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The mini proceedings of the "Fourth International Workshop on the Extension Project for the J-PARC Hadron Experimental Facility (HEF-ex 2024) [https://kds.kek.jp/event/46965]" held at J-PARC, February 19-21, 2024, are presented. The workshop was devoted to discussing the physics case that connects both the present and the future Hadron Experimental Facility at J-PARC, covering a wide range of topics in flavor, hadron, and nuclear physics related to both experimental and theoretical activities being conducted at the facility.

In May 2024, the scientific community observed intense solar eruptions that resulted in an extreme geomagnetic storm and auroral extension, highlighting the need to document and quantify these events. This study mainly focuses on their quantification. The source active region (AR 13664) evolved from 113 to 2761 millionths of the solar hemisphere between 4 May and 14 May 2024. AR 13664's magnetic free energy surpassed 1033 erg on 7 May 2024, triggering 12 X-class flares. Multiple interplanetary coronal mass ejections (ICMEs) came out from this AR, accelerating solar energetic particles toward Earth. At least four ICMEs seemingly piled up to disturb the interplanetary space, according to the satellite data and interplanetary scintillation data. The shock arrival at 17:05 UT on 10 May 2024 significantly compressed the magnetosphere down to ~ 5.04 R_E, and triggered a deep Forbush decrease. GOES satellite data and ground-based neutron monitors confirmed a ground-level enhancement from 2 UT to 10 UT on 11 May 2024. The ICMEs induced extreme geomagnetic storms, peaking at a Dst index of -412 nT at 2 UT on 11 May 2024, marking the sixth-largest storm since 1957. The AE and AL indices showed extreme auroral extensions that located the AE/AL stations into the polar cap. We gathered auroral records at that time and reconstructed the equatorward boundary of the visual auroral oval to 29.8{\deg} invariant latitude. We compared naked-eye and camera auroral visibility, providing critical caveats on their difference. We also confirmed global enhancements of storm-enhanced density of the ionosphere., Comment: 39 pages, 20 figures, and 2 tables. Figures 15 and 17 will appear on the record version. Under Review

An HPGe detector equipped with a transistor reset preamplifier and readout with a CAEN DT5781 fast pulse digitizer was employed in the measurement of X-rays from kaonic lead at the DA$\Phi$NE $e^+e^-$ collider at the Laboratori Nazionali di Frascati of INFN. A thin scintillator in front of a lead target was used to select kaons impinging on it and to form the trigger for the HPGe detector. We present the results of the kaonic lead feasibility measurement, where we show that the resolution of the HPGe detector in regular beam conditions remains the same as that without the beam and that a satisfactory background reduction can be achieved. This measurement serves as a test bed for future dedicated kaonic X-rays measurements for the more precise determination of the charged kaon mass., Comment: 14 pages, 7 figures

This paper examines a trade execution game for two large traders in a generalized price impact model. We incorporate a stochastic and sequentially dependent factor that exogenously affects the market price into financial markets. Our model accounts for how strategic and environmental uncertainties affect the large traders' execution strategies. We formulate an expected utility maximization problem for two large traders as a Markov game model. Applying the backward induction method of dynamic programming, we provide an explicit closed-form execution strategy at a Markov perfect equilibrium. Our theoretical results reveal that the execution strategy generally lies in a dynamic and non-randomized class; it becomes deterministic if the Markovian environment is also deterministic. In addition, our simulation-based numerical experiments suggest that the execution strategy captures various features observed in financial markets.

In 1966, Pierre-Gilles de Gennes proposed a non-volatile mechanism for switching superconductivity on and off in a magnetic device. This involved a superconductor (S) sandwiched between ferromagnetic (F) insulators in which the net magnetic exchange field could be controlled through the magnetisation-orientation of the F layers. Because superconducting switches are attractive for a range of applications, extensive studies have been carried out on $F/S/F$ structures. Although these have demonstrated a sensitivity of the superconducting critical temperature ($T_{c}$) to parallel (P) and antiparallel (AP) magnetisation-orientations of the F layers, corresponding shifts in $T_c$ (i.e., ${\Delta}T_c = T_{c,AP} - T_{c,P}$) are lower than predicted with ${\Delta}T_c$ only a small fraction of $T_{c,AP}$, precluding the development of applications. Here, we report $EuS/Au/Nb/EuS$ structures where EuS is an insulating ferromagnet, Nb is a superconductor and Au is a heavy metal. For P magnetisations, the superconducting state in this structure is quenched down to the lowest measured temperature of 20 mK meaning that ${\Delta}T_c/T_{c,AP}$ is practically 1. The key to this so-called absolute switching effect is a sizable spin-mixing conductance at the $EuS/Au$ interface which ensures a robust magnetic proximity effect, unlocking the potential of $F/S/F$ switches for low power electronics.

From 1998 to 2017, neutron monitors located at an altitude of 4300 m on the Tibetan plateau detected 127 long-duration bursts of high-energy radiation in association with thunderclouds. These bursts typically lasted for 10 to 40 minutes, and 89\% of them occurred between 10:00 and 24:00 local time. They were also found to be more likely to occur at night, especially during 18:00$-$06:00 local time period. The observed diurnal and seasonal variations in burst frequency were consistent with the frequencies of lightning and precipitation on the Tibetan plateau. Based on 19 years of data, the present study suggests that an annual variation in burst frequency has a periodicity of $\sim$16 years and a lag of $\sim$3 years relative to solar activity., Comment: 28 pages, accepted for publication in Progress in Earth and Planetary Science

We conducted measurements of $K^- + {^3{\rm He}} \to \pi \!Y \!N + N'$ reactions using a $1~{\rm GeV}/c$ $K^-$-beam, with the objective of understanding the broad decay width of $\bar{K} \!N \!N$ (approximately twice as broad as that of $\Lambda(1405)$ considered to be the $\bar{K} \!N$ quasi-bound state). We successfully reproduced distributions of the $\pi \! Y \! N$ invariant mass and momentum transfer for $\pi \! Y \! N$ using model fitting functions for $\bar{K} \!N \!N$ formation and quasi-free $\bar{K}$ absorption (${\rm QF}_{\bar{K}-{\rm abs}}$) processes. The model can describe the experimental data quite well, and four $\bar{K} \! N \! N \to \pi \! Y \! N $ cross-sections were obtained. The results indicate that mesonic decay is the dominant decay branch of $\bar{K} \! N \! N$. The results also suggest that $\Gamma_{\pi \Lambda N} \sim \Gamma_{\pi \Sigma N}$, which indicates that the $I_{\bar{K} \! N}=1$ absorption channel, in addition to the $I_{\bar{K} \! N}=0$ absorption channel, substantially contribute to the $\bar{K} \! N \! N$ decay, making the $\bar{K} \! N \! N$ state approximately twice as unstable as $\Lambda$(1405).

We examine the $\Lambda$-${}^4\mathrm{He}$ ($\alpha$) momentum correlation in high-energy collisions to elucidate the interaction between Lambdas ($\Lambda$) and nucleons ($N$). We compare phenomenological $\Lambda\alpha$ potentials with different strengths at short range. In addition to the conventional Gaussian-type potentials, we construct the $\Lambda\alpha$ potentials by substituting the nucleon density distribution in $\alpha$ into the Skyrme-type $\Lambda$ potentials. We find that the dependence on the employed potential models is visible in the correlation functions from a small-size source. This indicates that the $\Lambda\alpha$ momentum correlation could constrain the property of the $\Lambda N$ interaction at high densities, which is expected to play an essential role in dense nuclear matter. Also, we verify that the Lednicky-Lyuboshits formula can yield erroneous results for a small-size source with a potential which has a large interaction range, like the $\Lambda\alpha$ system., Comment: 8 pages, 6 figures, Published version in PRC, typos are fixed

Iterative learning control (ILC) is capable of improving the tracking performance of repetitive control systems by utilizing data from past iterations. The aim of this paper is to achieve both task flexibility, which is often achieved by ILC with basis functions, and the performance of frequency-domain ILC, with an intuitive design procedure. The cost function of norm-optimal ILC is determined that recovers frequency-domain ILC, and consequently, the feedforward signal is parameterized in terms of basis functions and frequency-domain ILC. The resulting method has the performance and design procedure of frequency-domain ILC and the task flexibility of basis functions ILC, and are complimentary to each other. Validation on a benchmark example confirms the capabilities of the framework.

We have experimentally investigated the mechanism of the exchange bias in the 2D van der Waals (vdW) ferromagnets by means of the anomalous Hall effect (AHE) together with the dynamical magnetization property. The temperature dependence of the AC susceptibility with its frequency response indicates a glassy transition of the magnetic property for the Te-rich FeGeTe vdW ferromagnet. We also found that the irreversible temperature dependence in the anomalous Hall voltage follows the Almeida-Thouless line. Moreover, the freezing temperature of the spin-glass-like phase is found to correlate with the disappearance temperature of the exchange bias. These important signatures suggest that the emergence of magnetic exchange bias in the 2D van der Waals ferromagnets is induced by the presence of the spin-glass-like state in FeGeTe. The unprecedented insights gained from these findings shed light on the underlying principles governing exchange bias in vdW ferromagnets, contributing to the advancement of our understanding in this field., Comment: 21 pages, 4 figures

We estimate the spacetime profile of the electric field in head-on heavy-ion collisions at intermediate collision energies $\sqrt{s_{\rm NN}} = {\mathcal O}(3 \;-\; 10\;{\rm GeV})$. Using a hadronic cascade model (JAM; Jet AA Microscopic transport model), we numerically demonstrate that the produced field has strength $eE = {\mathcal O}((30 \;-\; 60\;{\rm MeV})^2)$, which is supercritical to the Schwinger limit of QED and is non-negligibly large compared even to the hadron/QCD scale, and survives for a long time $\tau = {\mathcal O}(10\;{\rm fm}/c)$ due to the baryon stopping. We show that the produced field is nonperturbatively strong in the sense that the nonperturbativity parameters (e.g., the Keldysh parameter) are sufficiently large. This is in contrast to high-energy collisions $\sqrt{s_{\rm NN}} \gtrsim 100 \;{\rm GeV}$, where the field is extremely short-lived and hence is perturbative. Our results imply that the electromagnetic field may have phenomenological impacts on hadronic/QCD processes in intermediate-energy heavy-ion collisions and that heavy-ion collisions can be used as a new tool to explore strong-field physics in the nonperturbative regime., Comment: 15 pages, 4 figures. v2: version to be published in PRC. Animations available on the author's website https://hidetoshitaya.github.io/misc/EMfieldinHIC.html

Potential contribution from gamma-ray sources to the Galactic diffuse gamma rays observed above 100 TeV (sub-PeV energy range) by the Tibet AS{\gamma} experiment is an important key to interpreting recent multi-messenger observations. This paper reveals a surprising fact: none of the 23 Tibet AS{\gamma} diffuse gamma-ray events above 398TeV within the Galactic latitudinal range of |b| < 10 deg. come from the 43 sub-PeV gamma-ray sources reported in the 1LHAASO catalog, which proves that these sources are not the origins of the Tibet AS{\gamma} diffuse gamma-ray events. No positional overlap between the Tibet AS{\gamma} diffuse gamma-ray events and the sub-PeV LHAASO sources currently supports the diffusive nature of the Tibet AS{\gamma} diffuse gamma-ray events, although their potential origin in the gamma-ray sources yet unresolved in the sub-PeV energy range cannot be ruled out., Comment: 5 pages, 2 figures Accepted for publication from The Astrophysical Journal Letters. arXiv admin note: text overlap with arXiv:2309.16078

Computational models are an essential tool for the design, characterization, and discovery of novel materials. Hard computational tasks in materials science stretch the limits of existing high-performance supercomputing centers, consuming much of their simulation, analysis, and data resources. Quantum computing, on the other hand, is an emerging technology with the potential to accelerate many of the computational tasks needed for materials science. In order to do that, the quantum technology must interact with conventional high-performance computing in several ways: approximate results validation, identification of hard problems, and synergies in quantum-centric supercomputing. In this paper, we provide a perspective on how quantum-centric supercomputing can help address critical computational problems in materials science, the challenges to face in order to solve representative use cases, and new suggested directions., Comment: 60 pages, 14 figures; comments welcome

Path signatures have been proposed as a powerful representation of paths that efficiently captures the path's analytic and geometric characteristics, having useful algebraic properties including fast concatenation of paths through tensor products. Signatures have recently been widely adopted in machine learning problems for time series analysis. In this work we establish connections between value functions typically used in optimal control and intriguing properties of path signatures. These connections motivate our novel control framework with signature transforms that efficiently generalizes the Bellman equation to the space of trajectories. We analyze the properties and advantages of the framework, termed signature control. In particular, we demonstrate that (i) it can naturally deal with varying/adaptive time steps; (ii) it propagates higher-level information more efficiently than value function updates; (iii) it is robust to dynamical system misspecification over long rollouts. As a specific case of our framework, we devise a model predictive control method for path tracking. This method generalizes integral control, being suitable for problems with unknown disturbances. The proposed algorithms are tested in simulation, with differentiable physics models including typical control and robotics tasks such as point-mass, curve following for an ant model, and a robotic manipulator., Comment: 48 pages, 21 figures

We present a quantum-classical hybrid algorithm for calculating the ground state and its energy of the quantum many-body Hamiltonian by proposing an adaptive construction of a quantum state for the quantum-selected configuration interaction (QSCI) method. QSCI allows us to select important electronic configurations in the system to perform CI calculation (subspace diagonalization of the Hamiltonian) by sampling measurement for a proper input quantum state on a quantum computer, but how we prepare a desirable input state has remained a challenge. We propose an adaptive construction of the input state for QSCI in which we run QSCI repeatedly to grow the input state iteratively. We numerically illustrate that our method, dubbed \textit{ADAPT-QSCI}, can yield accurate ground-state energies for small molecules, including a noisy situation for eight qubits where error rates of two-qubit gates and the measurement are both as large as 1\%. ADAPT-QSCI serves as a promising method to take advantage of current noisy quantum devices and pushes forward its application to quantum chemistry., Comment: 14 pages

In this paper we present the results of a new kaonic helium-4 measurement with a 1.37 g/l gaseous target by the SIDDHARTA-2 experiment at the DA{\Phi}NE collider. We measured, for the first time, the energies and yields of three transitions belonging to the Mseries. Moreover, we improved by a factor about three, the statistical precision of the 2p level energy shift and width induced by the strong interaction, obtaining the most precise measurement for gaseous kaonic helium, and measured the yield of the L{\alpha} transition at the employed density, providing a new experimental input to investigate the density dependence of kaonic atoms transitions yield., Comment: 12 pages, 5 figures, 3 tables

Cygnus-X is considered a region of interest for high-energy astrophysics, since the Cygnus OB2 association has been confirmed as a PeVatron in the Cygnus cocoon. In this research note, we present new high-resolution (16'') $^{12,13}$CO(J=1$\rightarrow$0) and C$^{18}$O (J=1$\rightarrow$0) observations obtained with the Nobeyama 45-m radiotelescope, to complement the Nobeyama Cygnus-X Survey. We discovered 19 new C$^{18}$O clumps associated with the star-forming regions DR-6W, DR-9, and DR13S. We present the physical parameters of these clumps, which are consistent with the neighboring covered regions. We confirm the clumpy nature of these regions and of a filament located between DR6 and DR6W. These results strongly suggest that star formation occurs in these regions with clumps of sizes $\sim$10$^{-1}$ pc, masses $\sim$10$^2$ M$_\odot$, and H$_2$ densities of $\sim$10$^4$ cm$^{-3}$., Comment: 8 pages, 3 Figures, 1 Table. https://pos.sissa.it/444/631/pdf

The SIDDHARTA-2 collaboration at the INFN Laboratories of Frascati (LNF) aims to perform groundbreaking measurements on kaonic atoms. In parallel and beyond the ongoing kaonic deuterium, presently running on the DA$\Phi$NE collider at LNF, we plan to install additional detectors to perform further kaonic atoms' studies, taking advantage of the unique low energy and low momentum spread $K^-$ beam delivered by the at-rest decay of the $\phi$ meson. CdZnTe devices are ideal for detecting transitions toward both the upper and lower levels of intermediate-mass kaonic atoms, like kaonic carbon and aluminium, which have an important impact on the strangeness sector of nuclear physics. We present the results obtained in a set of preliminary tests conducted on DA$\Phi$NE, in view of measurements foreseen in 2024, with the twofold aim to tune the timing window required to reject the extremely high electromagnetic background, and to quantify the readout electronics saturation effect due to the high rate, when placed close to the Interaction Region (IR). In the first test we used commercial devices and electronics, while for the second one both were customized at the IMEM-CNR of Parma and the University of Palermo. The results confirmed the possibility of finding and matching a proper timing window where to identify the signal events and proved better performances, in terms of energy resolution, of the custom system. In both cases, strong saturation effects were confirmed, accounting for a loss of almost 90\% of the events, which will be overcome by a dedicated shielding structure foreseen for the final experimental setup.

Integration of quantum chemistry simulations, machine learning techniques, and optimization calculations is expected to accelerate material discovery by making large chemical spaces amenable to computational study; a challenging task for classical computers. In this work, we develop a combined quantum-classical computing scheme involving the computational-basis Variational Quantum Deflation (cVQD) method for calculating excited states of a general classical Hamiltonian, such as Ising Hamiltonian. We apply this scheme to the practical use case of generating photochromic diarylethene (DAE) derivatives for photopharmacology applications. Using a data set of 384 DAE derivatives quantum chemistry calculation results, we show that a factorization-machine-based model can construct an Ising Hamiltonian to accurately predict the wavelength of maximum absorbance of the derivatives, $\lambda_{\rm max}$, for a larger set of 4096 DAE derivatives. A 12-qubit cVQD calculation for the constructed Ising Hamiltonian provides the ground and first four excited states corresponding to five DAE candidates possessing large $\lambda_{\rm max}$. On a quantum simulator, results are found to be in excellent agreement with those obtained by an exact eigensolver. Utilizing error suppression and mitigation techniques, cVQD on a real quantum device produces results with accuracy comparable to the ideal calculations on a simulator. Finally, we show that quantum chemistry calculations for the five DAE candidates provides a path to achieving large $\lambda_{\rm max}$ and oscillator strengths by molecular engineering of DAE derivatives. These findings pave the way for future work on applying hybrid quantum-classical approaches to large system optimization and the discovery of novel materials., Comment: 13pages, 9 figures

The fraction of the contribution from yet-unresolved gamma-ray sources in the Galactic diffuse gamma rays observed by the Tibet air shower array is an important key to interpreting recent multi-messenger observations. This paper shows a surprising fact: no Tibet diffuse events above 398TeV come from the gamma-ray sources newly detected above 100 TeV by LHAASO. Based on this observational fact, the contribution of sources unresolved by LHAASO to the Tibet diffuse events is estimated to be less than 31% above 398TeV with a 99% confidence level. Our result shows that unresolved sources make only a sub-dominant contribution to the Tibet diffuse events above 398 TeV and a large fraction of the events are truly a diffusive nature., Comment: Calculations in Eq-(2) should have used the probability p that a Tibet diffuse gamma-ray event is of unresolved-source origin, but the parameter p in Eq-(2) is the probability that a gamma-ray event above 398 TeV from a source marginally detected by LHAASO is detected by the Tibet. This mistake leads to a wrong estimate of the limit on the source fraction to the Tibet diffuse gamma-ray events

The path optimization method, which is proposed to control the sign problem in quantum field theories with continuous degrees of freedom by machine learning, is applied to a spin model with discrete degrees of freedom. The path optimization method is applied by replacing the spins with dynamical variables via the Hubbard-Stratonovich transformation, and the sum with the integral. The one-dimensional (Lenz-)Ising model with a complex coupling constant is used as a laboratory for the sign problem in the spin model. The average phase factor is enhanced by the path optimization method, indicating that the method can weaken the sign problem. Our result reproduces the analytic values with controlled statistical errors., Comment: 8 pages, 5 figures, version accepted for publication in Phys. Rev. D

Gamma rays from HESS J1849$-$000, a middle-aged TeV pulsar wind nebula (PWN), are observed by the Tibet air shower array and the muon detector array. The detection significance of gamma rays reaches $4.0\, \sigma$ and $4.4\, \sigma$ levels above 25 TeV and 100 TeV, respectively, in units of Gaussian standard deviation $\sigma$. The energy spectrum measured between $40\, {\rm TeV} < E < 320\, {\rm TeV}$ for the first time is described with a simple power-law function of ${\rm d}N/{\rm d}E = (2.86 \pm 1.44) \times 10^{-16}(E/40\, {\rm TeV})^{-2.24 \pm 0.41}\, {\rm TeV}^{-1}\, {\rm cm}^{-2}\, {\rm s}^{-1}$. The gamma-ray energy spectrum from the sub-TeV ($E < 1\, {\rm TeV}$) to sub-PeV ($100\, {\rm TeV} < E < 1\, {\rm PeV}$) ranges including the results of previous studies can be modeled with the leptonic scenario, inverse Compton scattering by high-energy electrons accelerated by the PWN of PSR J1849$-$0001. On the other hand, the gamma-ray energy spectrum can also be modeled with the hadronic scenario in which gamma rays are generated from the decay of neutral pions produced by collisions between accelerated cosmic-ray protons and the ambient molecular cloud found in the gamma-ray emitting region. The cutoff energy of cosmic-ray protons $E_{\rm p\, cut}$, cut is estimated at ${\rm log}_{10}(E_{\rm p,\, cut}/{\rm TeV}) = 3.73^{+2.98}_{-0.66}$, suggesting that protons are accelerated up to the PeV energy range. Our study thus proposes that HESS J1849$-$000 should be further investigated as a new candidate for a Galactic PeV cosmic-ray accelerator, PeVatron., Comment: 10 pages, 2 figures, Accepted for publication from the Astrophysical Journal

HESS J1843$-$033 is a very-high-energy gamma-ray source whose origin remains unidentified. This work presents, for the first time, the energy spectrum of gamma rays beyond $100\, {\rm TeV}$ from the HESS J1843$-$033 region using the data recorded by the Tibet air shower array and its underground muon detector array. A gamma-ray source with an extension of $0.34^{\circ} \pm 0.12^{\circ}$ is successfully detected above $25\, {\rm TeV}$ at $(\alpha,\, \delta) = (281.09^{\circ}\pm 0.10^{\circ},\, -3.76^{\circ}\pm 0.09^{\circ})$ near HESS J1843$-$033 with a statistical significance of $6.2\, \sigma$, and the source is named TASG J1844$-$038. The position of TASG J1844$-$038 is consistent with those of HESS J1843$-$033, eHWC J1842$-$035, and LHAASO J1843$-$0338. The measured gamma-ray energy spectrum in $25\, {\rm TeV} < E < 130\, {\rm TeV}$ is described with ${\rm d}N/{\rm d}E = (9.70\pm 1.89)\times 10^{-16} (E/40\, {\rm TeV})^{-3.26\pm 0.30}\, {\rm TeV}^{-1} {\rm cm}^{-2} {\rm s}^{-1}$, and the spectral fit to the combined spectra of HESS J1843$-$033, LHAASO J1843$-$0338, and TASG J1844$-$038 implies the existence of a cutoff at $49.5\pm 9.0\, {\rm TeV}$. Associations of TASG J1844-038 with SNR G28.6$-$0.1 and PSR J1844-0346 are also discussed in detail for the first time., Comment: 11 pages, 4 figures, 1 table

Within the TMEP, we present a detailed study of the performance of different transport models in Sn+Sn collisions at $270A$ MeV, and put particular emphasis on the production of pions and $\Delta$ resonances, which have been used as probes of the nuclear symmetry energy. We prescribe a common and rather simple physics model, and follow in detail the results of 4 BUU models and 6 QMD models. The nucleonic evolution of the collision and the nucleonic observables in these codes do not completely converge, but the differences among the codes can be understood as being due to several reasons: the basic differences between BUU and QMD models in the representation of the phase-space distributions, computational differences in the mean-field evaluation, and differences in the adopted strategies for the Pauli blocking in the collision integrals. For pionic observables, we find that a higher maximum density leads to an enhanced pion yield and a reduced $\pi^-/\pi^+$ yield ratio, while a more effective Pauli blocking generally leads to a slightly suppressed pion yield and an enhanced $\pi^-/\pi^+$ yield ratio. We specifically investigate the effect of the Coulomb force, and find that it increases the total $\pi^-/\pi^+$ yield ratio but reduces the ratio at high pion energies, although differences in its implementations do not have a dominating role in the differences among the codes. Taking into account only the results of codes that strictly follow the homework specifications, we find a convergence of the codes in the final charged pion yield ratio to a $1\sigma$ deviation of about $5\%$. However, the uncertainty is expected to be reduced to about $1.6\%$ if the same or similar strategies and ingredients, i.e., an improved Pauli blocking and calculation of the non-linear term in the mean-field potential, are similarly used in all codes., Comment: 39 pages, 17 figures

The repulsive three-body force between the lambda ($\Lambda$) hyperon and medium nucleons is a key element in solving the hyperon puzzle in neutron stars. We investigate the binding energies of $\Lambda$ hyperon in hypernuclei to verify the repulsive $\Lambda$ potentials from the chiral effective field theory ($\chi$EFT) employing the Skyrme Hartree-Fock method. We find that the $\chi$EFT $\Lambda$ potential with the $\Lambda NN$ three-body forces reproduces the existing hypernuclear binding energy data, whereas the $\Lambda$ binding energies are overestimated without the $\Lambda NN$ three-body force. Additionally, we search for the parameter space of the $\Lambda$ potentials by varying the Taylor coefficients of the $\Lambda$ potential and the effective mass of $\Lambda$ at the saturation density. Our analysis demonstrates that the parameter region consistent with the $\Lambda$ binding energy data spans a wide range of the parameter space, including even more repulsive potentials than the $\chi$EFT prediction. We confirm that these strong repulsive $\Lambda$ potentials suppress the presence of $\Lambda$ in the neutron star matter. We found that the $\Lambda$ potentials repulsive at high densities are favored when the depth of the $\Lambda$ potential at the saturation density, $U_\Lambda(\rho_0)=J_\Lambda$, is $J_\Lambda\gtrsim-29~\text{MeV}$, while attractive ones are favored when $J_\Lambda \lesssim -31~\text{MeV}$. This suggests that the future high-resolution data of hypernuclei could rule out the scenario in which $\Lambda$s appear through the precise determination of $J_\Lambda$ within the accuracy of $1~\text{MeV}$., Comment: 15 pages, 11 figures, 3 tables, figures updated and extended, (Published in Physical Review C)