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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.

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 present a new measurement of the $^4_\Lambda$H hypernuclear lifetime using in-flight $K^-$ + $^4$He $\rightarrow$ $^4_\Lambda$H + $\pi^0$ reaction at the J-PARC hadron facility. We demonstrate, for the first time, the effective selection of the hypernuclear bound state using only the $\gamma$-ray energy decayed from $\pi^0$. This opens the possibility for a systematic study of isospin partner hypernuclei through comparison with data from ($K^-$, $\pi^-$) reaction. As the first application of this method, our result for the $^4_\Lambda$H lifetime, $\tau(^4_\Lambda \mathrm{H}) = 206 \pm 8 (\mathrm{stat.}) \pm 12 (\mathrm{syst.})\ \mathrm{ps}$, is one of the most precise measurements to date. We are also preparing to measure the lifetime of the hypertriton ($^3_\Lambda$H) using the same setup in the near future.

We measured a set of $\pi^\pm\Sigma^\mp$, $\pi^0\Sigma^0$, and $\pi^-\Sigma^0$ invariant mass spectra below and above the $\bar{K}N$ mass threshold in $K^-$-induced reactions on deuteron. We deduced the $S$-wave $\bar{K}N\rightarrow\pi\Sigma$ and $\bar{K}N\rightarrow\bar{K}N$ scattering amplitudes in the isospin 0 channel in the framework of a $\bar{K}N$ and $\pi\Sigma$ coupled channel. We find that a resonance pole corresponding to $\Lambda(1405)$ is located at 1417.7$^{+6.0}_{-7.4}$(fitting errors)$^{+1.1}_{-1.0}$(systematic errors) + $[-26.1^{+6.0}_{-7.9}$(fitting errors)$^{+1.7}_{-2.0}$(systematic errors)]$i$ MeV/$c^2$, closer to the $\bar{K}N$ mass threshold than the value determined by the Particle Data Group., Comment: 8 pages, 5 figures

$\bar K$-nuclear bound systems, kaonic nuclei, have been widely discussed as products of the strongly attractive $\bar K N$ interaction in $I = 0$ channels. Recently, we demonstrated that kaonic nuclei can be produced via in-flight $(K^-,N)$ reactions using the low-momentum DC kaon beam at the J-PARC E15 experiment. We observed the simplest kaonic nuclei, $K^-pp$, having a much deeper binding energy than normal nuclei. For further studies, we have proposed a series of experimental programs for the systematic investigation of light kaonic nuclei, from $\bar K N$ ($\Lambda(1405)$) to $\bar K NNNN$. In the new experiment approved as J-PARC E80, we will measure the $\bar K NNN$ ($A=3$) system as a first step toward a comprehensive study., Comment: 10 pages, 5 figures, proceedings of the 8th Asia-Pacific Conference on Few-Body Problems in Physics (APFB2020), accepted for publication in Fwe-Body Systems

We have performed an exclusive measurement of the $K^{-}+\! ~^{3}{\rm He} \to \Lambda pn$ reaction at an incident kaon momentum of $1\ {\rm GeV}/c$.In the $\Lambda p$ invariant mass spectrum, a clear peak was observed below the mass threshold of $\bar{K}\!+\!N\!+\!N$, as a signal of the kaonic nuclear bound state, $\bar{K}NN$.The binding energy, decay width, and $S$-wave Gaussian reaction form-factor of this state were observed to be $B_{K} = 42\pm3({\rm stat.})^{+3}_{-4}({\rm syst.})\ {\rm MeV}$, $\Gamma_{K} = 100\pm7({\rm stat.})^{+19}_{-9}({\rm syst.})\ {\rm MeV}$, and $Q_{K} = 383\pm11({\rm stat.})^{+4}_{-1}({\rm syst.})\ {\rm MeV}/c$, respectively. The total production cross-section of $\bar{K}NN$, determined by its $\Lambda p$ decay mode, was $\sigma^{tot}_{K} \cdot BR_{\Lambda p} = 9.3\pm0.8({\rm stat.})^{+1.4}_{-1.0}({\rm syst.})\ \mu{\rm b}$.We estimated the branching ratio of the $\bar{K}NN$ state to the $\Lambda p$ and $\Sigma^{0}p$ decay modes as $BR_{\Lambda p}/BR_{\Sigma^{0}p} \sim 1.7$, by assuming that the physical processes leading to the $\Sigma N\!N$ final states are analogous to those of $\Lambda pn$., Comment: 13 pages, 12 figures

Hadron scattering and production uncertainties are a limiting systematic on accelerator and at-mospheric neutrino flux predictions. New hadron measurements are necessary for neutrino fluxpredictions with well-understood and reduced uncertainties. We propose a new compact experimentto measure hadron scattering and production cross sections at beam energies that are inaccessibleto currently operating experiments. These measurements can reduce the current 10% neutrino fluxuncertainties by an approximate factor of two.

This write-up document is a summary of International workshop on the project for the extended hadron experimental facility which was held from March 26 to 28, 2018 at KEK Tokai Campus. This document is a collection of Letter Of Intents (LOIs) related to the proposed beam lines in the extended hadron experimental facility at J-PARC.

We observed a distinct peak in the $\Lambda p$ invariant mass spectrum of $^{3}{\rm He}(K^-, \, \Lambda p)n$, well below the mass threshold of $m_K + 2 m_p$. By selecting a relatively large momentum-transfer region $q = 350 \sim 650$ MeV/$c$, one can clearly separate the peak from the quasi-free process, $\overline{K}N \rightarrow \overline{K}N$ followed by the non-resonant absorption by the two spectator-nucleons $\overline{K}NN \rightarrow \Lambda N $. We found that the simplest fit to the observed peak gives us a Breit-Wigner pole position at $B_{\rm {\it Kpp}} = 47 \pm 3 \, (stat.) \,^{+3}_{-6} \,(sys.)$ MeV having a width $\Gamma_{\rm {\it Kpp}} = 115 \pm 7 \, (stat.) \,^{+10}_{-9} \,(sys.)$ MeV, and the $S$-wave Gaussian reaction form-factor parameter $Q_{\rm {\it Kpp}} = 381 \pm 14 \, (stat.)\,^{+57}_{-0} \,(sys.)$ MeV/$c$, as a new form of the nuclear bound system with strangeness -- "$K^-pp$"., Comment: 17 pages, 4 figures

To search for an S= -1 di-baryonic state which decays to $\Lambda p$, the $ {\rm{}^3He}(K^-,\Lambda p)n_{missing}$ reaction was studied at 1.0 GeV/$c$. Unobserved neutrons were kinematically identified from the missing mass $M_X$ of the $ {\rm{}^3He}(K^-,\Lambda p)X$ reaction in order to have a large acceptance for the $\Lambda pn$ final state. The observed $\Lambda p n$ events, distributed widely over the kinematically allowed region of the Dalitz plot, establish that the major component comes from a three nucleon absorption process. A concentration of events at a specific neutron kinetic energy was observed in a region of low momentum transfer to the $\Lambda p$. To account for the observed peak structure, the simplest S-wave pole was assumed to exist in the reaction channel, having Breit-Wigner form in energy and with a Gaussian form-factor. A minimum $\chi^2$ method was applied to deduce its mass $M_X\ =$ 2355 $ ^{+ 6}_{ - 8}$ (stat.) $ \pm 12$ (syst.) MeV/c$^2$, and decay-width $\Gamma_X\ = $ 110 $ ^{+ 19}_{ - 17}$ (stat.) $ \pm 27$ (syst.) MeV/c$^2$, respectively. The form factor parameter $Q_X \sim$ 400 MeV/$c$ implies that the range of interaction is about 0.5, Comment: 12pages, 8 figures

The antikaon-nucleon interaction close to threshold provides crucial information on the interplay between spontaneous and explicit chiral symmetry breaking in low-energy QCD. In this context the importance of kaonic deuterium X-ray spectroscopy has been well recognized, but no experimental results have yet been obtained due to the difficulty of the measurement. We propose to measure the shift and width of the kaonic deuterium 1s state with an accuracy of 60 eV and 140 eV respectively at J-PARC. These results together with the kaonic hydrogen data (KpX at KEK, DEAR and SIDDHARTA at DAFNE) will then permit the determination of values of both the isospin I=0 and I=1 antikaon-nucleon scattering lengths and will provide the most stringent constraints on the antikaon-nucleon interaction, promising a breakthrough. Refined Monte Carlo studies were performed, including the investigation of background suppression factors for the described setup. These studies have demonstrated the feasibility of determining the shift and width of the kaonic deuterium atom 1s state with the desired accuracy of 60 eV and 140 eV., Comment: 12 pages, 9 figures

In the 2001-2002 running period of the Relativistic Heavy Ion Collider (RHIC), transversely polarized protons were accelerated to 100 GeV for the first time, with collisions at sqrt{s} = 200 GeV. We present results from this run for single transverse spin asymmetries for inclusive production of neutral pions, photons and neutrons of the energy region 20 - 100 GeV for forward and backward production for angles between 0.3 mrad and 2.2 mrad with respect to the polarized proton direction. An asymmetry of A_N = (-0.090 +- 0.006 +- 0.009) x (1.0^{+0.47}_{-0.24}) was observed for forward neutron production, where the errors are statistical and systematic, and the scale error is from the beam polarization uncertainty. The forward photon and pi^0, and backward neutron, photon, and pi^0 asymmetries were consistent with zero. The large neutron asymmetry indicates a strong interference between a spin-flip amplitude, such as one pion exchange which dominates lower energy neutron production, and remaining spin non-flip amplitudes such as Reggeon exchange., Comment: 6 pages, 5 figures, 1 table, submitted to Phys. Lett. B

The invariant mass spectra of $\phi \to K^{+}K^{-}$ are measured in 12 GeV $p+A$ reactions in order to search for the in-medium modification of $\phi$ mesons. The observed $K^{+}K^{-}$ spectra are well reproduced by the relativistic Breit-Wigner function with a combinatorial background shape in three $\beta\gamma$ regions between 1.0 and 3.5. The nuclear mass-number dependence of the yields of the $K^{+}K^{-}$ decay channel is compared to the simultaneously measured $e^{+}e^{-}$ decay channel for carbon and copper targets. We parameterize the production yields as $\sigma (A) = \sigma_0 \times A^\alpha$ and obtain $\alpha_{\phi\to K^+K^-} - \alpha_{\phi\to e^+e^-}$ to be 0.14 $\pm$ 0.12. Limits are obtained for the partial decay widths of $\phi$ mesons in nuclear matter., Comment: 5 pages, 4 figures

The inclusive production of omega and phi mesons is studied in the backward region of the interaction of 12 GeV protons with polyethylene, carbon, and copper targets. The mesons are measured in e^+ e^- decay channels. The production cross sections of the mesons are presented as functions of rapidity y and transverse momentum p_T. The nuclear mass number dependences (A dependences) are found to be A^{0.710 +/- 0.021(stat) +/- 0.037(syst)} for omega mesons and A^{0.937 +/- 0.049(stat) +/- 0.018(syst)} for phi mesons in the region of 0.9 < y < 1.7 and p_T < 0.75 GeV/c., Comment: 12 pages, 8 figures; typos added

Invariant mass spectra of e+e- pairs have been measured in 12 GeV p+A reactions to detect possible in-medium modification of vector mesons. Copper and carbon targets are used to study the nuclear-size dependence of e+e- invariant mass distributions. A significant excess on the low-mass side of the phi meson peak is observed in the low beta gamma (=beta/sqrt(1-beta^2)) region of phi mesons (beta gamma < 1.25) with copper targets. However, in the high beta gamma region (beta gamma > 1.25), spectral shapes of phi mesons are well described by the Breit-Wigner shape when experimental effects are considered. Thus, in addition to our earlier publication on rho / omega modification, this study has experimentally verified vector meson mass modification at normal nuclear density., Comment: 4 pages, 4 figures

The invariant mass spectra of e+e- pairs produced in 12-GeV proton-induced nuclear reactions are measured at the KEK Proton-Synchrotron. On the low-mass side of the omega meson peak, a significant enhancement over the known hadronic sources has been observed. The mass spectra, including the excess, are well reproduced by a model that takes into account the density dependence of the vector meson mass modification, as theoretically predicted., Comment: 4 pages, 3 figures, Version accepted for Physical Review Letter

We have measured invariant mass spectra of electron-positron pairs in the target rapidity region of 12GeV p+A reactions. We have observed a significant difference in the mass spectra below the $\omega$ meson between p+C and p+Cu interactions. The difference is interpreted as a signature of the $\rho/\omega$ modification at normal nuclear-matter density., Comment: 8 pages, 3 figures, submitted to Phys. Rev. Letters. all the figures changed to Postscript format, text not changed