior to our study, there is no straightforward way of distinguishing even the lowest channel threshold-enhancement of the nucleon-nucleon system using only the cross-sections. The difficulty lies in the proximity of either a bound or virtual state pole to the threshold which creates an almost identical structure in the scattering region. Identifying the nature of the pole causing the enhancement falls under the general classification problem and supervised machine learning using a feed-forward neural network is known to excel in this task. In this study, we discuss the basic idea behind deep neural network and how it can be used to identify the nature of the pole causing the enhancement. The applicability of the trained network can be explored by using an exact separable potential model to generate a validation dataset. We find that within some acceptable range of the cut-off parameter, the neural network gives high accuracy of inference. The result also reveals the important role played by the background singularities in the training dataset. Finally, we apply the method to nucleon-nucleon scattering data and show that the network was able to give the correct nature of pole, i.e. virtual pole for ${}^1S_0$ partial cross-section and bound state pole for ${}^3S_0$.

hep-ph↗

arXiv2021

Unveiling the pole structure of S-matrix using deep learning

Particle scattering is a powerful tool to unveil the nature of various subatomic phenomena. The key quantity is the scattering amplitude whose analytic structure carries the information of the quantum states. In this work, we demonstrate our first step attempt to extract the pole configuration of inelastic scatterings using the deep learning method. Among various problems, motivated by the recent new hadron phenomena, we develop a curriculum learning method of deep neural network to analyze coupled channel scattering problems. We show how effectively the method works to extract the pole configuration associated with resonances in the $πN$ scatterings.

hep-ph↗

arXiv2021

Model independent analysis of coupled-channel scattering: a deep learning approach

We develop a robust method to extract the pole configuration of a given partial-wave amplitude. In our approach, a deep neural network is constructed where the statistical errors of the experimental data are taken into account. The teaching dataset is constructed using a generic S-matrix parametrization, ensuring that all the poles produced are independent of each other. The inclusion of statistical error results into a noisy classification dataset which we should solve using the curriculum method. As an application, we use the elastic $πN$ amplitude in the $I(J^P)=1/2(1/2^{-})$ sector where $10^6$ amplitudes are produced by combining points in each error bar of the experimental data. We fed the amplitudes to the trained deep neural network and find that the enhancements in the $πN$ amplitude are caused by one pole in each nearby unphysical sheet and at most two poles in the distant sheet. Finally, we show that the extracted pole configurations are independent of the way points in each error bar are drawn and combined, demonstrating the statistical robustness of our method.

hep-ph↗

arXiv2020

Classifying Pole of Amplitude Using Deep Neural Network

Most of exotic resonances observed in the past decade appear as peak structure near some threshold. These near-threshold phenomena can be interpreted as genuine resonant states or enhanced threshold cusps. Apparently, there is no straightforward way of distinguishing the two structures. In this work, we employ the strength of deep feed-forward neural network in classifying objects with almost similar features. We construct a neural network model with scattering amplitude as input and nature of pole causing the enhancement as output. The training data is generated by an S-matrix satisfying the unitarity and analyticity requirements. Using the separable potential model, we generate a validation data set to measure the network's predictive power. We find that our trained neural network model gives high accuracy when the cut-off parameter of the validation data is within $400$-$800\mbox{ MeV}$. As a final test, we use the Nijmegen partial wave and potential models for nucleon-nucleon scattering and show that the network gives the correct nature of pole.

hep-ph↗

arXiv2020

Neutron-neutron scattering length from $π^+$ photoproduction on the deuteron

We discuss the possibility of extracting the neutron-neutron scattering length $a_{nn}$ and effective range $r_{nn}$ from cross section data ($d^2σ/dM_{nn}/dΩ_π$), as a function of the $nn$ invariant mass $M_{nn}$, for $π^+$ photoproduction on the deuteron ($γd\to π^+nn$). The analysis is based on a $γd\to π^+nn$ reaction model in which realistic elementary amplitudes for $γp\to π^+n$, $NN\to NN$, and $πN\to πN$ are built in. We show that $M_{nn}$ dependence (lineshape) of a ratio $R_{\rm th}$, $d^2σ/dM_{nn}/dΩ_π$ normalized by $dσ/dΩ_π$ for $γp\toπ^+ n$ and the nucleon momentum distribution inside the deuteron, at the kinematics with $θ_π=0^\circ$ and $E_γ\sim 250$ MeV is particularly useful for extracting $a_{nn}$ and $r_{nn}$ from the corresponding data $R_{\rm exp}$. It is found that $R_{\rm exp}$ with 2% error, resolved into the $M_{nn}$ bin width of 0.04 MeV (corresponding to the $p_π$ bin width of 0.05 MeV$/c$), can determine $a_{nn}$ and $r_{nn}$ with uncertainties of $\pm 0.21$ fm and $\pm 0.06$ fm, respectively, for the case of $a_{nn}=-18.9$ fm and $r_{nn}=2.75$ fm. The requirement of such narrow bin widths indicates that the momenta of the incident photon and the emitted $π^+$ have to be measured with high resolutions. This can be achieved by utilizing virtual photons of very small $Q^2$ from electron scattering at Mainz MAMI facility. The proposed method for determining $a_{nn}$ and $r_{nn}$ from $γd\to π^+ nn$ has a great experimental advantage over the previous one utilizing $π^- d\toγnn$ for being free from the formidable task of controlling the neutron detection efficiency and its uncertainty.

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arXiv2019

Momentum distribution of the electron pair from the charged lepton flavor violating process $μ^-e^-\to e^-e^-$ in muonic atoms with a polarized muon

The $μ^-e^-\to e^-e^-$ process in a muonic atom is one of the promising probes to study the charged lepton flavor violation (CLFV). We have investigated the angular distribution of electrons from the polarized muon of the atomic bound state. The parity violating asymmetric distribution of electrons is analyzed by using lepton wave functions under the Coulomb interaction of a finite nuclear charge distribution. It is found that the asymmetry parameters of electrons are very sensitive to the chiral structure of the CLFV interaction and the contact/photonic interaction. Therefore, together with the atomic number dependence of the decay rate studied in our previous work, the angular distribution of electrons from a polarized muon should be a very useful tool to constrain the model beyond the standard model.

hep-ph↗

arXiv2017

Improved analysis for $μ^-e^-\to e^-e^-$ in muonic atoms by photonic interaction

Studies of the charged lepton flavor violating process of $μ^-e^-\to e^-e^-$ in muonic atoms by the four Fermi interaction [Y. Uesaka \textit{et al}., Phys. Rev. D {\bf 93}, 076006 (2016)] are extended to include the photonic interaction. The wave functions of a muon and electrons are obtained by solving the Dirac equation with the Coulomb interaction of a finite nuclear charge distribution. We find suppression of the $μ^-e^-\to e^-e^-$ rate over the initial estimation for the photonic interaction, in contrast to enhancement for the four Fermi interaction. It is due to the Coulomb interaction of scattering states and relativistic lepton wave functions. This finding suggests that the atomic number dependence of the $μ^-e^-\to e^-e^-$ rate could be used to distinguish between the photonic and the four Fermi interactions.

hep-ph↗

arXiv2016

Improved analyses for $μ^-e^-\rightarrow e^-e^-$ in muonic atoms by contact interactions

The charged lepton flavor violating (CLFV) processes of $μ^-e^-\rightarrow e^-e^-$ decay by four Fermi contact interactions in a muonic atom for various atoms are investigated. The wave functions of bound and scattering state leptons are properly treated by solving Dirac equations with Coulomb interaction of the finite nuclear charge distributions. This new effect contributes significantly in particular for heavier atoms, where the obtained decay rate is about one order of magnitude larger than the previous estimation for $^{208}$Pb. We find that, as the atomic number $Z$ increases, the $μ^-e^-\rightarrow e^-e^-$ decay rates increase more rapidly than the result of the previous work of $Z^3$, suggesting this decay as one of the promising processes to search for CLFV interaction.

hep-ph↗

arXiv2015

Improved analysis of the CLFV decay of muonic atoms $μ^-e^-\rightarrow e^-e^-$

Koike et al. proposed the charged lepton flavor violation (CLFV) decay of the muonic atom $μ^-e^-\rightarrow e^-e^-$ as one of the promising processes to search for new physics beyond the standard model. It was found that the attractive interaction of leptons with the nucleus enhances the transition rate of the $μ^-e^-\rightarrow e^-e^-$ process. We report on our improved analysis of this process by taking into account the distortion of the out-going electrons in the nuclear Coulomb potential and the relativistic treatment of the muon and the electrons. As results, we found significant enhancement of the transition rate. The transition rate for $^{208}$Pb becomes about 7 times larger than the previous estimation, which enhances the sensitivity of this process to discover the CLFV interaction. We also report on the energy spectrum of the out-going electron.

hep-ph↗

arXiv2015

Extraction of Neutrino Flux from the Inclusive Muon Cross Section

We have studied a method to extract neutrino flux from the data of neutrino-nucleus reaction by using maximum entropy method. We demonstrate a promising example to extract neutrino flux from the inclusive cross section of muon production without selecting a particular reaction process such as quasi-elastic nucleon knockout.

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arXiv2014

Linear programming analysis of the $R$-parity violation within EDM-constraints

The constraint on the $R$-parity violating supersymmetric interactions is discussed in the light of current experimental data of the electric dipole moment of neutron, $^{129}$Xe , $^{205}$Tl, and $^{199}$Hg atoms, and YbF and ThO molecules. To investigate the constraints without relying upon the assumption of the dominance of a particular combination of couplings over all the rest, an extensive use is made of the linear programming method in the scan of the parameter space. We give maximally possible values for the EDMs of the proton, deuteron, $^3$He nucleus, $^{211}$Rn, $^{225}$Ra, $^{210}$Fr, and the $R$-correlation of the neutron beta decay within the constraints from the current experimental data of the EDMs of neutron, $^{129}$Xe, $^{205}$Tl, and $^{199}$Hg atoms, and YbF and ThO molecules using the linear programming method. It is found that the $R$-correlation of the neutron beta decay and hadronic EDMs are very useful observables to constrain definite regions of the parameter space of the $R$-parity violating supersymmetry.

hep-ph↗