Single π+ Electroproduction on the Proton in the First and Second Resonance Regions at 0.25 GeV2 < Q2 < 0.65 GeV2 Using CLAS H. Egiyan,1,2 I.G. Aznauryan,4 V.D. Burkert,1 K.A. Griffioen,2 K. Joo,11,1 R. Minehart,3 L.C. Smith,3 G. Adams,34 P. Ambrozewicz,14 E. Anciant,6 M. Anghinolfi,19 B. Asavapibhop,26 G. Audit,6 T. Auger,6 H. Avakian,1,18 H. Bagdasaryan,31 J.P. Ball,5 N. Baltzel,37 S. Barrow,15 M. Battaglieri,19 K. Beard,23 M. Bektasoglu,30,∗ M. Bellis,34 N. Benmouna,16 N. Bianchi,18 A.S. Biselli,34,8 S. Boiarinov,1 B.E. Bonner,35 S. Bouchigny,20 R. Bradford,8 D. Branford,13 W.J. Briscoe,16 W.K. Brooks,1 C. Butuceanu,2 J.R. Calarco,28 S.L. Careccia,31 D.S. Carman,30 B. Carnahan,9 C. Cetina,16 S. Chen,15 P.L. Cole,38 A. Coleman,2 D. Cords,1 P. Corvisiero,19 D. Crabb,3 H. Crannell,9 J.P. Cummings,34 E. DeSanctis,18 R. DeVita,19 P.V. Degtyarenko,1 H. Denizli,32 6 L. Dennis,15 K.V. Dharmawardane,31 C. Djalali,37 G.E. Dodge,31 J. Donnely,17 D. Doughty,10,1 P. Dragovitsch,15 0 M. Dugger,5 S. Dytman,32 O.P. Dzyubak,37 M. Eckhause,2 K.S. Egiyan,4 L. Elouadrhiri,1 A. Empl,34 P. Eugenio,15 0 2 R. Fatemi,3 G. Fedotov,27 G. Feldman,16 R.J. Feuerbach,8 T.A. Forest,31 H. Funsten,2 S.J. Gaff,12 M. Gai,11 G. Gavalian,31 S. Gilad,25 G.P. Gilfoyle,36 K.L. Giovanetti,23 P. Girard,37 G.T. Goetz,7 C.I.O. Gordon,17 n a R. Gothe,37 M. Guidal,20 M. Guillo,37 N. Guler,31 L. Guo,1 V. Gyurjyan,1 C. Hadjidakis,20 R.S. Hakobyan,9 J J. Hardie,10,1 D. Heddle,10,1 F.W. Hersman,28 K. Hicks,30 R.S. Hicks,26 I. Hleiqawi,30 M. Holtrop,28 J. Hu,34 5 C.E. Hyde-Wright,31 Y. Ilieva,16 D.G. Ireland,17 B. Ishkhanov,27 M.M. Ito,1 D. Jenkins,40 H.G. Juengst,16 J.H. Kelley,12 J.D. Kellie,17 M. Khandaker,29 D.H. Kim,24 K.Y. Kim,32 K. Kim,24 M.S. Kim,24 W. Kim,24 2 v A. Klein,31 F.J. Klein,1,9 A..V. Klimenko,31 M. Klusman,34 M. Kossov,22 L.H. Kramer,14 Y. Kuang,2 7 V. Kubarovsky,34 S.E. Kuhn,31 J. Kuhn,8 J. Lachniet,8 J.M. Laget,6,1 J. Langheinrich,37 D. Lawrence,26 Ji Li,34 0 K. Livingston,17 A. Longhi,9 K. Lukashin,1,9 J.J. Manak,1 C. Marchand,6 S. McAleer,15 B. McKinnon,17 0 1 J.W.C. McNabb,8 B.A. Mecking,1 S. Mehrabyan,32 J.J. Melone,17 M.D. Mestayer,1 C.A. Meyer,8 K. Mikhailov,22 0 M. Mirazita,18 R. Miskimen,26 V. Mokeev,27,1 L. Morand,6 S.A. Morrow,6,20 V. Muccifora,18 J. Mueller,32 6 L.Y. Murphy,16 G.S. Mutchler,35 J. Napolitano,34 R. Nasseripour,14 S.O. Nelson,12 S. Niccolai,16,20 G. Niculescu,30 0 I. Niculescu,23,16 B.B. Niczyporuk,1 R.A. Niyazov,1 M. Nozar,1 G.V. O’Rielly,16 M. Osipenko,19 K. Park,24 / x E. Pasyuk,5 G. Peterson,26 S.A. Philips,16 N. Pivnyuk,22 D. Pocanic,3 O. Pogorelko,22 E. Polli,18 S. Pozdniakov,22 e - B.M. Preedom,37 J.W. Price,7 Y. Prok,3 D. Protopopescu,17 L.M. Qin,31 B.A. Raue,14 G. Riccardi,15 G. Ricco,19 cl M. Ripani,19 B.G. Ritchie,5 F. Ronchetti,18,33 G. Rosner,17 P. Rossi,18 D. Rowntree,25 P.D. Rubin,36 F. Sabati´e,6 u K. Sabourov,12 C. Salgado,29 J.P. Santoro,40 V. Sapunenko,19 M. Sargsyan,14 R.A. Schumacher,8 V.S. Serov,22 n A. Shafi,16 Y.G. Sharabian,4,1 J. Shaw,26 S. Simionatto,16 A.V. Skabelin,25 E.S. Smith,1 D.I. Sober,9 : v M. Spraker,12 A. Stavinsky,22 S. Stepanyan,1,31 P. Stoler,34 I.I. Strakovsky,16 S. Strauch,16 M. Taiuti,19 i X S. Taylor,35 D.J. Tedeschi,37 U. Thoma,1,21 R. Thompson,32 A. Tkabladze,30 L. Todor,8 C. Tur,37 r M. Ungaro,34 M.F. Vineyard,39,36 A.V. Vlassov,22 K. Wang,3 L.B. Weinstein,31 H. Weller,12 D.P. Weygand,1 a C.S. Whisnant,37,23 E. Wolin,1 M.H. Wood,37 A. Yegneswaran,1 J. Yun,31 J. Zhang,31 J. Zhao,25 and Z. Zhou25 (The CLAS Collaboration) 1 Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606 2 College of William and Mary, Williamsburg, Virginia 23187-8795 3 University of Virginia, Charlottesville, Virginia 22901 4 Yerevan Physics Institute, 375036 Yerevan, Armenia 5 Arizona State University, Tempe, Arizona 85287-1504 6 CEA-Saclay, Service de Physique Nucl´eaire, F91191 Gif-sur-Yvette, France 7 University of California at Los Angeles, Los Angeles, California 90095-1547 8 Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 9 Catholic University of America, Washington, D.C. 20064 10 Christopher Newport University, Newport News, Virginia 23606 11 University of Connecticut, Storrs, Connecticut 06269 12 Duke University, Durham, North Carolina 27708-0305 13 Edinburgh University, Edinburgh EH9 3JZ, United Kingdom 14 Florida International University, Miami, Florida 33199 15 Florida State University, Tallahassee, Florida 32306 16 The George Washington University, Washington, DC 20052 17 University of Glasgow, Glasgow G12 8QQ, United Kingdom 18 INFN, Laboratori Nazionali di Frascati, Frascati, Italy 19 INFN, Sezione di Genova, 16146 Genova, Italy 20 Institut de Physique Nucleaire ORSAY, Orsay, France 2 21 Institute fu¨r Strahlen und Kernphysik, Universit¨at Bonn, Germany 22 Institute of Theoretical and Experimental Physics, Moscow, 117259, Russia 23 James Madison University, Harrisonburg, Virginia 22807 24 Kungpook National University, Daegu 702-701, South Korea 25 Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307 26 University of Massachusetts, Amherst, Massachusetts 01003 27 Moscow State University, Skabeltsin Nuclear Physics Institute, 119899 Moscow, Russia 28 University of New Hampshire, Durham, New Hampshire 03824-3568 29 Norfolk State University, Norfolk, Virginia 23504 30 Ohio University, Athens, Ohio 45701 31 Old Dominion University, Norfolk, Virginia 23529 32 University of Pittsburgh, Pittsburgh, Pennsylvania 15260 33 Universita’ di ROMA III, 00146 Roma, Italy 34 Rensselaer Polytechnic Institute, Troy, New York 12180-3590 35 Rice University, Houston, Texas 77005-1892 36 University of Richmond, Richmond, Virginia 23173 37 University of South Carolina, Columbia, South Carolina 29208 38 University of Texas at El Paso, El Paso, Texas 79968 39 Union College, Schenectady, NY 12308 40 Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061-0435 (Dated: February 8, 2008) The ep → e′π+n reaction was studied in the first and second nucleon resonance regions in the 0.25 GeV2 < Q2 < 0.65 GeV2 range using the CLAS detector at Thomas Jefferson National Ac- celerator Facility. For the first time the absolute cross sections were measured covering nearly the full angular range in the hadronic center-of-mass frame. The structure functions σTL, σTT and the linear combination σT +ǫσL were extracted by fitting the φ-dependenceof the measured cross sections, and were compared to theMAID and Sato-Lee models. PACSnumbers: INTRODUCTION polarization parameter ǫ: θ Q2 =4E E sin2 e, (1) i f 2 ν2 θ −1 ǫ= 1+2 1+ tan2 e , (2) Q2 2 (cid:20) (cid:18) (cid:19) (cid:21) ν =E E , (3) i f − where E and E are the initial and final energies of the The structureofthe nucleonandits excitedstateshas i f electronandθ istheelectronscatteringangle. Themass been one of the most extensively studied subjects in nu- e of the hadronic system is given by: clear and particle physics for many years. It allows us to understand important aspects of the underlying the- W = M2+2Mν Q2, (4) − ory of the strong interaction, QCD, in the confinement whereM istheprotonpmass. Thetwohadronproduction regime where solutions are very difficult to obtain. Elas- angles θ and φ are defined in the center-of-mass (c.m.) tic electron scattering experiments provide information reference frame, with θ being the angle between the out- on the ground state of the nucleon, while studying the going pion and the direction of the three-momentum Q2 evolution of the transition amplitudes from the nu- transfer,andφbeingtheanglebetweentheelectronscat- cleongroundstateintotheexcitedstatesprovidesinsight tering plane and the hadron production plane. The un- intotheinternalstructureoftheexcitednucleon. Single- polarized cross section for single-pion electroproduction pion electroproduction is one of the most suitable pro- can be written as [2]: cesses for studying the transitions to states with masses below1.7GeVbecauseofthelargeπN couplingforthese ∂5σ dσ =Γ , (5) states[1]. Thedetectionoftwooutofthreeoutgoingpar- ∂E ∂Ω ∂Ω∗ · dΩ∗ f e π π ticles is sufficient to achieve a complete measurement of α (W2 M2)E 1 the differential crosssections in orderto attempt the ex- Γ= − f , (6) 2π2Q2 ME 1 ǫ i traction of the amplitudes for the individual resonances. − dσ The kinematic quantities of the ep e′π+n reaction is =σ +ǫσ + → dΩ∗ T L shown in Fig. 1. The virtual photon is described by the π four-momentum transfer Q2, energy transfer ν and the ǫσ cos2φ+ 2ǫ(1+ǫ)σ cosφ, (7) TT TL p 3 e- e- e- e- e’ γ* π+ γ* π+ e γ* N* p φ* p n p n a) b) π+ θ* e- e- e- e- γ* γ* π+ π+ n π+ ρ p n p n c) d) FIG.2: (Color online) Someofthemaindiagrams contribut- ing to single π+ electroproduction. FIG.1: (Coloronline)Kinematicdiagramofsingle-pionelec- troproduction. A and S . The first two are due to the coupling of 3/2 1/2 transverse photons with the proton resulting in a com- where Γ is the virtual photon flux, and dσ is the vir- dΩ∗ bined helicity h = 1 or h = 3 respectively. The S tual photoproduction cross section. The σπ , σ , σ 2 2 1/2 T L TT amplitudeispresentduetothe possibilityofalongitudi- andσ structurefunctions arebilinearcombinationsof TL nal polarization for virtual photons. Alternatively, pion the helicity amplitudes, depending only on the variables electroproduction can be described using multipole am- Q2, W and θ. The analysis of the angular distributions plitudes El±, Ml± and Sl±. The l-index represents the providesinformationforextractingtheelectroproduction orbital angular momentum of the πN system, and the amplitudes for different resonances. sign indicates how the nucleon spin is coupled to the The main tree-level Feynman diagrams contributing ±orbital momentum. For each excited state the helicity to the ep e′π+n process are shown in Fig. 2. The amplitudes can be expressed in terms of multipole am- → s-channel resonance excitation process is represented by plitudes and vice versa [2]. the diagram in Fig. 2a. The hadronic vertex of this pro- Quarkmodelspredictthatthe E1+ and S1+ ratiosfor cessisknownfromπN elasticscatteringexperiments[3]. M1+ M1+ the P (1232)are small at low Q2 [4, 5], while perturba- Thereforestudies ofpionelectroproductioncanyieldthe 33 Q2 evolutionofthe photocouplingamplitudes describing tiveQCDpredicts ME11++ =1andMS11++ isindependentofQ2 theγ∗NN∗ vertex. Forthepurposeofstudyingtheexci- as Q2 [6]. A transition between these two regimes → ∞ tationofnucleonresonances,theotherdiagramsarecon- isexpectedatsomefiniteQ2. AtlowQ2thedeviationsof sideredasphysicalbackground. Thelargestnon-resonant theseratiosfromzerocanbeinterpretedasnon-spherical contributiontothecrosssectioncomesfromthet-channel deformation of the nucleon or the ∆(1232) [7]. Usually pion exchange diagram, shown in Fig. 2c. Although this these ratios for ∆(1232) are obtained through measure- process mainly contributes in the forward region due to ments inthe π0p decaychannelwithanassumptionthat the pion propagator pole, it still accounts for a signifi- the uncertainty due to the isospin I = 1 background is 2 cant part of the cross section even at large angles. The negligible. High quality data in the π+n channel will diagrams in Fig. 2b and Fig. 2d correspond to the s- enable us to separate the isospin I = 1 and I = 3 com- 2 2 channel nucleon pole and t-channel ρ-meson exchange ponents of the transition form-factors for the P (1232) 33 amplitudes. Sophisticated analysis procedures are nec- and to determine these ratios with smaller uncertainties essary to separate the resonant contributions from the coming from non-resonant contributions. non-resonant background, and to extract the resonant The second resonance region is dominated by the amplitudes for different overlapping excited states. The three known isospin I = 1 states, P (1440), D (1520) 2 11 13 extraction of resonance multipoles is beyond the scope and S (1535). These resonances, produced in electron- 11 of this paper. In this contribution we describe the ex- proton scattering, are twice as likely to decay through periment and data analysis, and the extraction of fully the π+n channelthanthroughπ0p. Therefore,crosssec- exclusive and differential cross sections, and determina- tionmeasurementsoftheep e′π+nprocessarecrucial → tion of response functions. forunderstandingthe propertiesofthesestates. Thena- Electroexcitation of a nucleon resonance can be de- ture of the P (1440) resonance is not understood in the 11 scribedintermsofthreephotocouplingamplitudesA , framework of the constituent quark model (CQM) [8], 1/2 4 and there are suggestions that the Roper resonance may be a hybrid state [9] or a small quark core with a large vector meson cloud [10]. The Q2 evolution of the A 1/2 photocouplingamplitudefortheRoperispredictedtobe differentfor3-quarkandhybridstates. Previousanalyses [11, 12] indicate a rapid fall-off of A between Q2 = 0 1/2 and Q2 = 0.5 GeV2, therefore high quality data in this region will be very valuable in understanding the nature of the P (1440). 11 The experimental data for the A transition ampli- 1/2 tude for S (1535) show a significantly slower Q2 fall-off 11 than predicted by constituent quark models. Most of these results are obtained through analysis of η-meson electroproduction data, where there can be no I = 3 2 background. TheproximityoftheS (1535)masstothe 11 η-production threshold complicates the analysis of the FIG. 3: Three dimensional view of CLAS. data. Highqualitysingleπ+ datacurrently existonly at the photoproduction point, and there is very little data fornon-zeroQ2. The resultsfromanalysesofpionandη photoproductiondataaresignificantlydifferent[13], and the source of these discrepancies is still not understood. New electroproductiondata will allow for a similar com- parison between the results from the two channels from Apparatus CLAS to check the consistency of the analysis frame- works. These data will also allow for a future combined analysis of pion and η production data, which will pro- vide more stringent constraints on the fit. The main magnetic field of CLAS is provided by six superconducting coils, which produce an approximately Until now there have only been three experiments toroidalfieldintheazimuthaldirectionaroundthebeam [14, 15, 16] measuring single π+ electroproduction cross axis. The gaps between the cryostats are instrumented section in the resonance regions in this range of Q2. In withsixidenticaldetectorpackages,alsoreferredto here all of these experiments the lack of angular coverage in as “sectors”, as shown in Fig 3. Each sector consists the center-of-mass reference frame significantly reduced of three regions (R1, R2, R3) of Drift Chambers (DC) the sensitivity to the resonant amplitudes. The aim of [18]todeterminethetrajectoriesofthechargedparticles, thepresentexperimentistoprovidedifferentialcrosssec- Cˇerenkov Counters (CC) [19] for electron identification, tions for the π+n channel over a large kinematic region Scintillator Counters (SC) [20] for chargedparticle iden- and with high statistical accuracy, that can be used to- tification using the Time-Of-Flight (TOF) method, and getherwithotherchannelstoobtainmorereliableresults Electromagnetic Calorimeters (EC) [21] used for elec- on the resonance photocoupling amplitudes. tronidentificationanddetectionofneutralparticles. The liquid-hydrogentargetwaslocatedinthecenterofthede- tector on the beam axis. To reduce the electromagnetic background resulting from Møller scattering off atomic EXPERIMENT electrons, a second smaller normal-conducting toroidal magnet (mini-torus) was placed symmetrically around The measurement was carried out using the CE- the target. This additional magnetic field prevented the BAFLargeAcceptanceSpectrometer(CLAS)[17]atthe Møller electrons from reaching the detector volume. A Thomas Jefferson National Accelerator Facility (Jeffer- totally absorbing Faraday cup, located at the very end son Lab), located in Newport News, Virginia. CLAS is of the beam line, was used to determine the integrated a nearly 4π detector, providing almost complete angular beam charge passing through the target. The CLAS de- coverage for the ep e′π+n reaction in the center-of- tectorcanprovide δp <0.5%momentumresolution,and → p mass frame. It is well suited for conducting experiments 80% of 4π solid-angle coverage. The efficiency of de- ≈ which require detection of two or more particles in the tectionandreconstructionforstable chargedparticlesin finalstate. Suchadetectorandthecontinuousbeampro- fiducialregionsofCLASisǫ>95%. Thecombinedinfor- duced by CEBAF provide excellent conditions for mea- mationfromthetrackingintheDCandtheTOFsystems suringtheep e′π+nelectroproductioncrosssectionby allowsustoreliablyseparateprotonsfrompositivepions → detecting the outgoing electron and pion in coincidence. for momenta up to 3 GeV. 5 Matching Tolerance )0.6 TRK⊗EC 30 cm eV TRK⊗CC 5o G 102 EC⊗CC 5o ( EC0.4 E TABLE I: Cuts for the geometrical matching in the offline 10 analysis software. 0.2 1 energy in the electromagnetic calorimeter in coincidence 00 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 with a signal in the Cˇerenkov counter in the same sec- P (GeV) tor. Additional requirements were applied in the off-line e analysis to select events containing an electron. First, a geometrical matching was required between the EC and FIG. 4: Energy deposited by the electron candidates in the electromagneticcalorimeterversustheirmomenta. Theblack CC hits and the associated negatively charged tracks in lines show thecut applied for theelectron identification. thedriftchambers. Thevaluesofthe geometricalcutsin thesoftwarearegiveninTableI. Asamplingfractioncut wasimposedonthe dependence ofthe ECvisible energy onthemomentumtorejectthe backgroundcomingfrom Data taking and data reduction negativepions(seeFig.4). Theelectronidentificationin the off-line analysis can be summarized by: The data were taken in the spring of 1999 as part of the experimental program of the CLAS collaboration. EID =TRK CC EC SF, (8) The CEBAF 1.5 GeV electron beam was incident on ⊗ ⊗ ⊗ a 5-cm long liquid hydrogen target at 20.5 K temper- ature. The data were taken at 3 nA nominal beam cur- where TRK stands for track reconstruction in the drift rent,with 0.04nA currentfluctuations, atluminosities chambers, CC and EC are the Cˇerenkov counter and of 4 1±033 cm−2s−1. The size of the beam spot at the calorimeter geometrically matched hits and SF is ∼ × the target was 0.2 mm, with position fluctuations of the sampling fraction cut described above. In order to ∼ 0.04 mm. The main torus current was set at 1500 A, avoid inefficiencies due to the trigger threshold in the ± which created a magnetic field of about 0.8 Tesla in the electromagnetic calorimeter, only events containing an forward direction. The magnetic field of the spectrom- electron with at least 500 MeV momentum were used in eter is significantly lower at large angles. The CLAS the analysis. In addition, fiducial cuts, discussed later, event readout was triggered by a coincidence of signals wereappliedtoselectonlyelectronsintheregionswhere from the electromagnetic calorimeter and the Cˇerenkov the Cˇerenkov counter efficiency was greater than 92%. counters in a single sector, generating an event rate of The final cross sections were correctedfor the remaining 2 kHz. The total number of accumulated triggers at inefficiency of the Cˇerenkov counters [19]. ∼ thesedetectorsettingswasabout4.5 108. Therawdata × Charged hadron identification in the CLAS detector were written onto a tape silo of the Jefferson Lab Com- is accomplished using the momentum determined from puterCenter. Duringtheoff-lineprocessingeachfilewas the tracking and the timing information from the scin- retrievedfromthetapesiloandanalyzedtoproducefiles tillation counters. Fig. 5 shows the distribution of posi- for general use containing 4-vectors of the reconstructed tively charged particles at 1.515 GeV electron beam en- particles. ROOT [22] files, containing the specific in- ergy plotted versus velocity β and momentum P. Bands formation relevant for single π+ electroproduction, were due to positrons, pions, protons and deuterons can be created and stored on a disk. These files were further easily identified. At low momentum the muon band is analyzed to extract the differential cross sections for the visible as well. The deuterons are produced from elec- ep e′π+n reaction. → tron scattering on the aluminum windows of the target cell. All positive particles in the region outlined by the dashed lines were considered as π+. Positrons can be Particle identification separatedfrompionsatlowmomenta,butathighermo- menta the pion and positron bands merge. Background Oneofthekeyissuesinelectronscatteringexperiments due to muons and positrons is significantly reduced by is the ability of the detector to reliably identify elec- the missing mass and vertex cuts described below. The trons. Electron identification at the trigger level was ac- remainingcontaminationisevaluatedasasystematicun- complishedbyrequiringaminimumamountofdeposited certainty. 6 Momentum corrections V)0.04 V)0.04 e a) e b) G0.03 G0.03 When extracting the resonant parameters for excited (Mn0.02 (Mn0.02 svtaartiaesn,titmiassismopfotrhteanhtadtorohnaivcesttahteec.oTrrheecrtevfoarlue,eiftoirstnheeceins-- - ss0.01 - ss0.01 mi mi saryto measurethe electronmomentum with highaccu- M 0 M 0 racy. For this reasonadditional corrections were applied -0.01 -0.01 totheelectronmomentumreconstructedbythestandard -0.02 -0.02 CLAS software package. These corrections were deter- -0.03 -0.03 mined using elastic scatteringeventsfromthe same runs -0.04 -0.04 0 50 100150 200250300 350 0 50 100150200250300350 that were used in the single pion analysis. It was found φ (deg) φ (deg) e e that the missing mass determined from the elastically scattered electrons is typically 5 MeV below the pro- FIG.6: Positionofthemissingmasspeakintheep→e′π+X ∼ tonmassMp =0.938GeV.Assumingthatthescattering reaction versus φe in the lab frame: a) - before, b) - after angle of the electron is measured correctly, and using: momentum corrections are applied. The error bars represent thewidth of thedistribution around theneutron mass. 2ME (W2 M2) E = i− − (9) f 2M +4E sin2 θe i 2 the momentum correction factor can be found as: reaction was within 2.0 MeV of the neutron mass for ± 1.1 GeV< W < 1.6 GeV range. Fig. 6 shows the differ- C δEf = W2−M2, (10) ence between the missing mass in ep e′π+X reaction p ≡ Ef − 2MEi and the neutron mass with and withou→t momentum cor- rections. The six gaps between the points are due to the where E is the electronbeamenergy andW is the mea- i six coils of the magnet. The dependence of the peak po- sured recoil mass. This quantity was calculated for dif- ferentbinsinθ [15◦,55◦]andφ∗ [ 30◦,+30◦]inthe sition on φe is practically eliminated by this procedure, e ∈ e ∈ − andthe peakislocatedmuchclosertotheneutronmass. laboratory frame for each sector and stored in a look-up table. The azimuthalangleφ∗ is definedwithin a sector, e withφ∗ =0correspondingtothemid-planeofthesector. e Themomentaoftheelectronsfromsingleπ+ production Fiducial cuts datawerecorrectedusingthistableonanevent-by-event basis. This procedure relies on the fact that the relative AlthoughCLASisanearly4πdetector,itstillcontains momentumoffsetisindependentofW forafixedvalueof significant inactive volumes without particle detectors. θ . Itwasfoundthatafterthesecorrectionswereapplied, Inaddition,someofthedetectioninefficienciesintheac- e theneutronpeakinthemissingmassoftheep e′π+X → FIG.5: Distributionofthenumberofpositivelychargedpar- ticlesversusβ andp. Thevisiblebandsareduetopositrons, FIG.7: Cˇerenkovcounterefficiencyversustheθe andφe elec- muons, pions, protons and deuterons. All positive particles tron angles in the laboratory frame for Sector 4. The black withintheareaoutlinedbythedashedlinesareconsideredas curvesindicatetheouteredgesoftheelectronfiducialregions. π+’s in this analysis. Each momentum bin is 200 MeV wide. 7 tivevolumesarenotadequatelyreproducedinthedetec- torsimulationsoftware. Theseareasareneartheedgesof the electromagnetic calorimeter, Cˇerenkov counter mir- 10000 χχ22 // nnddff 330022..22 // 1177 χχ22 // nnddff 334466..66 // 5577 CCoonnssttaanntt 99665577 ±± 3377..22 4000 CCoonnssttaanntt 44009966 ±± 1144..55 rors, the main torus and mini-torus coils, regions with MMeeaann 00..99339911 ±± 00..00000000 MMeeaann --00..0055886699 ±± 00..0000111100 broken wires in the drift chambers, and malfunctioning SSiiggmmaa 00..000099888888 ±± 00..000000003388 SSiiggmmaa 00..33666611 ±± 00..00001111 3000 phototubesintheTOFsystem. Toeliminateeventswith particles traveling through these regions, a set of fidu- 5000 2000 cial cuts was developed. For electrons the main bound- ary of the fiducial region was defined by the efficiency of the Cˇerenkov counters and the edges of the electromag- 1000 netic calorimeter. Fig. 7 shows the dependence of the Cˇerenkovcounterefficiencyversustheθ andφ electron 0 0 e e 0.8 1 1.2 1.4 -4 -2 0 2 4 6 anglesinthe laboratoryframe forsix 200MeVwide mo- Missing Mass (GeV) Zπ - Ze (cm) mentum bins in Sector 4. Due to the optics design of the CLAS Cˇerenkov counters [19] there are areas with FIG. 8: Missing mass spectrum (a) and the distribution of relatively lower efficiency shown with the lighter shade. theeventsversusZπ−Ze (b). Thearrows representthecuts applied in the data analysis. The solid lines are gaussian fits These features are difficult to implement in the detec- to thedata. tor simulation. Only events in the regions within the black curves and with the Cˇerenkov counter efficiency above 92% were used in the analysis. An additional set ofgeometricalcutswasappliedtorejectelectronshitting malfunctioning scintillatorcountersortraversingregions with missing or inefficient wires in the drift chambers. Two sets of fiducial cuts were used to define the outer boundary of the fiducial regions for the positive pions. The first set, similar to the electron cuts, was defined in such a way that the φlab distributions of the number of π events be uniform within the fiducial region. The sec- ond set of cuts was applied to ensure equivalent solid angle coverage for pions in the Monte-Carlo simulation and the realdata. This mismatch was due to distortions oftheminitoruscoilswhichwerenotimplementedinthe detector simulation package. As in the case with the electrons,tracksinthe regionswithmalfunctioning scin- FIG.9: Distributionofthenumberofsingleπ+eventsversus: tillatorcountersorbrokenwireswererejectedbyanother Q2 and W - left; φ and θ center-of-mass angles - right. set of fiducial cuts. Kinematic cuts difference of the Z-coordinates along the beam-line for the electron and the pion tracks in the same event (see The exclusive final state was selected by detecting the Fig.8b). This ledto areductioninthe numberofevents outgoing electron and the π+, and by requiring that the with decaying π+ to 4% with less than 1% losses in the missing particle be a neutron. The missing-mass spec- number of events when the pion did not decay. trum in Fig. 8a shows a prominent neutron peak as well aseventsfromtheradiativetailandfrommulti-pionpro- The kinematic coverageofthis experimentis shownin duction channels. The arrows indicate the cuts used in Fig. 9. The grating on the figures shows the binning of the analysis. The number of rejected events in the tails the data. In the first resonance region this experiment is recoveredby imposing the same cuts on the simulated covers a Q2 range from 0.25 GeV2 to 0.65 GeV2, while events in the acceptance calculations. in the second resonance region the upper boundary of GEANT-basedMonte-Carlostudiesshowedthatabout the Q2 coverage is reduced to 0.45 GeV2. The angular 18%ofthepositivepionsdecayin-flightintoµ+ν . Most coverage in the hadronic center-of-mass frame is nearly µ of the momentum of the original pion is carried by the complete,withtheexceptionoftheregionθ >140◦. This µ+,whichis,therefore,oftendetectedandreconstructed limitation at larger angles is related to the fact that the as a π+ with a significantly different momentum vector. CLAScoverageforchargedparticlesislimitedto140◦ in Inordertoreducethenumberoftheeventswithdecaying laboratoryframe. The number and the sizes of the cross pions, a vertex cut Z Z <2 cm was applied on the section bins are given in Table II. π e | − | 8 Variable # of bins Lower limit Upperlimit Width Q2 4 0.25 GeV2 0.65 GeV2 0.10 GeV2 e0.25 e0.25 c a) c b) W 25 1.1 GeV 1.6 GeV 20 MeV n n θ 12 0◦ 180◦ 15◦ pta 0.2 pta 0.2 φ 12 0◦ 360◦ 30◦ ce ce c0.15 c0.15 A A TABLEII:Thenumberandthesizesofthedatabins. Values 0.1 0.1 for thelimits indicate theupper and lower edges of the bins, rather than thebin centers. 0.05 0.05 0 0 Acceptance corrections 0 50 100 θ 1(d50eg) 0 100 200 φ 3(d00eg) In order to relate the experimental yields to cross sec- FIG. 10: Sample plots of acceptance corrections versus θ tions, acceptance correction factors were calculated us- and φ pion angles in the center-of-mass frame in the Q2 = ing the Monte-Carlo method. The GEANT-based de- 0.3 GeV2 and W = 1.23 GeV bin. The θ-dependence (a) is tectorsimulationpackageGSIMincorporatedthe survey shownatφ=116.25◦ andtheφ-dependenceisatθ=108.75◦. The width of the curves represent the statistical uncertainty geometry of CLAS, realistic drift chamber and timing for the acceptance. resolutions along with missing wires and malfunctioning photomultiplier tubes. Because CLAS is a complicated detector covering almost 4π of solid angle, it is virtually impossible to separate the efficiency calculations from in Fig. 10. The θ-dependence of the acceptance (see the geometrical acceptance calculations. In this work Fig. 10a) exhibits a dip at 45◦, which is due to the ∼ the term acceptance correctionrefers to a combined cor- forward beam pipe. Six sectors of CLAS can be clearly rection factor due to the geometry of the detector and identified in the plot showing acceptance versus φ-angle the inefficiencies of the detection and reconstruction. It (see Fig. 10b). The width of the curves in these graphs is defined as the ratio of the number of reconstructed representthe statistical error bands. Since a single cross Monte-Carloeventstothenumberofsimulatedeventsin section bin contains sixteen acceptance bins, the contri- a given bin: butionofthe acceptance statisticalerrorto the totalun- certainty of cross sections is on average approximately N A= rec. (11) four times smaller than the errors seen in these plots. N sim With this definition of the acceptance it is desirable to Radiative corrections have a realistic physics model in the event generator be- cause of the finite bin sizes and bin migration effects, which are described later. In this work the MAID2000 In addition to processes which result in the exclusive model [23], which reasonably reproduces both pπ0 [24] e′π+n final state, there are radiative processes repre- andthecurrentnπ+ CLASdata,wasusedasaninputto sentedbyFeynmandiagramssimilartotheoriginalsingle theMonte-Carloeventgenerator. Thesimulated200mil- photon exchange diagrams, but with an additional pho- lioneventswereprocessedusingthe same softwarepack- tonleg,thatalsocontributetothecrosssections. Theex- ageandanalyzedwiththesamecutsthatwereappliedto perimentally measured cross sections must be corrected the realdata. An acceptance table with 8 25 24 48 forsuchprocesses,alsoknownasinternalradiation. The × × × bins in Q2, W, θ and φ, respectively, was calculated us- radiative cross section for an exclusive process can be ing the definition in Eq. (11). The fine binning of the written as [25] : acceptance look-up table reduces the model dependence (4πα)3dQ2dW2dΩ∗ of the cross sections. The statistical errors for the ac- dσr = 2(4π)7S2W2 π × ceptance corrections were estimated using the binomial v√λ distribution: dΩ dv WL(r)W , (13) k f2 Q4 µν µν A (1 A ) Z W δA = bin − bin , (12) where S 2E M , dΩ∗ is the differential center-of-mass bin s Ngen−1 solid ang≡le of ithepπ+,πv M2 M2, L(r) and W are ≡ X − n µν µν whereN isthenumberoftheMonte-Carloeventsgen- the leptonic and the hadronic tensors respectively, and gen erated in the bin. These errors are included in the sta- λ (W2 m2 M2 )2 4m2 W2 (14) tistical error of the final cross sections. W ≡ − π+ − miss − π+ f W E +p (cosθ cosθ TheacceptanceofCLASforsingle-pionelectroproduc- W π π π k ≡ − tion at Q2 = 0.3 GeV2 and W = 1.23 GeV is shown +sinθ sinθ cos(φ φ )). (15) π k π k − 9 Corrections for binning effects R R 1.6 θ=82.5, φ=105 1.6 W=1.23, φ=105 1.4 1.4 Because of the finite detector resolution and finite bin 1.2 1.2 size,themeasuredvaluesofthecrosssectioninthecenter 1 1 ofthedatabincanbedistortedbyupto10%. Theexper- 0.8 0.8 imentallymeasuredquantityisthecrosssectionaveraged 1.1 1.2 1.3 1.4 1.5 1.6 0 50 100 150 W (GeV) θ (deg) over a full data bin, while usually it is more desirable to determine the value of the cross section at the center of R R 1.6 W=1.23, θ=82.5 1.6 W=1.53, φ=105 the bin. To account for such distortions, multiplicative 1.4 1.4 corrections were introduced as the ratio of the cross sec- 1.2 1.2 tion in the center of a bin to the averagecross section in 1 1 that bin: 0.80 100 200 300 0.80 50 100 150 dσ φ (deg) θ (deg) B = dΩ∗π |ctr . (16) dσ FIG. 11: Sampleplots of theradiative correction factor R at dΩ∗π |avg Q2=0.3GeV2. Thedottedlinesaretheexternalcorrections, The averaged cross sections were evaluated using two the dashed lines are internal corrections, and the solid lines models: the Q2 dependence of the cross sections was show the combined radiative correction. taken from the MAID2000 model [23], while the cross sections at fixed values of Q2 were obtained using a uni- tary isobar [27] fit to these data in the first iteration. Here, θ , φ , θ and φ are the pion and radiated π π k k photon’s angles in the hadronic center-of-mass reference Normalization frame. The integral in Eq. (15) is taken over the photon angles and variable v. The integrated charge of the electron beam passing In addition, there is also a nonzero probability that through the target was measured using the Faraday cup in the presence of the electromagnetic field of the atoms located at the end of the Hall B beam line. It generated of the target the electron will emit one or more photons pulseswithafrequencyproportionaltothebeamcurrent before or after interacting with the nucleus of the target with10Hzper1nAlinearslopeparameter. Thecalibra- (external radiation). The probability of emitting a real tion parameters of this device are known with less than photonofaparticularenergyis proportionalto the path 0.5% uncertainty. The measured charge was corrected length of the electron in the target material. The size for the data acquisition live-time, calculated as the ra- of the external radiative corrections for these measure- tio of the counts from two scalers. These scalers were ments was significantlysmaller thanfor internalbecause connected to a single 100 kHz pulse generator. One of of the small amount of the target material (t = 0.5% of them was ungated, while the other one was gatedby the radiation length). data acquisition “live” signal. To ensure the quality of Theinternalradiativecorrectionsforthecrosssections theanalyzeddatasample,softwarecutswereimposedon werecalculatedusingtheExcluRad program[25]asmul- the live-time, elastic scatteringandsingle π+ electropro- tiplicative correction factors for each data bin. The ex- duction rates. The portions of the runs for which these ternal radiative corrections were done using the Mo and quantities were outside of the imposed limits were ex- Tsaiformalism[26]. The unradiatedstructurefunctions, cluded from the analysis, with the corresponding beam needed as an input for the correction procedure, were charge being subtracted from the total charge. As was calculatedusingaparameterizationofthe multipole am- mentioned above, the Cˇerenkov counter efficiencies were plitudes using a fit of these CLAS data based on the parameterizedduringthecalibrationprocedure[19],and unitary isobar model [27]. The size of the required cor- theappropriatecorrectionswereappliedtothecrosssec- rections varied up to 55%, depending on the kinematics. tions. The comparisonofthe elastic scatteringcrosssec- Fig. 11 shows dependences of the radiative corrections tions versus θ from CLAS and the model calculation e R σrad onthevariablesW,θandφatQ2 =0.3GeV2. using a parameterization[28] for the elastic form factors ≡ σBorn The dotted line shows the correction due to external ra- is showninFig.12. The modelcrosssectionincludes ra- diation, and the dashed line is the correction factor ob- diative effects, according to the Mo and Tsai formalism tainedusingtheExcluRad program. Thesolidlineisthe [26]. Theerrorbarsonthedatapointsrepresentstatisti- combined correction factor calculated as the product of caluncertainties only. The solid line at R=1.015shows the two. Because of the short length of the target, the the result of fitting a constant to the ratio of the mea- external radiative corrections are much smaller than the sured cross sections to the parameterization [28]. The internal corrections. fluctuations aroundthis line can be used to estimate the 10 calculations. Aswasmentionedabove,weusemissingmassandver- R1.1 texcutstoselectthesingle-pionproductioneventsandto reduce the number of events with decaying pions. These 1.05 cuts cause losses of some single-pion events as well. The true number ofevents is expectedto be recoveredby ap- plying the acceptance corrections by using exactly the 1 same cuts on the Monte-Carlo data. The remaining sys- tematic errorsassociatedwith these cuts were estimated 0.95 by varying the sizes of the windows. The absolute value of the cross section variations calculated with different 0.9 cut windows, averagedoverφ at fixed Q2, W andθ, was 20 25 30 35 40 45 50 θ (deg) consideredasthesystematicuncertaintyforallφforthat e fixed Q2, W and θ. Oneofthe possiblesourcesofsystematicerrorsinthis FIG. 12: The ratio of the measured elastic cross section to experimentis the uncertaintyinthe normalization. This the parameterization of the world data [28]. The error bars can arise from miscalibrations of the Faraday cup, tar- represent the statistical uncertainty only. The solid line is get density variations, errors in determining the target from the fit of the data pointsto a constant. length and its temperature along with data acquisition live-timeandotherfactors. However,the presenceofthe elastic events in the data set allows us to account for systematic uncertainty of electron detection and recon- the normalization uncertainties of the cross sections by struction. comparingthe elasticcrosssectionsto the parameteriza- The contributions from scattering off the target cell tion of the world data [28]. This way we were able to walls was estimated to be 1.5%using empty targetruns. combine the normalization, electron detection, electron This correctionfactor was appliedto the crosssectionin trackingandelectronidentificationerrorsintooneglobal every data bin. uncertainty factor. A comparison of the measured elas- tic cross sections for different θ and φ electron angles e e allowedustoassigna5.2%globaluncertaintyduetothe SYSTEMATIC ERRORS STUDIES normalization and electron efficiency uncertainties. The systematic uncertainty due to the model used in A number of studies were carried out to estimate the the radiative corrections was estimated by performing a systematic uncertainties on the measured cross sections. seconditeration. The radiativelycorrectedexperimental The primary method used in these studies was to vary crosssections fromCLAS were fitted once more,and us- different independent parameters of the analysis to de- ingthefitthenewcorrectionfactorswerecalculatedand termine the corresponding change in the resulting cross compared with the previous iteration. The comparison sections and the structure functions. indicated an uncertainty on the order of 2% due to the Becauseofthefinitebinsize,theresultofaveragingthe model dependence of the radiative corrections. acceptanceoveranacceptancebindependsonthedistri- Usingthekinematicallyover-determinedreactionep bution of events in that bin. If the physics model used e′π+π−p allows us to determine the π+ efficiency by d→e- inthe Monte-Carlosimulationdiffers fromthe realdata, tecting the outgoing electron, π− and proton. The effi- then the averaging over a bin may result in an incorrect ciencyoftheπ+detectioncanbefoundastheratioofthe crosssection. Theintroducederrordependsontheshape numberofeventswheretheπ+ wasdetectedtothenum- of the acceptance function and the cross sections as well ber of events where the π+ was expected to be detected. asontheacceptancebinsize. Inaddition,becauseofthe A comparison of the pion efficiency calculated from the finite detector resolution, some of the events produced realdata withthe efficiency fromGEANT-basedMonte- inone acceptancebin willbe reconstructedin adifferent Carlo simulation lead to a systematic error estimate of bin. This may cause significant distortions in the final 2.5%. cross section distributions. In order to correctly account In order to estimate the background coming from for these effects, a realistic physics generator and detec- two-pion production, a sample of two-pion Monte-Carlo tor simulation are required. To estimate the errors of eventswasprocessedasifitweretheactualdatasample. the final results due to the modelused in the acceptance Theanalysisoftheseeventsshowedthatthisbackground calculations,wecalculatedtheacceptancetablewithtwo would contribute less than 1% uncertainty to the differ- different models. The comparisonof the results with the ential cross sections. The systematic error due to the twoacceptancecorrectionsallowedustoestimatethesys- π+ misidentification was estimated to be about 0.5% ∼ tematicerrorsduetothephysicsmodelintheacceptance by varying the cut in the proton-pion separation in the