Λ polarization measurement of the π − p → K 0 Λ reaction in J-PARC E40 experiment

. We performed the J-PARC E40 experiment to measure the Σ p scattering cross sections from 2018 to 2020. Together with the π − p → K + Σ − data, the π − p → K 0 Λ data were accumulated as a byproduct. The analysis con ﬁ rmed that Λ could be identi ﬁ ed with an S / N ratio of ∼ 2 . 67. The polarization of Λ ( P Λ ) was preliminarily derived as 1 . 009 ± 0 . 049 for the K 0 angular range of 0 . 7 < cos θ K 0 , CM < 0 . 8. It is more accurate than the past data [1]. The high polarization enables us to measure not only the di ﬀ erential cross section but also spin observables of the Λ p scattering in the future J-PARC experiment.


Introduction
The nucleon-nucleon (NN) interaction is the foundation of nuclear physics. The nuclear force has an attractive potential in the long-range region, which is well described by the oneboson exchange (OBE) model. In contrast, it has a repulsive core in the short-range region. Although the origin of the core is still unknown, it is expected that the quark-gluon dynamics would dominate because the two nucleons overlap in this range. That is why most of us are engaging in hypernuclear physics to expand the nuclear force study by adding strange quarks.
Representative baryon-baryon (BB) interation models are, for example, Nijmegen model [2], quark cluster model [3], and chiral EFT [4] [5]. To update the theories based on experimental results, precise two-body hyperon-nucleon (Y N) data are necessary to make the Y N interaction models more realistic. Furthermore, accurate binding energy and level scheme of hypernuclei are also important to compare with hypernuclear calculations based on the Y N interaction.
Historically, many hypernuclear experiments in KEK, Jefferson Lab, J-PARC, etc., have accumulated many hypernuclear data. In addition, precise two-body Y N data should be taken by Y N scattering and hypertriton experiments as the fundamental information. The realistic Y N interactions would be established by feeding back two-body Y N data into theories. Such Y N interactions will derive from many-body interactions in the hypernuclear data.
The J-PARC E40 (Σp scattering) experiment recently pioneered the Y N scattering technique in J-PARC [6]. We now plan the next-generation Λp scattering experiment (J-PARC E86) using the same procedure as the E40 experiment. The J-PARC E86 aims to measure many scattering observables such as the differential cross section (dσ/dΩ) Λp , analyzing power (A y ), and depolarization (D y y ).
2 Λ polarization measurement for the J-PARC E86

Λp scattering observables and Λ polarization
In the momentum range of 0.4 − 0.8 GeV/c, The J-PARC E86 will measure the Λp scattering observables, such as the differential cross section ((dσ/dΩ) Λp ), analyzing power (A y ), and depolarization (D y y ). The Λ beam should be polarized in this measurement. Besides, we need to measure the Λ beam polarization (P Λ ) for deriving A y and D y y . It is desirable to confirm the high polarization of Λ produced in the π − p → K 0 Λ reaction and to establish the analysis method in advance. Therefore, we analyzed the π − p → K 0 Λ data accumulated as a byproduct in the J-PARC E40. Although the past experiment reported P Λ in the π − p → K 0 Λ reaction is ∼ 100% for the forward angular range of K 0 [1], its statistic is not enough. Hence, our re-measurement of P Λ would be valuable.

Analysis of the reaction
The J-PARC E40 measured the Σp scattering and pioneered the new hyperon scattering experimental technique. It was performed at the K1.8 beamline of the J-PARC Hadron Experimental Facility. The detector setup is shown in Figure 1. In its byproduct data of the (π − , K 0 ) reaction, K 0 was reconstructed from π + and π − . They are detected by the KURAMA spectrometer, and CATCH system [7], respectively. Λ was tagged by calculating the missing mass of the π − p → K 0 X reaction. The detail of detector configuration and K 0 reconstruction is described in Ref. [9]. The J-PARC E40 byproduct data includes enough Λ beam yield for the P Λ analysis of 2.80 × 10 4 with the S/N ratio of ∼ 2.67. These values were calculated by requiring the Λ → pπ − decay detection with the CATCH system.

Λ polarization calculation
As we mentioned, the Λ → pπ − decay was identified with the CATCH system. Due to the parity violation in the Λ → pπ − decay, the emission angle of decay proton (θ p ) distributes asymmetrically. By measuring the θ p distribution in the rest frame of Λ, we obtain P Λ from the following equation, Here, N 0 is the yield of the decay proton, and α is the asymmetry parameter (which is recently updated as 0.750 ± 0.009 ± 0.004 [10]). The raw θ p distribution was corrected by the acceptance of the CATCH system, estimated by a Geant4-based Monte Carlo simulation. Figure 2 shows the θ p distribution after the acceptance correction in the K 0 angular range of 0.7 < cos θ K 0 , CM < 0.8. Due to parity violation in the Λ → pπ − decay, a clear asymmetry called "Up-Down asymmetry" can be seen. We calculated the P Λ for the K 0 angular range of 0.6 < cos θ K 0 , CM < 1.0 by fitting the cos θ K 0 , CM distribution with Eq. (1). The comparison between the present values of P Λ Figure 1. The schematic of K 0 reconstruction and Λ identification in the J-PARC E40 byproduct data of the (π − , K 0 ) reaction. The cylindrical detector cluster (CATCH) is represented by pink parts, and the forward magnetic spectrometer (KURAMA), blue ones. The detail of the analysis technique is described in Ref. [9]. and the past experiment is shown in Figure 3. Here, the past data are replotted with the updated asymmetry parameter. The higher statistics of the Λ production in the J-PARC E40 allowed us to get smaller error bars. This result indicates that the Λ produced in the reaction π − p → K 0 Λ has high polarization.

Conclusion
To establish the realistic Y N interactions, we need feedback on two-body Y N data into theories. Such realistic Y N interactions are necessary to derive many-body interactions in the https://doi.org/10.1051/epjconf/202227102008 EPJ Web of Conferences 271, 02008 (2022) HYP2022 Figure 3. Λ beam polarization (P Λ ) in the reaction π − p → K 0 Λ. The present value (the J-PARC E40 byproduct data) is marked by red points, and the past data [1], by blue points. hypernuclear data. J-PARC E40 (Σp scattering) recently pioneered the hyperon scattering experimental technique for the first time. Following this success, we plan the next-generation Λp scattering experiment, J-PARC E86. It aims to measure the spin observables and the differential cross section of the Λp scattering precisely. In the spin observables measurement, we need the highly polarized Λ beam. Although the past experiment reported that the Λ polarization (P Λ ) was ∼ 100% for the forward angular region of K 0 [1], its accuracy is not enough due to the low statistics. Therefore, we decided to re-measure P Λ .
In the P Λ analysis, we used the (π − , K 0 ) reaction data accumulated as a byproduct in the J-PARC E40. We have identified the Λ beam yield of 2.80 × 10 4 with the S/N ratio of ∼ 2.67. By measuring the θ p distribution in the rest frame of Λ, P Λ was derived from its slope. Now, P Λ was preliminarily derived as 1.009 ± 0.049 for the K 0 angular range of 0.7 < cos θ K 0 , CM < 0.8. Using such a highly-polarized Λ beam, Λp spin observables measurement is possible in J-PARC E86.