Photoproduction of η mesons off the proton for 1.2< E γ <4.7 GeV using CLAS at Jefferson Laboratory
T. Hu, Z. Akbar, V. Crede, K.P. Adhikari, S. Adhikari, M.J. Amaryan, G. Angelini, G. Asryan, H. Atac, C. Ayerbe Gayoso, L. Barion, M. Battaglieri, I. Bedlinskiy, F. Benmokhtar, A. Bianconi, A.S. Biselli, F. Bossu, S. Boiarinov, W.J. Briscoe, W.K. Brooks, D.S. Carman, J. Carvajal, A. Celentano, P. Chatagnon, T. Chetry, G. Ciullo, L. Clark, B.A. Clary, P.L. Cole, M. Contalbrigo, R. Cruz-Torres, A. D'Angelo, N. Dashyan, R. De Vita, M. Defurne, A. Deur, S. Diehl, C. Djalali, M. Dugger, R. Dupre, H. Egiyan, M. Ehrhart, A. El Alaoui, L. El Fassi, P. Eugenio, G. Fedotov, R. Fersch, A. Filippi, G. Gavalian, G.P. Gilfoyle, F.X. Girod, D.I. Glazier, E. Golovatch, R.W. Gothe, K.A. Griffioen, M. Guidal, L. Guo, K. Hafidi, H. Hakobyan, C. Hanretty, N. Harrison, M. Hattawy, T.B. Hayward, D. Heddle, K. Hicks, A. Hobart, M. Holtrop, Y. Ilieva, I. Illari, D.G. Ireland, B.S. Ishkhanov, E.L. Isupov, D. Jenkins, H.S. Jo, K. Joo, S. Joosten, D. Keller, M. Khachatryan, A. Khanal, M. Khandaker, A. Kim, C.W. Kim, W. Kim, F.J. Klein, V. Kubarovsky, L. Lanza, M. Leali, P. Lenisa, K. Livingston, I.J.D. MacGregor, D. Marchand, N. Markov, V. Mascagna, M.E. McCracken, B. McKinnon, C.A. Meyer, Z.E. Meziani, T. Mineeva, V. Mokeev, A. Movsisyan, et al. (51 additional authors not shown)
PPhotoproduction of η mesons off the proton for . < E γ < . GeV using CLAS atJefferson Laboratory
T. Hu, Z. Akbar, ∗ V. Crede, † K.P. Adhikari, ‡ S. Adhikari, M.J. Amaryan, G. Angelini, G. Asryan, H. Atac, C. Ayerbe Gayoso, L. Barion, M. Battaglieri,
42, 20
I. Bedlinskiy, F. Benmokhtar, A. Bianconi,
45, 23
A.S. Biselli, F. Boss`u, S. Boiarinov, W.J. Briscoe, W.K. Brooks, D.S. Carman, J. Carvajal, A. Celentano, P. Chatagnon, T. Chetry, G. Ciullo,
18, 13
L. Clark, B.A. Clary, P.L. Cole,
28, 17
M. Contalbrigo, R. Cruz-Torres, A. D’Angelo,
21, 38
N. Dashyan, R. De Vita, M. Defurne, A. Deur, S. Diehl, C. Djalali,
34, 40
M. Dugger, R. Dupre, H. Egiyan, M. Ehrhart, A. El Alaoui, L. El Fassi,
30, 1
P. Eugenio, G. Fedotov, § R. Fersch, A. Filippi, G. Gavalian,
42, 35
G.P. Gilfoyle, F.X. Girod,
42, 7
D.I. Glazier, E. Golovatch, R.W. Gothe, K.A. Griffioen, M. Guidal, L. Guo,
14, 42
K. Hafidi, H. Hakobyan,
43, 51
C. Hanretty, N. Harrison, M. Hattawy, T.B. Hayward, D. Heddle,
8, 42
K. Hicks, A. Hobart, M. Holtrop, Y. Ilieva, I. Illari, D.G. Ireland, B.S. Ishkhanov, E.L. Isupov, D. Jenkins, H.S. Jo, K. Joo, S. Joosten,
1, 41
D. Keller,
49, 34
M. Khachatryan, A. Khanal, M. Khandaker, ¶ A. Kim, C.W. Kim, W. Kim, F.J. Klein, V. Kubarovsky, L. Lanza, M. Leali,
45, 23
P. Lenisa,
13, 18
K. Livingston, I.J.D. MacGregor, D. Marchand, N. Markov, V. Mascagna,
44, 23, ∗∗ M.E. McCracken, B. McKinnon, C.A. Meyer, Z.E. Meziani,
1, 41
T. Mineeva, V. Mokeev, A. Movsisyan, E. Munevar, †† C. Munoz Camacho, P. Nadel-Turonski,
42, 6
S. Niccolai, G. Niculescu, T. O’Connell, M. Osipenko, A.I. Ostrovidov, M. Paolone, L.L. Pappalardo,
13, 18
R. Paremuzyan, E. Pasyuk, W. Phelps, O. Pogorelko, J. Poudel, J.W. Price, Y. Prok, D. Protopopescu, B.A. Raue,
14, 42
M. Ripani, J. Ritman, A. Rizzo,
21, 38
G. Rosner, J. Rowley, F. Sabati´e, C. Salgado, A. Schmidt, ‡‡ R.A. Schumacher, Y.G. Sharabian, U. Shrestha, Iu. Skorodumina,
40, 39
D. Sokhan, O. Soto, N. Sparveris, S. Stepanyan, P. Stoler, I.I. Strakovsky, S. Strauch, J.A. Tan, N. Tyler, M. Ungaro,
42, 9
L. Venturelli,
45, 23
H. Voskanyan, E. Voutier, D.P. Watts, K. Wei, X. Wei, M.H. Wood, N. Zachariou, J. Zhang,
49, 35 and Z.W. Zhao
10, 35 (The CLAS Collaboration) Argonne National Laboratory, Argonne, Illinois 60439, USA Arizona State University, Tempe, Arizona 85287-1504, USA California State University, Dominguez Hills, Carson, California 90747, USA Canisius College, Buffalo, New York 14208, USA Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA Catholic University of America, Washington, DC 20064, USA IRFU, CEA, Universit´e Paris-Saclay, F-91191 Gif-sur-Yvette, France Christopher Newport University, Newport News, Virginia 23606, USA University of Connecticut, Storrs, Connecticut 06269, USA Duke University, Durham, North Carolina 27708-0305, USA Duquesne University, Pittsburgh, Pennsylvania 15282, USA Fairfield University, Fairfield, Connecticut 06824, USA Universit`a di Ferrara, 44121 Ferrara, Italy Florida International University, Miami, Florida 33199, USA Florida State University, Tallahassee, Florida 32306, USA The George Washington University, Washington, DC 20052, USA Idaho State University, Pocatello, Idaho 83209, USA 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 f¨ur Kernphysik, 52425 J¨ulich, Germany James Madison University, Harrisonburg, Virginia 22807, USA Kyungpook National University, Daegu 41566, Republic of Korea Lamar University, 4400 MLK Blvd, P.O. Box 10009, Beaumont, Texas 77710, USA Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA Mississippi State University, Mississippi State, Mississippi 39762-5167, USA National Research Centre Kurchatov Institute - ITEP, Moscow, 117259, Russia University of New Hampshire, Durham, New Hampshire 03824-3568, USA Norfolk State University, Norfolk, Virginia 23504, USA a r X i v : . [ nu c l - e x ] J un Ohio University, Athens, Ohio 45701, USA Old Dominion University, Norfolk, Virginia 23529, USA Rensselaer Polytechnic Institute, Troy, New York 12180-3590, USA University of Richmond, Richmond, Virginia 23173, USA Universit`a 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, USA Temple University, Philadelphia, Pennsylvania 19122, USA Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606, USA 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 Virginia Tech, Blacksburg, Virginia 24061-0435, USA University of Virginia, Charlottesville, Virginia 22901, USA College of William and Mary, Williamsburg, Virginia 23187-8795, USA Yerevan Physics Institute, 375036 Yerevan, Armenia (Dated: Received: June 15, 2020/ Revised version:)Photoproduction cross sections are reported for the reaction γp → pη using energy-tagged photonsand the CLAS spectrometer at Jefferson Laboratory. The η mesons are detected in their dominantcharged decay mode, η → π + π − π , and results on differential cross sections are presented for incidentphoton energies between 1.2 and 4.7 GeV. These new η photoproduction data are consistent withearlier CLAS results but extend the energy range beyond the nucleon resonance region into theRegge regime. The normalized angular distributions are compared with the experimental resultsfrom several other experiments, and with predictions of η -MAID 2018 and the latest solution of theBonn-Gatchina coupled-channel analysis. Differential cross sections dσ/dt are presented for incidentphoton energies E γ > . W > . t -channel (Regge models). The data confirm the expecteddominance of ρ , ω vector-meson exchange in an analysis by the Joint Physics Analysis Center. PACS numbers: 13.60.Le, 13.60.-r, 14.20.Gk, 25.20.Lj
I. INTRODUCTION
The photoproduction of pseudoscalar mesons on thenucleon has remained of interest in recent years for thestudy of meson production in hadronic reactions acrossa wide range of energies. At low energies using incidentphoton energies below 3.0 GeV, information about thenucleon excitation spectrum can be extracted, whereasat higher energies above E γ ≈ t -channel exchange ofmassive quasi-particles known as Reggeons can be stud-ied [1]. These two regimes are analytically connected, but ∗ Present address: University of Virginia, Charlottesville, Virginia22901, USA † Corresponding author: [email protected] ‡ Present address: Mississippi State University, Mississippi State,Mississippi 39762-5167, USA § Present address: Ohio University, Athens, Ohio 45701, USA ¶ Present address: Idaho State University, Pocatello, Idaho 83209,USA ∗∗ Present address: Universit`a degli Studi di Brescia, 25123 Brescia,Italy †† Present address: Thomas Jefferson National Accelerator Facility,Newport News, Virginia 23606, USA ‡‡ Present address: The George Washington University, Washing-ton, DC 20052, USA the scarcity of cross section and polarization data for theenergy range 3–6 GeV have thus far hindered our un-derstanding of the transition from the baryon resonanceregime to high-energy photoproduction.In the nucleon resonance region, abundant data on η photoproduction on the proton are available from thereaction threshold at W thres . ≈ .
49 GeV up to the fourthresonance region just below W ≈ η mesons is a selective probe for the study of nu-cleon excitations. Although photons incident on protonscouple to both isospin I = 0 , η mesonin the final state serves as an isospin filter for baryon ex-citations since isospin I = 3 / N η final states.Near the production threshold, the dominance of thetwo nucleon resonances N (1535) 1 / − and N (1650) 1 / − in η photoproduction is undisputed [7, 8]. Small con- FIG. 1. Dominant contributions to η photoproduction off thenucleon: s -channel intermediate nucleon resonance excitation(left) and t -channel exchange of Reggeons (right). tributions have also been observed in ( γ, η ) from the N (1520) 3 / − state, which itself couples strongly to the N η decay mode. The state was identified mainly fromthe S - D interference term in the description of thephoton-beam asymmetry [9–12] indicating the impor-tance of polarization observables. Also available areresults from MAMI for the transverse target asymme-try T , and the beam-target asymmetry F [13]. The he-licity asymmetry E was reported by the CLAS Collabo-ration at Jefferson Lab [14] and the A2 Collaboration atMAMI [15]. More recently, results on the target asymme-try T and the double-polarization observables E , G (lon-gitudinal target polarization) as well as P , H (transversetarget polarization) in the photoproduction of η mesonsoff protons were reported by the CBELSA/TAPS Col-laboration at ELSA [16].In their bi-annual editions, the listing of nucleon res-onances by the Particle Data Group (PDG) in the Re-view of Particle Physics [17] has undergone significantupgrades based on the recent photoproduction data fromthe above facilities with almost no N ∗ resonance leftuntouched since 2010. Several new nucleon states havebeen added, some of which show strong couplings to N η .Above 1700 MeV in overall center-of-mass energy, a third1 / − state, N (1895) 1 / − , is now listed as a new reso-nance with a four-star rating indicating its existence iscertain in both its overall status and its N η decay mode.In the 1 / + wave, a large contribution in ( γ, η ) is ob-served from the N (1710) 1 / + resonance, the status ofwhich has been upgraded to three stars in its N η de-cay mode. In the fourth resonance region and above,discrepancies occur in various amplitude analyses. Suchambiguities are not surprising in light of the remaining incompleteness of the η photoproduction database. Theexperimental status of η photoproduction from nucleonsand nuclei, as well as phenomenological progress was re-cently reviewed in Ref. [18].The theoretical description of high-energy photopro-duction provides constraints on the amplitudes utilized inlow-energy meson photoproduction to extract the spec-trum of excited baryons [19]. Moreover, understandingthe meson photoproduction mechanism at high energiesis a crucial component of a broader program to search for gluonic excitations in the meson spectrum, which isthe primary goal of the GlueX experiment in Hall D atJefferson Lab [20, 21]. The dominant contributions to η photoproduction are shown in Fig. 1.In this paper, differential cross sections are presentedfor the reaction γp → pη from CLAS at Jefferson Lab,where the η was identified through the detection of itsdecay products π + π − π . The new data reported herecover an incident photon energy range E γ from 1.2 GeVup to 4.7 GeV.This paper has the following structure. A summaryof previous measurements in η photoproduction is pre-sented in Sec. II. Section III gives an introduction to theCLAS-g12 experimental setup. The data reconstructionand event selection are discussed in Sec. IV and the ex-traction of the cross sections is described in Sec. V. Fi-nally, the experimental results and a discussion of thephysics, as well as the observed resonance contributionsare presented in Secs. VI and VII. II. PREVIOUS MEASUREMENTS
Cross sections for the reaction γp → pη were mea-sured at many different laboratories over a wide kine-matic range and in various η decay modes using eithertagged-photon beams produced in Compton scattering oflaser photons off electrons in the accelerator [11, 22, 23] orvia the bremsstrahlung technique [24–29]. A whole “in-dustry” of photoproduction experiments recorded datafor several meson-production channels in the 60s and 70s.Results were mostly published at higher energies and onlya few data points bridge the gap down to the resonanceregion below E γ ≈ η photoproduction cross sections from thenucleon is given in Table I. The current status of single- η meson production using photon beams is reviewed inRef. [30], and in particular the information that can beobtained on the spectrum of light, non-strange baryons. A summary of older experiments (1960s and 1970s)
At the 5 GeV electron synchrotron NINA at the Dares-bury Laboratory, a linearly polarized bremsstrahlungbeam was used to extract differential cross sectionsfor the reaction γp → pη at incident photon ener-gies of 2.5 GeV and 3.0 GeV, and for various t -valuesbetween − . and − . [31]. The inci-dent photon intensity as a function of energy was de-rived from a quantameter, together with the shape ofthe spectrum as measured with a pair spectrometer.At the Deutsches Elektronen-Synchrotron (DESY), abremsstrahlung beam was produced on a tungsten targetand the flux was measured with a gas-filled quantameter.Cross section results for η photoproduction were reportedat mean photon energies of 4 and 6 GeV in the momen-tum transfer range between zero and 1.4 GeV [32]. Fi-nally, a bremsstrahlung beam from a tungsten target wasused at the Cambridge Electron Accelerator (CEA) atthe Massachusetts Institute of Technology (MIT). Thebeam was monitored with a quantameter that was cali-brated against a Faraday cup and whose output was mea-sured with a current integrator [33]. Results for η pho-toproduction at 4 GeV were published in Ref. [34].Measurements at higher incident photon energiesin the range 6.0–16.0 GeV were performed at theStanford Linear Accelerator Center (SLAC) using abremsstrahlung beam [35]. The beam was monitoredby detecting Cherenkov light of e + e − pairs from a con-verter in the beam. The Cherenkov monitor was cali-brated against a precision calorimeter [36]. In Ref. [37],the overall uncertainty in normalization was estimated at10 %; other references give even smaller uncertainties, seee.g. Ref. [36]. The SLAC high-power quantameter wasused for the measurement of the incident photon flux andis described in Ref. [38]. A. Experiments using Compton backscattering
The GRenoble Anneau Accelerateur Laser (GRAAL)experiment measured the differential η photoproductioncross sections from threshold up to 1100 MeV [22] and upto 1500 MeV [11] in incident photon laboratory energyand for cos θ c . m . < .
85 of the η meson in the overallcenter-of-mass (c.m.) frame. The facility was located atthe European Synchrotron Radiation Facility (ESRF) inGrenoble, France. For a detailed description of the facil-ity, see Ref. [5]. The tagged and polarized γ -ray beamwas produced by Compton scattering of laser photons offthe 6 GeV electrons circulating in the storage ring. Thephoton energy was provided by an internal tagging sys-tem consisting of silicon microstrips for the detection ofthe scattered electron and a set of plastic scintillators fortime-of-flight (TOF) measurements [11]. A thin monitorwas used to measure the beam flux (typically 10 γ /s).The monitor efficiency of (2 . ± .
03) % was estimatedby comparing with the response of a lead/scintillatingfiber calorimeter at a low rate.At the SPring-8/LEPS facility, the photon beam wasproduced by backward-Compton scattering of laser pho-tons off electrons with an energy of 8 GeV. Data were ac-cumulated with 1 . × photons at the target and crosssection results on the reaction γp → pη were extractedfor the incident photon energy range E γ ∈ [ 1 . , . θ c . m . < − .
6) [23].
B. Experiments using bremsstrahlung photons
At the ELectron Stretcher Accelerator (ELSA) [3], twovery different experimental setups extracted cross section data for the photo-produced pη final state. In 2001, theCB-ELSA detector recorded data and η photoproductionwas studied in the neutral decays of the η meson into γγ and π π π [24, 25]. The original experiment consisted ofthe CsI(Tl)-based Crystal Barrel (CB) calorimeter cov-ering 97.8 % of the 4 π solid angle [39]. For the 2000/2001data taking, electrons were extracted in two separateexperiments at energies of 1.4 and 3.2 GeV, coveringtagged-photon energies from 0.3 up to about 3.0 GeV,with a typical intensity of 1–3 × tagged photons/s.The experimental setup was later modified and in a se-ries of measurements in 2002/2003, a combination of theCB calorimeter and the BaF TAPS detector in the for-ward direction was used. Results of the CBELSA/TAPSsetup on single- η cross section measurements off the pro-ton can be found in Ref. [27]. The data provide improvedangular coverage in the forward and backward directionin the c.m. system.At the upgraded Mainz Microtron (MAMI-C), an ex-perimental setup using a combination of the NaI(Tl)Crystal Ball and BaF TAPS multi-photon spectrometersrecorded high-quality data on the reaction γp → pη in theenergy range from the production threshold at 707 MeVto 1.4 GeV [28, 29]. The NaI(Tl) crystals were arrangedin two hemispheres that covered 93 % of the 4 π solid angleand the TAPS calorimeter subtended the full azimuthalrange for polar angles from 1 ◦ to 20 ◦ . Since the TAPScalorimeter was installed 1.5 m downstream of the Crys-tal Ball center, the resolution of TAPS in the polar an-gle θ was better than 1 ◦ . For an electron beam energyof 1508 MeV, a tagger channel in this experiment had awidth of about 2 MeV at 1402 MeV and about 4 MeV atthe η -photoproduction threshold of E γ = 707 MeV.At the Continuous Electron Beam Accelerator Facility(CEBAF) at Jefferson Laboratory (Jefferson Lab), theCEBAF Large Acceptance Spectrometer (CLAS) was op- Reaction W [ GeV ] − t [ GeV ] Reference γp → pη − A2 [28, 29]1.55 – 2.80 − CLAS [26, 44]1.51 – 2.55 − CB-ELSA [24, 25]1.57 – 2.38 − CBELSA/TAPS [27]1.49 – 1.92 − GRAAL [11, 22]1.97 – 2.32 − LEPS [23]2.36 & 2.55 0.2 – 1.2 Daresbury [31]2.90 & 3.48 0.0 – 1.4 DESY [32]2.90 < . γn → nη − A2 [41]1.50 – 2.18 − CBELSA/TAPS [42]1.59 – 2.07 − CBELSA/TAPS [43]TABLE I. Summary of experimental data on cross sectionsfor η photoproduction off the nucleon. Fig. 2. Side view of the CLAS detector in Hall B with beamline and associated equipment. B . A . M ec k i ng e t a l. / N u c l e a rI n s t r u m e n t s and M e t hod s i n P hy s i c s R e s e a r c h A FIG. 2. Side view of the CLAS detector in Hall B at Jefferson Lab including the photon tagging facility upstream of CLAS.Reproduced figure with permission from Ref. [2]. Copyright 2003 by Elsevier. timized for charged-particle tracking. A detailed descrip-tion of the spectrometer and its various detector compo-nents is given below and in Ref. [2]. The CLAS “g1”experiment accumulated data in 1998 (g1a) and in 1999(g1c) using electron beam energies of 2.49 and 2.45 GeV,respectively. These experiments used a single-prong trig-ger configuration. Results for the reaction γp → pη wereonly published from the CLAS “g1a” experiment [44].For the absolute normalization of the η channel, theSAID-SM02 solution [45] was used. The normalizationuncertainty for all incident photon energies below 2 GeVwas estimated at 3 % [44].The CLAS “g11a” experiment accumulated a high-statistics data sample in 2004 of about 20 × triggeredevents. An electron beam of energy E e − = 4 .
023 GeVwas used to generate tagged photons with energies be-tween 0.81 and 3.81 GeV covering center-of-mass energiesup to √ s ≈ .
84 GeV. Results on η cross section mea-surements for E γ < . III. EXPERIMENTAL SETUP
The γp → pη measurements discussed here were per-formed at Jefferson Lab from March to June 2008 us-ing the CLAS spectrometer [2] in Hall B. The experi-mental setup is shown in Fig. 2. The incident tagged,bremsstrahlung photon beam was produced from a 60–65 nA electron beam of energy E e − = 5 .
715 GeV de-livered by the CEBAF accelerator. These measurementswere part of the CLAS-g12 experiment, which was a high-luminosity data-taking period. The tagging system pro- vided a circularly polarized, real-photon beam with thehighest available photon energies of any CLAS experi-ment of up to E γ ≈ . E e − . The photons impinged upon a 40-cm longunpolarized liquid-hydrogen target, which was moved up-stream by 90 cm from the center of the CLAS spectro-meter to enhance the acceptance of charged tracks inthe forward direction. Various results from the CLAS-g12 experiment have been recently published and arediscussed in Refs. [47–50]. First cross section measure-ments have been presented in short papers on the re-action γp → pπ → pe + e − ( γ ) [48] and on the reaction γp → K + K + ( X ) [50] in the search for excited Ξ baryons.A brief overview of the CLAS performance is givenin the following section; a full description of the CLASspectrometer can be found in Ref. [2]. The remainingsections describe at greater length those components ofthe experimental setup that differ from previous CLASexperiments or are particularly relevant for the cross sec-tion measurements. A. Overview
The charged tracks in the experiment were detectedin the CLAS spectrometer, which provided coverage forcharged particles in the polar-angle range 8 ◦ < θ lab < ◦ . The three momentum components of the parti-cles were reconstructed from their tracks in the toroidalmagnetic field of the spectrometer by a set of threedrift-chamber packages [51]. Time-of-flight (TOF) in-formation was available from plastic scintillators [52] lo-cated about 5 m from the center of CLAS. The spec-trometer provided a momentum and angle resolution of∆ p/p ≈ θ ≈ ◦ – 2 ◦ , respectively. A set of plas-tic scintillation counters close to the target (referred toas the start counter) provided event start times [53]. Forthis experiment, coincident signals from the photon tag-ger, start counter, and time-of-flight system constitutedthe event trigger that required a coincidence between ascattered-electron signal from the photon tagger and anenergy-dependent number of charged tracks in CLAS (seeSection III E for details). B. The tagging system
The bremsstrahlung beam was produced from a thingold radiator and photons were tagged by detectingenergy-degraded electrons, which were deflected in themagnetic field of a single dipole magnet. The CLAS tag-ging system used a hodoscope that contained two planararrays of plastic scintillators [54]. The first layer of 384partially overlapping small scintillators (E-counters) pro-vided the photon energy resolution of ∼ × − , whilethe second layer of 61 larger scintillators (T-counters)provided the timing resolution of about 160 ps necessaryto form a coincidence with the corresponding chargedparticles that were produced in the nuclear interactiontriggered by the tagged photon.The arrangement of the E-counters is relevant for thediscussion of the cross-section results presented here. Thewidths of the counters ranged from 6 to 18 mm in order toprovide approximately constant momentum intervals of0 . E e − . Since each counter optically overlapped its ad-jacent neighbors by one-third of their respective widths,a total of 767 separate incident photon energy bins wasavailable with an energy resolution of r = 0 . E e − . As-suming equal acceptance along the length of each paddle,the element for the photon energy in the covariance ma-trix is given by: σ E γ = 12 r r (cid:90) − r E dE = r . The CLAS-g12 experiment recorded data at the high-est possible CEBAF energies of E e − = 5 .
715 GeV andtherefore, σ E γ = 3 . W was chosenfor W < . E e − ,the width of the W bins translates into the smallest binwidth in incident photon energy for the entire analyzedenergy range. This resolution effect, combined with ob-served small fluctuations in our extracted cross sectionsat the lower end of the tagging range, which are believedto originate from the measured incident photon flux, re-quired additional adjustments of the chosen E γ binning. [ns] TGPB t ∆ -4 -2 0 2 4 C oun t s × FIG. 3. (Color online) Distribution of the tagger-start countercoincidence times. The 2-ns bunch structure is visible. Eventswere considered for further analysis only if a single photoncandidate remained after a timing cut of ∆ t TGPB < C. Particle identification
Particle identification (PID) of charged final-statehadrons in this experiment was based on the combinedinformation from the drift chamber and TOF systems.A value for β , defined as the ratio of the particle speedrelative to the speed of light, could be measured in twodifferent ways:1. An empirically measured value for each particle, β m = v/c , was based on timing information fromthe time-of-flight and start counter systems, and2. Independently, a value for each particle, β c = p/E ,could be determined from the measured momen-tum using the CLAS drift chambers and the PDGmass [17] for the particle.PID could then proceed by evaluating the distributionof ∆ β = | β c − β m | values and defining proper event-by-event selection criteria.The CEBAF electrons were delivered to the CLAS-g12 experiment in 2-ns bunches. Several bunches arrivedat the tagger within the trigger coincidence window andeach bunch contained many electrons. Therefore, manyphoton candidates were recorded for each event; randomhits could also occur from background sources, e.g. cos-mic radiation. To determine the correct initial-state pho-ton, the time differences were used between the eventvertex-time based on the final-state tracks and the tag-ger vertex-time for each photon candidate.The event vertex-time, t event , was given as an averageover the event’s track times t track = t ST − dc β m , where t ST denotes the start-counter time and d is thedistance from the interaction point to the correspondingstart-counter paddle. The time, t γ , for each photon can-didate is given by the recorded electron-triggered taggertime corrected for the propagation from the target centerto the event vertex along the beam axis. Figure 3 showsthe coincidence time ∆ t TGPB = t event − t γ . The 2-nstime structure is clearly visible. In the CLAS-g12 ex-periment, selecting photons from the central coincidencepeak and discarding events with more than one photoncandidate resulted in a remaining non-negligible acciden-tal background of about 13 % due to the relatively highelectron beam current of 60–65 nA. D. The liquid-hydrogen target
In the CLAS-g12 experiment, the liquid-hydrogen tar-get was not positioned at the center of CLAS but wasmoved upstream by 90 cm to allow for the enhanced de-tection of peripherally produced mesons off the protonwith the goal to search for and study excited mesons atthe highest available CEBAF energies. The target cellwas 40 cm in length and 2 cm in diameter. The z -vertexdistributions (coordinate along the beamline) for dataand Monte Carlo events are shown in Fig. 4. The targetlength and the position offset from the CLAS center areclearly visible.In the CLAS-g12 experiment, the target temperatureand pressure were sampled continuously throughout eachrun. Since the overall uncertainty in the target densitywas smaller than the geometrical uncertainty in the di-mensions of the Kapton cell, the uncertainty in the liquid-hydrogen density was not considered a factor in the bud-get of the various systematic uncertainties. E. Trigger
The entire CLAS-g12 data set was classified into manydifferent groups of runs according to their trigger config-urations. Some of these configurations applied a tagger pre-scaling to enhance events with high photon energies.For this analysis, we used a fraction of the total statis-tics that was not subject to pre-scaling to avoid addi-tional complications in the absolute normalization of themeasured angular distributions.The TOF counters generated signals for the CLASlevel-1 trigger. These detectors were positioned out-side the CLAS tracking system in a symmetric six-sector arrangement, geometrically defined by the coilsof the CLAS toroidal magnet. For the data presentedhere, the trigger required a scattered electron in the z Vertex [ cm ]-120 -100 -80 -60 C oun t s FIG. 4. (Color online) The z -vertex distribution of γp → pη Monte Carlo (black) and data events (blue). The targetlength of 40 cm is clearly visible. In this experiment, thetarget cell was moved upstream from the CLAS center by90 cm. The vertical lines define the range of the z -vertex cut. bremsstrahlung tagger in coincidence with either (a) (atleast) three charged tracks in different sectors with norestrictions on any photon energy, or (b) only two tracksin different sectors with the additional requirement of ob-serving at least one tagger photon with an energy above3.6 GeV. Along with several ancillary trigger conditions,these requirements resulted in a livetime of the data-acquisition system of about 87 %. About 20–30 recordedphotons per event were observed using a trigger coinci-dence window of approximately 100 ns. IV. CALIBRATION AND EVENTRECONSTRUCTION
The calibration of the individual spectrometer compo-nents followed the CLAS standard procedures [55]. In theprocess, inefficient TOF paddles were identified and laterremoved from the analysis in a standardized approach forreal data and simulated events. The latter is particularlyimportant for the trigger simulation. The details of theMonte Carlo simulations are described in Section IV A.Charged particles emerging from the event vertex in-teract with various detector components and materials,e.g. target, beam pipe, and start counter, and there-fore, are subject to energy loss along their trajectories.The standard CLAS ELoss-package [56] was applied toaccount for these interactions. Each particle track alsoneeded to be momentum corrected owing to small mis-alignments of the three CLAS drift chamber regions andfluctuations in the toroidal magnetic field. The momen-tum corrections for each charged particle were deter- bD -0.1 0 0.1 C oun t s · = 0.009 s bD -0.1 0 0.1 C oun t s · = 0.011 s × p [ GeV ] m β ± π proton FIG. 5. (Color online) Left and middle: ∆ β = | β c − β m | distributions for protons and positively charged pions, respectively.The blue area indicates the 3 σ cut according to Eq. (1). Right: The distribution of β m vs. particle momentum after the 3 σ cut.Note that the momentum range is limited to p < . mined in kinematic fitting for the exclusive γp → pπ + π − reaction, where the mean values of the corresponding mo-mentum pull distributions were tuned in an iterative pro-cedure. The corrections were small and typically of theorder of a few MeV. The set of simulated events did notundergo any momentum corrections. A. Preparation of the π + π − π final state The reconstruction of the pη channel was based onpreparing a data set of photoproduced pπ + π − π events.The same data set was also used to extract the crosssections for the reactions γp → pω → p ( π + π − π ) ω and γp → K Σ + → ( π + π − ) K ( pπ ) Σ + , which will be dis-cussed in subsequent publications. The only major dif-ference in extracting the cross sections for these threereactions was the subtraction of background events. Forthis reason, the next section will focus on the reconstruc-tion of the general reaction γp → p π + π − π , followed bya separate section on describing the background subtrac-tion. The preparation of the pη event sample resulted inthe reconstruction of 269,308 η → π + π − π events for theincident photon energy range 1 . < E γ < .
72 GeV or1 . < W < .
12 GeV in center-of-mass energy.
Event reconstruction and selection criteria
The CLAS spectrometer was optimized for detectingand measuring charged particles. However, the overcon-strained event kinematics allows for the reconstruction ofa single neutral meson. The reaction γp → pπ + π − ( π )with a missing π was identified in a first step by re-quiring exactly one proton track and two charged-piontracks. Positively and negatively charged pions weredistinguished by their track curvatures in the toroidalfield. The acceptance of π − mesons was smaller than for π + mesons since they were bent toward the beamline and a large fraction escaped through the forward hole of theCLAS spectrometer. The π meson was later identifiedin kinematic fitting.Standard particle identification was then improved byevaluating ∆ β distributions and applying a 3 σ cut oneither the proton or the π + meson:∆ β = | β c − β m | = (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (cid:115) p m + p − β m (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) < σ , (1)where β m and β c are based on information from the TOFand the drift-chamber system, respectively, as defined inSection III C. While the quantity ∆ β depends on par-ticle momentum, the ∆ β distribution is approximatelyGaussian when summed over all β m values, with width σ = 0 .
009 and 0 .
011 for the proton and pions, respec-tively. Figure 5 shows the ∆ β distributions for protons(left) and charged pions (center). The tail on the left sideof the ∆ β peak for pions originates from misidentifiedelectrons. Also shown in Fig. 5 (right) is the distributionof β m versus particle momentum after the 3 σ cut accord-ing to Eq. (1). Clear bands for the proton and the pionsare visible.Standard fiducial cuts [55] geometrically suppressedevents outside of the active detector regions where theacceptance was well behaved and reliably reproducedin simulations. For example, the magnetic field variedrapidly close to the torus coils rendering these regionsdifficult to simulate. This effect was more dramatic inthe forward direction, where the coils occupied a largeramount of the solid angle for small polar angles. Suchregions were studied for charged hadrons with exclusive γp → pπ + π − events and defined as upper and lower lim-its of the azimuthal angle φ lab from the center of a givensector. Due to the hyperbolic geometry of CLAS and thepresence of a toroidal magnetic field, the fiducial bound-aries of φ lab are functions of a track’s momentum, charge,and polar angle. Moreover, events were removed fromthis analysis if the primary interaction z -vertex was veryclose to the downstream boundary of the liquid-hydrogen CL (Monte Carlo)0 0.2 0.4 0.6 0.8 1 C oun t s · CL (data)0 0.2 0.4 0.6 0.8 1 C oun t s · Normalized Slopes-1 -0.5 0 0.5 1 C oun t s FIG. 6. (Color online) Confidence-level distribution for the missing- π hypothesis after all corrections for Monte Carlo (MC)events (left) and CLAS-g12 data (center). The covariance matrix for both data and MC events was initially tuned using fullyexclusive γp → p π + π − events. Right: Distribution of normalized slopes for data events, see text for more details. target. Figure 4 shows that these regions could not besufficiently well reproduced in the Monte Carlo simula-tions. A cut of −
110 cm < z -vertex < −
72 cm wasapplied to the final event sample.The exclusive pπ + π − channel was identified as a domi-nant background source. This charged double-pion reac-tion has a significantly larger cross section than any othercompeting reaction leading to an additional π meson inthe final state. In this analysis, pπ + π − leakage into theselected pπ + π − ( π ) data sample was observed due tothe relatively small difference in the missing masses ofthese two final states. If an incorrect initial-state pho-ton candidate was selected with an energy higher thanthe correct incident photon, this additional energy and z -momentum would allow for the reconstruction of anartificial π in the final state that would move along theincident photon-beam direction. Therefore, leakage fromthe γp → pπ + π − channel was observed as an excess of π mesons in the very forward direction. To reduce thecontribution from γp → pπ + π − background, only eventswith cos θ π c . m . < .
99 were retained for further analysis.In a final step, all events were subject to kinematic fit-ting. Events were tested for energy and momentum con-servation in a four-constraint (4C) fit for detected par-ticles and in a one-constraint (1C) fit for a missing π .The exclusive reaction γp → pπ + π − was used to tunethe covariance matrix using run-group-recommended pa-rameters in order to secure Gaussian pull distributionsand a flat confidence-level (CL) distribution, where theCL denotes the goodness of fit of the statistical model ap-plied to the data and is defined as the integral over the χ probability density function in the range [ χ , ∞ ] [57].Figure 6 (center) shows the confidence-level distribu-tion for the missing- π hypothesis after all corrections;the distribution is fairly flat. In addition to the qualityof the global CL and pull distributions, the flat shapeof the CL distributions was also checked in all relevantkinematic regions by considering the normalized slope of each distribution: ¯ a = aa/ b , (2)where a is the slope and b is the y intercept obtained byfitting the confidence-level distribution to a first-orderpolynomial. Figure 6 (right) shows the respective nor-malized slopes integrated over all analyzed energies and η center-of-mass angles. The distribution is symmetricand centered at zero demonstrating the relative flatnessof the CL distributions in all kinematic bins and thus, thegood understanding of the measurement uncertainties.Events in this analysis were retained with a confidence-level cut of p > . Monte Carlo simulations
The performance of the experimental setup was stud-ied in GEANT3-based [58] Monte-Carlo (MC) simula-tions. The acceptance for the reaction γp → pη → p π + π − π was determined by generating events, whichwere evenly distributed across the available phase space.The MC events were then analyzed using the same re-construction and selection criteria, which were appliedto the measured data events. The simulated tracks werecorrected for the energy loss along their trajectories butwere not subject to any momentum corrections since allthe DC components were perfectly positioned in the sim-ulations and a homogeneous magnetic field was used.The same hypotheses were tested in the kinematic fitsand events selected with the same confidence level cut.The acceptance for each kinematic bin was then definedas the ratio of the number of generated to reconstructedMC events: A γp → pη = N rec , MC N gen , MC . Information about the trigger condition was encodedin the so-called trigger word, which was available in the0data stream for every event. The trigger (in)efficiencywas studied by using a sample of exclusive γp → p π + π − events, where each final-state particle was detected in adifferent sector of CLAS. Since one of the trigger con-ditions required only (at least) two charged tracks intwo different sectors (see Section III E), any inefficienciescould be studied by comparing with the encoded triggerinformation. The trigger efficiency for three-track eventswas then given as the fraction of events where a thirdparticle could be reconstructed in a different sector butthe information was not recorded in the correspondingtrigger bit. Trigger efficiency maps were developed foreach particle type (proton, π + , π − ) as a function of sec-tor ID, TOF counter, and azimuthal angle, φ . Thesemaps were applied in the Monte Carlo simulations bygenerating random numbers for each track. B. Background subtraction
In the determination of the η photoproduction crosssections reported here, non-signal background eventswere removed in a probabilistic event-based approachcalled the “ Q -factor method,” which is fully describedin Ref. [59]. A brief summary of the method and itsapplication to the data from CLAS-g12 is given in thissection.For every event in this analysis, a quality factor (or Q value) was determined that describes the probabilityfor an event to be a signal event as opposed to back-ground. The approach used the unbinned maximum-likelihood technique. For every selected γp → pη eventand its N c kinematically nearest neighbors, the invariant M π + π − π mass distribution was fit according to f ( x ) = N · [ f s · S ( x ) + (1 − f s ) · B ( x )] , (3)where S ( x ) and B ( x ) denote the signal and the back-ground probability density functions, respectively, and x = M π . A double-Gaussian profile was chosen for thesignal and the background shape was modeled with asecond-order Chebyshev polynomial. The parameter N in Eq. (3) is a normalization constant and f s is the signalfraction with a value between 0 and 1.The kinematically nearest neighbor events were se-lected by defining a distance metric for the phase spacespanned by a set of kinematic variables O k . These inde-pendent quantities were chosen to becos θ η c . m . , cos θ HEL , φ
HEL , φ η lab , λ , (4)where cos θ η c . m . denotes the cosine of the polar angle ofthe η in the center-of-mass frame, cos θ HEL and φ HEL arethe two angles of the η in the helicity frame, and φ η lab isthe azimuthal angle of the η in the laboratory frame. Thevariable λ = | (cid:126)p π + × (cid:126)p π − | / λ max is defined in terms ofthe pion momenta in the η rest frame and is proportionalto the η → π + π − π decay amplitude as a consequence of isospin conservation [60], with λ max defined as [61] λ max = K (cid:18) K
108 + mK m (cid:19) , (5)for a totally symmetric decay, where K = T + T + T is the sum of the π ± , kinetic energies and m is the π ± mass.Initially defined for vector mesons, λ has a limitedphysics interpretation for pseudoscalar mesons but stillserves as an independent kinematic variable in this analy-sis. The background subtraction described in this sectionwas performed simultaneously for the ω and η meson de-caying to the same π + π − π final state. Results on crosssection measurements for γp → pω will be presented ina forthcoming publication [62]. The parameter λ variesbetween 0 and 1 and shows a linearly increasing behaviorfor vector mesons, whereas a flat distribution is expectedfor the η meson. This is nicely observed in Fig. 7. Usingthe quantities listed in Eq. (4), the kinematic distancebetween two events i and j is defined as d ij = (cid:88) k =1 (cid:18) O ik − O jk ∆ k (cid:19) , (6)where the O k denotes the set of kinematic variables forthe two events i and j , and ∆ k is the full range for thekinematic variable k .The Q value for a selected γp → pη event is finallygiven as the signal component at the event’s invariant π + π − π mass in the overall mass distribution of the event λ C oun t s FIG. 7. (Color online) Typical example of a normalized λ = | (cid:126)p π + × (cid:126)p π − | distribution for the center-of-mass energybin W ∈ [ 2360 ,
450 500 550 600 C oun t s c.m. η θ -0.2 < cos 450 500 550 600 < 0.1 c.m. η θ [ MeV/c π - π + π m450 500 < 0.8 c.m. η θ FIG. 8. (Color online) Examples of π + π − π mass distributions for the center-of-mass energy range W ∈ [ 1 . , .
92 ] GeVfor events that were subject to the Q -factor fitting (background subtraction). These events survived all kinematic cuts. Theinvariant 3 π mass of each event weighted by 1 − Q gives the blue area (background), whereas the signal peak comes from theinvariant mass weighted by Q . and its N c nearest neighbors: Q = s ( x ) s ( x ) + b ( x ) , (7)where x is again the invariant mass of the π + π − π sys-tem, s ( x ) = f s · S ( x ), and b ( x ) = (1 − f s ) · B ( x ) (see alsoEq. (3)).The Q values were then used as weight factors forvarious kinematic distributions in this analysis. Fig-ure 8 shows examples of the resulting separation of signaland background in the invariant π + π − π mass distri- ] [ MeV/c π - π + π M450 500 550 600 650 C oun t s × FIG. 9. (Color online) Total invariant π + π − π mass distri-bution for the center-of-mass energy W ∈ [ 1 . , .
36 ] GeVcorresponding to the combined γp → pη event statistics ofFigs. 10–12. bution. Three angle bins are presented in the energyrange W ∈ [ 1 . , .
92 ] GeV. The sum of the signal(white area) and the background (blue area) is identi-cal to the total unweighted mass distribution, whereasthe invariant 3 π mass of each event weighted by 1 − Q gives the background alone. Figure 9 shows the total in-variant π + π − π mass distribution for the energy range W ∈ [ 1 . , .
36 ] GeV representing the underlying eventstatistics in Figs. 10–12. An excellent signal / backgroundseparation is observed.
V. EXTRACTION OF CROSS SECTIONS
The differential cross sections, d σ /dΩ, for the reaction γp → pη are determined according tod σ dΩ = N γ p → p η A γ p → p η N γ ρ target , (8)where ρ target : target area density N γ p → p η : number of reconstructed data eventsin a ( W , cos θ c . m . ) bin N γ : number of photons in an incident E γ bin A γ p → p η : acceptance in a ( W , cos θ c . m . ) bin∆Ω : solid-angle interval ∆Ω = 2 π ∆cos ( θ c . m . )BR : decay branching fraction.The target area density, i.e. the number of atoms inthe target material per cross-sectional area (orthogonalto the photon beam), is given by ρ target = 2 ρ (H ) N A LM mol (H ) = 16 . · − µ b − , (9)where ρ (H ) = 0 . [55] is the average density, M mol = 2 . ,2and L = 40 . N A = 6 . · mol − is Avogadro’snumber. The factor of two accounts for the molecularcomposition of hydrogen (H ).The solid angle in steradians equals the area of asegment of a unit sphere. The full solid angle of asphere measured from any point in its interior is thus2 · π = 4 π sr, where 2 π originates from integratingover the azimuthal angle and the factor of two from inte-grating over sin θ d θ (polar angle). Since the differentialcross sections are integrated over φ lab but are binnedin cos θ c . m . , ∆Ω = 2 π ∆cos ( θ c . m . ) was used in Eq. (8)and ∆cos ( θ c . m . ) = 2 / ( . η → π + π − π of Γ π + π − π / Γ = (22 . ± .
28) % was takenfrom Ref. [17], where Γ = (1 . ± .
05) keV [17].
A. Normalization
The photon flux for the absolute normalization of theextracted angular distributions was determined usingstandard CLAS procedures. The method is describedin Ref. [63] and based on comparing the number of“good” electrons in the tagger with the number of pho-tons traversing the liquid-hydrogen target measured witha total absorption counter (TAC) placed directly in thephoton beam. Such normalization runs were carried outat about 10 % of the production beam current using athinner bremsstrahlung radiator to determine the tag-ging ratio (cid:15) T of each T-counter. The tagging ratio isapproximately between 75 % and 80 %. Photons can belost on the way from the tagger to the target due to dis-persion of the beam, collimation, and Møller scattering,for instance. The number of “good” electrons is given byintegrating the observed electron rates at the tagger overthe data aquisition (DAQ) livetime of the experiment,which is measured with a clock. The number of taggedphotons per T-counter is then given by: N T γ = N Te − × (cid:15) T − α , (10)where the photon attenuation factor, α , denotes the smallfractional loss of photons from the liquid-hydrogen targetto the TAC. B. Systematic uncertainties
The statistical uncertainties were determined from thenumber of pη events in each ( W , cos θ η c . m . ) or ( W , − t ) bin,and are included in the uncertainties shown for all datapoints. In this analysis, the effective number of eventsin each kinematic bin was given by summing over all Q values of the contributing events. The overall systematic uncertainty includes uncer-tainties in the normalization, as well as contributionsfrom reconstruction-related sources and the background-subtraction method. An overview of the different frac-tional contributions (% uncertainties) is given in Table II.These contributions are not included in the following re-sults figures. A brief discussion of the contribution fromthe background-subtraction method is given in this sec-tion below. Such contributions are included in the un-certainty shown for each data point (added in quadratureto the statistical uncertainty). Other absolute contribu-tions to the overall systematic uncertainty are given asan uncertainty band at the bottom of each distribution.An individual event’s Q value is based on a fit to theinvariant π + π − π mass distribution that is formed by theevent and its kinematically nearest neighbors using themaximum-likelihood technique. The covariance matrix, C η , for the set of fit parameters, (cid:126)η , was used to determinethe uncertainty of the Q value for the given event: σ Q = (cid:88) i, j ∂Q∂η i (cid:0) C − η (cid:1) ∂Q∂η j . (11)The Q factor method naturally led to some correlationsamong events and their nearest neighbors because eventscould serve as neighbors for many seed events. The sys-tematic “correlation” uncertainty of the η yield in eachkinematic bin due to the method as such was given by: σ ω = (cid:88) i, j σ iQ ρ ij σ jQ , (12)where the sum i, j was taken over all the events in thekinematic bin, σ iQ and σ jQ denote the fit uncertainties forevents i and j , and ρ ij represents the correlation factorbetween events i and j . The correlation factor is sim-ply the fraction of shared nearest-neighbor events and anumber between zero and one . In high-statistics eventsamples, the correlation among events is typically smalland the corresponding contribution to the overall system-atic uncertainty is negligible, whereas in low-statisticssamples, the contribution can quickly exceed the basicstatistical uncertainty.The contribution from the Q -factor method was thenadded to the statistical uncertainty in quadrature to ob-tain the total “statistics-based” uncertainty that is shown Source of Uncertainty % UncertaintySector-by-sector relative acceptance 5.9Fiducial cuts 2.5 z -vertex cut 0.4Kinematic fitting (CL cut) 1.6Liquid-hydrogen target 0.5Normalization uncertainty 2.5Branching fraction ( η → π + π − π ) 0.28TABLE II. Summary of the fractional contributions to theoverall systematic uncertainty. c.m. θ cos b / s r ] µ [ Ω / d σ d FIG. 10. (Color online) The differential cross sections d σ /dΩ for three 40-MeV-wide center-of-mass energy W bins. The newCLAS data are shown as the black solid circles ( • ) and the uncertainties associated with each point comprise the statisticaluncertainty and contributions from the Q -value correlation uncertainty added in quadrature. Also shown for comparisonare data from CLAS-g11a [26] ( (cid:4) ), the A2 Collaboration at MAMI [29] ( (cid:72) ) using their published center-of-bin energies of W = 1 .
78 GeV (left), 1.82 GeV (center), 1.86 GeV (right), and the CBELSA/TAPS Collaboration at ELSA [27] ( (cid:78) ). The bluesolid and purple dashed curves denote the η -MAID 2018 [65] and the BnGa 2019 [16] description of the γp → pη cross section,respectively. for each data point in subsequent figures: σ = σ η + σ . (13)An additional CL cut of p > .
05 was examined andthe resulting cross section results compared with the orig-inal results when a nominal cut of just p > .
01 was used.Both the difference and ratio distributions were observedto be symmetric and Gaussian reflecting a change in theresults, which is mostly statistical in nature due to theloss of events when using a larger p value. The con-tribution from the liquid hydrogen target to the overallsystematic uncertainty accounts for effects such as thecontraction, length, etc. Previous CLAS experimentshave determined that the effect is approximately at the0.5 % level [55]. VI. EXPERIMENTAL RESULTS
The cross section data presented in this section havebeen analyzed in three different energy ranges. Angulardistributions for all energies are shown in Figs. 10–14.Representations in terms of W and momentum transfer − t are given in Figs. 15–17. The uncertainty associatedwith each data point comprises contributions from thestatistical uncertainty and the Q -value correlation un-certainty added in quadrature. A. Differential cross sections d σ /d Ω Figure 10 shows the differential cross sections d σ /dΩfor the W range [ 1 . , .
88 ] GeV in 40-MeV-wide energy bins and 0.1-wide angle bins in cos θ η c . m . of the η me-son in the center-of-mass frame. The CLAS-g12 dataare given as the black data points. For comparison, thedistributions also show the earlier published CLAS-g11adata [26] as the red points. These data are available in 20-MeV-wide energy bins and therefore, adjacent bins wereaveraged. The agreement is very good within the givenuncertainties. Moreover, data from the A2 Collaborationat MAMI [29] are shown as the blue points with the pub-lished center-of-bin W energy closest to any of the center-of-bin energies presented in the figure. The overall agree-ment is good. Finally, data from CBELSA/TAPS [27] aregiven as the green points. Again, the overall agreement ofall four data sets ranges from fair to very good. Some dis-crepancies can be attributed to small energy mismatchesin the presentation of the data. The CLAS-g12 datatend to by systematically lower in the backward direc-tion for cos θ η c . m . < − .
5. A possible explanation is thepoor CLAS acceptance in this kinematic range since thetarget was significantly shifted upstream for this experi-ment. The A2 and CBELSA/TAPS data seem to slightlyunderestimate the CLAS data in the forward direction for1 . < W < .
84 GeV. However, no significant normal-ization discrepancy is observed in any of these W bins.The set of angular distributions for the energy range W ∈ [ 1 . , .
36 ] GeV corresponding to the incident pho-ton energy E γ ∈ [ 1 . , .
50 ] GeV is shown in Figs. 11and 12 in 20-MeV-wide W bins and 0.1-wide angle binsin cos θ η c . m . . For comparison, as before, the CLAS-g11a [26] and CBELSA/TAPS [27] data are also shown;MAMI data are only available below E γ < .
45 GeVand therefore, are not included in these figures. The ear-lier CLAS data have not been averaged for these distri-butions since they were published in 20-MeV-wide bins.4 θ cos b / s r ] µ [ Ω / d σ d FIG. 11. (Color online) The differential cross sections d σ /dΩ in 20-MeV-wide center-of-mass bins for W ∈ [ 1 . , .
12 ] GeV.The new CLAS data are shown as the black solid circles ( • ) and the uncertainties associated with each point comprisethe statistical uncertainty and contributions from the Q -value correlation uncertainty added in quadrature. Also shown forcomparison are data from CLAS-g11a [26] ( (cid:4) ) and from the CBELSA/TAPS Collaboration at ELSA [27] ( (cid:78) ). The blue solidand purple dashed curves denote the η -MAID 2018 [65] and the BnGa 2019 [16] description of the γp → pη cross section,respectively. While the agreement of the two CLAS data sets is excel-lent, the CBELSA/TAPS data tend to be systematicallyhigher. The CBELSA/TAPS data had to be convertedto W bins and for this reason, some discrepancies can beexplained in terms of small energy mismatches. Never-theless, the ELSA data seem to be systematically higherespecially in the very forward and backward directionabove E γ ≈ . W ≈ . ω photoproduc-tion [64]. The latter suggests an energy-dependent nor-malization issue of unknown nature but it is also worthemphasizing that the calorimeter-based CBELSA/TAPSexperimental setup has better acceptance in the very for-ward direction. Given the excellent agreement of the twoCLAS data sets, the reason for this discrepancy remainsunclear, though. The shapes of the angular distributions are indica-tive of nucleon resonance production in the entire energyrange presented in Figs. 11 and 12. Moreover, the veryprominant forward-peaking develops around and above W ≈ .
96 GeV, which suggests that t -channel processesbecome increasingly relevant.Finally, differential cross section results for the en-ergy range W ∈ [ 2 . , .
12 ] GeV corresponding to in-cident photon energy E γ ∈ [ 2 . , .
71 ] GeV are shownin Fig. 13 in 40-MeV-wide W bins and 0.1-wide angle binsin cos θ η c . m . . Note that the vertical axis switches from alinear to a logarithmic scale for W > .
56 GeV (secondrow), seemingly changing the shape of the angular dis-tributions and visibly increasing the reported uncertain-ties. The agreement with the CLAS-g11a data remainsvery good. Above W = 2 .
72 GeV ( E γ ≈ . θ cos b / s r ] µ [ Ω / d σ d FIG. 12. (Color online) The differential cross sections d σ /dΩ in 20-MeV-wide center-of-mass bins for W ∈ [ 2 . , .
36 ] GeV.The new CLAS data are shown as the black solid circles ( • ) and the uncertainties associated with each point comprisethe statistical uncertainty and contributions from the Q -value correlation uncertainty added in quadrature. Also shown forcomparison are data from CLAS-g11a [26] ( (cid:4) ) and from the CBELSA/TAPS Collaboration at ELSA [27] ( (cid:78) ). The blue solidand purple dashed curves denote the η -MAID 2018 [65] and the BnGa 2019 [16] description of the γp → pη cross section,respectively. are not available for 2 . < W < .
60 GeV caused byan established tagger inefficiency in the detectors of thetagger focal plane in this region. Figure 14 is similar toFig. 13 but for the same W range of [ 2 . , .
12 ] GeV,only shows the forward direction 0 . < cos θ η c . m . < . t -channel production of η mesons beyond the baryonresonance regime and to compare the measured angulardistributions with the model described in Ref. [66]. B. Differential cross sections d σ /d t In an effort to study η photoproduction beyond thebaryon resonance regime, the differential cross sectionshave been extracted also in a ( E γ , − t ) representation.This approach facilitates the comparison of the datawith Regge models that aim at describing the reactionin terms of the t -channel exchange of massive quasi-particles. These new CLAS results are particularly im-portant since they provide the missing data link in theenergy range E γ ∈ [ 3 . , . σ /d t for the energy range W ∈ [ 2 . , .
12 ] GeV correspond-ing to incident photon energies E γ ∈ [ 2 . , .
72 ] GeV6 -2 -1 -2 -1 -2 -1
10 -1 -0.5 0 10.5-1 -0.5 0 0.5-1 -0.5 0 0.5-1 -0.5 0 0.5-1 -0.5 0 0.5 c.m. θ cos b / s r ] µ [ Ω / d σ d FIG. 13. (Color online) The differential cross sections d σ /dΩ in 40-MeV-wide center-of-mass bins for W ∈ [ 2 . , .
12 ] GeV.The new CLAS data are shown as black solid circles ( • ) and the uncertainties associated with each point comprise the statisticaluncertainty and contributions from the Q -value correlation uncertainty added in quadrature. Also shown for comparison aredata from CLAS-g11a [26] ( (cid:4) ). The blue solid curve denotes the η -MAID 2018 [65] description of the γp → pη cross section. using 0.2-GeV -wide − t bins for 0 < − t < . Alsoshown in the figure are older data from DESY [32], theCambridge Electron Accelerator at MIT [34], and Cor-nell [40], which are all only available at W = 2 . − t < . at these fairly lowenergies in the Regge regime. The comparison betweenthe data from the 1960s and 1970s, and the CLAS data isalso presented in Fig. 16 using a linear scale. While theRegge model of Ref. [66] describes the DESY and Cornelllow- t data fairly well, the prediction clearly overestimatesthe experimental data points for − t > . .The full set of new data points is shown in Fig. 17for the entire analyzed − t range, 0 < − t < ,on a logarithmic scale. The almost linear fall-off of thedifferential cross sections in the low − t region is expectedand can clearly be observed. Comparison with previous CLAS data
Figure 18 shows a comparison of the new CLAS datawith the previously published CLAS data on η photo-production [26] in the form of a normalized differencedistribution: (cid:0) dσd Ω (cid:1) g12 − (cid:0) dσd Ω (cid:1) g11a (cid:113) (∆ σ ) + (∆ σ ) , (14)where the uncertainties in the denominator are comprisedonly of statistical and Q -value correlation uncertainties.With the exception of a small structure around − . θ cos b / s r ] µ [ Ω / d σ d FIG. 14. (Color online) The differential cross sections d σ /dΩ in 40-MeV-wide center-of-mass bins for W ∈ [ 2 . , .
12 ] GeVand just the forward direction cos θ η c . m . > .
5. The new CLAS data are shown as the black solid circles ( • ) and the uncertaintiesassociated with each point are comprised of the statistical uncertainty and contributions from the Q -value correlation uncertaintyadded in quadrature. The blue solid curve denotes the η -MAID 2018 description [65] of the γp → pη cross section, whereas thered long-dashed curve represents the Regge model discussed in Ref. [66]. ture. The Gaussian width of σ = 1 .
13 suggests that theuncertainties in the denominator of Eq. (14) are slightlyunderestimated.As a matter of fact, no additional uncertainties are in-cluded beyond those listed in Table II to guarantee con-sistency between the two data sets. However, the differ-ence distribution is slightly shifted toward positive val-ues. Figure 19 shows the unweighted ratio distributionof the same two data sets. This distribution is also fairlysymmetric with an RMS value of 1.06. The latter indi-cates that an overall increase of about 6 % is observed inthe new data. The electron rates detected by the tag-ger and used to compute the number of photons incidenton the target are typically integrated over the live timeof the experiment. In Ref. [26], the clock-based livetimecalculation was checked by using the counts of a Fara- day cup located downstream of CLAS. Despite high sta-tistical uncertainties in these secondary measurements,a current-dependent livetime was observed and at max-imum electron beam current, the deadtime was deter-mined to be about a factor of two higher than the onegiven by the clock-based measurement used for the fluxnormalization. The corresponding correction resulted inthe largest single-source contribution to the overall sys-tematic uncertainty. Such a current-dependent livetimewas not observed for the data reported here. The reasonfor this effect in the previous CLAS experiment remainspoorly understood. However, the observed overall scalediscrepancy between the two CLAS measurements of the γp → pη cross sections is well within the reported uncer-tainties for these two experiments.8 -3 -2 -1 -3 -2 -1 -3 -2 -1
101 0 210 10 10 10 1 ] -t [GeV ] b / G e V µ / d t [ σ d FIG. 15. (Color online) The differential cross sections d σ /d t in 40-MeV-wide center-of-mass bins for W ∈ [ 2 . , .
12 ] GeVand for the − t range [ 0 , . The new CLAS data are shown as the black solid circles ( • ) and the uncertainties associatedwith each point are comprised of the statistical uncertainty and contributions from the Q -value correlation uncertainty added inquadrature. In the energy range 2 . < W < .
92 GeV, also shown for comparison are data from DESY [32] ( (cid:78) ), MIT [34] ( (cid:4) ),and Cornell [40] ( (cid:72) ). The red long-dashed curve represents the Regge model discussed in Ref. [66] and the blue solid curvedenotes the η -MAID 2018 description [65]. VII. PHYSICS DISCUSSION
Various theoretical and phenomenological approacheshave been applied and studied in order to describe η pho- -t [ GeV ] b / G e V µ / d t [ σ d FIG. 16. (Color online) The differential cross section d σ /d t for W ∈ [ 2 . , .
92 ] GeV and for the − t range [ 0 , using a linear scale. For the color code and an explanation ofthe curves, see the caption of Fig. 15. toproduction on the nucleon, in particular to understandnucleon resonance contributions to this reaction, e.g. ef-fective field theory [67], dispersion theoretical calcula-tions [68], and Regge models [69, 70].A special group of models are isobar models, e.g. [71–73], which treat nucleon resonances in terms of s -channelBreit-Wigner parametrizations using energy-dependentwidths due to their couplings with other decay chan-nels. The non-resonant background amplitude is typ-ically written as a sum of Born terms and t -channelmeson-exchange contributions. In η photoproduction,Born terms are usually suppressed because their cou-pling constants are fairly small. In such isobar models,the double-counting of terms due to the quark-hadronduality is often concerning since the sum of an infiniteseries of s -channel resonances is equivalent to an infi-nite sum of t -channel meson-exchange amplitudes. Inthe η -MAID 2018 isobar model described in Ref [65], thedouble-counting is removed by introducing a dampingfactor to the Regge amplitudes. Moreover, despite theminor role of Born terms, their couplings are determinedfrom fitting experimental data.9 -3 -2 -1 -3 -2 -1 -3 -2 -1
101 0 420 20 20 20 2 ] -t [GeV ] b / G e V µ / d t [ σ d FIG. 17. The differential cross sections d σ /d t in 40-MeV-wide center-of-mass bins for W ∈ [ 2 . , .
12 ] GeV and for the fullrange − t ∈ [ 0 , . The new CLAS data are shown as the black solid circles ( • ) and the uncertainties associated witheach point are comprised of the statistical uncertainty and contributions from the Q -value correlation uncertainty added inquadrature. The latest η -MAID 2018 solution is shown as a bluesolid curve in Figs. 10–16. The experimental data aredescribed very well over the entire energy range. Allknown N ∗ states listed in the RPP [17] were used to de-scribe the resonance regime from the γp → pη thresh-old up to W < . W > . γp → pη : The N (2040) 3 / + resonance, aone-star state only observed by BES II in J/ψ decays to
N N π [74, 75], and the N (2220) 9 / + resonance. In theirdescription, the reaction is dominated by the 1 / − par-tial wave that is associated with contributions from the N (1535) 1 / − , N (1650) 1 / − , and N (1895) 1 / − states.In the fourth resonance region, the most significant con-tributions beyond the 1 / − partial wave come from the N (1875) 3 / − , N (1900) 3 / + , and the N (1860) 5 / + nu-cleon resonances. The multi-channel Bonn-Gatchina (BnGa) partialwave analysis (PWA) uses a large experimental database,which includes data on pion- and photo-induced meson-production reactions, with up to two pseudoscalarmesons in the final state [76]. The approach is based on afully relativistically invariant operator expansion methodand combines the analysis of different reactions imposingdirectly analyticity and unitarity constraints [77]. TheFigures 10–12, show the BnGa solution BnGa 2019 asa purple curve; more details are discussed in Ref. [77].Overall, the BnGa curve describes the experimental datavery well. Deviations from the η -MAID 2018 solutioncan be observed, mostly in the forward direction above W ≈ / − partial wave also dominates the BnGa descrip-0 CLAS g12 - g11a (normalized)-5 0 5 C oun t s = 1.13 s = 0.42x FIG. 18. (Color online) Comparison between the new andthe published [26] CLAS data in form of a difference distri-bution normalized to their uncertainties. See text for moredetails.
CLAS g12 / g11a0.5 1 1.5 C oun t s = 1.06x FIG. 19. (Color online) Unweighted ratio distribution of thenew and the published [26] CLAS data. tion of the γp → pη reaction. However, in the fourthresonance region, the N (1900) 3 / + resonance plays asignificantly more important role than in η -MAID 2018,whereas contributions from the other two states foundsignificant in η -MAID, N (1875) 3 / − and N (1860) 5 / + ,are practically negligible [78]. The identification of signif-icant contributions from different nucleon resonances in η photoproduction is not surprising since the polarizationobservables are still scarce.The high-energy regime above E γ = 4 GeV is stud-ied in terms of Regge amplitudes in Ref. [66]. Whileeach Regge exchange has a known energy dependence,the t behavior is a priori unknown. In the approach ofthe Joint Physics Analysis Center (JPAC) [66], informa- tion from the resonance region is used through disper-sion relations and finite-energy sum rules (FESR) to ex-tract the t -dependence of the differential cross sectionsat high energies. Data from DESY [32] and Cornell [40]for 0 < − t < were used to constrain the JPACmodel. The available data sets and the model are shownin Fig. 16 for E γ ≈ . t -channel exchanges associated with observed meson-resonances are considered, whereas the second model in-cludes exchanges that correspond to, as yet, unobservedmesons. The latter approach explores the possible im-pact of a 2 −− exchange that would result in increasedcross sections and in a beam asymmetry smaller thanone. However, these new CLAS data and recent resultson the beam asymmetry in η photoproduction at high en-ergies reported by the GlueX Collaboration [20, 79] arein clear contradiction with these predictions.In conclusion, the experimental data confirm the ex-pectation that the γp → pη reaction proceeds primarilythrough ρ and ω vector-meson 1 −− exchange. These andother data also confirm the predicted rapid decline of thecross sections in the very forward direction of the η me-son in the center-of-mass frame, which is related to thedifferential cross sections at very small values of − t . Forcos θ c . m . = 1 or t (cid:48) = t − t min = 0 GeV , conservation ofangular momentum requires conservation of helicities: λ γ − λ proton = λ η − λ proton (cid:48) , where the right-hand side denotes the helicity of the re-coiling proton with λ η = 0. In Regge models, this im-poses an even stronger constraint since conservation ofangular momentum is required at the top ( γ - η ) ver-tex and at the bottom ( N - N ) vertex (see right side ofFig. 1). Since the helicity of a real photon, λ = ± λ = 0 for the η meson, the amplitudeneeds to vanish and the cross section decreases to zero .In Regge pole theory, this behavior is thus built into thetop vertex by factorization [1]. In contrast, using virtualphotons, the cross section in the very forward directionproceeds primarily via the photon’s longitudinal compo-nent. VIII. SUMMARY
Photoproduction cross sections have been presentedfor the reaction γp → pη using tagged photons and theCLAS spectrometer at Jefferson Laboratory. The resultsare shown for incident photon energies between about1.2 and 4.7 GeV. These new η photoproduction data are1consistent with earlier CLAS results but extend the en-ergy range beyond the nucleon resonance regime. Crosssections dσ/dt are also presented for W > .
52 GeV andstudied in terms of the dominant Regge exchange ampli-tudes. While axial vector exchanges are negligible, thedata confirm the expected dominance of vector-mesonexchanges. Calculations using finite-energy sum rules(FESR) indicate that the 2 −− exchange could be relevantbut predictions are inconsistent with the differential crosssection data presented here and with beam-asymmetryresults recently reported by the GlueX Collaboration. Acomparison of the differential cross sectrions d σ /dΩ inthe baryon resonance regime with predictions of the iso-bar model η -MAID 2018 and the BnGa coupled-channelanalysis confirms the dominance of the 1 / − partial waveclose to the reaction threshold. The unambiguous iden-tification of resonance contributions in the fourth reso-nance region is still challenging owing to the lack of po-larization observables around W ≈ ACKNOWLEDGMENTS
The authors thank the technical staff at Jefferson Lab-oratory and at all the participating institutions for their invaluable contributions to the success of the experi-ment. This research is based on work supported bythe U. S. Department of Energy, Office of Science, Of-fice of Nuclear Physics, under Contract No. DE-AC05-06OR23177. The group at Florida State University ac-knowledges additional support from the U.S. Departmentof Energy, Office of Science, Office of Nuclear Physics,under Contract No. DE-FG02-92ER40735. This workwas also supported by the US National Science Founda-tion, the State Committee of Science of Republic of Ar-menia, the Chilean Comisi´on Nacional de Investigaci´onCient´ıfica y Tecnol´ogica (CONICYT), the Italian Isti-tuto Nazionale di Fisica Nucleare, the French CentreNational de la Recherche Scientifique, the French Com-missariat a l’Energie Atomique, the Scottish UniversitiesPhysics Alliance (SUPA), the United Kingdom’s Scienceand Technology Facilities Council, and the National Re-search Foundation of Korea. [1] A. C. Irving and R. P. Worden, Phys. Rept. , 117(1977).[2] B. A. Mecking et al. , Nucl. Instrum. Meth. A , 513(2003).[3] W. Hillert, Eur. Phys. J. A , 139 (2006).[4] B. A. Mecking, Eur. Phys. J. A , 209 (2006).[5] O. Bartalini et al. [GRAAL Collaboration], Eur. Phys. J.A , 399 (2005).[6] N. Muramatsu et al. [LEPS Collaboration], Nucl. In-strum. Meth. A , 184 (2014).[7] B. Krusche et al. , Phys. Rev. Lett. , 3736 (1995).[8] B. Krusche et al. , Phys. Lett. B , 171 (1997).[9] J. Ajaka et al. , Phys. Rev. Lett. , 1797 (1998).[10] D. Elsner et al. [CBELSA and TAPS Collaborations],Eur. Phys. J. A , 147 (2007).[11] O. Bartalini et al. [GRAAL Collaboration], Eur. Phys. J.A , 169 (2007).[12] P. Collins et al. [CLAS Collaboration], Phys. Lett. B ,213 (2017).[13] C. S. Akondi et al. [A2 at MAMI Collaboration], Phys.Rev. Lett. , 102001 (2014).[14] I. Senderovich et al. [CLAS Collaboration], Phys. Lett.B , 64 (2016).[15] L. Witthauer et al. [A2 Collaboration], Phys. Rev. C ,055201 (2017).[16] J. Mller et al. [CBELSA/TAPS Collaboration], Phys.Lett. B , 135323 (2020).[17] M. Tanabashi et al. [Particle Data Group], Phys. Rev. D , 030001 (2018).[18] B. Krusche and C. Wilkin, Prog. Part. Nucl. Phys. ,43 (2014).[19] V. Mathieu et al. , Phys. Rev. D , 074004 (2015). [20] H. Al Ghoul et al. [GlueX Collaboration], Phys. Rev. C , 042201 (2017).[21] S. Adhikari et al. , [arXiv:2005.14272 [physics.ins-det]].[22] F. Renard et al. [GRAAL Collaboration], Phys. Lett. B , 215 (2002).[23] M. Sumihama et al. [LEPS Collaboration], Phys. Rev. C , 052201 (2009).[24] V. Crede et al. [CB-ELSA Collaboration], Phys. Rev.Lett. , 012004 (2005).[25] O. Bartholomy et al. [CB-ELSA Collaboration], Eur.Phys. J. A , 133 (2007).[26] M. Williams et al. [CLAS Collaboration], Phys. Rev. C , 045213 (2009).[27] V. Crede et al. [CBELSA/TAPS Collaboration], Phys.Rev. C , 055202 (2009).[28] E. F. McNicoll et al. [Crystal Ball at MAMI Collabora-tion], Phys. Rev. C , 035208 (2010) Erratum: [Phys.Rev. C , 029901 (2011)].[29] V. L. Kashevarov et al. [A2 Collaboration], Phys. Rev.Lett. , 212001 (2017).[30] D. G. Ireland, E. Pasyuk and I. Strakovsky, Prog. Part.Nucl. Phys. , 103752 (2020).[31] P. J. Bussey et al. , Phys. Lett. , 479 (1976).[32] W. Braunschweig et al. , Phys. Lett. , 236 (1970).[33] V. B. Elings et al. , Phys. Rev. , 1433 (1967).[34] D. Bellenger, S. Deutsch, D. Luckey, L. S. Osborne andR. Schwitters, Phys. Rev. Lett. , 1205 (1968).[35] R. L. Anderson et al. , Phys. Rev. Lett. , 384 (1968).[36] A. Boyarski et al. , Phys. Rev. Lett. , 300 (1968).[37] A. Boyarski et al. , Phys. Rev. Lett. , 1131 (1969).[38] R. L. Anderson, Nucl. Instrum. Meth. , 195 (1968). [39] E. Aker et al. [Crystal Barrel Collaboration], Nucl. In-strum. Meth. A , 69 (1992).[40] J. Dewire, B. Gittelman, R. Loe, E. C. Loh, D. J. Ritchieand R. A. Lewis, Phys. Lett. , 326 (1971).[41] D. Werthmller et al. [A2 Collaboration], Phys. Rev. C , 015205 (2014).[42] I. Jaegle et al. [CBELSA/TAPS Collaboration], Eur.Phys. J. A , 89 (2011).[43] L. Witthauer et al. [CBELSA/TAPS Collaboration], Eur.Phys. J. A , 58 (2017).[44] M. Dugger et al. [CLAS Collaboration], Phys. Rev. Lett. , 222002 (2002) [Erratum-ibid. , 249904 (2002)].[45] R. A. Arndt et al., http://gwdac.phys.gwu.edu .[46] V. Crede and W. Roberts, Rept. Prog. Phys. , 076301(2013).[47] S. Chandavar et al. [CLAS Collaboration], Phys. Rev. C , 025203 (2018).[48] M. C. Kunkel et al. [CLAS Collaboration], Phys. Rev. C , 015207 (2018).[49] J. Bono et al. [CLAS Collaboration], Phys. Lett. B ,280 (2018).[50] J. T. Goetz et al. [CLAS Collaboration], Phys. Rev. C , 062201 (2018).[51] M. D. Mestayer et al. , Nucl. Instrum. Meth. A , 81(2000).[52] E. S. Smith et al. , Nucl. Instrum. Meth. A , 265(1999).[53] Y. G. Sharabian et al. , Nucl. Instrum. Meth. A , 246(2006).[54] D. I. Sober et al. , Nucl. Instrum. Meth. A , 263(2000).[55] CLAS-g12 Run Group, CLAS-NOTE 2017-002, 2017, https://misportal.jlab.org/ul/Physics/Hall-B/clas/viewFile.cfm/2017-002?documentId=756 .[56] E. Pasyuk, Jefferson Laboratory Report No. CLAS-NOTE 2007-016, 2007, https://misportal.jlab.org/ul/physics/Hall-B/clas/viewFile.cfm/2007-016.pdf?documentId=423 [57] S. Brandt, Data Analysis (Springer-Verlag New York,1999), ISBN 0-387-98498-4.[58] R. Brun, F. Bruyant, F. Carminati, S. Giani,M. Maire, A. McPherson, G. Patrick and L. Urban,doi:10.17181/CERN.MUHF.DMJ1.[59] M. Williams, M. Bellis and C. A. Meyer, J. Instrum. ,P10003 (2009).[60] M. Williams et al. [CLAS Collaboration], Phys. Rev. C , 065208 (2009).[61] P. Weidenauer et al. [ASTERIX Collaboration], Z. Phys.C , 387 (1993).[62] Z. Akbar et al. [CLAS Collaboration], in preparation.[63] J. Ball and E. Pasyuk, CLAS Note 2005-002, 2005, .[64] A. Wilson et al. [CBELSA/TAPS Collaboration], Phys.Lett. B , 407 (2015).[65] L. Tiator et al. , Eur. Phys. J. A , 210 (2018).[66] J. Nys et al. [JPAC Collaboration], Phys. Rev. D ,034014 (2017).[67] D. Rui, M. Mai and U. G. Meissner, Phys. Lett. B ,659 (2011).[68] I. G. Aznauryan, Phys. Rev. C , 065204 (2003).[69] A. Sibirtsev, J. Haidenbauer, S. Krewald and U.-G. Meissner, Eur. Phys. J. A , 359 (2010).[70] V. L. Kashevarov, M. Ostrick and L. Tiator, Phys. Rev.C , 035207 (2017).[71] W. T. Chiang, S. N. Yang, L. Tiator and D. Drechsel,Nucl. Phys. A , 429 (2002).[72] W. T. Chiang, S. N. Yang, L. Tiator, M. Vanderhaeghenand D. Drechsel, Phys. Rev. C , 045202 (2003).[73] V. A. Tryasuchev, Eur. Phys. J. A , 97 (2004).[74] M. Ablikim et al. [BES Collaboration], Phys. Rev. Lett. , 062001 (2006).[75] M. Ablikim et al. [BES Collaboration], Phys. Rev. D ,052004 (2009).[76] http://pwa.hiskp.uni-bonn.de/baryon_x.htm [77] A. V. Anisovich et al. , Eur. Phys. J. A , 284 (2016).[78] A. V. Anisovich et al. , Phys. Rev. C , 055202 (2017).[79] S. Adhikari et al. [GlueX Collaboration], Phys. Rev. C100