arXiv subjects

Wren Yamada

Publications and source records attributed to Wren Yamada.

5 recordsLinked to original sources

arXiv2026

$\bar{D}$-meson Nucleon Scattering from Lattice QCD at the Physical Point

We report the first lattice QCD study of the $s$-wave scattering of the $\bar{D}$-meson and the nucleon at the physical point, utilizing (2+1)-flavor configurations generated by the HAL QCD collaboration with a pion mass of $m_\pi\simeq 137$ MeV and a lattice spacing of $a\simeq0.084$ fm. By applying the HAL QCD method to the four-point correlation function of the $\bar{D}N$ system, we obtain a leading-order potential of the derivative expansion of the interaction kernel, which is then used to extract the $s$-wave phase shifts of low-energy $\bar{D}N$ scattering. Both the isospin $I=0$ and $I=1$ channels have a short-range repulsive core and a shallow attractive pocket in the intermediate to long-range region, though the $I=0$ channel is more attractive than the $I=1$ channel. We also observe that the $\bar{D}N$ potential exhibits more attraction than the $KN$ potential, which is its analog in the strange sector. In terms of the $s$-wave phase shifts, the $I=0$ channel shows a weak attractive behavior in the low-energy region with a positive scattering length of $0.246 \pm 0.105 (_{-0.051}^{+0.084})$ fm, whereas the $I=1$ channel shows repulsion with a negative scattering length of $-0.086 \pm 0.050 (_{-0.001}^{+0.037})$ fm. No bound states are found in both isospin channels, indicating the absence of a pentaquark state in the $s$-wave $\bar{D}N$ system.

hep-lat↗

arXiv2025

$S$-wave kaon-nucleon interactions from lattice QCD at the physical point

We investigate S-wave kaon-nucleon ($KN$) interactions with strangeness $S=+1$ in lattice QCD using the time-dependent HAL QCD method. Employing the $(2+1)$-flavor gauge configuration with $m_{\pi}\approx 137~\textrm{MeV}$ and $m_{K}\approx 502~\textrm{MeV}$, we calculate the $KN$ potentials at the leading order in the derivative expansion. The potentials in both isospin channels ($I=1$ and $I=0$) exhibit repulsion at short distances, while only the $I=0$ potential has a small attractive pocket at intermediate distances. From these potentials, we compute the phase shifts as well as the low-energy scattering parameters. The obtained phase shifts show no signals corresponding to resonances or bound states in both isospin channels, suggesting the absence of the $\Theta^{+}(1540)$ pentaquark in the S-wave $KN$ systems. The results for $I=0$ suggest that the scattering amplitudes in this channel are dominated by P-wave components rather than S-wave.

hep-lat↗

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↗

arXiv2021

Application of the Uniformized Mittag-Leffler Expansion to $Λ(1405)$

We study the pole properties of $Λ(1405)$ in a model-independent manner by applying the Uniformized Mittag-Leffler expansion proposed in our previous paper. The resonant energy, width and residues are determined by expanding the observable as a sum of resonant-pole pairs under an appropriate parameterization which expresses the observable to be single-valued, and fitting it to experimental data of the invariant-mass distribution of $π^+Σ^-$, $π^-Σ^+$, $π^0Σ^0$ final states in the reaction, $γp \rightarrow K^+ πΣ$, and the elastic and inelastic cross section, $K^-p\to K^-p$, $\bar{K}^0n$, $π^+Σ^-$, $π^-Σ^+$. As we gradually increase the number of pairs from one to three, the first pair converges while the second and third pairs emerge further and further away from the first pair, implying that the Uniformized Mittag-Leffler expansion with three pairs is almost convergent in the vicinity of the $Λ(1405)$. The broad peak structure between the $πΣ$ and $\bar{K} N$ thresholds regarded to be $Λ(1405)$ is explained by a single pair with a resonant energy of 1420 $\pm$ 1 MeV, and a half width of 48 $\pm$ 2 MeV, which is consistent with the single-pole picture of $Λ(1405)$. We conclude that the Uniformized Mittag-Leffler expansion turns out to be a very powerful method to obtain resonance energy, width and residues from the near-threshold spectrum.

hep-ph↗

arXiv2020

A New Method to Extract Information of Near-Threshold Resonances: Uniformized Pole-Sum Representation of Green's Function and T-matrix

We propose a new, simple model-independent method to extract information of near-threshold resonances, such as complex energies and residues. The method is based on the observation that the Green's function and the T-matrix can be represented as the sum of all poles, both bound and resonant poles, in the complex plane of a variable in which the Green's function and the T-matrix are single-valued functions. The symmetries of poles, which arise from the unitarity of the S-matrix, naturally impose the sum to obey the proper threshold behaviors. The imaginary part of Green's function and the T-matrix are directly related to observables such as scattering cross sections or invariant or missing mass distributions of hadron resonances. Thus we can determine their pole positions and residues by fitting their imaginary part to observables. We also test the new method by regarding the imaginary part of the $T$-matrix calculated exactly in a model theory as virtual experimental data. As a model theory, we take double-channel meson-baryon scatterings in the chiral unitary model with channels, $\overline{K}N (I=0)$, and $πΣ(I=0)$. By fitting the imaginary part of the $T$-matrix calculated in the model theory by that of the uniformized pole-sum, we obtain the pole positions and residues. Comparing the obtained results with those of the exact calculation in the model theory, we conclude that our new method works very well.

hep-ph↗