Beam Asymmetry Σ for the Photoproduction of η and η ′ Mesons at E γ =8.8 GeV
GlueX Collaboration, S. Adhikari, A. Ali, M. Amaryan, A. Austregesilo, F. Barbosa, J. Barlow, A. Barnes, E. Barriga, R. Barsotti, T. D. Beattie, V. V. Berdnikov, T. Black, W. Boeglin, M. Boer, 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, N. Gevorgyan, 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, P. Mattione, V. Matveev, M. McCaughan, M. McCracken, W. McGinley, C. A. Meyer, R. Miskimen, R. E. Mitchell, F. Nerling, L. Ng, 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, et al. (34 additional authors not shown)
BBeam Asymmetry Σ for the Photoproduction of η and η (cid:48) Mesonsat E γ = . S. Adhikari, A. Ali, M. Amaryan, A. Austregesilo, F. Barbosa, J. Barlow,
3, 5
A. Barnes,
3, 5
E. Barriga, R. Barsotti, T. D. Beattie, V. V. Berdnikov, T. Black, W. Boeglin, M. Boer, 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, N. Gevorgyan, 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,
25, 26
D. Mack, H. Marukyan, P. Mattione, V. Matveev, M. McCaughan, M. McCracken, W. McGinley, C. A. Meyer, ∗ R. Miskimen, R. E. Mitchell, F. Nerling, L. Ng, 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, A. Yu. Semenov, I. A. Semenova, K. K. Seth, X. Shen, M. R. Shepherd, E. S. Smith, D. I. Sober, A. Somov, S. Somov, O. Soto, M. Staib, J. R. Stevens, I. I. Strakovsky, K. Suresh, V. V. Tarasov, A. Teymurazyan, A. Thiel, G. Vasileiadis, T. Whitlatch, N. Wickramaarachchi, M. Williams, T. Xiao, Y. Yang, J. Zarling, Z. Zhang, G. Zhao, 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 a r X i v : . [ nu c l - e x ] N ov University of Connecticut, Storrs, Connecticut 06269, 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 ExperimentalPhysics NRC Kurchatov Institute, Moscow, 117218, Russia Thomas Jefferson National Accelerator Facility,Newport News, Virginia 23606, USA University of Massachusetts, Amherst, Massachusetts 01003, USA Massachusetts Institute of Technology,Cambridge, Massachusetts 02139, USA National Research Nuclear University MoscowEngineering 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: November 12, 2019)
Abstract
We report on the measurement of the beam asymmetry Σ for the reactions (cid:126)γp → pη and (cid:126)γp → pη (cid:48) from the GlueX experiment, using an 8.2–8.8 GeV linearly polarized tagged photon beam incidenton a liquid hydrogen target in Hall D at Jefferson Lab. These measurements are made as afunction of momentum transfer − t , with significantly higher statistical precision than our earlier η measurements, and are the first measurements of η (cid:48) in this energy range. We compare the resultsto theoretical predictions based on t –channel quasi-particle exchange. We also compare the ratioof Σ η to Σ η (cid:48) to these models, as this ratio is predicted to be sensitive to the amount of s ¯ s exchangein the production. We find that photoproduction of both η and η (cid:48) is dominated by natural parityexchange with little dependence on − t . ∗ Corresponding author:[email protected] η and η (cid:48) mesons has been important in the search for isospin baryonresonances, with both cross section and spin observables providing input in this endeavor.In the nucleon resonance region, the s –channel baryon production is mixed with t –channelReggeon exchange, while at high energy (above 7 GeV), reactions are dominated by the t –channel contributions [1, 2]. Of particular interest in the high-energy region is the photonbeam asymmetry Σ, measured using linearly polarized photons. This observable is sensitiveto the naturality of the exchange particle [3], and a determination of the beam asymmetriesfor the η and η (cid:48) (Σ η and Σ η (cid:48) , respectively) at high energy directly constrains these samecontributions at lower energies. While Σ η and Σ η (cid:48) provide valuable information on theirown, the ratio of the two can shed light on the contributions of hidden strangeness exchange( s ¯ s states, such as the φ and h (cid:48) ) and axial vector meson ( b and h ) exchange [4].There is substantial literature of photon beam asymmetry measurements for the η below4 GeV beam energies [5–11]. A more limited set of Σ η (cid:48) measurements exists in the sameenergy region [11, 12], however, only one measurement of Σ η above 7 GeV exists [13].In this paper, we extend our earlier measurement of the linearly polarized photon beamasymmetry of the η meson [13] in (cid:126)γp → pη with more precise measurements. We also reportthe first measurement of the beam asymmetry of the η (cid:48) photoproduction in the photonenergy range 8 . − . . . − collected at a beam pulse repetition rate of 250 MHzin GlueX.Tagged photons are produced through the processes of bremsstrahlung and coher-ent bremsstrahlung by passing the 11 . µ m thick diamond radiator and measuring the energy of each recoil electron using ahighly segmented hodoscope, which covers the 8.2–8.8 GeV energy range of the coherentbremsstrahlung peak and allows us to determine each photon’s energy with an accuracyof ≈
10 MeV. Four orientations of the diamond radiator are used to produce two sets oforthogonal linear polarizations, one set parallel and perpendicular to the lab floor (referredto as ‘0/90’), and a second set, rotated by 45 ◦ from the first (‘-45/45’). About 10% ofthe data have been collected using a 30 µ m thick aluminum radiator, while the remainingdata are equally divided among the four diamond orientations. Data were taken by cycling4hrough each of the five configurations, with about two hours of data collection in eachconfiguration, per cycle.The produced photons travel 75 m before passing through a 5 mm diameter collimator,which removes off-axis photons from the beam. This enhances the fraction of coherentlyproduced photons, yielding a photon beam with peak linear polarization of 40%, as shownin Fig. 1. The energy and flux of the photon beam are measured by a pair spectrometer [14],which detects pair production of e + e − in a 75 µ m thick beryllium converter. The polarizationof the photons is measured using a triplet polarimeter [15] using the process (cid:126)γe − → e − e + e − .The high-energy pair is measured in the pair spectrometer, while the low-energy recoilelectron is detected in a 1 mm thick silicon detector. The photon polarization P γ is obtainedfrom the azimuthal angular distribution φ e of the low-energy electron via dσdφ e ∝ [1 − P γ λ cos 2 ( φ e − φ γ )] , (1)where φ γ is the orientation of the linear polarization and λ is the analyzing power, whichis fully determined by quantum electrodynamics. The measured linear polarization, as afunction of the photon energy, is shown for each of the four diamond orientations in Fig. 1.The average polarization in each orientation is determined from the average of measurementsin the coherent peak region, weighted by the beam energy distribution for reconstructed η or η (cid:48) events. The statistical uncertainties of the average polarizations are driven by the yield oftriplet production events in the data sample, while the systematic uncertainty in the designand operation of the triplet polarimeter is 1.5% [15]. This uncertainty contributes to theoverall relative uncertainty of 2.1% discussed later.The GlueX detector is nearly hermetic and azimuthally symmetric, and optimized fora fixed target photoproduction experiment. It is based on a ∼ ∼ e + e − pairs) generated in the target to within a smallradius of the photon beamline. Inside the bore of the solenoid, the incident photons interactin a 30 cm long liquid hydrogen target that is located 65 cm from the upstream end of thesolenoid. The target is surrounded by a scintillator-based Start Counter (ST) that recordsthe time of charged particles [16], and a Central Drift Chamber (CDC) that contains 28layers of 1 . . (GeV) γ E − P o l a r i z a t i on ° PARA (0 ) ° PERP (90 ) ° PARA (-45) ° PERP (45
FIG. 1. The measured degree of linear polarization for the four diamond orientations is plotted asa function of the photon energy, offset from one another in energy for clarity. Events with energybetween 8.2–8.8 GeV are selected, as demarcated by the vertical lines. chambers (FDC) [18, 19]. Charged particle tracks are reconstructed with momentum reso-lution between 1% and 7%, depending on their angle and momentum. The drift chambersalso provide energy-loss information which allows for π - p separation up to about 1 GeV/cmomentum. A lead–scintillating-fiber barrel calorimeter (BCAL) encompasses all the driftchambers and measures the position, energy, and time of all incident particles [20]. Down-stream past the solenoid is a scintillator-based time-of-flight (TOF) wall that measures thearrival time of charged particles. A forward calorimeter (FCAL) is located downstream ofthe TOF wall and measures the energy, position, and time of particles in a 2800-elementarray of lead-glass blocks [21].The data for this study were reconstructed in two exclusive final states: (cid:126)γp → pγγ for the η decaying to γγ , and (cid:126)γp → pπ + π − γγ for the η (cid:48) decaying to ηπ + π − . The final states wereselected by choosing events with an associated topology: one positively charged track andtwo photons for the η , and two positively and one negatively charged track together withtwo photons for the η (cid:48) . Protons are identified using momentum and energy-loss informationfrom the drift chambers in the central region, and through time-of-flight in the forwarddirection.Initial event selection requires a primary event vertex inside the GlueX target, no photons6ear the edges of the calorimeters where shower reconstruction is incomplete, and protonmomentum above 250 MeV/c (to ensure that it can be consistently detected in the driftchambers). The time of the primary interaction is determined by hits in the ST matched tothe recoil proton track, and is used to specify which beam bunch of electrons is associatedwith the event, as the accelerator delivers one bunch of electrons every 4 ns. Photons associ-ated with the primary interaction are selected using the difference between the bunch’s time(provided by the accelerator) and the tagged photon’s time, ∆ t = | t photon − t bunch | < < | ∆ t | <
18 ns, corresponding to six out-of-time beambunches (three early and three late), is also selected to account for photons accidentallyassociated with the primary interaction.To ensure reaction channel exclusivity, a condition is placed on the square of the missingmass of the event, defined as MM = | p in − p fin | , where p in is the sum of the initial state four-momentum vectors (beam photon and target proton), and p fin is the sum of the final statefour-momentum vectors ( p and two γ s for the η , and p , π + , π − , and two γ s for the η (cid:48) ). Themissing mass squared is required to be consistent with zero, | MM | ≤ .
05 (GeV /c ) , whichreduces contributions from massive particles not detected in the event. As an additionalcondition of exclusivity, both channels excluded events containing extra photons that didnot appear to be part of the reconstructed event.Next, kinematic fitting is performed on the two exclusive final states. In the case of the η , a four-constraint fit requiring energy and momentum conservation is performed assuming γp → pγγ . In the case of the η (cid:48) , an eight-parameter fit is performed for the hypothesis γp → pπ + π − ( η → γγ ), applying energy and momentum conservation and constraining theevent vertex and mass of the η . Selection cuts are placed on the resulting χ from the fitsto isolate the desired final states. The cut values are the result of detailed studies of thetwo reactions to optimize signal to background in each channel. Finally, the energy of thebeam photon must be in the coherent peak. Detailed Monte Carlo studies of non-exclusive η and η (cid:48) production processes limit the level of peaking background satisfying all the eventselection criteria to less than one part in a thousand.The same analysis is performed on the out-of-time event sample, and the resulting out-of-time signal is subtracted (with a weight of ) from the in-time signal. The resulting massspectra for η and η (cid:48) candidates are shown in Fig. 2. Pronounced particle peaks are observedat the expected η and η (cid:48) masses, both on top of a small amount of background, described7n more detail below. The final event sample is selected by choosing the events between thetwo vertical lines surrounding the η and η (cid:48) mass peaks. The treatment of the backgroundcontribution to the measured beam asymmetry is discussed later. ) Invariant Mass (GeV/c γγ ) C oun t s / . ( M e V / c a) ) Invariant Mass (GeV/c η - π + π ) C oun t s / . ( M e V / c b) FIG. 2. The 2 γ (a) and π + π − η (b) invariant mass distributions are graphed after all selection cutsare applied. The η and η (cid:48) ‘peak region’ samples consist of the events between the solid verticallines. The ‘side-band region’ samples include events between the vertical dashed lines and are usedto evaluate the background asymmetry. The dashed curve on (a) is a Monte Carlo calculation ofthe reaction γp → pω where the ω → π γ and one of the resulting photons is not detected. Using these selection criteria, the yields of η and η (cid:48) are shown as a function of themomentum transfer − t in Fig. 3. The diminishing yield approaching − t = 0 . mainlyarises from the 250 MeV/c cut on the momentum of the recoil proton. The evaluation ofthe acceptance is based on a Regge model describing the underlying physics in terms of8 -channel meson exchange and is found to give a reasonable description of the data. MonteCarlo (MC) simulations are performed and compared with data to determine the detectoracceptance as a function of the momentum transfer − t (see Fig. 3). Other than the fall-off at − t near zero, the acceptance is approximately flat, demonstrating that it does not introduceany significant distortion to the yield distributions. ) -t (GeV × ) C oun t s / ( M e V a) A cce p t a n ce ) -t (GeV × ) C oun t s / ( M e V b) A cce p t a n ce FIG. 3. The yields of η (a) and η (cid:48) (b) events are plotted as a function of − t after all selection cutsare applied. The acceptance functions for γp → ηp ( pγγ ) and γp → η (cid:48) p ( pπ + π − γγ ), shown as thedashed curves, are determined from Monte Carlo simulation using a Regge model. The analyses are reported in more detail elsewhere [22, 23], while their key steps are sum-marized herein. For the photoproduction of pseudoscalar mesons with a linearly polarizedphoton beam and an unpolarized target, the polarized cross section σ pol is related to the9eam asymmetry through Eq. 2, σ pol ( φ, φ γ ) = σ (1 − P γ Σ cos [2( φ − φ γ )]) , (2)where σ is the unpolarized cross section, P γ is the magnitude of the photon beam polar-ization, φ is the azimuthal angle of the production plane, and φ γ is the azimuthal angle ofthe photon beam’s linear polarization plane determined by the orientation of the diamondradiator. In general, the azimuthal ( φ ) distribution of the event yield is given by Y (cid:107) ( φ, φ γ = 0) ∝ N (cid:107) (cid:2) σ A ( φ ) (cid:0) − P (cid:107) Σ cos 2 φ (cid:1)(cid:3) (3) Y ⊥ ( φ, φ γ = 90) ∝ N ⊥ [ σ A ( φ ) (1 + P ⊥ Σ cos 2 φ )] , (4)where A ( φ ) is an arbitrary function for the φ -dependent detector acceptance and efficiency,and N ⊥ ( (cid:107) ) is the flux of photons in two orthogonal orientations.The GlueX detector is designed to be symmetric in φ and thus have a uniform acceptanceand efficiency, but here we consider the general case of an arbitrary φ -dependent detectoracceptance and define the method for extracting Σ that cancels this detector acceptance.We choose the diamond radiator orientation such that we have two sets of orthogonallypolarized data, which causes the detector acceptance effects to cancel when forming the yield asymmetry , as in Eq. 5: Y ⊥ ( φ ) − F R Y (cid:107) ( φ ) Y ⊥ ( φ )+ F R Y (cid:107) ( φ ) = ( P ⊥ + P (cid:107) )Σ cos 2 ( φ − φ )2+( P ⊥ − P (cid:107) )Σ cos 2 ( φ − φ ) . (5)In this equation we introduce the phase offset φ which accounts for slight misalignment inthe orientation of the polarization plane ( φ γ ) away from its nominal value. The value os φ is found to be small (about 3 ◦ ).The flux normalization ratio F R = N ⊥ N (cid:107) is the ratio of the integrated photon flux for the twoorthogonal orientations of the photon polarization. For the 0/90 set, F R = 1 . ± . F R = 0 . ± . η and η (cid:48) in bins of − t , and Σ is extracted in each bin through fits of Eq. 5 to the asymmetry data,where Σ is the only free parameter. Fig. 4(a) shows the yields, Y ⊥ and Y (cid:107) , for the η events(integrated over all values of − t ) as a function of the angle φ . The oscillations of the twopolarization orientations are 90 ◦ out of phase. Fig. 4(b) shows the yield asymmetry givenby Eq. 5 and the resulting fit to the data.In order to correct for possible asymmetries from background events under the η and η (cid:48) events, the same asymmetry analysis is carried out for background events in the side-band10 − − − (deg) φ × C oun t s / ( deg ) a) ) ° PARA (0 ) ° PERP (90 − − − (deg) φ − − − Y i e l d A sy mm e t r y b) FIG. 4. (a) The yields integrated over the full range of − t , Y ⊥ and Y (cid:107) , are shown for the η eventsusing one set of orthogonally polarized data, and (b) the yield asymmetry is shown, fitted with a χ / ndf = 25 . / regions as shown in Fig. 2. The side-band asymmetry Σ SB and the dilution factor f (thefractional background under the peak) are extracted. The corrected beam asymmetry Σ COR is then given by Eq. 6: Σ
COR = Σ peak − f Σ SB − f (6)where Σ peak is the asymmetry measured in the peak region. This correction shifts theasymmetry values by a few percent in the lowest − t bin, falling to a negligible amount atlarge − t . 11its to the invariant mass spectra (Fig. 2) are carried out to extract f for each bin of − t .Σ SB is estimated from a fit of Eq. 5 to the yield asymmetry in the side-band region data.The binning in − t is optimized so that each bin contains an approximately equal numberof events; the higher statistics η channel allows finer binning than the η (cid:48) channel. Sincethe background under the η peak is almost entirely due to ω → π γ events with a missingphoton [13] (as shown in Fig. 2a), the Σ asymmetry for background events under the η peakis assumed to be identical to the Σ asymmetry of events in the ω peak. Therefore, the side-band region chosen to determine the η background asymmetry, 0 . < M γ < .
84 GeV/ c ,encompasses the ω peak. A systematic uncertainty on Σ η , associated with the Σ SB correction,is assigned to each − t bin and is between 0 . . η (cid:48) peak comesfrom multiple, higher lying channels, and the measured asymmetry in the side-band regionis mass-dependent. Thus, the assumption that the asymmetry in a mass side-band region isthe same as the asymmetry of the background events under the peak may not be completelyvalid. However, due to low statistics at high − t , a wide mass range is used for the side-bandregion, 1 . < M π + π − η < . c . With this wide range, mass-dependent effects to theasymmetry are encapsulated in a systematic uncertainty on Σ η (cid:48) for each − t bin, between0 . . − t bins and are tabulated in Tab. I. When theuncertainty varies between − t bins, a range is reported. The largest of these systematic un-certainties is associated with the event selection, and is found by evaluating the asymmetriesin each − t bin under varied selection criteria. The errors on the flux normalization ratios, F R , manifest as systematic uncertainties on the η and η (cid:48) asymmetries, and, finally, there isan uncertainty associated with the phase offset, φ . None of these systematic uncertaintiesare correlated, so they are added in quadrature to give the total systematic uncertainty. Inaddition to the systematic uncertainties in the analysis, there is a 2 .
1% relative uncertaintyassociated with the photon beam polarization that would result in an overall shift in themeasured beam asymmetries. We do not combine this with the other uncertainties.The final photon beam asymmetry results are the weighted averages of the two indepen-dent polarization data sets plotted as functions of − t . The results for Σ η are shown in Fig. 5,where they are compared to earlier GlueX data [13] as well as several theoretical predictions(values can be found in Ref. [24]). For values of − t below 0 . /c ) , the Laget [25, 26],12 ABLE I. Summary of the systematic uncertainties assigned to Σ η and Σ η (cid:48) . See the text fordetails. UncertaintiesSource Σ η Σ η (cid:48) Event Selection 1 . .
5% 3 . . SB Correction 0 . .
4% 0 . . .
2% 0 . .
1% 0 . . .
5% 3 . . JPAC [3] and EtaMAID [27] models describe the data. For − t larger than 0 . /c ) ,the Laget and JPAC models appear to overestimate Σ η , while the EtaMAID is in betteragreement with the data which suggests that the beam asymmetry may be decreasing withincreasing − t . The older model by Goldstein [28] predicts a lower value of Σ η than is ob-served, as well as significant structure, which is not observed. In terms of the models, valuesof Σ η near one indicate the reaction is dominated by natural parity exchange mechanisms,while values below one suggest a contribution from unnatural parity exchange as well.The photon beam asymmetry Σ η (cid:48) is shown as a function of − t in Fig. 6 (values can befound in Ref. [24]). The results are systematically smaller than one, averaging at around 0 . − t . This indicates that while the production of η (cid:48) is dominated by naturalparity exchanges, there must be some unnatural parity exchange contributions as well. Theonly theoretical prediction, from JPAC [4], is consistent with these results, but appears tobe systematically high.In addition to Σ η (cid:48) , the JPAC model [4] also predicts the ratio of the beam asymmetries,Σ η (cid:48) / Σ η . We show this ratio in Fig. 7, along with the JPAC prediction (values can be foundin Ref. [24]). Because of strong correlations between systematic uncertainties in the twochannels, we estimate the systematic on the ratio as the uncorrelated part of the η (cid:48) systematicuncertainty. In the JPAC model, a deviation of the ratio from one or even a slope in thedistribution suggests that s ¯ s exchanges ( φ and h (cid:48) ) are important in the production. As themeasured ratio is consistent with unity, the reactions proceed predominantly through ρ and ω vector meson exchange. At this time, however, our data are not sensitive enough to be13 ) -t (GeV η Σ This WorkGlueX (2017)LagetJPACEtaMAIDGoldstein
FIG. 5. The photon beam asymmetry Σ η is shown as a function of − t for (cid:126)γp → pη . The verticalerror bars represent the total errors and the horizontal error bars represent the RMS widths of the − t distributions in each bin. Previous GlueX (2017) results [13] are shown along with predictionsfrom several Regge theory calculations: Laget [25, 26], JPAC [3], EtaMAID [27] and Goldstein [28].The 2.1% relative uncertainty is due largely to the polarization measurement. ) -t (GeV ' η Σ This WorkJPAC
FIG. 6. The photon beam asymmetry Σ η (cid:48) is shown for (cid:126)γp → pη (cid:48) . The vertical error bars representthe total errors and the horizontal error bars represent the RMS widths of the − t distributions ineach bin. The Regge theory calculation from JPAC [4] is shown. The 2.1% relative uncertainty isdue largely to the polarization measurement. ) -t (GeV η Σ / ' η Σ This WorkJPAC
FIG. 7. The photon beam asymmetry ratio Σ η (cid:48) / Σ η is plotted. The vertical error bars representtotal errors. The horizontal error bars represent the RMS widths of the − t distributions in eachbin. The Regge theory calculation from JPAC [4] is shown. We have measured the photon beam asymmetry Σ for both η and η (cid:48) photoproduction inthe GlueX experiment using an 8.2–8.8 GeV linearly polarized tagged photon beam. Thesemeasurements were made as a function of momentum transfer − t and, in the case of the η , are of significantly greater precision than our earlier η measurements [13]. For the η (cid:48) ,these represent the first measurements of Σ η (cid:48) in this energy range. The beam asymmetriesand their ratio are compared to theoretical predictions based on t –channel quasi-particleexchange. The data show that the asymmetries and ratio are close to unity, which impliesthat the reactions proceed primarily through ρ and ω vector meson exchange. The analysisin this article was supported by the Natural Sciences and Engineering Research Council ofCanada grant SAPPJ-2018-00021 and by the U.S. Department of Energy, Office of Science,Office of Nuclear Physics under contract DOE Grant No. DE-FG02-87ER40315. We wouldlike to acknowledge the outstanding efforts of the staff of the Accelerator and the PhysicsDivisions at Jefferson Lab that made the experiment possible. This work was also sup-ported in part by the U.S. Department of Energy, the U.S. National Science Foundation,the German Research Foundation, GSI Helmholtzzentrum f¨ur Schwerionenforschung GmbH,the Russian Foundation for Basic Research, the UK Science and Technology Facilities Coun-15il, the Chilean Comisi´on Nacional de Investigaci´on Cient´ıfica y Tecnol´ogica, the NationalNatural Science Foundation of China, and the China Scholarship Council. This material isbased upon work supported by the U.S. Department of Energy, Office of Science, Office ofNuclear Physics under contract DE-AC05-06OR23177. [1] I. S. Barker, A. Donnachie, and J. K. Storrow, Nucl. Phys. B95 , 347 (1975).[2] V. Mathieu, I. V. Danilkin, C. Fernndez-Ramrez, M. R. Pennington, D. Schott, A. P. Szczepa-niak, and G. Fox, Phys. Rev.
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