Differential cross sections for Λ(1520) using photoproduction at CLAS
U. Shrestha, T. Chetry, C. Djalali, K. Hicks, S.i. Nam, K.P. Adhikari, S. Adhikari, M.J. Amaryan, G. Angelini, H. Atac, L. Barion, M. Battaglieri, I. Bedlinskiy, F. Benmokhtar, A. Bianconi, A.S. Biselli, M. Bondi, F. Bossu, S. Boiarinov, W.J. Briscoe, W.K. Brooks, D. Bulumulla, V.D. Burkert, D.S. Carman, J.C. Carvajal, A. Celentano, P. Chatagnon, G. Ciullo, P.L. Cole, M. Contalbrigo, V. Crede, A. De Angelo, N. Dashyan, R. De Vita, M. Defurne, A. Deur, S. Diehl, M. Dugger, R. Dupre, H. Egiyan, M. Ehrhart, L. El Fassi, P. Eugenio, G. Fedotov, S. Fegan, A. Filippi, G. Gavalian, Y. Ghandilyan, G.P. Gilfoyle, F.X. Girod, D.I. Glazier, R.W. Gothe, K.A. Griffioen, M. Guidal, L. Guo, K. Hafidi, H. Hakobyan, M. Hattawy, T.B. Hayward, D. Heddle, M. Holtrop, Q. Huang, D.G. Ireland, E.L. Isupov, H.S. Jo, K. Joo, S. Joosten, D. Keller, A. Khanal, M. Khandaker, A. Kim, W. Kim, F.J. Klein, A. Kripko, V. Kubarovsky, L. Lanza, M. Leali, P. Lenisa, K. Livingston, I.J.D. MacGregor, D. Marchand, L. Marsicano, V. Mascagna, M.E. McCracken, B. McKinnon, V. Mokeev, A. Movsisyan, E. Munevar, C. Munoz Camacho, P. Nadel Turonski, 5 K. Neupane, S. Niccolai, G. Niculescu, T. O'Connell, M. Osipenko, A.I. Ostrovidov, L.L. Pappalardo, R. Paremuzyan, K. Park, E. Pasyuk, et al. (33 additional authors not shown)
aa r X i v : . [ h e p - e x ] J a n Differential cross sections for
Λ(1520) using photoproduction at CLAS
U. Shrestha, ∗ T. Chetry, C. Djalali, K. Hicks, S. i. Nam, K.P. Adhikari, † S. Adhikari, M.J. Amaryan, G. Angelini, H. Atac, L. Barion, M. Battaglieri,
41, 19
I. Bedlinskiy, F. Benmokhtar, A. Bianconi,
44, 22
A.S. Biselli, M. Bondi, F. Boss`u, S. Boiarinov, W.J. Briscoe, W.K. Brooks, D. Bulumulla, V.D. Burkert, D.S. Carman, J.C. Carvajal, A. Celentano, P. Chatagnon, G. Ciullo,
17, 12
P.L. Cole,
27, 16
M. Contalbrigo, V. Crede, A. D’Angelo,
20, 37
N. Dashyan, R. De Vita, M. Defurne, A. Deur, S. Diehl,
34, 8
M. Dugger, R. Dupre, H. Egiyan,
41, 30
M. Ehrhart, L. El Fassi,
28, 1
P. Eugenio, G. Fedotov, ‡ S. Fegan, A. Filippi, G. Gavalian,
41, 33
Y. Ghandilyan, G.P. Gilfoyle, F.X. Girod,
41, 6
D.I. Glazier, R.W. Gothe, K.A. Griffioen, M. Guidal, L. Guo,
13, 41
K. Hafidi, H. Hakobyan,
42, 49
M. Hattawy, T.B. Hayward, D. Heddle,
7, 41
M. Holtrop, Q. Huang, D.G. Ireland, E.L. Isupov, H.S. Jo, K. Joo, S. Joosten, D. Keller,
47, 32
A. Khanal, M. Khandaker, § A. Kim, W. Kim, F.J. Klein, A. Kripko, V. Kubarovsky, L. Lanza, M. Leali,
44, 22
P. Lenisa,
17, 12
K. Livingston, I .J .D. MacGregor, D. Marchand, L. Marsicano, V. Mascagna,
43, 22, ¶ M.E. McCracken, B. McKinnon, V. Mokeev,
41, 38
A Movsisyan, E. Munevar, ∗∗ C. Munoz Camacho, P. Nadel-Turonski,
41, 5
K. Neupane, S. Niccolai, G. Niculescu, T. O’Connell, M. Osipenko, A.I. Ostrovidov, L.L. Pappalardo,
R. Paremuzyan, K. Park, ∗∗ E. Pasyuk,
41, 2
W. Phelps, N. Pivnyuk, O. Pogorelko, J. Poudel, Y. Prok,
33, 47
M. Ripani, J. Ritman, A. Rizzo,
20, 37
G. Rosner, J. Rowley, F. Sabati´e, C. Salgado, A. Schmidt, R.A. Schumacher, Y.G. Sharabian, O. Soto, N. Sparveris, S. Stepanyan, I.I. Strakovsky, S. Strauch, N. Tyler, M. Ungaro,
41, 8
L. Venturelli,
44, 22
H. Voskanyan, E. Voutier, D.P. Watts, K. Wei, X. Wei, M.H. Wood,
3, 39
B. Yale, N. Zachariou, J. Zhang,
47, 33 and Z.W. Zhao
9, 39 (The CLAS Collaboration) Argonne National Laboratory, Argonne, Illinois 60439 Arizona State University, Tempe, Arizona 85287-1504 Canisius College, Buffalo, NY Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 Catholic University of America, Washington, D.C. 20064 IRFU, CEA, Universit´e Paris-Saclay, F-91191 Gif-sur-Yvette, France Christopher Newport University, Newport News, Virginia 23606 University of Connecticut, Storrs, Connecticut 06269 Duke University, Durham, North Carolina 27708-0305 Duquesne University, 600 Forbes Avenue, Pittsburgh, PA 15282 Fairfield University, Fairfield CT 06824 Universita’ di Ferrara , 44121 Ferrara, Italy Florida International University, Miami, Florida 33199 Florida State University, Tallahassee, Florida 32306 The George Washington University, Washington, DC 20052 Idaho State University, Pocatello, Idaho 83209 INFN, Sezione di Ferrara, 44100 Ferrara, Italy INFN, Laboratori Nazionali di Frascati, 00044 Frascati, Italy INFN, Sezione di Genova, 16146 Genova, Italy INFN, Sezione di Roma Tor Vergata, 00133 Rome, Italy INFN, Sezione di Torino, 10125 Torino, Italy INFN, Sezione di Pavia, 27100 Pavia, Italy Universit’e Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France Institute fur Kernphysik (Juelich), Juelich, Germany James Madison University, Harrisonburg, Virginia 22807 Kyungpook National University, Daegu 41566, Republic of Korea Lamar University, 4400 MLK Blvd, PO Box 10046, Beaumont, Texas 77710 Mississippi State University, Mississippi State, MS 39762-5167 National Research Centre Kurchatov Institute - ITEP, Moscow, 117259, Russia University of New Hampshire, Durham, New Hampshire 03824-3568 Norfolk State University, Norfolk, Virginia 23504 Ohio University, Athens, Ohio 45701 Old Dominion University, Norfolk, Virginia 23529 II Physikalisches Institut der Universitaet Giessen, 35392 Giessen, Germany Pukyong National University, Busan 48513, Republic of Korea University of Richmond, Richmond, Virginia 23173 Universita’ di Roma Tor Vergata, 00133 Rome Italy Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, 119234 Moscow, Russia University of South Carolina, Columbia, South Carolina 29208 Temple University, Philadelphia, PA 19122 Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606 Universidad T´ecnica Federico Santa Mar´ıa, Casilla 110-V Valpara´ıso, Chile Universit`a degli Studi dell’Insubria, 22100 Como, Italy Universit`a degli Studi di Brescia, 25123 Brescia, Italy University of Glasgow, Glasgow G12 8QQ, United Kingdom University of York, York YO10 5DD, United Kingdom University of Virginia, Charlottesville, Virginia 22901 College of William and Mary, Williamsburg, Virginia 23187-8795 Yerevan Physics Institute, 375036 Yerevan, Armenia (Dated: January 18, 2021)The reaction γp → K + Λ(1520) using photoproduction data from the CLAS g
12 experiment atJefferson Lab is studied. The decay of Λ(1520) into two exclusive channels, Σ + π − and Σ − π + ,is studied from the detected K + , π + , and π − particles. A good agreement is established for theΛ(1520) differential cross sections with the previous CLAS measurements. The differential crosssections as a function of CM angle are extended to higher photon energies. Newly added are thedifferential cross sections as a function of invariant 4-momentum transfer t , which is the naturalvariable to use for a theoretical model based on a Regge-exchange reaction mechanism. No new N ∗ resonances decaying into the K + Λ(1520) final state are found.
I. INTRODUCTION
Resonance structures are the signatures of excited va-lence quarks inside the nucleon. These excited reso-nances can then decay to a lower energy configuration byemitting a quark-antiquark pair. Hadron spectroscopysearches for these ground state and excited state baryons( qqq ), and their decay channels into mesons ( qq ). Themain objective is to identify the different quantum states(resonances) that come from analysis of their energies,widths, and characteristic line profiles. The study ofbaryon spectra is crucial to understanding QuantumChromo-Dynamics (QCD).Non-relativistic constituent quark models (NRCQMs)[1, 2] can be considered as a naive and solvable approachto formulate hadronic wave functions in order to makepredictions for the properties of baryonic ground statesand excited states. They are, however, not so accurateat higher mass hadron spectra, when compared to ex-perimental results [3]. Lattice QCD calculations [4] haveshown “missing resonances” [5] and other excited states,and are able to predict masses in the hadron spectra, butthe currently available calculations are made at higherthan physical masses because of the computational costand therefore have limited accuracy. The systematicstudy of different decay channels is critical to the searchfor these missing resonances. Different studies have been ∗ Corresponding author: [email protected] † Current address:Hampton University, Hampton, VA 23668 ‡ Current address:Ohio University, Athens, Ohio 45701 § Current address:Idaho State University, Pocatello, Idaho 83209 ¶ Current address:Universit`a degli Studi di Brescia, 25123 Brescia,Italy ∗∗ Current address:Thomas Jefferson National Accelerator Facility,Newport News, Virginia 23606 carried out at Jefferson Lab. One approach has beento measure the strangeness photoproduction into two-body final states. Another one has shown the importanceof three-body final states in order to study higher massmissing resonances [6].Photoproduction is an important mechanism to deci-pher information that identifies the dynamical basis be-hind ground state and excited state resonance structureformation. This study aims to deliver a better under-standing of photoproduction of the hyperon resonance,Λ(1520).The framework of this paper is the following. Sec-tion II presents a brief summary of previous experimen-tal and theoretical studies on the photoproduction of theΛ(1520) hyperon. Section III introduces the experimen-tal set up that provided the data for this study. Sec-tion IV outlines the details of the event selection, simu-lation, and yield extraction procedures for cross sectionsin Sections IV A, IV B, and IV C. The measured crosssections are displayed in Section V. Section VI gives anaccount of the systematic uncertainties for this study.The comparison of the results with the theoretical pre-dictions are discussed and our conclusions are providedin Section VII.
II. PREVIOUS STUDIES ON
Λ(1520)
The Λ(1520) has been well studied [7]. The Laser Elec-tron Photon Experiment at SPring (LEPS) Collaborationstudied the photoproduction of Λ(1520) and measureddifferential cross sections and photon-beam asymmetrieswith linearly polarized photon beams in the energy range1 . < E γ < . W ≃ .
11 GeV sug-gesting a nucleon resonance or a new reaction process.Another photoproduction study [9] for this hyperon byLEPS with liquid hydrogen and deuterium targets at sim-ilar photon energies, showed a reduced production fromneutrons compared to protons at backward angles.A recent study on Λ(1520) photoproduction was com-pleted by Moriya et al . [10]. As part of the g
11 experi-ment, this was done at the CEBAF Large AccepteanceSpectrometer (CLAS) with an unpolarized real photonbeam at energies up to 4.0 GeV striking a liquid hydro-gen target. They studied all of the three Σ π decay modes,measuring the kaon angular distributions, which were flatat threshold ( W ≃ . etal . [12] for the Λ(1520), our results will extend the crosssections to higher photon energies using the g
12 experi-ment at CLAS, where the current theoretical models ofRegge exchange are expected to be more accurate [12].The photoproduction of Λ(1520) off a proton targethas been studied theoretically by Nam et al . [12]. Theauthors investigated the Λ(1520)3 / − , or Λ ∗ , photopro-duction in an effective-Lagrangian approach using Bornterms where they use the Rarita-Schwinger formalism toaccount for the spin-3/2 fermion field. They introducedhadron form factors that represent spatial distributionsfor hadrons, and in order to preserve gauge invarianceof the invariant amplitude, they also include a contactterm [13]. One of several free parameters in their model,the vector-kaon coupling constant g K ∗ N Λ ∗ , has been con-strained by data, along with the anomalous magnetic mo-ment of the Λ ∗ , κ Λ ∗ , for photon energies below 3 GeV.Regge theory accounts for the analytic properties ofscattering as a function of angular momentum. The the-ory uses Regge trajectory functions α ( s , t ), where s and t are Mandelstam variables, that can correlate certain se-quences of particles or resonances. Regge theory accountsfor the exchange of entire families of hadrons, with iden-tical internal quantum numbers but different spins J . Inorder to extend their model to higher energy, Nam et al .[12] have implemented the Regge contributions in Λ ∗ pho-toproduction by considering mesonic Regge trajectories,corresponding to all the meson exchanges with the samequantum numbers but different spins in the t channel attree level.He and Chen [11] also studied an effective-Lagrangianapproach model for the Λ(1520), which takes into con-sideration the vector meson K ∗ exchanged in the t chan-nel, which has proven to be significant at high energy(11 GeV). Besides the Born terms, the inclusion of thecontact term and s , u , and K exchanged t channels haveimportant contribution at all energies. They report acontribution from the nucleon resonance N (2080)3 / − in Λ(1520) photoproduction that suggests the need foranother resonance at a nearby mass. Studies of Λ ∗ photo-production help to strengthen the idea that the effective-Lagrangian approach is a valid theoretical model. Moriya et al . [10] compared their cross sections with the model FIG. 1. Schematic diagram for the reaction, γp → K + Λ ∗ ,assuming t -channel dominance. Λ ∗ here represents Λ(1520). calculation from Nam et al . [12] and He et al . [11], andconcluded that the latter model, because of the addi-tional interaction ingredients, had a slightly better agree-ment with their data.Regge exchange ( t -channel) models are expected to bemore accurate as the beam energy goes above the reso-nance region. For W > . s -channel) are significant, and hence the g
12 data will provide a more stringent test of the modelof Nam et al . [12]. A. Λ(1520)
Photoproduction
Photoproduction off a proton can create a K + -mesonand a Λ ∗ resonance, Λ(1520), see Fig. 1, which can decayvia Σ π channels, e.g. , Σ + π − , Σ − π + , and Σ π . For thetwo charged decay channels, Σ ± gives off a neutron and a π ± . Both the Σ + and Σ − branches of the photoproducedΛ(1520) have K + , π + , and π − as the detected final stateparticles. III. EXPERIMENTAL SETUPA. The CLAS Detector
The data set used in this analysis of Λ(1520) photo-production is taken from the g
12 experiment performedby the CLAS Collaboration at the Thomas Jefferson Na-tional Accelerator Facility (TJNAF). Located in NewportNews, Virginia, Jefferson Lab houses four experimentalhalls, namely, A, B, C, D, and the Continuous ElectronBeam Accelerator Facility (CEBAF). The CLAS detectorwas installed inside the Hall B and was decommissionedin 2012.The design of the CLAS detector was based on atoroidal magnetic field that had the ability to measurecharged particles with good momentum resolution, pro-vide geometrical coverage of charged particles over a largelaboratory angular range, and keep a magnetic field-freeregion around the target to allow the use of dynamicallypolarized targets [14]. Six superconducting coils aroundthe beamline produced a field in the azimuthal direction.Drift chambers (DC) for charged particle trajectories, gasCherenkov counters for electron identification, scintilla-tion counters for time-of-flight (TOF), and electromag-netic calorimeters (EC) to detect showering electrons,photons, and neutrons, were the major components ofthe detector’s particle identification (PID) system [14].The accelerated electron beam producedbremsstrahlung photons when passed through athin gold radiator. The photon tagger system at CLASused a hodoscope with two scintillator planes (energyand timing counters) that enabled photon tagging bythe detection of energy-degraded electrons, which weredeflected in the tagger magnetic field [14]. The startcounter, surrounding the target, recorded the start timeof the outgoing particles that originated in the target. B. g -Run The data set used in this analysis was acquired fromthe CLAS g
12 experiment that was performed in thesummer of 2008. This CLAS experiment was a high-luminosity, high-energy, real-photon run. This run usedan electron beam current of 60-65 nA that producedbremsstrahlung photons. The photons continued forwardtowards the 40 cm LH (liquid hydrogen) target. Thephoton energy for the run was up to 5.7 GeV. Detailsof the g
12 experiment, the running conditions, and theformulated standard procedures for the data analysis canbe found on
The g12 Analysis Procedure, Statistics, andSystematics document [15].
IV. DATA ANALYSIS
For the reaction γp → K + Λ(1520) → K + Σ ± π ∓ , twoexclusive decay channels, Λ(1520) → Σ ± π ∓ → nπ ± π ∓ ,were identified by detecting K + , π + , and π − . The un-measured Σ ± and n were reconstructed from the missingmass ( M M ) approach.
A. Event Selection
1. Photon Selection
For the g
12 experiment, the accelerator delivered elec-trons in packets of 2-ns bunches into Hall B, wherebremsstrahlung photons were then produced. A reactioninside the target was triggered by an incident photon. Anevent was recorded when a triggered reaction was associ-ated with a specific photon candidate. Since there wereseveral potential photon contenders for a recorded eventdue to background sources, it was necessary to determinethe correct photon that created a specific event. - - - - - · [ns] g - t event = t coinc t D C oun t s FIG. 2. The photon coincident-time distribution, ∆ t coinc , forthe events with K + , π + , and π − as the detected particlesis shown. The 2-ns bunching of the photon beam is appar-ent. Events with ∆ t coinc = | t event − t γ | < In order to find the correct photon, the coincidencetime , ∆ t coinc , was defined per photon as the differencebetween the Tagger time ( t γ ) and the Start Counter time( t event ) extrapolated to the interaction point,∆ t coinc = t event − t γ . (1)The Tagger time, also known as the photon time, is thetime at which a photon reached at the point of interac-tion or the event vertex point, whereas the Start Countertime, also known as the event time, is understood as theaverage of the time per track of the particle, when de-tected by the Start Counter, at the same vertex point.Figure 2 shows a distribution of the coincidence time,where multiple photon candidates per event can be seen.A photon peak selection cut of ∆ t coinc = | t event − t γ | < | ∆ t coinc | < γ corr = 1 .
03, was obtained byexamining photon multiplicities in both data and simula-tion, and was applied in the calculation of the differentialcross sections.
2. Particle Identification
The particle identification (PID) process used the in-formation signature left by a particle when it hit a de-tector in order to identify that particle. Proper particleidentification was vital to reduce backgrounds and im-prove measurement resolution. The PID information wasaccessed and the data were passed through the skimmingprocess where events that included the topologies withthe final state particles were selected. PID process wasrefined by employing the time-of-flight technique to iden-tify particles. The measured time of flight ( t meas ) for any - - (a) | [GeV] + K |p t [ n s ] d - - (b) | [GeV] + p |p t [ n s ] d - - (c) | [GeV] - p |p t [ n s ] d FIG. 3. The timing versus momentum distributions used for particle identification for K + , π + , and π − in (a), (b), and (c),respectively, for the data as a function of the particle’s momentum are shown. Straight cuts of | δt | < ± . σ momentum-dependent timing cut around the centroid of δt in each momentum bin are employed in identifyingthe particles coincident with a single photon. particle produced during an event was compared with thecalculated time of flight ( t calc ) for the known path ( d path )for the measured momentum ( p ) and an assumed mass( m ). The measured and calculated time of flight informa-tion used the measured and calculated β values, β meas ,and β calc , respectively. The β meas was obtained fromthe CLAS-measured momentum p of a particle duringthe data skimming process, whereas β calc is a theoreti-cal value calculated from that measured momentum andthe particle’s assumed mass. The time difference ( δt ) be-tween the measured time ( t meas ) and the calculated time( t calc ) is given by, δt = t meas − d path c Ep = d path c (cid:18) β meas − β calc (cid:19) , (2)where E = p p + m is the total energy of a particle.The δt is recalculated for each particle based on its massand charge.For the first-order PID, the three detected particles, K + , π + , and π − , were selected with a timing cut of | δt | < δt = 0 ns, into several momentum bins and then fit-ting with a Gaussian function for π ± or a Gaussian func-tion over an exponential background for K + . The ex-tracted centroid and width parameters were used to ap-ply a ± . σ timing cut for both data and simulations tothe original 1-ns timing-momentum distribution of thedetected particles. Figure 3 shows the timing versus mo-mentum distributions of the three detected particle afterthe PID cuts.
3. Minimum | p | , z -vertex, Fiducial, and Paddle Cuts The detection efficiency of low momentum particleswas not large and not so accurately known. Such par- ticles were eliminated by applying minimum momen-tum cuts | p K + | < .
35 GeV, | p π + | < .
15 GeV, and | p π − | < .
17 GeV, where | p | represents the magnitudeof the particle momentum.The g
12 experiment used a liquid hydrogen (LH ) tar-get measuring 40 cm in length and 2 cm in diameter.The target was not centered around the CLAS detector, z = 0 cm, but was shifted 90 cm upstream in order to in-crease the detector acceptance in the forward direction.Charged tracks from the target were selected in recon-struction by requiring that they came from the z range(coordinate along the beamline) from -100 to -70 cm.The geometry of the CLAS detector and the presenceof the toroidal magnetic field could cause inaccurate re-construction of particle tracks at the edges of the driftchambers, thereby resulting in uncertainties in the de-tector efficiency. We introduced fiducial boundaries thatencompass a well-behaved and predictable acceptance re-gion in azimuthal angle, φ , of the detector for each par-ticle depending upon its momentum, charge, and polarangle, θ . Hence, a standard geometric fiducial cut proce-dure [15] was applied for each detected particle in all sixsectors, both for the data and for the simulation.Scintillation counters were used to determine the timeof flight of charged particles. Counter with very low pho-tomultiplier gain resulted in poor timing resolution andpoor efficiency. These bad paddles were identified and re-moved from the data analysis during the event selectionprocess [15].
4. Missing Mass Cuts
A series of missing mass cuts was applied to isolate andfilter events corresponding to the two topologies for theΛ(1520). In both of its charged decay channels, Λ(1520)branches into π + , π − , and n . Since, π + and π − are thedetected particles, the missing mass distribution given · ) [GeV] - p + p + MM(K C oun t s FIG. 4. The missing mass distribution used to reconstructthe missing n is shown. A 0 . ≤ MM ( K + ππ )[GeV] ≤ . by, M M ( K + π + π − ) = q ( P γ + P p − P K + − P π + − P π − ) , (3)was constructed to select the missing n , where P γ , P p , P K + , P π + , and P π − are the four-momenta of the incom-ing photon, target proton, and the outgoing particles, K + , π + , and π − , respectively. The missing n peak canbe seen in Fig. 4 and the corresponding events with a n were selected by making the cuts indicated in the figure.A small structure seen at around 0.85 GeV to the leftof the n peak in Fig. 4 is due to π + tracks incorrectly re-constructed as K + tracks. Events from the three pion re-action, γp → π + π + π − n , can have one of the π + misiden-tified as a K + . These events form a nearly uniform back-ground, and do not contribute to the yield of the Λ(1520)as shown below. The side structure at 0.85 GeV relativeto the n peak is reduced in size by applying more strin-gent cuts in the particle identification process.It is important to consider the nK decay of Λ(1520).The K can decay to a π + π − pair. Hence, the n -cutselected events mentioned earlier can have charged pi-ons contribution to the final state particles. In order toexclusively look for the Λ(1520) photoproduction fromthe Σ ± π ∓ channel, events from a possible nK channelwere excluded by removing events in the K peak in theinvariant mass distribution plot for π + π − , given by, IM ( π + π − ) = p ( P π + + P π − ) , (4)as seen in Fig. 5.After applying the above-mentioned cuts, the analy-sis branches into the two exclusive reaction channels forthe Λ(1520), Λ(1520) → Σ + π − and Λ(1520) → Σ − π + .This was done by by plotting the missing mass distri-butions, M M ( K + π − ) and M M ( K − π + ) for the Σ + andΣ − channels, respectively. Straight cuts were applied toselect events with Σ + and Σ − in their respective missing · ) [GeV] - p + p IM( C oun t s FIG. 5. Removing K → π + π − (Λ(1520) → nK channel)by cutting out events with 0 . ≤ IM ( π + π − )[GeV] ≤ .
51 asindicated by the dotted lines. mass distributions, as shown in Fig. 6. Even though theΣ + and Σ − event distributions in the data show somebackground, the background will not form a peak at theΛ(1520). Some of the background in the data comesfrom generic background processes and reactions, suchas γp → K ∗ Σ + ( K ∗ → K + π − ) and γp → π + π + π − n (where π + is misidentified as K + ). The latter reactionmakes a smooth background under the Σ peaks.Now the Λ ∗ resonances can be seen in the M M ( K + )distributions for the two channels as shown in Fig. 7.The peaks at around 1.40 GeV and 1.52 GeV corre-spond to the Λ(1405) and Λ(1520). The smooth peaknear 1.68 GeV represents the two higher mass resonancesΛ(1670) and Λ(1690). The analysis of those flavor-octetresonances is being carried out and will be the subject ofa future publication.The difference in the strengths of the backgrounds, asseen in Fig. 7, is caused by the unequal contributionsfrom the K ∗ in the two measured Σ π channels. Figure 8shows calculations that include K ∗ background contri-butions to the cross sections of the two decay channelsof the Λ ∗ resonances. These calculations represented inthe figure clarify that the intermediate K ∗ → K + π − decay is significantly responsible for introducing morebackground to the data in the Σ + π − decay channel thanin the Σ − π + decay channel for the Λ(1520). Therefore,these predictions provide an explanation to the contrast-ing backgrounds in the two channels, as seen in Fig. 7 andFig. 10. Very similar mass distributions of the Λ ∗ reso-nances for the Σ ± π ∓ decay channels can be seen in thestudy of the reaction K − p → Λ(1520) π for the Σ + π − π and Σ − π + π final states by J. Griselin et al . (1975) [16].The Λ(1520) events were selected by cutting onthe M M ( K + ) distribution in the range from 1.44 to1.60 GeV. This cut around the Λ(1520) peak for the datais based on the particle data mass range for the Λ(1520)and is consistent with the range of the Λ(1520) peak ob-tained from our simulation of events for the two decay · (a) ) [GeV] - p + MM(K C oun t s · (b) ) [GeV] + p + MM(K C oun t s FIG. 6. Selection of the Σ + (a) and Σ − (b) in the event distributions by making cuts 1 . ≤ MM ( K + π − ) [GeV] ≤ .
25 and1 . ≤ MM ( K + π + ) [GeV] ≤ .
25, respectively. The cuts are shown by the dotted lines. The two decay branches are analyzedseparately for further analysis. · (a) ) [GeV] + MM(K C oun t s · (b) ) [GeV] + MM(K C oun t s FIG. 7. Λ ∗ resonances for the Σ + and Σ − channels are shown in (a) and (b), respectively. The data distributions show the Λ ∗ resonances Λ(1405) and Λ(1520). The wider peak around 1.68 GeV is due to higher-mass resonances Λ(1670) and Λ(1690). branches.
5. Dalitz Plots
The invariant mass ( IM ) distributions of differentcombinations of the final-state particles for our reactionwere used with the goal of looking for physics back-grounds that could contribute to our final state. Plotsof the decay Λ(1520) → nπ + π − were studied by investi-gating the 2-D correlations of IM ( nπ − ) vs IM ( nπ + ) forboth data and simulation as shown in Fig. 9.A remarkable similarity is seen between the data andthe Monte-Carlo (MC) simulations. Figure 9 showsthat there are clear bands corresponding to the Σ + andΣ − baryons, with very little overlap at the intersection.Events were assigned to only one branch, depending onwhether the IM was closer to the known mass of the Σ + or Σ − (for both data and MC). Studies using the MCshow that only about 1% of events were misclassified,and the leakage was the same (within statistics) bothways.The IM ( nπ − ) vs. IM ( nπ + ) plots for both the dataand the simulation showed a region at the intersectionthat did not contribute to the Λ(1520) peak. A diagonalcut was made to eliminate these events, which improvedthe signal-to-background ratio. B. Simulation
A GEANT3-based Monte Carlo (MC) [17] was used tosimulate events for our experiment with the same final-state particles. Since, the acceptance of a detector is re-action dependent, the simulation for the two-decay chan-nels of the Λ(1520), the Σ + π − and Σ − π + , was indepen- ) [Gev] pS M( b / G e V ] m [ d M s d FIG. 8. Model predictions [12] to understand the differencein the K ∗ background contributions to the decay of Λ ∗ intothe two channels, Σ + π − and Σ − π + , shown as short dashedand dotted curves, respectively. The predictions are shown asa function of Σ π invariant mass, M (Σ π ). dently generated for the processes γp → K + Λ(1520) → K + Σ + π − → K + π + π − ( n ) and γp → K + Λ(1520) → K + Σ − π + → K + π + π − ( n ), respectively.The MC event generator was based on the user inputparameters and settings that include beam position, tar-get material, reaction products, decay channels, and the t -slope parameter [15]. The differential cross sections canbe modeled as a function of t -slope by, dσdt = σ e − bt , (5)where dσdt is the differential cross section, b is the t -slopeparameter, and σ is the amplitude of the cross section.In order to best estimate the b -value for the simulation sothat it matched our data, different values of b were usedto generate different sets of Monte-Carlo simulations,which were compared with the data distributions versus t . As a result, detector acceptance (or efficiency) was cal-culated with simulated events using b = 1 . − and b = 2 . − for W ≤ .
85 GeV and
W > .
85 GeV,respectively.There were multiple triggers set up during the g
12 ex-periment. The trigger relevant to our reaction is the onewhere events were recorded with three charged particlesdetected in three different sectors of CLAS. Due to thecomplex trigger configuration, the efficiency of the trig-ger was studied and accounted for by including it intothe MC simulation. The same cuts, described previouslyfor the data, were also applied for the simulations. (a) ) [GeV] + p IM(n ) [ G e V ] - p I M ( n + S - S (b) ) [GeV] + p IM(n ) [ G e V ] - p I M ( n + S - S FIG. 9. The IM ( nπ − ) vs. IM ( nπ + ) distribution for datain (a) and simulation in (b) with the vertical and horizontalstrips reflecting Σ + and Σ − , respectively are shown. C. Yield, Acceptance & Luminosity
1. Kinematic Binning
The events that made it through the event selectionprocedure, representing the Λ(1520), were sorted intobins of center-of-mass (CM) energy ( W ) and azimuthalangle for the K + in the CM frame, cos θ c.m.K + . The CMenergy, W , is a function of photon energy, E γ , and themass of the proton target, m p .Events were also binned in center-of-mass (CM) en-ergy, W , and squared four-momentum transfer t . Themomentum transfer value is obtained from the Mandel-stam t -variable for the reaction γp → K + Λ(1520), t = ( P γ − P K + ) , (6)where P γ and P K + are the four-momenta of the incident (a) ) [GeV] + MM(K C oun t s (b) ) [GeV] + MM(K C oun t s FIG. 10. The yield extract fits for the Λ(1520) peak in the MM ( K + ) distribution for 2 . < W [GeV] ≤ .
35 and 0 . ≤ cos θ c.m.K + ≤ . → Σ + π − and Λ(1520) → Σ − π + , in (a) and (b), respectivelyare shown. The sum of the signal fit with a Voigtian function (dashed curve), along with the background estimated with apolynomial function (dotted curve), gives the total function (solid curve). The yield of the signal events is given by the integralof the signal fit curve. photon and the detected K + , respectively.For the differential cross sections as a function ofCM angle, 10 W -bins were taken in the range 2 . 25, each of 100 MeV width. Each W binwas studied with cos θ c.m.K + bins of width, ∆cos θ c.m.K + = 0 . − . ≤ cos θ c.m.K + ≤ . 9. For the cross sections as a func-tion of t , nine W -bins were taken in the range 2 . ≤ W [GeV] ≤ . 15, each of 100 MeV width, where each W bin was studied with various t bins, − . ≤ t [GeV ] ≤− . t = 0 . ]. Due to bad photonTagger scintillators, the events with W -values between2.55 GeV and 2.6 GeV were omitted so that, the fourth W -bin has a 50 MeV width (2 . < W [GeV] ≤ . 2. Yield Extraction The Λ(1520) peak in the M M ( K + ) distribution wasfit with a Gaussian-convoluted non-relativistic Breit-Wigner function, known as the Voigtian profile. Asecond-order polynomial function was chosen to estimatethe smooth background. Figure 10 shows fitting samplesfor a particular kinematic bin. The Voigtian centroid pa-rameter limits are set between 1.510 - 1.525 GeV, whereasthe non-relativistic Breit-Wigner width is limited to 14.6- 16.6 MeV. Both parameters are related to mass and fullwidth values for the Λ(1520) [3, 18]. The backgroundsubtracted signal yield Y ( W, cos θ c.m.K + or t ) was obtainedby integrating the Voigtian function, as shown above bythe region within the dashed curve in Fig. 10. 3. Acceptance The accepted number of events out of the total gen-erated events, from the MC simulation provide a scalefactor to correct the number of events in each kine-matic bin ( W, cos θ c.m.K + or t ). Hence, an acceptance value, A ( W, cos θ c.m.K + or t ), was calculated as the ratio of theMC events that were accepted to the total generatedevents and is given by A ( W, cos θ c.m.K + or t ) = Y acc N gen , (7)where Y acc is the accepted yield of the simulated eventsand N gen is the total number of generated events.The accepted events distributions were obtained us-ing the MC accepted files for both the channels. Thesesimulated files underwent a similar treatment to that ofthe data, including the cuts and corrections. Since theMC generates only the signal, the accepted event dis-tribution was fit using a Voigtian function only. Thenon-relativistic Breit-Wigner width, σ L , of the Voigtianfunction was kept fixed (for the MC fits only) at the phys-ical width of the Λ(1520), Γ Λ(1520) = 15 . 4. Luminosity The luminosity or flux, L ( W ), was evaluated as, L ( W ) = ρ p N A l t A p N γ ( W ) , (8)where N γ ( W ) is the number of incident photons in agiven W range, ρ p = 0 . is the density of0the proton target, l t = 40 cm is the target length, N A is Avogadro’s number, and A p = 1 . V. DIFFERENTIAL CROSS SECTIONS The differential cross sections for the reaction γp → K + Λ(1520) were calculated in cos θ c.m.K + bins using dσd cos θ c.m.K + = Y ( W, cos θ c.m.K + ) τ ∆ cos θ c.m.K + A ( W, cos θ c.m.K + ) L ( W ) × γ corr , (9)where Y ( W, cos θ c.m.K + ) is the yield value and A ( W, cos θ c.m.K + ) is the detector acceptance, L ( W ) isthe luminosity as a function of the center-of-mass ( W )energy, and τ accounts for the branching ratio factors.The differential cross sections were also obtained as afunction of t as, dσdt = Y ( W, t ) τ ∆ tA ( W, t ) L ( W ) × γ corr , (10)where Y ( W, t ) is the yield value and A ( W, t ) is the detec-tor acceptance. The kinematic bin widths, ∆ cos θ c.m.K + =0 . t = 0 . / c , represent the size of eachcos θ c.m.K + -bin and t -bin, respectively. The photon multi-plicity correction factor, γ corr , is 1.03.The decay modes of the Λ(1520) include a branchingratio factor (b.r.) of 0.42 via the Σ π channel into Σ + π − ,Σ − π + or Σ π . Using Clebsch-Gordon Coefficients, theindividual b.r. factor for the Σ π channels comes out to be0.14. The Σ + decays to a n and π + with a b.r. factor of0.48, whereas the Σ − decays to a n and a π − with a b.r. of1.0. Hence, the branching ratio used in Eqs. 9 and 10for the Λ(1520) → Σ + π − channel is 0.0672, whereas thebranching ratio factor used for Λ(1520) → Σ − π + chan-nel is 0.14. The branching ratio factors, τ , were appliedseparately to each decay channel in order to obtain theΛ(1520) differential cross sections for each decay mode.The differential cross sections for the two branches arethen averaged to obtain the Λ(1520) differential crosssections. The uncertainties were determined by standardpropagation of errors.The differential cross sections as a function of cos θ c.m.K + are shown in Fig. 11. The figure shows the current analy-sis in comparison with previous CLAS results [10] (hollowsquares). The results by Moriya et al . [10], uses a W binwidth of 100 MeV and cos θ c.m.K + bin width of 0.1. It canbe seen that there is good agreement between the differ-ential cross sections for the Λ(1520) between this analysisand previous CLAS results. The theoretical calculationsprovided by Seung-il Nam are also shown (as the dashedcurves) in the figure.Similarly, the differential cross sections as a functionof t are shown in Fig. 12. The theoretical calculationsprovided by Seung-il Nam are also shown (as the dashedcurves) in the figure. VI. SYSTEMATIC UNCERTAINTIES The systematic uncertainties for this study were es-timated by making variations on the different cuts andtaking the average relative difference in the final result.Hence, the systematic uncertainty is understood as theshift of the average of the relative differences from zero;zero being no net change in the result after a variation.The variation in the parameters was done by observingthe data and making an estimate of what range is a rea-sonable choice for each systematic uncertainty. For in-stance, a first-order polynomial function was taken as avariation to the nominal choice of second-order polyno-mial function for estimating the background. Similarly,tighter fiducial boundaries on the active region of thedetector were used as a deviation from the normal cuton those boundaries to determine the uncertainty due tothe fiducial cut. Similar variations are used for the otherparameters.The systematic uncertainties for this analysis, bothgeneral and specific, are summarized in Table I. The gen-eral systematic uncertainties that refer to the uncertain-ties due to the g 12 run conditions, for instances, fluxconsistency/luminosity, sector-by-sector, and target, areoutlined in [15]. For instance, the sector-by-sector uncer-tainty is computed by the deviation of the acceptance-corrected yields in each sector of the CLAS detector[14] from the average acceptance-corrected yield of allsix sectors. Similarly, the uncertainty from the targetaccounts for the variations of the pressure and temper-ature throughout the g 12 data-taking period. The re-action specific uncertainties that depend on the analysisprocess, cuts, and corrections performed during the studyare also reported. Each of the systematic effects has itscontribution to the total systematic uncertainty of thisanalysis. The total systematic uncertainty of 10.05% iscalculated by the sum in quadrature of all systematic un-certainties, assuming that they are independent of eachother. TABLE I. Summary of the systematic uncertainties calculatedin this analysis. Source Uncertainty t -slope dependence 0.78%Timing cut 4.11%Minimum | p | cut 0.20% z -vertex cut 1.28%Fiducial cut 3.13%Background function 2.07%Signal integral range 0.43%Flux consistency/luminosity [15] 5.70%Sector-by-sector [15] 5.90%Target [15] 0.50% Total Systematic Uncertainty 10.05% - - - - - 10 110 £ [GeV] W - - - - - 10 110 £ [GeV] W - - - - - 10 110 £ [GeV] W - - - - - 10 110 £ [GeV] W - - - - - 10 110 £ [GeV] W - - £ [GeV] W - - £ [GeV] W - - £ [GeV] W - - £ [GeV] W - - £ [GeV] W c.m. + K q cos b ] m [ c . m . + K q d c o s s d FIG. 11. Differential cross sections for γp → K + Λ(1520) are shown as solid circles for 10 center-of-mass energies ( W ) between2 . ≤ W [GeV] ≤ . 25 as a function of cos θ c.m.K + . The hollow squares show the previous CLAS results by Moriya et al .[10]. The theoretical calculations from the model of [12] are shown by the dashed curves. The error bars represent statisticaluncertainties. VII. DISCUSSION AND CONCLUSIONS As seen in Figs. 11 and 12, the model calculations byNam are in good agreement with our experimental re-sults. The theory calculations, represented by dashedcurves, are the numerical results without the N ∗ contri-bution, and conserve gauge invariance [12]. The calcula- tions with the N ∗ contribution (not shown in Figs 11and 12) indicate that the N ∗ contribution in the s -channel process is very small [12], and only slightlychanges the calculation in the first W bin. This is be-cause only N ∗ resonances with mass below 2.2 GeV areincluded in such calculations. For the u -channel, wherethere is intermediate Λ ∗ exchange, such an approach is2 - - - - - - 10 110 £ [GeV] W - - - - - - 10 110 £ [GeV] W - - - - - - 10 110 £ [GeV] W - - - £ [GeV] W - - - £ [GeV] W - - - £ [GeV] W - - - £ [GeV] W - - - £ [GeV] W - - - £ [GeV] W ] t [GeV ] b / G e V m [ d t s d FIG. 12. Differential cross sections for γp → K + Λ(1520) are shown as solid circles for 9 center-of-mass energies ( W ) between2 . ≤ W [GeV] ≤ . 15 as a function of momentum transfer t . The theoretical calculations from the model of [12] are shownby the dashed curves. The error bars represent statistical uncertainties. not needed to explain the experimental data as it doesnot significantly contribute to the calculation due to thesmall coupling constant of the proton-hyperon vertex.Consequently, even for the higher-energy region up to W = 3 . K -exchangediagram, as shown in Fig. 1, qualitatively reproducethe data without Regge, K ∗ , and hyperon resonances.Hence, we can conclude that the simplest theoreticalmodel with a pseudoscalar K -meson exchange, assuming t -channel dominance, is sufficient to explain the broadfeatures of our data, without the need for the inclusionof other reaction processes.The slight increases above the theory observed in thedata in the backward scattering region could be improvedby the inclusion of hyperon resonances in the u -channel, although the theoretical uncertainties, such as the EMtransition couplings between the hyperons, are consid-erable for the u -channel. Also, some small deviationsof the model compared to the data at forward anglesfor W > . N ∗ resonances and theRegge trajectories. Although not shown here, a more de-tailed theoretical study [12] has concluded that the K ∗ - N -Λ(1520) coupling must be very small in order to re-produce the data.Even though the theoretical calculations are adequateto explain the broad behavior of the experimental crosssections, we can say that there is an indication that athigher W there is a possibility for K ∗ exchange or a possi-ble interference of a K ∗ -exchange with the K -exchange.These future improvements may introduce a small cor-rection to the theoretical predictions. Hence, this studycan contribute to a better understanding of the Λ(1520)using higher-energy photoproduction data.Although our results do not show any evidence forhigher-mass N ∗ resonances decaying to the K + Λ(1520)final state, the lack of such evidence is useful in itself.One question that has surrounded the “missing reso-nances” problem is whether an N ∗ could have a strongpreference to decay into strangeness channels. For ex-3ample, there is some evidence from photoproduction of K ∗ + Λ that a few higher-mass N ∗ states have a significantdecay branch to that final state [19]. The present resultsindicate that these same higher-mass N ∗ states, if con-firmed, do not contribute to the K + Λ(1520) final state.The lack of N ∗ states contributing in the s -channel tothe current cross sections is a constraint on the branchingratios of possible higher-mass N ∗ states. Further explo-ration of the “missing resonances” at higher mass wouldbe better done using either the K ∗ Λ or the γp → π + π − p reaction [6]. A systematic study of the latter reaction, us-ing virtual photons, is being carried out with the CLAS12detector [20] (an upgrade of the CLAS detector) at Jef-ferson Lab and also at other facilities.We acknowledge the staff of the Accelerator andPhysics Divisions at the Thomas Jefferson National Ac-celerator Facility who made this experiment possible. This work was supported in part by the Chilean Comisi´onNacional de Investigaci´on Cient´ıfica y Tecnol´ogica (CON-ICYT), the Italian Istituto Nazionale di Fisica Nucleare,the French Centre National de la Recherche Scientifique,the French Commissariat `a l’Energie Atomique, the U.S.Department of Energy, the National Science Founda-tion, the Scottish Universities Physics Alliance (SUPA),the United Kingdom’s Science and Technology FacilitiesCouncil, and the National Research Foundation of Ko-rea. The Southeastern Universities Research Association(SURA) operates the Thomas Jefferson National Acceler-ator Facility for the United States Department of Energyunder contract DE-AC05-06OR23177. Appendix A: Data Table TABLE II: Differential cross sections for γp → K + Λ(1520), as a functionof CM angle. The uncertainties represent only the statistical contribu-tions. W [GeV] cos θ c.m.K + dσ/d cos θ c.m.K + [ µ b](2.25, 2.35) ( − − ± − − ± − − ± − − ± − ± ± ± ± ± − − ± − − ± − − ± − − ± − ± ± ± ± ± − − ± − − ± − − ± − − ± − ± ± ± ± ± − − ± − − ± − ± ± ± ± ± − − ± − − ± − ± ± ± Table II Continued.. W [GeV] cos θ c.m.K + dσ/d cos θ c.m.K + [ µ b](2.65, 2.75) (0.5, 0.7) 0.445 ± ± − − ± − − ± − ± ± ± ± ± − − ± − ± ± ± ± ± ± ± ± ± ± ± ± ± ± γp → K + Λ(1520) as a functionof t . The uncertainties represent only the statistical contributions. W [GeV] t [GeV ] dσ/dt [ µ b/GeV ](2.25, 2.35) ( − − ± − − ± − − ± − − ± − − ± − − ± − − ± − − ± − − ± − − ± − − ± − − ± − − ± − − ± − − ± − − ± − − ± − − ± − − ± − − ± − − ± − − ± − − ± − − ± − − ± − − ± − − ± − − ± − − ± − − ± − − ± − − ± Table III Continued.. 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