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Measurement of $^{3,4}$He($K^-, π^0$)$^{3,4}_Λ$H reaction cross section and evaluation of hypertriton binding energy

T. Akaishi, H. Asano, X. Chen, A. Clozza, C. Curceanu, R. Del Grande, C. D. Han, T. Hashimoto, M. Iliescu, K. Inoue, S. Ishimoto, K. Itahashi, M. Iwasaki, Y. Ma, R. Murayama, H. Noumi, H. Ohnishi, S. Okada, H. Outa, K. Piscicchia, A. Sakaguchi, F. Sakuma, M. Sato, A. Scordo, K. Shirotori, D. Sirghi, F. Sirghi, S. Suzuki, K. Tanida, T. Toda, T. Yamaga, X. Yuan, P. Zhang, Y. Zhang, H. Zhang

TL;DR

This work reports the first production cross sections for the light hypernuclei $^{3}_{\Lambda}\text{H}$ and $^{4}_{\Lambda}\text{H}$ produced via the in-flight $(K^-, \pi^0)$ reaction at $p_K=1.0$ GeV/$c$, using the J-PARC E73 setup with forward-tagging of the $\pi^0$ via a PbF$_2$ calorimeter and CDS tracking of the $\pi^-$ from two-body decays. From the measured cross sections and their ratio, and by comparing with DWIA-based predictions, the authors extract a $\Lambda$ binding energy for hypertriton, $B_\Lambda \approx 0.063^{+0.029}_{-0.023}$ (stat) $^{+0.025}_{-0.021}$ (syst) MeV, supporting a loosely bound system. The cross-section ratio $R_{34} \approx 0.30$ implies a ground-state spin $J=1/2$ for $^{3}_{\Lambda}\text{H}$ and corroborates a spin-non-flip production mechanism. The results help address the hypertriton lifetime puzzle by providing an independent, theory-guided pathway to constrain $B_\Lambda$ and the $\Lambda N$ interaction, with ongoing analyses to further reduce uncertainties and refine lifetime estimates.

Abstract

Light $s$-shell hypernuclei ($^{3,4}_Λ\text{H}$) and their ground-state properties are crucial benchmarks in hypernuclear physics. In particular, comparing the production cross sections of $^{3}_Λ\text{H}$ and $^{4}_Λ\text{H}$ provides insights into the $ΛN$ interaction in different isospin configurations, which can help address recent discrepancies in the reported $Λ$ binding energy of hypertriton. We present the first measurement of the production cross sections for $^{3}_Λ\text{H}$ and $^{4}_Λ\text{H}$ using the in-flight $(K^-, π^0)$ reaction at a beam momentum of 1.0 GeV/$c$ with an identical experimental setup. The production cross sections in the laboratory frame, for the angular range from 0$^{\circ}$ to 20$^{\circ}$, are measured to be $15.0~\pm~2.6~(\text{stat.})~^{+2.4}_{-2.8}~(\text{syst.})~μ\text{b} $ and $49.9~\pm~2.1~(\text{stat.})~^{+7.8}_{-8.0}~(\text{syst.})~μ\text{b}$ for the ground-state of $^{3}_Λ\text{H}$ and $^{4}_Λ\text{H}$, respectively. Using the ratio of these cross sections and comparing it with theoretical calculations, we evaluate the $Λ$ binding energy of hypertriton, yielding a value consistent with the picture of a loosely bound system.

Measurement of $^{3,4}$He($K^-, π^0$)$^{3,4}_Λ$H reaction cross section and evaluation of hypertriton binding energy

TL;DR

This work reports the first production cross sections for the light hypernuclei and produced via the in-flight reaction at GeV/, using the J-PARC E73 setup with forward-tagging of the via a PbF calorimeter and CDS tracking of the from two-body decays. From the measured cross sections and their ratio, and by comparing with DWIA-based predictions, the authors extract a binding energy for hypertriton, (stat) (syst) MeV, supporting a loosely bound system. The cross-section ratio implies a ground-state spin for and corroborates a spin-non-flip production mechanism. The results help address the hypertriton lifetime puzzle by providing an independent, theory-guided pathway to constrain and the interaction, with ongoing analyses to further reduce uncertainties and refine lifetime estimates.

Abstract

Light -shell hypernuclei () and their ground-state properties are crucial benchmarks in hypernuclear physics. In particular, comparing the production cross sections of and provides insights into the interaction in different isospin configurations, which can help address recent discrepancies in the reported binding energy of hypertriton. We present the first measurement of the production cross sections for and using the in-flight reaction at a beam momentum of 1.0 GeV/ with an identical experimental setup. The production cross sections in the laboratory frame, for the angular range from 0 to 20, are measured to be and for the ground-state of and , respectively. Using the ratio of these cross sections and comparing it with theoretical calculations, we evaluate the binding energy of hypertriton, yielding a value consistent with the picture of a loosely bound system.

Paper Structure

This paper contains 8 sections, 5 equations, 5 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Experiment Setup
  3. Data analysis
  4. Event selection
  5. Decomposition of $\pi^-$ momentum spectra
  6. Acceptance and efficiency correction
  7. Discussion
  8. Summary

Figures (5)

  • Figure 1: Schematic view of the experimental setup with a timing counter (T0), a Beam Profile Chamber (BPC), a cryogenic system for the liquid $^{3,4}\text{He}$ target; high-energy $\gamma$-rays are tagged with a PbF$_2$ calorimeter; Cylindrical Detector System(CDS) is a tracking device to measure $\pi^-$ from the $^{3,4}_\Lambda$H MWD.
  • Figure 2: Contour plots of the $\pi^-$ momentum versus $\gamma$-ray energy measured with the PbF$_2$ calorimeter. (a) $^4\text{He}$ target. (b) $^3\text{He}$ target. The red horizontal dashed line at 550 MeV indicates the threshold for the event selection.
  • Figure 3: The $\pi^-$ momentum spectra with fitting components. (a) $^4\text{He}$ dataset. (b) $^3\text{He}$ dataset. The black points show the experimental data. The orange line denotes the peak from the two-body MWD of hypernucleus while the purple line denotes the peak from the three-body MWD. The red dashed line represents the contribution from in-flight $\Lambda$ decay, located in the region 0.07--0.15 GeV/$c$, the blue dashed line from in-flight $\Sigma^0$ decay, located in the same region, the magenta dashed line from in-flight $\Sigma^-$ decay, located in the region 0.15--0.25 GeV/$c$, and the cyan dashed line from beam $K^-$ decay, located in the region 0.07--0.22 GeV/$c$. The green line represents the total spectrum obtained when applying “quasi-free $\Lambda$ + continuum” in the fit.
  • Figure 4: Distributions of the $\gamma$-ray energy. (a) $^4\text{He}$ dataset. (b) $^3\text{He}$ dataset. Line colors as in Fig. \ref{['fig:pion_mom_fit_final']}. The vertical red dashed line indicates the selected energy value of 550 MeV.
  • Figure 5: The calculated production cross section ratio $R_{34} = \sigma_{^3_{\Lambda}\text{H}}/\sigma_{^4_{\Lambda}\text{H}}$ varying the assumed $\Lambda$ binding energy of hypertriton. The horizontal red line indicates the measured ratio $R_{34}$, the long dashed lines show the range of the statistical errors, and the short dashed lines show the total errors obtained as the quadratic sum of the statistical and systematic errors. The dots represent the calculated ratios. The theoretical calculation by Harada harada2023private is plotted to illustrate the consistency or discrepancy between the experimental result and the theoretical expectation.