Measurement of the Photon Beam Asymmetry in γ ⃗ p→ K + Σ 0 at E γ =8.5 GeV
GlueX Collaboration, S. Adhikari, A. Ali, M. Amaryan, A. Austregesilo, F. Barbosa, J. Barlow, E. Barriga, R. Barsotti, T. D. Beattie, V. V. Berdnikov, T. Black, W. Boeglin, W. J. Briscoe, T. Britton, W. K. Brooks, B. E. Cannon, N. Cao, E. Chudakov, S. Cole, O. Cortes, V. Crede, M. M. Dalton, T. Daniels, A. Deur, S. Dobbs, A. Dolgolenko, R. Dotel, M. Dugger, R. Dzhygadlo, H. Egiyan, T. Erbora, A. Ernst, P. Eugenio, C. Fanelli, S. Fegan, A. M. Foda, J. Foote, J. Frye, S. Furletov, L. Gan, A. Gasparian, C. Gleason, K. Goetzen, A. Goncalves, V. S. Goryachev, L. Guo, H. Hakobyan, A. Hamdi, G. M. Huber, A. Hurley, D. G. Ireland, M. M. Ito, N. S. Jarvis, R. T. Jones, V. Kakoyan, G. Kalicy, M. Kamel, C. Kourkoumelis, S. Kuleshov, I. Larin, D. Lawrence, D. I. Lersch, H. Li, W. Li, B. Liu, K. Livingston, G. J. Lolos, V. Lyubovitskij, D. Mack, H. Marukyan, V. Matveev, M. McCaughan, M. McCracken, W. McGinley, C. A. Meyer, R. Miskimen, R. E. Mitchell, F. Nerling, L. Ng, H. Ni, A. I. Ostrovidov, Z. Papandreou, M. Patsyuk, C. Paudel, P. Pauli, R. Pedroni, L. Pentchev, K. J. Peters, W. Phelps, E. Pooser, N. Qin, J. Reinhold, B. G. Ritchie, L. Robison, D. Romanov, C. Romero, C. Salgado, A. M. Schertz, R. A. Schumacher, et al. (27 additional authors not shown)
MMeasurement of the Photon Beam Asymmetryin (cid:126)γp → K + Σ at E γ = 8 . S. Adhikari, A. Ali, M. Amaryan, ∗ A. Austregesilo, F. Barbosa, J. Barlow, E. Barriga, R. Barsotti, T. D. Beattie, V. V. Berdnikov, T. Black, W. Boeglin, W. J. Briscoe, T. Britton, W. K. Brooks, B. E. Cannon, N. Cao, E. Chudakov, S. Cole, O. Cortes, V. Crede, M. M. Dalton, T. Daniels, A. Deur, S. Dobbs, A. Dolgolenko, R. Dotel, M. Dugger, R. Dzhygadlo, H. Egiyan, T. Erbora, A. Ernst, P. Eugenio, C. Fanelli, S. Fegan, A. M. Foda, J. Foote, J. Frye, S. Furletov, L. Gan, A. Gasparian, C. Gleason, K. Goetzen, A. Goncalves, V. S. Goryachev, L. Guo, H. Hakobyan, A. Hamdi, G. M. Huber, A. Hurley, D. G. Ireland, M. M. Ito, N. S. Jarvis, R. T. Jones, V. Kakoyan, G. Kalicy, M. Kamel, C. Kourkoumelis, S. Kuleshov, I. Larin, D. Lawrence, D. I. Lersch, H. Li, W. Li, B. Liu, K. Livingston, G. J. Lolos, V. Lyubovitskij,
27, 28
D. Mack, H. Marukyan, V. Matveev, M. McCaughan, M. McCracken, W. McGinley, C. A. Meyer, R. Miskimen, R. E. Mitchell, F. Nerling, L. Ng, H. Ni, A. I. Ostrovidov, Z. Papandreou, M. Patsyuk, C. Paudel, P. Pauli, R. Pedroni, L. Pentchev, K. J. Peters, W. Phelps, E. Pooser, N. Qin, J. Reinhold, B. G. Ritchie, L. Robison, D. Romanov, C. Romero, C. Salgado, A. M. Schertz, R. A. Schumacher, J. Schwiening, K. K. Seth, X. Shen, M. R. Shepherd, E. S. Smith, D. I. Sober, A. Somov, S. Somov, O. Soto, J. R. Stevens, I. I. Strakovsky, K. Suresh, V. V. Tarasov, S. Taylor, A. Teymurazyan, A. Thiel, G. Vasileiadis, T. Whitlatch, N. Wickramaarachchi, † M. Williams, T. Xiao, Y. Yang, J. Zarling, Z. Zhang, Q. Zhou, X. Zhou, and B. Zihlmann (The GlueX
Collaboration) Arizona State University, Tempe, Arizona 85287, USA National and Kapodistrian University of Athens, 15771 Athens, Greece Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA The Catholic University of America, Washington, D.C. 20064, USA University of Connecticut, Storrs, Connecticut 06269, USA Duke University, Durham, North Carolina 27708, USA Florida International University, Miami, Florida 33199, USA Florida State University, Tallahassee, Florida 32306, USA The George Washington University, Washington, D.C. 20052, USA University of Glasgow, Glasgow G12 8QQ, United Kingdom GSI Helmholtzzentrum f¨ur Schwerionenforschung GmbH, D-64291 Darmstadt, Germany Institute of High Energy Physics, Beijing 100049, People’s Republic of China Indiana University, Bloomington, Indiana 47405, USA Alikhanov Institute for Theoretical and Experimental Physics NRC Kurchatov Institute, Moscow 117218, Russia Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606, USA Forschungszentrum Juelich Nuclear Physics Institute, 52425 Juelich, Germany University of Massachusetts, Amherst, Massachusetts 01003, USA Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA National Research Nuclear University Moscow Engineering Physics Institute, Moscow 115409, Russia Norfolk State University, Norfolk, Virginia 23504, USA North Carolina A&T State University, Greensboro, North Carolina 27411, USA University of North Carolina at Wilmington, Wilmington, North Carolina 28403, USA Northwestern University, Evanston, Illinois 60208, USA Old Dominion University, Norfolk, Virginia 23529, USA University of Regina, Regina, Saskatchewan, Canada S4S 0A2 Universidad T´ecnica Federico Santa Mar´ıa, Casilla 110-V Valpara´ıso, Chile Tomsk State University, 634050 Tomsk, Russia Tomsk Polytechnic University, 634050 Tomsk, Russia A. I. Alikhanian National Science Laboratory (Yerevan Physics Institute), 0036 Yerevan, Armenia College of William and Mary, Williamsburg, Virginia 23185, USA Wuhan University, Wuhan, Hubei 430072, People’s Republic of China (Dated: May 13, 2020)We report measurements of the photon beam asymmetry Σ for the reaction (cid:126)γp → K + Σ (1193)using the GlueX spectrometer in Hall D at Jefferson Lab. Data were collected using a linearlypolarized photon beam in the energy range of 8.2-8.8 GeV incident on a liquid hydrogen target. The a r X i v : . [ nu c l - e x ] M a y beam asymmetry Σ was measured as a function of the Mandelstam variable t , and a single value ofΣ was extracted for events produced in the u -channel. These are the first exclusive measurementsof the photon beam asymmetry Σ for the reaction in this energy range. For the t -channel, themeasured beam asymmetry is close to unity over the t -range studied, − t = (0 . − .
4) (GeV/ c ) ,with an average value of Σ = 1.00 ± K ∗ (892) Regge trajectory. A value of Σ = 0.41 ± u -channel integrated up to − u = 2 . c ) . I. INTRODUCTION
The GlueX experiment at Thomas Jefferson NationalAccelerator Facility (Jefferson Lab) was designed tostudy the light quark meson spectrum and to searchfor exotic resonances. It uses a high-intensity linearly-polarized photon beam impinging on a liquid hydrogentarget and is able to access a broad range of final states.The interpretation of experimental data from photopro-duction of pseudoscalar mesons requires a deep under-standing of the production mechanism, which is compli-cated by the possible excitation of baryon resonances.In this experiment, we study photoproduction of thestrange pseudoscalar meson K + in the (cid:126)γp → K + Σ re-action, above the baryon resonance region. While thehigh-energy domain in photoproduction of pseudoscalarmesons is relatively well understood in the framework ofRegge theory, precise experimental data for the photo-production of many different final states at high energyare scarce. In this analysis, we focus on the photopro-duction reaction (cid:126)γp → K + Σ to study the mechanism ofstrange Reggeon exchange and measure the relative con-tributions of natural and unnatural parity exchange viabeam asymmetry measurements.Our understanding of the photoproduction of kaons atthese energies is based predominantly on measurementsfrom SLAC [1, 2]. These measurements were not fullyexclusive - the beam was untagged bremsstrahlung andonly the final state K + was detected. The first paperreported measurements of beam asymmetry for the sumof the two photoproduction reactions, K + Λ and K + Σ.It was found to be close to unity. In the later paper, theauthors used the ratio of the cross sections, which wasalso close to unity, to extract separate asymmetries forthe two processes as a function of t -Mandelstam. Priorto this current publication, these were the only availablemeasurements above the baryon resonance region.Theoretical models [3–7] are necessary for extractinginformation from the more detailed measurements ob-tained at lower beam energy, such as the beam asymme-try measurements from both proton and neutron targetswith a photon beam at 1.5-2.4 GeV by LEPS [8, 9], themeasurements below 1.5 GeV at GRAAL [10, 11], andthe recent CLAS results [12], which provide extensivemeasurements of many observables for hadronic mass W from 1.71 to 2.19 GeV. ∗ Corresponding author:[email protected] † Corresponding author:[email protected]
These measurements have been important for resolvingnew states and also the status of many excited baryonstates, however the precision of the existing high-energydata limited the accuracy of some of the modeling neededfor the baryon studies. The new and more precise datareported here will make an impact on models used in thelower energy studies.Below, we present the first exclusive measurement ofthe photon beam asymmetry Σ in the reaction (cid:126)γp → K + Σ beyond the resonance region. The analysis wasperformed with approximately 20% of the data collectedin the first phase of the GlueX experiment, which corre-sponds to a luminosity of 20.8 pb − in the beam energyrange between 8.2 and 8.8 GeV. II. THEORY
The Mandelstam variables s , t and u in the reaction (cid:126)γp → K + Σ are defined as: s = ( p beam + p target ) , (1) t = ( p beam − p K + ) , (2) u = ( p target − p K + ) , (3)where p beam , p target and p K + are the four-momenta ofthe incoming photon beam, the target proton and theproduced K + meson respectively.The observables of the photoproduction reaction arediscussed in terms of s -channel helicity amplitudes withdefinite parity in the t -channel to leading order in s de-fined in Ref. [3]: f = f , ,f = f , − ,f = f − , ,f = f − , − , (4)where in f ab,cd the subscripts a, b, c, d represent the he-licities of the incoming photon, the target proton, theproduced spin-zero meson and the recoiling baryon, re-spectively. The following combinations can be formed: f ± = 12 ( f ± f ) ,f ± = 12 ( f ∓ f ) , (5)where the superscript +( − ) indicates natural (unnatural)parity exchange in the t -channel. In Regge theory, forthe reaction of interest, (cid:126)γp → K + Σ , these are realizedvia exchange of K ∗ (892) and K (494) trajectories for thenatural and unnatural parity exchanges, respectively.The polarized photon beam asymmetry is given byΣ = (cid:104) dσ ⊥ dt − dσ (cid:107) dt (cid:105)(cid:46)(cid:104) dσ ⊥ dt + dσ (cid:107) dt (cid:105) = ( | f +1 | + | f +2 | − | f − | − | f − | )( | f +1 | + | f +2 | + | f − | + | f − | ) , (6)where dσ ⊥ dt ( dσ (cid:107) dt ) is the cross section with a photon beampolarized perpendicular (parallel) to the reaction plane.The experimental value of Σ provides a direct measure-ment of the relative contributions of the natural and un-natural parity exchange mechanisms to the photoproduc-tion of the K + Σ final state. III. EXPERIMENT
The measurements were performed using the GlueXspectrometer, which is located in Hall D at JeffersonLab. An 11.6 GeV electron beam from the Continu-ous Electron Beam Accelerator Facility is used to cre-ate a tagged linearly polarized photon beam by coherentbremsstrahlung off a diamond radiator. The polarizationapproaches 40% in the region of the coherent peak, from8.2 to 8.8 GeV. The scattered electrons are directed intothe Tagger Detector, a scintillating-fiber array which, bymeasuring the momenta of the recoil electrons, enables ameasurement of the energy of the produced photons to0.1% precision within the region of the coherent peak.The photon beam passes through a collimator in orderto suppress the incoherent part, a triplet polarimeter [13]and a pair spectrometer [14], which provide continuous,non-invasive measurements of the photon beam polariza-tion and the relative flux, respectively, before reachingthe liquid hydrogen target. The target is surroundedby a scintillator start counter [15], a straw-tube centraldrift chamber [16] and a lead and scintillating-fiber barrelcalorimeter [17], all inside the bore of a superconductingsolenoid. Four sets of planar wire drift chambers [18] arealso located inside the solenoid, downstream of the cen-tral drift chamber. A time-of-flight scintillator wall anda forward lead-glass calorimeter [19] are located furtherdown the beamline and outside of the solenoid. The driftchambers provide measurements of momentum and spe-cific energy loss for charged particles, while the calorime-ters provide energy and position measurements for show-ers caused by both charged and neutral particles. Time-of-flight measurements for particle identification are pro-vided by the start counter, the calorimeters and the time-of-flight wall. The trigger signal is generated for eventsthat deposit sufficient energy in the calorimeters. Thespectrometer has a nearly hermetic angular coverage.The data used in this analysis were collected in spring2017. Four orientations of the diamond radiator wereused to produce bremsstrahlung photons in two sets with orthogonal linear polarization, one set parallel and per-pendicular to the lab floor (referred to as 0/90), and asecond set, rotated by 45 ◦ from the first one (-45/45).The two different sets of orientations allow an indepen-dent check of systematic uncertainties. IV. EVENT SELECTION
The exclusive reaction (cid:126)γp → K + Σ was selected usingthe subsequent decays of Σ → Λ γ and Λ → pπ − . Can-didate events for this reaction were required to containat least two positively charged tracks, one negative trackand one photon candidate. Extra tracks, showers andtagged beam photons were also permitted in the initialevent selection. The proton was identified via its spe-cific energy loss dE/dx in the central drift chamber, andtime-of-flight information was used to refine the selectionof all the charged-particle tracks. The absolute value ofthe squared missing mass for the reaction was limitedto less than 0.08 (GeV/ c ) . A kinematic fit was usedto select particle combinations satisfying conservation ofenergy and momentum with a constraint on the eventvertex. Following the kinematic fit, further event selec-tion required that the vertex of the K + track originatewithin 1 cm from the beamline and within the target vol-ume, while the pion and proton from the Λ decay werepermitted to originate from a detached vertex. A qualityrequirement was placed on neutral showers in the for-ward calorimeter in order to reduce the likelihood thatthey were caused by split-off clusters from charged par-ticle showers [20].The beam photons were selected from the coherentpeak region, between 8.2 and 8.8 GeV, where the polar-ization was highest. Figure 1 shows the measured polar-ization as a function of the photon energy averaged overthe four diamond orientations. Dashed vertical lines indi-cate the photon beam energy range used in this analysis.The energy of the beam photon initiating the eventwas defined by the position of the fired tagger counter inthe Tagger Detector. The candidates were selected usingthe time difference | ∆ t | between the timing of the sig-nal in the counter, projected to the vertex location, andthe vertex time. The electron beam had a 4 ns bunchstructure but the vertex timing resolution permitted theassociation of the events with a particular bunch, thusimproving the | ∆ t | resolution. Prompt beam candidateswere selected in the range | ∆ t | < < | ∆ t | <
18 ns.Figure 2 shows the correlation between the invariantmass of the pπ − γ system and its pπ − subsystem. A clearenhancement can be seen in the overlap region betweenthe masses of Σ (1193) and Λ (1116), respectively. Theone-dimensional pπ − mass distribution in Fig. 3 showsthe Λ peak. This distribution was fitted using a Voigtian (GeV) g E P o l a r i za ti on FIG. 1. Photon beam polarization as a function ofbeam energy, as measured by the triplet polarimeter,averaged over the four different diamond orientations.Dashed vertical lines indicate the beam energy rangeused for this analysis. Vertical error bars show thestatistical uncertainty and inner shaded regions showthe systematic uncertainty due to the 1.5% relativeuncertainty from the polarimeter analyzing power.The polarizations for the individual orientations arepresented in Ref. [21]. function for the signal and a first order Chebyshev poly-nomial for the background. The fit shows a mean valueof M Λ = 1116 MeV/ c and has a corresponding Gaus-sian width σ = 3 MeV/ c . Events within the range | M pπ − − M Λ | < σ were selected as shown in Fig. 3 bydashed vertical lines to reconstruct the invariant mass ofΛ γ . ) c (GeV/ - p p M ) c ( G e V / g - p p M FIG. 2. Invariant mass of pπ − γ vs. invariant mass of pπ − after all cuts. The enhancement in the overlapregion corresponds to the Λ (1116) and Σ (1193). Figure 4 shows the invariant mass of the Λ γ system.It was fitted using a Voigtian function for the signal anda first order Chebyshev polynomial for the background.A mean value of M Σ = 1193 MeV/ c and a correspond-ing Gaussian width of σ = 8 MeV/ c were obtained forthe Σ peak. The range | M Λ γ − M Σ | < σ is indicated ) c (GeV/ - p p M c C oun t s / M e V / FIG. 3. Invariant mass of pπ − (solid circles). Thesolid curve is the sum of a Voigtian and a first orderChebyshev polynomial (dashed curve) fitted to thedata. The selection region of Λ signal events isindicated by the vertical dashed lines. ) c (GeV/ gL M c C oun t s / M e V / FIG. 4. The invariant mass of Λ γ (solid circles). Thesolid curve is the sum of a Voigtian and a first orderChebyshev polynomial (dashed curve) fitted to thedata. The selection region of Σ events for furtheranalysis is indicated by the vertical dashed lines. by dashed vertical lines. The events within this range,1.169 GeV/ c < M Λ γ < c , were used for thebeam asymmetry analysis. The fraction of backgroundevents within 3 σ of the peak was found to be approxi-mately constant with t at about 2%.Figure 5 shows the yields of K + Σ events as a functionof − t and − u within the range of 1.169 GeV/ c < M Λ γ < c . The acceptances are shown in the samefigure as dashed lines. They were obtained by passinga sample of generated events through a GEANT3 [22]model of the detector and applying the same selectioncriteria as used in the analysis. ) c / -t (GeV c / C oun t s / . G e V A cce p t a n ce a) ) c / -u (GeV c / C oun t s / . G e V A cce p t a n ce b) FIG. 5. Event yields for (cid:126)γp → K + Σ (solid circles)and detector acceptance (dashed lines): (a) as afunction of − t and (b) as a function of − u . V. PHOTON BEAM ASYMMETRY
The event yields for the orthogonal orientations Y (cid:107) and Y ⊥ are given by Eqs. 7 and 8, where φ is the angle be-tween a plane parallel to the laboratory floor and the K + production plane, σ is the unpolarized cross section, A ( φ ) is a function representing the detector acceptance, N (cid:107) ( N ⊥ ) is the flux of photons, P (cid:107) ( P ⊥ ) is the magni-tude of the photon beam polarization and Σ is the beamasymmetry. Y (cid:107) ( φ ) ∝ N (cid:107) [ σ A ( φ )(1 − P (cid:107) Σ cos 2 φ )] (7) Y ⊥ ( φ ) ∝ N ⊥ [ σ A ( φ )(1 + P ⊥ Σ cos 2 φ )] (8)Figure 6 shows the yields for the photon polarizationplanes oriented at 0 ◦ ( Y (cid:107) ) and 90 ◦ ( Y ⊥ ), integrated overthe t region used in the analysis and Fig. 7 showsthe yields for the other orientation set, − ◦ ( Y (cid:107) ) and45 ◦ ( Y ⊥ ). Assuming that there is no background, theseyields can be used to obtain a polarization-dependentyield asymmetry, given by Y ⊥ − F R Y (cid:107) Y ⊥ + F R Y (cid:107) = ( P ⊥ + P (cid:107) )Σ cos 2( φ − φ )2 + ( P ⊥ − P (cid:107) )Σ cos 2( φ − φ ) (9) where F R = N ⊥ N (cid:107) is the ratio of the integrated photon fluxfor the two orthogonal orientations. A phase offset φ ac-counts for a possible small misalignment of the beam po-larization from its nominal orientation and the additional45 ◦ offset for the -45/45 dataset. The flux normalizationratio F R was found to be 1.038 for the 0/90 dataset and0.995 for the -45/45 dataset. The yield asymmetry allowsthe beam asymmetry Σ to be extracted without requir-ing any correction for instrumental acceptance. The yieldasymmetries for the 0/90 and -45/45 orientation sets areshown in Figs. 8 and 9 respectively. (deg) f - - C oun t s FIG. 6. Yield of (cid:126)γp → K + Σ events versus φ integrated over t for the 90 ◦ (open upward triangles)and 0 ◦ (closed downward triangles) polarizationorientations. (deg) f - - C oun t s FIG. 7. Yield of (cid:126)γp → K + Σ events versus φ integrated over t for the 45 ◦ (open upward triangles)and − ◦ (closed downward triangles) polarizationorientations. After fitting the yield asymmetry with the functiongiven in Eq. 9, the beam asymmetry Σ was extracted asthe only free parameter in the fit. The yield asymme-try was measured in four bins of t , with roughly equalstatistics in each bin. The beam asymmetry values forthe 0/90 and -45/45 orientations were combined using (deg) f - - Y i e l d A s y mm e t r y - - - - FIG. 8. The yield asymmetry for the 0/90 orientationset, corresponding to the data in Fig. 6 with a fit ofEq. 9 (solid curve). See text for details. (deg) f - - Y i e l d A s y mm e t r y - - - - FIG. 9. The yield asymmetry for the -45/45orientation set, corresponding to the data in Fig. 7with a fit of Eq. 9 (solid curve). See text for details. weighted averages.Systematic uncertainties were estimated by varying theevent selection criteria, the phase offset φ , the flux nor-malization, and the minimum shower energy. They arelisted in Tables I and II.For the event selection, the invariant mass cuts for π − p and Λ γ were varied within the Gaussian 2 σ and 4 σ range,where 3 σ is the nominal range. For the other cuts in theevent selection, they are varied between ranges such thatthe signal yield was not allowed to change by more than10% from the nominal range to avoid statistical effects.The systematic uncertainty due to the phase offset φ was found by letting φ be a free parameter in the fitand extracting beam asymmetry Σ values. The flux nor-malization was varied ±
5% from the nominal value andthe systematic uncertainty found using the correspondingΣ values.The minimum detection threshold for shower energy inthe barrel calorimeter is 50 MeV [17]. The acceptance forradiated photons from low momentum Σ decay is sensi- tive to this energy threshold at low − t . The systematicuncertainty was found by varying this minimum radiativephoton energy to 55 MeV and 60 MeV. For the low − u domain, the Σ has high momentum leading to higherradiative photon energies, making the acceptance insen-sitive to the minimum shower energy around 50 MeV.Therefore the systematic uncertainty due to this is esti-mated for the low − t domain only.The uncertainty from the 2% background was esti-mated by measuring beam asymmetry for events in theregion 1.23 GeV/ c < M Λ γ < . c . These areevents from K + Λ combined with an uncorrelated shower.The systematic uncertainty from this background is 0.4%for both t and u regions.Since this reaction is studied in the fully exclusive fi-nal state, there is a potential bias arising from the non-uniform acceptance of decay products of the polarizedΛ. This leads the measured φ yields to be sensitive tounmeasured polarization observables of the recoiling hy-peron [12]. A conservative estimate of the uncertaintydue to this effect was made by convoluting the accep-tance of the decay proton, obtained from detailed MonteCarlo simulations, with a range of polarization observ-ables spanning a conservative range of values. The con-tribution of the hyperon decay dependence to the yieldasymmetry was found to be 3% or less for each bin in t . A uniform 3% systematic uncertainty was applied toall bins. The same approach was used for the u -channelproduction, for which 1.5% uncertainty was obtained.The dominant systematic uncertainties are due to thevariation in event selection criteria. A 2.1% relative un-certainty in the measurement of the photon beam po-larization comes from the combination of the 1.5% sys-tematic uncertainty in the instrument combined with thestatistical uncertainty in the number of detected tripletevents. This uncertainty applies to the overall scale of themeasured beam asymmetries and is not combined withthe other uncertainties.Table III gives the average values of the beam asym-metry, together with the statistical and systematic un-certainties for the low − t region. The combined system-atic uncertainty for each bin in t or u is taken to be thelarger of the systematic uncertainties from the two datasets, and the total uncertainties are found by adding thestatistical and systematic errors in quadrature.The extracted beam asymmetry results shown inFig. 10 are close to unity within errors in all four t bins.The mean value of Σ over the entire measured t range isfound to be Σ = 1 . ± . ± . ± . K + Σ . This result isconsistent with the theoretical predictions from RPR-2007 [6, 7] and Guidal et al. [5] where K + Σ photopro-duction proceeds via exchange of K ∗ (892), the lowestmember of the linear Regge trajectory for natural-parityexchange.The beam asymmetry for the measured low − u re-gion, − u < . c ) , is found to be Σ =0 . ± . ± . ± . − u = 0 . ± .
34 (GeV /c ) . ) c / -t (GeV S GlueXSLAC et al.
Corthals et al.
Guidal
FIG. 10. The beam asymmetry Σ for (cid:126)γp → K + Σ asa function of − t . The results from the 0/90 and-45/45 data sets are averaged (solid circles) wherehorizontal error bars indicate the RMS widths of the t bins and vertical error bars represent statistical andsystematic uncertainties added in quadrature. Anadditional 2.1% overall relative polarizationuncertainty is not included. The triangles areprevious SLAC results [2] at E γ = 16 GeV, the curvesshow predictions from RPR-2007 [6, 7] (solid) andGuidal et al. [5] (dashed) at E γ = 8 . − t (0 . < − t < . c ) ) region. Source 0/90 Set -45/45 SetEvent selection 3.1-5.9% 3.0-5.3%Phase offset 0.1% 0.7%Flux normalization 0.5% 0.4%Minimum shower energy 2.6% 2.9%Background 0.4% 0.4%Non-uniform acceptance 3.0% 3.0%Total 5.1-7.1% 5.2-6.8%
VI. CONCLUSIONS
We present experimental results for the first mea-surement of the photon beam asymmetry Σ in the ex-clusive reaction (cid:126)γp → K + Σ beyond the baryon reso-nance region, which have significantly higher precisionthan the earlier SLAC measurement [2]. The measuredbeam asymmetry as a function of t is consistent, within TABLE II. Summary of systematic uncertainties forthe low − u ( − u < . c ) ) region. Source 0/90 Set -45/45 SetEvent selection 5.0% 4.0%Phase offset 2.2% 2.1%Flux normalization 0.6% 0.2%Background 0.4% 0.4%Non-uniform acceptance 1.5% 1.5%Total 5.7% 4.8%
TABLE III. Average beam asymmetry Σ for the low − t region with statistical and systematicuncertainties. − t ((GeV/ c ) ) Σ0.27 0.99 ± ± ± ± ± ± ± ± − u < . /c ) has never been extracted before. Anaverage beam asymmetry of 0.41 ± u in-terval is obtained. In this kinematic domain, u -channelhyperon exchanges of both Σ ( J = 1 / Y ∗ ( J = 3 / K + Σ final state. Currently there is no predic-tion for the beam asymmetry as a function of u . Theseresults place significant new constraints on photoproduc-tion models for strangeness-exchange reactions. ACKNOWLEDGEMENTS
We would like to acknowledge the outstanding effortsof the staff of the Accelerator and the Physics Divisionat Jefferson Lab that made the experiment possible. Weappreciate useful communication with Jan Ryckebusch,Michel Guidal and Gary Goldstein.This work was supported in part by the U.S. Depart-ment of Energy, the U.S. National Science Foundation,the German Research Foundation, GSI Helmholtzzen-trum f¨ur Schwerionenforschung GmbH, the Natural Sci-ences and Engineering Research Council of Canada, theRussian Foundation for Basic Research, the UK Scienceand Technology Facilities Council, the Chilean Comisi´onNacional de Investigaci´on Cient´ıfica y Tecnol´ogica, theNational Natural Science Foundation of China and the China Scholarship Council. This material is based uponwork supported by the U.S. Department of Energy, Of-fice of Science, Office of Nuclear Physics under contractDE-AC05-06OR23177. [1] D. J. Quinn, J. P. Rutherfoord, M. A. Shupe, D. J. Sher-den, R. H. Siemann, and C. K. Sinclair, Phys. Rev. Lett. , 543 (1975).[2] D. J. Quinn, J. P. Rutherfoord, M. A. Shupe, D. J. Sher-den, R. H. Siemann, and C. K. Sinclair, Phys. Rev. D20 ,1553 (1979).[3] G. R. Goldstein, J. F. Owens III, and J. Rutherfoord,Nucl. Phys.
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