Study of the hyperon-nucleon interaction via ﬁnal-state interactions in exclusive reactions

A novel approach that allows access to long-sought information on the Hyperon-Nucleon (YN) interaction was developed by producing a hyperon beam within a few-body nuclear system, and studying ﬁnal-state interactions. The determination of polarisation observables, and speciﬁcally the beam spin asymmetry, in exclusive reactions allows a detailed study of the various ﬁnal-state interactions and provides us with the tools needed to isolate kinematic regimes where the YN interaction dominates. High-statistics data collected using the CLAS detector housed in Hall-B of the Thomas Jefferson laboratory allows us to obtain a large set of polarisation observables and place stringent constraints on the underlying dynamics of the YN interaction.


Introduction
One of the main goal of nuclear physics is to obtain a comprehensive picture of the strong interaction, which can be accessed by introducing the strangeness degree of freedom in the, now well-understood, nucleon-nucleon (N N ) interaction. The N N interaction has a long history of detailed studies, and currently phenomenological approaches can describe observed phenomena with high accuracy. On the other hand, the interaction between Hyperons (hadrons with one or more strange quarks) and Nucleons (Y N ) is very poorly constrained, mainly due to difficulties associated with performing high-precision scattering experiments involving short-lived hyperon beams. Because of these difficulties, complimentary approaches, including studies of hypernuclei and final-state interaction (FSI), have been developed to provide indirect access to information on the hyperon-nucleon interaction. Final state interactions in exclusive hyperon photoproduction reactions off deuterium impart an excellent tool to study the bare Y N interaction in an approach that is free from medium modifications and many-body effects. Figure 1: Four main mechanisms that contribute to the reaction γd → K + Λn according to theoretical models [1,2]: (a) quasi-free ΛK + photoproduction on the proton; (b) pion mediated production; (c) K + rescattering off the spectator neutron; (d) Λ rescattering off the spectator neutron.

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Available models [1,2] indicate that four mechanisms contribute in the exclusive reaction γd → K + Λn (see Fig. 1): (1) the quasi-free mechanism, which dominates the reaction cross section, (2) the pion mediated mechanism, (3) the kaon rescattering, and (4) the hyperon rescattering mechanism. The exclusivity of the reaction allows us to place kinematical constraints that minimise contributions from the quasi-free reaction, enabling detailed investigation of FSI. Linearly and circularly polarised photon beams in combination with the selfanalyticity of hyperons give access to a large set of polarisation observables that are crucial for constraining the dynamics of the Y N interaction. This is illustrated by the most comprehensive model for this reaction, which uses two Y N potentials (Nijmegen NSC89 and NSC97f -both of which correctly predict the hypertrition binding energy) [3] and provides calculations of the polarised differential cross section, allowing predictions for a set of polarisation observables. These calculations predict a strong sensitivity between the two main potentials, indicating that polarisation observables are crucial in our current understanding of the Y N interaction. A determination of a large set of polarisation observables will allow a model-dependent interpretation of the data, in which various FSI contribute. The beam-spin asymmetry, Σ, is a critical observable that allows direct insight on contributions from the different FSI.

Experimental setup
Recent developments in accelerator and detector technologies, allowed the collection of a large data sample of the exclusive reaction γd → K + Λn utilising the CEBAF [4] Large Acceptance Spectrometer (CLAS) [5] and the tagger spectrometer housed in Hall-B of the Thomas Jefferson Laboratory (JLab). The CLAS detector, which is comprised of a time-of-flight detector system, drift chambers, a superconducting magnet that produced a toroidal magnetic field, and electromagnetic calorimeters, provided us with an efficient detection of charged particles over a large fraction of the full solid angle. A schematic of the CLAS detector is shown in the left panel of Fig. 2.
Data for this analysis were collected from one of the largest photoproduction experiments conducted during the CLAS6 era (experiment E06-103 [6]), utilising both linearly and a circularly polarised tagged photon beams incident on a 40 cm long deuterium target. The tagger

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SciPost Phys. Proc. 3, 026 (2020) low rates and then used to monitor the flux at higher intensities.
The first of these secondary monitors is a pair spectrometer, operated with a thin conversion foil in front of the spectrometer. In the early rounds of CLAS experiments the pair spectrometer was situated 22 m behind the CLAS target, near the TASC (see Fig. 2). This arrangement was not ideal since at high photon rates additional pairs produced in the CLAS target, and in the medium between the target and the pair spectrometer, caused pair rates that were too high and made the monitoring unstable. In addition, a sizable correction had to be applied to account for the photons lost in these pair production processes. More recently, a pair spectrometer has been installed in front of the CLAS target. By operating the entire system in vacuum, and by using a thin pairconversion foil that removes less than 1% of the photons from the beam, it is possible to monitor the photon flux even at high flux rates.
A second method that uses out-of-time events allows the monitoring of any changes in the flux distribution of electrons associated with the production of tagged photons. Each time a photon-generated event is detected in CLAS, a TDC window, 200-ns long, is opened for each of the 64 timing detectors in the tagger hodoscope.
Only the correct detector will record the correct time, but the other detectors will see random events, out of time with the true signal. This random rate is proportional to the total photon rate in the detector. Because of the high rate in the detectors, this has allowed the measurement of small rate changes (less than 1%) in time periods of less than 5 min: 6. Operating conditions

Targets
Hall B experiments are grouped into running periods according to beam type and target. A variety of targets have been used to date, with dimensions adapted to the particular needs of either electron or photon running. The most common target used has been liquid H2: However, reactions have also been studied using liquid D2; 3 He; and 4 He; solid 12 C; Al, Fe, Pb, and CH2; and polarized NH3 and ND3 targets. All targets are positioned inside CLAS using support structures which are inserted from the upstream end, and are independent of the detector itself. A sketch of the insertion scheme for targets inside CLAS, together with the supporting equipment, is shown for the spectrometer (right panel of Fig. 2) allowed the tagging of photons with energies between 20 and 95% of the incident electron energy. A linearly polarised photon beam between 0.7 and 2.3 GeV produced via the coherent bremsstrahlung technique (electrons incident on a diamond radiator), gave access to the beam spin asymmetry Σ, as well as the polarisation transfer observables O x and O z . On the other hand, photons produced using an amorphous radiator and a polarised electron beam, were circularly polarised and gave access to the double polarisation observables C x and C z . Equation (1) shows how the cross section of the reaction γd → K + Λn depends on the set of polarisation observables this work focuses on: where φ is the azimuthal angle of the kaon, and P lin and P cir c is the degree of linear and circular polarisation respectively, and α is the self-analsing power of the Λ hyperon equal to 0.75 [7]. Figure 3 shows the frame definition used to determine all relevant polarisation observables.

Analysis
The reaction γd → K + Λn was fully reconstructed with the detection of all charged-tracks in the final state, utilising the large branching ratio of Λ → pπ − (63.9%). Particle identification was done based on time-of-flight and drift chamber information, and misidentified kaons were discarded with a requirement on the proton-pion invariant mass. Finally, the missing neutron was identified utilising the tagged photon-beam by constructing the missing-mass, M X , of the reaction γd → K + ΛX . Background contributions, mainly from Σ 0 (which decays into a Λ and a γ), were accounted for using a comprehensive event generator and a realistic detector simulation based on the GEANT package [8]. The left panel of Fig. 4 shows an example of the missing-mass distribution for a specific kinematic bin, indicating the various background contributions. Quasi-free and FSI-dominated samples were determined by selecting events with neutron momenta (reconstructed from the missing-momentum of the reaction γd → K + ΛX ) below and above 200 MeV/c, as indicated in the right panel of Fig. 4. The polarisation observables were determined using the maximum likelihood technique. Specifically, the likelihood function was established from the cross section of the reaction (see Eq. (1)). This allowed for a simultaneous extraction of a set of polarisation observables by maximising the log-likelihood calculated using the linearly and circularly polarised data.

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SciPost Phys. Proc ntum conservation, with the cut to select FSI indicated on the determined using a maximum likelihood technique. A multied on each of the linearly and circularly polarized data, and vables were determined. The likelihood function was modelled  (1)). The lower left panel shows the definition of θ z (and correspondingly θ x ) with which the double-polarization observables produce modulations. The main figure defines the kaon laboratory polar angle θ K + , and the hyperon angle θ Λ , which is with respect to an axis pointing along the momentum of the YN pair.
As indicated before, the beam-spin asymmetry plays a crucial role in this study, since it provides us with vital information that allows us to identify kinematic regimes where specific FSI mechanisms dominate. This observable can be determined using the azimuthal distribution of kaons, Σ K + , hyperons, Σ Λ , and neutrons, Σ n . In a quasi-free dominated sample, where the neutron is a spectator, the hyperon and kaon azimuthal distribution are expected to result in the same beam-spin asymmetries (i.e. Σ K + = Σ Λ ), which would also be consistent to the beamspin asymmetry determined using a free-proton target (any contributions from initial-state effects are expected to be small). Moreover, the neutron beam-spin asymmetry Σ n is expected to be consistent with zero as it does not participate in the reaction. In the case of a sample that is dominated by the pion-mediate reaction, the beam-spin asymmetries Σ K + and Σ Λ are expected to be consistent with zero, where the neutron beam-spin asymmetry, Σ n , is expected to be consistent with the well-known pion beam-spin asymmetries of the reactions γn → π 0 n or γp → π + n. For a kaon-rescattering dominated sample, the neutron beam-spin asymmetry, Σ n , is expected to be consistent with zero, where the hyperon beam-spin asymmetry, Σ Λ is expected to be consistent with the quasi-free value. In this case, the kaon beam-spin asymmetry Σ K + , should be diluted with respect to the quasi-free value due to the secondary scattering process. A similar situation is expected in a hyperon-rescattering dominated sample, where the beamspin asymmetry determined using the hyperon azimuthal distribution is expected to be diluted with respect to the quasi-free value, where the Σ K + should be consistent with the quasi-free value and Σ n consistent to zero. This information was extensively studied using generated samples from our comprehensive event generator that includes rescattering processes in a simplified two-step approach.

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SciPost Phys. Proc. 3, 026 (2020) was reconstructed through four-momentum conservation, with the cut to select FSI indicated on the bottom panel of Fig. 2.
The polarization observables were determined using a maximum likelihood technique. A multidimensional minimization was performed on each of the linearly and circularly polarized data, and from this, each set of polarization observables were determined. The likelihood function was modelled according to the polarized cross section where d d⌦ is the unpolarized cross section, P lin and P circ are the degree of linear and circular polar-

Results and discussion
Generated samples allowed us to study in great detail the various contributing FSI in a controlled manner. Specifically, the kinematic dependence of the beam-spin asymmetry was studied individually for all mechanisms. The beam spin asymmetry of the initial step was set at a specific value and the effect of the second step was investigated. Figure 5 shows the beam spin asymmetries as a function of the neutron momentum for the quasi-free reaction, pion mediated reaction, as well as the Kaon and Hyperon rescattering processes. It is evident from these studies that the beam-spin asymmetries determined using the azimuthal distribution of

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SciPost Phys. Proc. 3, 026 (2020) Figures 44-48 show the same results of ⌃, O x , and O z for the QF (black squares) an using K (red squares), ⇤ (blue up-triangles), and n (cyan down triangles).   Figure 44: Polarisation observables as a function of photon energy. The points show squares) and FSI results determined using K (red squares), ⇤ (blue up-triangles), an triangles).

CLAS-ANALYSIS 2016-003
⌃ K + QF < l a t e x i t s h a 1 _ b a s e 6 4 = " G s G s 6 6 d R J 8 l X A 9 C f w 0 z j N w w K J A g = " > A A A C A H i c b V D L S s N A F J 3 U V 6 2 v q A s X b g a L I A g l q Y L i q i C I 4 K Z F + 4 A m h s l 0 0 g 6 d S c L M R C w h G 3 / F j Q t F 3 P o Z 7 v w b p 2 0 W 2 n r g w u G c e 7 n 3 H j 9 m V C r L + j Y K C 4 t L y y v F 1 d L a + s b m l r m 9 0 5 J R I j B p 4 o h F o u M j S R g N S V N R x U g n F g R x n 5 G 2 P 7 w c + + 0 H I i S N w j s 1 i o n L U T + k A c V I a c k z 9 5 x b 2 u f I S 2 / u j z P o c D 9 6 T G H j K v P M s l W x J o D z x M 5 J G e S o e + a X 0 4 t w w k m o M E N S d m 0 r V m 6 K h K K Y k a z k J J L E C A 9 R n 3 Q 1 D R E n 0 k 0 n D 2 T w U C s 9 G E R C V 6 j g R P 0 9 k S I u 5 Y j 7 u p M j N Z C z 3 l j 8 z + s m K j h 3 U x r G i S I h n i 4 K E g Z V B M d p w B 4 V B C s 2 0 g R h Q f W t E A + Q Q F j p z E o 6 B H v 2 5 X n S q l b s k 0 q 1 c V q u X e R

y j h E 7 g a T Z Y = " > A A A C A X i c b V D L S s N
x a X 8 c m F l d W 1 9 w 9 z c a s g w F p j U c c h C 0 f K R J I w G p K 6 o Y q Q V C Y K 4 z 0 j T H 5 y P / O Y 9 E Z K G w a 0 a R s T l q B f Q L s V I a c k z d 5 w a 7 X H k J d d 3 h y l 0 u B 8 + J P C i d p V 6 Z t E q W W P A W W J n p A g y V D 3 z y + m E O O Y k U J g h K d u 2 F S k 3 Q U J R z E h a c G J J I o Q H q E f a m g a I E + k m 4 w 9 S u K + V D u y G Q l e g 4 F j 9 P Z E g L u W Q + 7 q T I 9 W X 0 9 5 I / M 9 r x 6 p 7 6 i Y 0 i G J F A j x Z 1 I 0 Z V C E c x Q E 7 V B C s 2 F A T h A X V t 0 L c R w J h p U M r 6 B D s 6 Z d n S a N c s o 9 K 5 Z v j Y u U s i y M P d s E e O A A 2 O A E V c A m q o A 4 w e A T P 4 B W 8 G U / G i / F u f E x a c 0 Y 2 s w 3 + w P j 8 A X j 5 l j s = < / l a t e x i t > ⌃ ⇤ FSI < l a t e x i t s h a 1 _ b a s e 6 4 = " I z r U v K W Z g + p n a 0 l Q t r C a Q P G F h 2 U = " > A A A C B X i c b V D L S s N A F J 3 U V 6 2 v q E t d D B b B V U m q o L g q C K L g o l L 7 g C a E y W T S D p 1 J w s x E L C E b N / 6 K G x e K u P U f 3 P k 3 T h 8 L b T 0 w c D j n H u 7 c 4 y e M S m V Z 3 0 Z h Y X F p e a W 4 W l p b 3 9 j c M r d 3 W j J O B S Z N H L N Y d H w k C a M R a S q q G O k k g i D u M 9 L 2 B x c j v 3 1 P h K R x d K e G C X E 5 6 k U 0 p B g p L X n m v t O g P Y 6 8 z L n R o Q D l 0 O F + / J D B y 8 Z 1 7 p l l q 2 K N A e e J P S V l M E X d M 7 + c I M Y p J 5 H C D E n Z t a 1 E u R k S i m J G 8 p K T S p I g P E A 9 0 t U 0 Q p x I N x t f k c N D r Q Q w j I V + k Y J j 9 X c i Q 1 z K I f f 1 J E e q L 2 e 9 k f i f 1 0 1 V e O Z m N E p S R S I 8 W R S m D K o Y j i q B A R U E K z b U B G F B 9 V 8 h 7 i O B s N L F l X Q J 9 u z J 8 6 R V r d j H l e r t S b l 2 P q 2 j C P b A A T g C N j g F N X A F 6 q A J M H g E z + A V v B l P specific particles for each mechanism follows the predicted trend as discussed above. Furthermore, the dilutions are enhanced at missing momenta P X , and a selection of data with missing momenta above 200 MeV/c is expected to reflect well such dilutions with respect to data with momenta below 200 MeV/c. Detailed studies of simulated data (generated using measurements of the polarised cross section) are well underway to establish the kinematical dependence of the dilutions of the beam-spin asymmetry. This allow us to obtain the relative ratios of the various FSI mechanisms to the quasi-free production from analysed data from the E06-103 experiment, using determined dilutions from our generated samples. Figure 6 shows the beam-spin asymmetry of real data using a QF-dominated sample (black points) and FSI dominated samples using the azimuthal distributions of kaon, hyperons and neutrons (red, blue and cyan respectively). It is evident that the pion mediated reaction, which results in large Σ n is not a major contributing mechanism in the FSI dominated sample. In addition, the photon energy regimes 1.1 -1.5 GeV and 2 -2.3 GeV are dominated by the Y N mechanism since Σ K + is consistent with its QF value and Σ Λ significantly diluted. Many-fold differential results in these regimes will allows us to place stringent constraints on the underlying dynamics of the YN interaction.