Study of the Hyperon-Nucleon Interaction via Final-State … · 2019-12-10 · The tagger spectrometer (right panel of Fig.2) allowed the tagging of photons with energies ... operated

SciPost Physics Proceedings Submission

Study of the Hyperon-Nucleon Interaction via Final-StateInteractions in Exclusive Reactions.

Nicholas Zachariou1?, Daniel Watts1, and Yordanka Ilieva2

for the CLAS collaboration.

1 University of York 2 University of South Carolina? [email protected]

December 10, 2019

Proceedings for the 24th edition of European Few Body Conference,Surrey, UK, 2-4 September 2019

Abstract

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 nuclearsystem, and studying final-state interactions. The determination of polarisation observables,and specifically the beam spin asymmetry, in exclusive reactions allows a detailed study ofthe various final-state interactions and provides us with the tools needed to isolate kinematicregimes where the YN interaction dominates. High-statistics data collected using the CLASdetector housed in Hall-B of the Thomas Jefferson laboratory allows us to obtain a large setof polarisation observables and place stringent constraints on the underlying dynamics ofthe YN interaction.

1 Introduction

One of the main goal of nuclear physics is to obtain a comprehensive picture of the strong in-teraction, which can be accessed by introducing the strangeness degree of freedom in the, nowwell-understood, nucleon-nucleon (NN) interaction. The NN interaction has a long history ofdetailed studies, and currently phenomenological approaches can describe observed phenomenawith high accuracy. On the other hand, the interaction between Hyperons (hadrons with one ormore strange quarks) and Nucleons (Y N) is very poorly constrained, mainly due to difficultiesassociated with performing high-precision scattering experiments involving short-lived hyperonbeams. Because of these difficulties, complimentary approaches, including studies of hypernucleiand final-state interaction (FSI), have been developed to provide indirect access to information onthe hyperon-nucleon interaction. Final state interactions in exclusive hyperon photoproductionreactions off deuterium impart an excellent tool to study the bare Y N interaction in an approachthat is free from medium modifications and many-body effects.

Available models [1, 2] indicate that four mechanisms contribute in the exclusive reactionγd → K+Λn (see Fig. 1): (1) the quasi-free mechanism, which dominates the reaction crosssection, (2) the pion mediated mechanism, (3) the kaon rescattering, and (4) the hyperon rescat-tering mechanism. The exclusivity of the reaction allows us to place kinematical constraints that

1

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Figure 1: Four main mechanisms that contribute to the reaction γd → K+Λn accordingto theoretical models [1,2]: (a) quasi-free ΛK+ photoproduction on the proton; (b) pionmediated production; (c) K+ rescattering off the spectator neutron; (d) Λ rescatteringoff the spectator neutron.

minimise contributions from the quasi-free reaction, enabling detailed investigation of FSI. Lin-early and circularly polarised photon beams in combination with the self-analyticity of hyperonsgive access to a large set of polarisation observables that are crucial for constraining the dynam-ics 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 predictthe hypertrition binding energy) [3] and provides calculations of the polarised differential crosssection, allowing predictions for a set of polarisation observables. These calculations predict astrong sensitivity between the two main potentials, indicating that polarisation observables arecrucial in our current understanding of the Y N interaction. A determination of a large set of po-larisation observables will allow a model-dependent interpretation of the data, in which variousFSI contribute. The beam-spin asymmetry, Σ, is a critical observable that allows direct insight oncontributions from the different FSI.

2 Experimental setup

Recent developments in accelerator and detector technologies, allowed the collection of a largedata sample of the exclusive reaction ~γd → K+Λn utilising the CEBAF [4] Large Acceptance Spec-trometer (CLAS) [5] and the tagger spectrometer housed in Hall-B of the Thomas Jefferson Lab-oratory (JLab). The CLAS detector, which is comprised of a time-of-flight detector system, driftchambers, a superconducting magnet that produced a toroidal magnetic field, and electromagneticcalorimeters, provided us with an efficient detection of charged particles over a large fraction ofthe 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 experimentsconducted during the CLAS6 era (experiment E06-103 [6]), utilising both linearly and a circu-larly polarised tagged photon beams incident on a 40 cm long deuterium target. The taggerspectrometer (right panel of Fig. 2) allowed the tagging of photons with energies between 20 and

2


low rates and then used to monitor the flux athigher intensities.

The first of these secondary monitors is a pairspectrometer, operated with a thin conversion foilin front of the spectrometer. In the early rounds ofCLAS experiments the pair spectrometer wassituated 22 m behind the CLAS target, near theTASC (see Fig. 2). This arrangement was not idealsince at high photon rates additional pairsproduced in the CLAS target, and in the mediumbetween the target and the pair spectrometer,caused pair rates that were too high and made themonitoring unstable. In addition, a sizable correc-tion had to be applied to account for the photonslost in these pair production processes. Morerecently, a pair spectrometer has been installed infront of the CLAS target. By operating the entiresystem in vacuum, and by using a thin pair-conversion foil that removes less than 1% of thephotons from the beam, it is possible to monitorthe photon flux even at high flux rates.

A second method that uses out-of-time eventsallows the monitoring of any changes in the fluxdistribution of electrons associated with theproduction of tagged photons. Each time aphoton-generated event is detected in CLAS, aTDC window, 200-ns long, is opened for each ofthe 64 timing detectors in the tagger hodoscope.

Only the correct detector will record the correcttime, but the other detectors will see randomevents, out of time with the true signal. Thisrandom rate is proportional to the total photonrate in the detector. Because of the high rate in thedetectors, this has allowed the measurement ofsmall rate changes (less than 1%) in time periodsof less than 5 min:

6. Operating conditions

6.1. Targets

Hall B experiments are grouped into runningperiods according to beam type and target. Avariety of targets have been used to date, withdimensions adapted to the particular needs ofeither electron or photon running. The mostcommon target used has been liquid H2: However,reactions have also been studied using liquid D2;3He; and 4He; solid 12C; Al, Fe, Pb, and CH2; andpolarized NH3 and ND3 targets. All targets arepositioned inside CLAS using support structureswhich are inserted from the upstream end, and areindependent of the detector itself. A sketch of theinsertion scheme for targets inside CLAS, togetherwith the supporting equipment, is shown for the

0 1 m 2 m 3 m

Radiator Magnet pole

PhotonsMagnet return yoke

Full-energy electrons

k/E0 = 0.95 0.90 0.80 0.700.60

0.500.40

0.300.20

384 E-counters

61 T-counters

Fig. 23. Hall B photon-tagging system.

B.A. Mecking et al. / Nuclear Instruments and Methods in Physics Research A 503 (2003) 513–553538

Figure 2: Left: A schematic of the CLAS detector. The kidney-shaped superconductingcoils are shown in yellow, drift chambers in blue, Cerenkov counters in magenta, time-of-flight scintillators in red, and electromagnetic calorimeters in green. Right: The Hall-Bphoton tagging system located upstream of the CLAS detector.

95% of the incident electron energy. A linearly polarised photon beam between 0.7 and 2.3 GeVproduced 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 Ox andOz . On the other hand, photons produced using an amorphous radiator and a polarised electronbeam, were circularly polarised and gave access to the double polarisation observables Cx andCz . Equation (1) shows how the cross section of the reaction γd → K+Λn depends on the set ofpolarisation observables this work focuses on:

dσdΩ

=

dσdΩ

0[1− Pl inΣ cos 2φ +α cosθx(−Pl inOx sin2φ − PcircCx)

−α cosθy(−Py + Pl inT cos2φ)−α cosθz(Pl inOz sin 2φ + PcircCz)], (1)

where φ is the azimuthal angle of the kaon, and Pl in and Pcirc is the degree of linear and circularpolarisation 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.

3 Analysis

The reaction γd → K+Λn was fully reconstructed with the detection of all charged-tracks in thefinal state, utilising the large branching ratio of Λ → pπ− (63.9%). Particle identification wasdone based on time-of-flight and drift chamber information, and misidentified kaons were dis-carded with a requirement on the proton-pion invariant mass. Finally, the missing neutron wasidentified utilising the tagged photon-beam by constructing the missing-mass, MX , of the reactionγd → K+ΛX . Background contributions, mainly from Σ0 (which decays into a Λ and a γ), wereaccounted for using a comprehensive event generator and a realistic detector simulation basedon the GEANT package [8]. The left panel of Fig. 4 shows an example of the missing-mass distri-bution for a specific kinematic bin, indicating the various background contributions. Quasi-freeand FSI-dominated samples were determined by selecting events with neutron momenta (recon-structed 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

3


21st International Conference on Few-Body Problems in Physics

FSIQF

Figure 2. Top panel: Missing-mass distribution of thereaction d ! K+X fitted with contributions fromd ! K+0X (green), d ! K+X (purple), and ac-cidental events (magenta) from simulated data. The ver-tical dotted lines indicate the cuts that select the eventsof interest and the fits are used to perform backgroundsubtraction. Bottom panel: Missing momentum of the re-action d ! K+X indicating the cut applied to selectFSI.

K+

x

zy

px

zy

z

K+

n

K+

Plin

d

-n

K+

d

n

rest frame

Lab frame

Figure 3. Reaction plane definition for d !K+n. The upper left panel shows the definitionof the kaon azimuthal angle in which producesa modulation (see Eq. [1]). The lower left panelshows the definition of z (and correspondingly x)in which the double-polarization observables pro-duce modulations. The main figure defines thekaon laboratory polar angle K+ , and the hyperonangle 0

, which is in respect to an axis pointing

along the momentum of the YN pair.

was reconstructed through four-momentum conservation, with the cut to select FSI indicated on thebottom panel of Fig. 2.

The polarization observables were determined using a maximum likelihood technique. A multi-dimensional minimization was performed on each of the linearly and circularly polarized data, andfrom this, each set of polarization observables were determined. The likelihood function was modelledaccording to the polarized cross section

dd

=dd

0

h1 Plin cos 2 + ↵ cos x(PlinOx sin 2 PcircCx)

↵ cos y(Py + PlinT cos 2) ↵ cos z(PlinOz sin 2 + PcircCz)i, (1)

where dd

0

is the unpolarized cross section, Plin and Pcirc are the degree of linear and circular polar-ization, respectively, and , Ox, Oz, Cx, Cz, Py, and T are the polarization observables. The angles ,and x,y,z are defined in Fig 3. The self-analyzing power of , which allows the determination of the polarization by studying the distribution of its decay products, is denoted by ↵.

3 Results and Discussion

Preliminary results for polarization observables of FSI in the reaction d ! K+n were determined.Specifically, , Ox, Oz, Cx, and Cz were determined for photon energies between 1.0 and 2.4 GeV,kaon momenta between 0.3 and 1.9 GeV/c, and 0

angles between 0 and 60 degrees as shown in Fig. 4.

Invaluable information on kinematic regions where specific FSI are enhanced can be extracted fromstudying the di↵erences between the observables determined for the QF reaction and FSI (see Fig. 4).

Figure 3: Reaction plane definition for γd → K+Λn. The upper left panel shows the def-inition of the kaon azimuthal angleφ with whichΣ produces a modulation (see Eq. (1)).The lower left panel shows the definition of θz (and correspondingly θx) with which thedouble-polarization observables produce modulations. The main figure defines the kaonlaboratory polar angle θK+ , and the hyperon angle θΛ′ , which is with respect to an axispointing along the momentum of the YN pair.

maximum likelihood technique. Specifically, the likelihood function was established from the crosssection of the reaction (see Eq. (1)). This allowed for a simultaneous extraction of a set of polar-isation observables by maximising the log-likelihood calculated using the linearly and circularlypolarised data.

As indicated before, the beam-spin asymmetry plays a crucial role in this study, since it pro-vides us with vital information that allows us to identify kinematic regimes where specific FSImechanisms dominate. This observable can be determined using the azimuthal distribution ofkaons, ΣK+ , hyperons, ΣΛ, and neutrons, Σn. In a quasi-free dominated sample, where the neu-tron is a spectator, the hyperon and kaon azimuthal distribution are expected to result in thesame beam-spin asymmetries (i.e. ΣK+ = ΣΛ), which would also be consistent to the beam-spinasymmetry determined using a free-proton target (any contributions from initial-state effects areexpected to be small). Moreover, the neutron beam-spin asymmetry Σn is expected to be consis-tent with zero as it does not participate in the reaction. In the case of a sample that is dominatedby the pion-mediate reaction, the beam-spin asymmetries ΣK+ and ΣΛ are expected to be con-sistent with zero, where the neutron beam-spin asymmetry, Σn, is expected to be consistent withthe well-known pion beam-spin asymmetries of the reactions γn → π0n or γp → π+n. For akaon-rescattering dominated sample, the neutron beam-spin asymmetry, Σn, is expected to be

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Figure 10: Fits on missing-mass for each photon-energy bins to determine the ratios rBi and rA

i

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aAr b

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Figure 11: Ratios determined from the missing-mass fits. Region 1 corresponds to 0.90 < Mx <0.98 GeV/c2 and region 2 corresponds to 0.98 < Mx < 1.08 GeV/c2.

CLAS Analysis Note 2016- page 23 of 60

Exclusivity of the Reactiond ! K+(n)

21st International Conference on Few-Body Problems in Physics

FSIQF

Figure 2. Top panel: Missing-mass distribution of thereaction d ! K+X fitted with contributions fromd ! K+0X (green), d ! K+X (purple), and ac-cidental events (magenta) from simulated data. The ver-tical dotted lines indicate the cuts that select the eventsof interest and the fits are used to perform backgroundsubtraction. Bottom panel: Missing momentum of the re-action d ! K+X indicating the cut applied to selectFSI.

K+

x

zy

px

zy

z

K+

n

K+

Plin

d

-n

K+

d

n

rest frame

Lab frame

Figure 3. Reaction plane definition for d !K+n. The upper left panel shows the definitionof the kaon azimuthal angle in which producesa modulation (see Eq. [1]). The lower left panelshows the definition of z (and correspondingly x)in which the double-polarization observables pro-duce modulations. The main figure defines thekaon laboratory polar angle K+ , and the hyperonangle 0

, which is in respect to an axis pointing

along the momentum of the YN pair.

was reconstructed through four-momentum conservation, with the cut to select FSI indicated on thebottom panel of Fig. 2.

The polarization observables were determined using a maximum likelihood technique. A multi-dimensional minimization was performed on each of the linearly and circularly polarized data, andfrom this, each set of polarization observables were determined. The likelihood function was modelledaccording to the polarized cross section

dd

=dd

0

h1 Plin cos 2 + ↵ cos x(PlinOx sin 2 PcircCx)

↵ cos y(Py + PlinT cos 2) ↵ cos z(PlinOz sin 2 + PcircCz)i, (1)

where dd

0

is the unpolarized cross section, Plin and Pcirc are the degree of linear and circular polar-ization, respectively, and , Ox, Oz, Cx, Cz, Py, and T are the polarization observables. The angles ,and x,y,z are defined in Fig 3. The self-analyzing power of , which allows the determination of the polarization by studying the distribution of its decay products, is denoted by ↵.

3 Results and Discussion

Preliminary results for polarization observables of FSI in the reaction d ! K+n were determined.Specifically, , Ox, Oz, Cx, and Cz were determined for photon energies between 1.0 and 2.4 GeV,kaon momenta between 0.3 and 1.9 GeV/c, and 0

angles between 0 and 60 degrees as shown in Fig. 4.

Invaluable information on kinematic regions where specific FSI are enhanced can be extracted fromstudying the di↵erences between the observables determined for the QF reaction and FSI (see Fig. 4).

pX [GeV/c]

Quasifree

MM(d ! K+X) [GeV/c2]<latexit sha1_base64="XmlXiTdlywK2kiYEdUbGPgMvarY=">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</latexit>

Figure 4: Left: Missing-mass distribution of γd → K+ΛX indicated the various sourcesof background (Σ channel with yellow, Σ∗ channel with cyan, and accidentals with ma-genta). Right: Missing momentum of the reaction indicating the typical cut applied toselect quasi-free or FSI- dominated samples.

consistent with zero, where the hyperon beam-spin asymmetry, ΣΛ is expected to be consistentwith the quasi-free value. In this case, the kaon beam-spin asymmetry ΣK+ , should be diluted withrespect to the quasi-free value due to the secondary scattering process. A similar situation is ex-pected in a hyperon-rescattering dominated sample, where the beam-spin asymmetry determinedusing the hyperon azimuthal distribution is expected to be diluted with respect to the quasi-freevalue, where the ΣK+ should be consistent with the quasi-free value and Σn consistent to zero.This information was extensively studied using generated samples from our comprehensive eventgenerator that includes rescattering processes in a simplified two-step approach.

4 Results and discussion

Generated samples allowed us to study in great detail the various contributing FSI in a controlledmanner. Specifically, the kinematic dependence of the beam-spin asymmetry was studied individ-ually for all mechanisms. The beam spin asymmetry of the initial step was set at a specific valueand the effect of the second step was investigated. Figure 5 shows the beam spin asymmetries as afunction of the neutron momentum for the quasi-free reaction, pion mediated reaction, as well asthe Kaon and Hyperon rescattering processes. It is evident from these studies that the beam-spinasymmetries determined using the azimuthal distribution of specific particles for each mechanismfollows the predicted trend as discussed above. Furthermore, the dilutions are enhanced at miss-ing momenta PX , and a selection of data with missing momenta above 200 MeV/c is expected to toreflect well such dilutions with respect to data with momenta below 200 MeV/c. Detailed studiesof simulated data (generated using measurements of the polarised cross section) are well under-way to establish the kinematical dependence of the dilutions of the beam-spin asymmetry. Thisallow us to obtain the relative ratios of the various FSI mechanisms to the quasi-free productionfrom analysed data from the E06-103 experiment, using determined dilutions from our generatedsamples. 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, hyperonsand neutrons (red, blue and cyan respectively). It is evident that the pion mediated reaction,which results in large Σn is not a major contributing mechanism in the FSI dominated sample.

5


0 0.1 0.2 0.3 0.4 0.5 [GeV/c]

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0

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nΣ stepst 1ΛΣ Λ +K → pγ

n Λ → n Λ

-n rescatteringΛ

Figure 5: Beam spin asymmetries as a function of the neutron momentum of generateddata for the four mechanisms that contribute to the reaction γd → K+Λn. The differentpoints show the asymmetries determined using the azimuthal distribution of the variousparticles as indicated in each caption.

In addition, the photon energy regimes 1.1 – 1.5 GeV and 2 – 2.3 GeV are dominated by the Y Nmechanism since ΣK+ is consistent with its QF value and ΣΛ significantly diluted. Many-fold dif-ferential results in these regimes will allows us to place stringent constraints on the underlyingdynamics of the YN interaction.

References

[1] Salam A. et al., K0photoproduction on the deuteron and the extraction of the elementaryamplitude. Phys. Rev. C 74 044004-8 (2006).

[2] Laget J. M., Pentaquark, cusp, and rescattering in single kaon photoproduction off deu-terium. Phys. Rev. C 75 014002-7 (2007).

[3] Miyagawa K. et al., Polarization observables in exclusive kaon photoproduction on thedeuteron. Phys. Rev. C 74 034002-11 (2006).

[4] Leemann C. W., Douglas D R and Krafft G A, The Continuous Electron Beam AcceleratorFacility: CEBAF at the Jefferson Laboratory, Annu. Rev. Nucl. Part. Sci. 51 413-50 (2001).

[5] Mecking B. A. et. al. The CEBAF large acceptance spectrometer (CLAS). Nucl. Instr. Meth. A503 513-53 (2003).

6

SciPost Physics Proceedings SubmissionFigures 44-48 show the same results of , Ox, and Oz for the QF (black squares) and FSI determinedusing K (red squares), (blue up-triangles), and n (cyan down triangles).

(GeV)γE1 1.2 1.4 1.6 1.8 2 2.2 2.4

Σ

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(GeV)γE1 1.2 1.4 1.6 1.8 2 2.2 2.4

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zO

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Figure 44: Polarisation observables as a function of photon energy. The points show the QF (blacksquares) and FSI results determined using K (red squares), (blue up-triangles), and n (cyan downtriangles).

CLAS-ANALYSIS 2016-003 page 65 of 115

K+ QF<latexit sha1_base64="GsGs66dRJ8lXA9Cfw0zjNwwKJAg=">AAACAHicbVDLSsNAFJ3UV62vqAsXbgaLIAglqYLiqiCI4KZF+4Amhsl00g6dScLMRCwhG3/FjQtF3PoZ7vwbp20W2nrgwuGce7n3Hj9mVCrL+jYKC4tLyyvF1dLa+sbmlrm905JRIjBp4ohFouMjSRgNSVNRxUgnFgRxn5G2P7wc++0HIiSNwjs1ionLUT+kAcVIackz95xb2ufIS2/ujzPocD96TGHjKvPMslWxJoDzxM5JGeSoe+aX04twwkmoMENSdm0rVm6KhKKYkazkJJLECA9Rn3Q1DREn0k0nD2TwUCs9GERCV6jgRP09kSIu5Yj7upMjNZCz3lj8z+smKjh3UxrGiSIhni4KEgZVBMdpwB4VBCs20gRhQfWtEA+QQFjpzEo6BHv25XnSqlbsk0q1cVquXeRxFME+OABHwAZnoAauQR00AQYZeAav4M14Ml6Md+Nj2low8pld8AfG5w/Z8ZXm</latexit>

K+ FSI<latexit sha1_base64="SR5fzLFLaykmhSsy4yjhE7gaTZY=">AAACAXicbVDLSsNAFJ3UV62vqBvBzWARBKEkVVBcFQRR3FRqH9DEMJlO26EzSZiZiCXEjb/ixoUibv0Ld/6N0zYLbT1w4XDOvdx7jx8xKpVlfRu5ufmFxaX8cmFldW19w9zcasgwFpjUcchC0fKRJIwGpK6oYqQVCYK4z0jTH5yP/OY9EZKGwa0aRsTlqBfQLsVIackzd5wa7XHkJdd3hyl0uB8+JPCidpV6ZtEqWWPAWWJnpAgyVD3zy+mEOOYkUJghKdu2FSk3QUJRzEhacGJJIoQHqEfamgaIE+km4w9SuK+VDuyGQleg4Fj9PZEgLuWQ+7qTI9WX095I/M9rx6p76iY0iGJFAjxZ1I0ZVCEcxQE7VBCs2FAThAXVt0LcRwJhpUMr6BDs6ZdnSaNcso9K5ZvjYuUsiyMPdsEeOAA2OAEVcAmqoA4weATP4BW8GU/Gi/FufExac0Y2sw3+wPj8AXj5ljs=</latexit>

FSI<latexit sha1_base64="IzrUvKWZg+pna0lQtrCaQPGFh2U=">AAACBXicbVDLSsNAFJ3UV62vqEtdDBbBVUmqoLgqCKLgolL7gCaEyWTSDp1JwsxELCEbN/6KGxeKuPUf3Pk3Th8LbT0wcDjnHu7c4yeMSmVZ30ZhYXFpeaW4Wlpb39jcMrd3WjJOBSZNHLNYdHwkCaMRaSqqGOkkgiDuM9L2Bxcjv31PhKRxdKeGCXE56kU0pBgpLXnmvtOgPY68zLnRoQDl0OF+/JDBy8Z17pllq2KNAeeJPSVlMEXdM7+cIMYpJ5HCDEnZta1EuRkSimJG8pKTSpIgPEA90tU0QpxINxtfkcNDrQQwjIV+kYJj9XciQ1zKIff1JEeqL2e9kfif101VeOZmNEpSRSI8WRSmDKoYjiqBARUEKzbUBGFB9V8h7iOBsNLFlXQJ9uzJ86RVrdjHlertSbl2Pq2jCPbAATgCNjgFNXAF6qAJMHgEz+AVvBlPxovxbnxMRgvGNLML/sD4/AHtDpgs</latexit>

n FSI<latexit sha1_base64="WvSQ8D5ltFbjl/+CeAY76jZikho=">AAAB/3icbVBNS8NAEN3Ur1q/ooIXL4tF8FSSKiieCoLorVLbCk0Im+22Xbq7CbsbscQc/CtePCji1b/hzX/jts1BWx8MPN6bYWZeGDOqtON8W4WFxaXlleJqaW19Y3PL3t5pqSiRmDRxxCJ5FyJFGBWkqalm5C6WBPGQkXY4vBj77XsiFY3ErR7FxOeoL2iPYqSNFNh7XoP2OQpSkUGPh9FDCi8b11lgl52KMwGcJ25OyiBHPbC/vG6EE06Exgwp1XGdWPspkppiRrKSlygSIzxEfdIxVCBOlJ9O7s/goVG6sBdJU0LDifp7IkVcqREPTSdHeqBmvbH4n9dJdO/MT6mIE00Eni7qJQzqCI7DgF0qCdZsZAjCkppbIR4gibA2kZVMCO7sy/OkVa24x5XqzUm5dp7HUQT74AAcARecghq4AnXQBBg8gmfwCt6sJ+vFerc+pq0FK5/ZBX9gff4Ah4aVwQ==</latexit>

Figure 6: Beam spin asymmetries as a function of the photon energy of real data. Thedifferent points show the asymmetries determined using the azimuthal distribution ofthe various particles as indicated in the caption. Specifically, the black points show thebeam-spin asymmetry of kaons using a QF-dominated sample (Px < 200 MeV/c), whereas the red blue and cyan points show the beam-spin asymmetries determined using thekaon, hyperon, and neutron azimuthal distribution of an FSI-dominated data sample(Px > 200 MeV/c)).

[6] Nadel-Turonski P. N. et. al., Kaon production on the deuteron using polarized photons. Jef-ferson Lab Experiment E06-103 (2006).

[7] M. Tanabashi et al., Particle Data Group, Phys. Rev. D 98, 030001 (2018) and 2019 update.

[8] E. Wolin, GSIM Documentation, http://www.jlab.org/Hall-B/document/gsim/userguide.html

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