Photoproduction of eta-mesons off nuclei for Eg < 2.2 GeV
T. Mertens, I. Jaegle, P. Muehlich, J.C.S. Bacelar, B. Bantes, O. Bartholomy, D.E. Bayadilov, R. Beck, Y.A. Beloglazov, R. Castelijns, V. Crede, H. Dutz, A. Ehmanns, D. Elsner, K. Essig, R. Ewald, I. Fabry, K. Fornet-Ponse, M. Fuchs, C. Funke, R. Gothe, R. Gregor, A.B. Gridnev, E. Gutz, S. Hoeffgen, P. Hoffmeister, I. Horn, J. Junkersfeld, H. Kalinowsky, S. Kammer, V. Kleber, Frank Klein, Friedrich Klein, E. Klempt, M. Konrad, M. Kotulla, B. Krusche, M. Lang, J. Langheinrich, H. Loehner, I.V. Lopatin, J. Lotz, S. Lugert, D. Menze, J.G. Messchendorp, V. Metag, C. Morales, U. Mosel, M. Nanova, D.V. Novinski, R. Novotny, M. Ostrick, L.M. Pant, H. van Pee, M. Pfeiffer, A.K. Radkov, A. Roy, S. Schadmand, C. Schmidt, H. Schmieden, B. Schoch, S. Shende, V. Sokhoyan, A. Suele, V.V. Sumachev, T. Szczepanek, U. Thoma, D. Trnka, R. Varma, D. Walther, C. Weinheimer, C. Wendel
aa r X i v : . [ nu c l - e x ] O c t EPJ manuscript No. (will be inserted by the editor)
Photoproduction of η -mesons off nuclei for E γ ≤ T. Mertens , I. Jaegle , P. M¨uhlich , J.C.S. Bacelar , B. Bantes , O. Bartholomy , D.E. Bayadilov , , R. Beck ,Y.A. Beloglazov , R. Castelijns , V. Crede , , H. Dutz , A. Ehmanns , D. Elsner , K. Essig , R. Ewald ,I. Fabry , K. Fornet-Ponse , M. Fuchs , C. Funke , R. Gothe , , R. Gregor , A.B. Gridnev , E. Gutz , S. H¨offgen ,P. Hoffmeister , I. Horn , J. Junkersfeld , H. Kalinowsky , S. Kammer , V. Kleber , Frank Klein , FriedrichKlein , E. Klempt , M. Konrad , M. Kotulla , , B. Krusche , M. Lang , J. Langheinrich , , H. L¨ohner ,I.V. Lopatin , J. Lotz , S. Lugert , D. Menze , J.G. Messchendorp , V. Metag , C. Morales , U. Mosel , M. Nanova ,D.V. Novinski , , R. Novotny , M. Ostrick , , L.M. Pant , , H. van Pee , , M. Pfeiffer , A.K. Radkov , A. Roy , ,S. Schadmand , , C. Schmidt , H. Schmieden , B. Schoch , S.V. Shende , V. Sokhoyan , A. S¨ule , V.V. Sumachev ,T. Szczepanek , U. Thoma , , D. Trnka , R. Varma , , D. Walther , C. Weinheimer , , and C. Wendel (The CBELSA/TAPS collaboration) Department Physik, Universit¨at Basel, Switzerland Institut f¨ur Theoretische Physik I, Universit¨at Giessen, Germany KVI, University of Groningen, The Netherlands Physikalisches Institut der Universit¨at Bonn, Germany Helmholtz-Institut f¨ur Strahlen- und Kernphysik der Universit¨at Bonn, Germany Petersburg Nuclear Physics Institute, Gatchina, Russia Department of Physics, Florida State University, Tallahassee, USA II. Physikalisches Institut, Universit¨at Giessen, Germany present address: University of South Carolina, USA present address: University of Mainz, Germany on leave from Nucl. Phys. Division, BARC, Mumbai, India on leave from Department of Physics, Indian Institute of Technology Mumbai, India present address: Institut f¨ur Kernphysik, Forschungszentrum J¨ulich, Germany present address: University of M¨unster, Germanythe date of receipt and acceptance should be inserted later Abstract.
Photoproduction of η mesons off C, Ca, Nb, and nat
Pb nuclei has been measured with atagged photon beam with energies between 0.6 and 2.2 GeV. The experiment was performed at the BonnELSA accelerator with the combined setup of the Crystal Barrel and TAPS calorimeters. It aimed at thein-medium properties of the S (1535) nucleon resonance and the study of the absorption properties ofnuclear matter for η mesons. Careful consideration was given to contributions from ηπ final states andsecondary production mechanisms of η -mesons e.g. from inelastic πN reactions of intermediate pions. Theanalysis of the mass number scaling shows that the nuclear absorption cross section σ Nη for η mesonsis constant over a wide range of the η momentum. The comparison of the excitation functions to dataoff the deuteron and to calculations in the framework of a BUU-model show no unexplained in-mediummodifications of the S (1535). PACS.
The study of possible in-medium modifications of the prop-erties of hadrons is a challenge for both theory and exper-iment. In contrast to any other composite system, most ofthe mass of hadrons is generated by dynamical effects fromthe interaction of the quarks. An important role is played
Correspondence to : B. Krusche, Klingelberstrasse 82, CH-4056Basel, Switzerland, e-mail:
[email protected] by the spontaneous breaking of chiral symmetry, the fun-damental symmetry of QCD. The symmetry breaking isreflected in a non-zero expectation value of scalar q ¯ q pairsin the vacuum, the chiral condensate. However, model cal-culations (see e.g. Ref. [1]) indicate a temperature anddensity dependence of the condensate which is connectedto a partial restoration of chiral symmetry. In this way,hadron in-medium properties are closely connected to thenon-perturbative aspects of low-energy QCD. While a di-rect relation between the quark condensate and the in- T. Mertens et al.: Photoproduction of η -mesons off nuclei medium masses and widths of hadrons is not known, an in-direct relation connects the QCD picture with the hadronpicture by QCD sum rules. In the hadron picture, the in-medium modifications arise from the coupling of mesonsto resonance - hole states and the coupling of the modi-fied mesons to resonances. The best known example is thetreatment of the ∆ in the framework of the ∆ -hole model(see e.g. Ref. [2,3]). The hadron in-medium spectral func-tions for π -, η -, and ρ -mesons and baryon resonances havebeen recently calculated by Post, Leupold, and Mosel [4]in a self-consistent coupled channel approach.The experimental investigation of hadron in-mediumproperties is complicated by initial and/or final state in-teractions. Since the present experiment uses photopro-duction of mesons, no initial but significant final state in-teraction effects must be considered. Here, the investiga-tion of these reactions also allows us to perform a detailedstudy of the meson - nucleus interactions which are re-sponsible for the final state interaction [5,6,7]. In case ofthe short-lived η meson the investigation of final state in-teraction effects is almost the only possibility to study the η -nucleon interaction.Experimentally, one of the clearest, although still notfully explained, in-medium effects has been observed inthe excitation function of the total photoabsorption reac-tion [8,9,10]. The bump in the elementary cross sectionsaround 700 MeV incident photon energy, correspondingto the second resonance region, namely the excitation ofthe P (1440), D (1520), and S (1535) resonances, is notseen in the nuclear data. Many different effects have beendiscussed in the literature including trivial explanationslike nuclear Fermi motion. Fermi motion certainly con-tributes to the broadening of the structure but cannot ex-plain its complete disappearance. Collisional broadeningof the resonances due to additional decay channels like N N ⋆ → N N has been studied in detail in the frameworkof transport models of the Boltzmann-Uehling-Uhlenbeck(BUU) type (see e.g. [11]) and can also not fully explainthe data. The situation is complicated by the fact that al-ready on the free nucleon the second resonance bump con-sists of a superposition of reaction channels with differentenergy dependencies [6]. Inclusive reactions like total pho-toabsorption do not allow to study in-medium propertiesof individual nucleon resonances. A study of the partial re-action channels is desirable, but their experimental identi-fication is more involved, and final state interaction effects[7] as well as experimental bias due to the averaging overthe nuclear density [12] must be accounted for (see Ref.[13] for a recent summary). Of special interest are mesonproduction reactions which are dominated in the energyregion of interest by one of the three resonances. Singleand double pion production reactions have been employedfor the study of the D resonance in the nuclear medium[6,14], although up to now without conclusive results.Photoproduction of η mesons in the second resonanceregion is an excellent tool for the study of the S (1535)resonance, which completely dominates this reaction [15,16]. Photoproduction of η mesons has been studied for thefree proton in great detail over a wide range of incident photon energies and for different observables [16,17,18,19,20,21,22,23,24]. The quasi-free reaction off the neutronbound in light nuclei has been investigated in detail forincident energies up to the peak position of the S (1535)( ≈
800 MeV) [25,26,27], quasi-free neutron/proton crosssection ratios for a few angular ranges up to photon en-ergies of 1 GeV have been reported in [28] and the co-herent photoproduction off light nuclei has been inves-tigated for the deuteron and Helium isotopes [26,28,29,30]. The combined result of these experiments (see [31]for a summary) was, that up to photon energies of ≈ (1535) with a constant cross section ra-tio σ n /σ p ≈ /
3. Only very recently, results from theGRAAL, ELSA, and Tohoku experiments [32,33,34,35]indicated a stronger contribution of a higher lying reso-nance to γn → ηn than to γp → ηp for photon energiesabove 1 GeV.A first search for possible in-medium effects on the S spectral function was done with the TAPS experiment atMAMI [5]. However, the experiment covered only incidentphoton energies up to 800 MeV, i.e. approximately up tothe peak position of the resonance. The experimental re-sults were in good agreement with BUU-model calcula-tions (see e.g. [11]). Subsequently, measurements at KEK[36] and Tohoku [37] extended the energy range up to1.1 GeV. The KEK experiment reported some collisionalbroadening of the S resonance. The Tohoku experimentpointed to a significant contribution of a higher lying res-onance to the γn → nη reaction. However, none of theseexperiments covered the full line shape of the S .Here, we report the measurement of η photoproduc-tion off carbon, calcium, niobium, and lead nuclei up toincident photon energies of 2.2 GeV, i.e. throughout andbeyond the S resonance range. For comparison, the re-action has been studied for the same energy range off deu-terium which provides an estimate for the average nucleoncross section. The experiment was performed at the electron stretcheraccelerator facility ELSA [38,39] in Bonn, using a 2.8 GeVelectron beam. Real photons were produced by Brems-strahlung off a copper foil of 0.3 % radiation length thick-ness. The photon energies were determined via the mo-mentum analysis of the scattered electrons by a mag-netic spectrometer. The tagging system, which is operatedin coincidence with the production detector viewing thetargets, is shown in Fig. 1. The direct electron beam isstopped in a beam dump while electrons having emittedBremsstrahlung are deflected into the detection system ofthe tagging facility. The system has 14 overlapping scin-tillator bars with 4 cm thickness which cover the photonenergy range between 22 % to 95 % of the incoming elec-tron beam energy E o . Better energy resolution is providedby a scintillating fiber detector which covers 18 % to 80 %of E o and a wire chamber (80 % to 92 %). In the presentexperiment only the scintillating fiber detector was used . Mertens et al.: Photoproduction of η -mesons off nuclei 3 magnetradiatorelectronbeam beamdumpfibersproportional wire chamber unscatteredelectrons beamphotonscintillatorselectronsscattered Fig. 1.
Setup of the tagging spectrometer. which provides an energy bin width of ≈
10 MeV for thelowest incident photon energies around 650 MeV and 2MeV at the high energy end of 2.2 GeV. The total rate inthe tagging system was 8 - 10 MHz for an incident electronbeam intensity of ≈ C (20 mm length), Ca (10 mm), Nb (1 mm), and nat
Pb (0.64 mm) were irradiated by thephoton beam. The lengths of the carbon, calcium, and leadtargets corresponded to 8 - 10 % of the respective radia-tion length X . The niobium target was somewhat thicker( ≈
17 % of X ), all targets were 30 mm in diameter. The η -mesons produced in the photonuclear reactions were de-tected via their η → π → γ decay (branching ratio32.5 %) with a two-component electromagnetic calorime-ter, covering 99 % of the full solid angle (see fig. 2). Thetargets were mounted in the center of the Crystal Barreldetector [40] which covered the full azimuthal angle forpolar angles between 30 ◦ and 168 ◦ . The Barrel consistedof 1290 CsI(Tl) crystals of 16 radiation lengths X . Insideit, around the target, a three-layer scintillating fiber detec-tor [41] (513 fibers of 2 mm diameter, three layers orientedwith respect to the z -axis by angles of -24.5 ◦ , +25.7 ◦ ,0 ◦ ) was mounted for charged particle identification. Com-pared to the standard setup of the Crystal Barrel whichwas used for the measurement of η -photoproduction offthe proton [21] (see [42] for a detailed description of thesetup), the 90 forward-most crystals have been removed.The forward angular range down to 4.5 ◦ was covered bythe TAPS detector [43,44]. This component consisted of528 BaF crystals of hexagonal shape with an inner diam-eter of 5.9 cm and a length of 25 cm corresponding to 12radiation lengths. They were arranged in a wall-like struc-ture as shown in the lower part of fig. 2. A 5 mm thick plas-tic scintillator was mounted in front of each BaF crystalfor the identification of charged particles. The front faceof the BaF wall was located 1.18 m from the center ofthe target. Both calorimeters have a comparable energyresolution of [40,44] σ E E ≈ − p E/GeV . (1)The impact points of photons are determined from thecenter of gravity of the electromagnetic showers, so that
Fig. 2.
Arrangement of the Crystal Barrel and TAPS detec-tors. Upper part: side view, lower part: front view of the TAPSwall: left hand side: logical segmentation for the LED-low trig-ger, right hand side: logical segmentation for the LED-hightrigger (see text). the angular resolution is better than the granularity ofthe crystals. It is 1.5 ◦ ( σ ) for the CB [40] for photonswith energies above 50 MeV and 1.25 ◦ in TAPS. The fastBaF modules were read out by photomultipliers, the CsIcrystals by photodiodes. Therefore, only information fromthe TAPS wall could be used for the first level trigger. Forthis purpose each module of the TAPS wall was equippedwith two independent leading edge discriminators whichwere combined in two different ways into logical groups(see Fig. 2). For the present experiment the thresholds ofthe first set of leading edge discriminators were set to 60MeV (LED-low) and the thresholds of the second set to 80MeV (LED-high). A valid first level trigger was acceptedif either at least two logical groups of the low-thresholdor at least one group of the high-threshold discriminatorshad fired. In the latter case, a second level trigger fromthe FAst Cluster Encoder (FACE) of the Crystal Barrel,indicating at least two separated hits in the Crystal Barrel,was required in addition. Due to the trigger conditionsonly the decay channel into six photons could be used forthe detection of the η mesons since the probability to findboth photons from a two photon decay in TAPS is almostnegligible. It should be noted that this restriction occursonly for measurements off nuclei where the recoil nucleoncan be a neutron. In case of a proton target the recoilproton can provide the trigger. T. Mertens et al.: Photoproduction of η -mesons off nuclei In the experiment, η -mesons have been identified via thedecay chain η → π π π → γ . Events with six detectedphotons without a condition on further detected chargedand/or neutral particles (recoil nucleons, pions) were se-lected. The photon reconstruction and identification inthe Crystal Barrel is discussed in detail in Ref. [42]. Itis based on a cluster search algorithm and uses the infor-mation from the three layer scintillating fiber detector forrejection of charged particles. The photon identification inTAPS is based on the information from the charged par-ticle veto detectors, on a time-of-flight analysis, and on apulse-shape analysis of the BaF signals. Details of thisanalysis procedure can be found in Ref. [45]. dataMC simu c oun t s [ a . u . ] M inv ( gg ) [ MeV ] Fig. 3.
Upper part: Invariant mass of photon pairs from eventswith six photons. All possible disjunct combinations of photonsare included. Solid line: data, dashed line: Monte Carlo simu-lation of η → π → γ . Bottom part: same data samples butonly ‘best’ combination selected by χ test is plotted (see text).The vertical lines indicate the cut applied to select candidatesfor the η → π decay. Even in the presence of intense charged particle back-ground, the analysis leads to a very clean photon sample.The following invariant mass analysis is based on the ex-cellent reproduction of the shapes of the invariant masspeaks by Monte Carlo simulations. In the first step for m(3 p ) [ MeV ] C oun t s / e i n [ a . u ] m(3 p ) [ MeV ] C oun t s / e i n [ a . u ] m(3 p ) [ MeV ] C oun t s / e i n [ a . u ] m(3 p ) [ MeV ] C oun t s / e i n [ a . u ] m(3 p ) [ MeV ] C oun t s / e i n [ a . u ] -0.500.511.522.533.54450 500 550 600 650 m(3 p ) [ MeV ] C oun t s / e i n [ a . u ] Fig. 4.
Identification of η -mesons via invariant mass. Upperrow: incident photon energies in the range 0.8 - 0.85 GeV, mid-dle: 1.4 - 1.6 GeV, bottom: 1.85 - 2.15 GeV. Left column: spec-tra with fitted background and η -peak. Right column: back-ground subtracted peaks compared to Monte Carlo line-shapes.Vertical lines: nominal position of η mass peak. All events havebeen corrected for detection efficiency (see text). events with six (or more) photons the invariant mass ofall possible disjunct photon pairs was calculated. In thecase of six photons 15 different combinations into pho-ton pairs are possible. The resulting two-photon invariantmass spectrum is shown in Fig. 4 (top part) together witha Monte Carlo simulation of the η → π → γ decay.Among the 15 combinations the ‘best’ combination waschosen via a χ analysis which minimizes the followingexpression χ = X k =1 ( m γγ ( i k , j k ) − m π ) ( ∆m γγ ( i k , j k )) (2)where i , ..., i , j , ...j represents a permutation of 1,...,6, m π is the pion mass, and the m γγ are the invariant massesof the photon pairs with their uncertainties ∆m γγ . The . Mertens et al.: Photoproduction of η -mesons off nuclei 5 resulting spectra for data and simulation are shown inFig. 4 (bottom part). In case of the simulation, wherethe background in the upper part of the figure is onlyof combinatorial nature, a clean, background-free π in-variant mass peak is recovered by this procedure. For thedata, some background from other reactions remains. Dueto the selection procedure of the ‘best’ combination thisbackground is also concentrated around the peak region.In the next step, events were selected where all three two-photon invariant masses of the best combination are lyingbetween 110 MeV and 160 MeV (indicated by the ver-tical lines in fig. 4). This cut is motivated by the shapeof the simulated invariant mass cut and removes only asmall fraction of ‘true’ events, which is determined fromthe simulation and taken into account for the extractionof the cross section.The nominal mass of the pion was then used as a con-straint to improve the experimental resolution. Since theangular resolution of the detector for photons is much bet-ter than the energy resolution, it was not necessary to usea kinematic fitting procedure. Instead, only the photonenergies were re-calculated from E ′ , = E , m π m γγ (3)where E , are the measured photon energies, E ′ , there-calculated, m π is the nominal π mass, and m γγ themeasured invariant mass. This procedure was applied toall three photon pairs combining to pions. In the last step,the invariant mass spectrum of the six photons is buildfrom their four-vectors, using the measured angles and there-calculated energies. Typical results for the η invariantmass peak for different incident photon energies are showin Fig. 4. The spectra can be fitted by a simple polyno-mial background (polynomial of second degree) and theline shape of the invariant mass peaks generated from aMonte Carlo simulation with the GEANT3 package [46].For the fit only the three parameters of the backgroundpolynomial and the amplitude of the simulated responsefunction were varied. Background subtracted spectra com-pared to the simulated line-shape are also shown in Fig.4. The shape of the invariant mass peaks is in excellentagreement with the results of the Monte Carlo simulation(see Fig. 4), where the same analysis procedure was ap-plied. The position of the invariant mass peak as functionof incident photon energy is rather stable, which is partlydue to the fact that the positions of the π and η invari-ant mass peaks have been used in an iterative procedurefor the energy calibration of the detector, and partly dueto the re-calculation of the photon energies from the π invariant masses. For differential cross sections, this pro-cedure must be applied to each bin. The detection effi-ciency, as discussed in the next section, was corrected onan event-by-event basis. Therefore, the fitting was not ac-tually done on the raw invariant mass distributions but onthe corresponding spectra with efficiency corrected events(shown in fig. 4).With the analysis discussed so far, the fully inclusivereaction γA → ηX is identified, where X may also in- D m [ MeV ] C oun t s / M e V D m [ MeV ] C oun t s / M e V Fig. 5.
Missing mass spectra for lead calculated under theassumption of quasi-free single η production. Left hand side:incident photon energies in the range 0.65 - 0.8 GeV, right handside: 1.3 - 1.5 GeV. Histograms: simulated detector responsefor quasi-free single η production. Arrow indicates cut for thisreaction. clude any (kinematically possible) number of pions. Se-lecting exclusive, single η -production without any furthermesons in the final state is not possible by simply vetoingevents with additional clusters in the detector. Additionalcharged mesons may go undetected (e.g. along the beamline), making the suppression incomplete. In case of theBarrel, charged pions cannot be distinguished from pro-tons and the condition would falsely suppress events withdetected recoil protons. Therefore, exclusive η -productioncan only be identified via the reaction kinematics. Here, itis assumed that the reaction occurs quasi-free off a boundnucleon. The initial momentum of the nucleon is neglectedand the missing mass ∆m of the reaction is calculatedfrom the nucleon mass m N , the energy of the incidentphoton E b , and the energies and momenta E γ i and P γ i ofthe six decay photons: ∆m = vuut ( E b + m N − X i =1 E γ i ) − ( P b − X i =1 P γ i ) − m N . (4)The resulting distributions are broadened by Fermi mo-tion, so that a perfect separation of the different reac-tion channels is not possible. Examples of missing massspectra are shown in fig. 5. The structures around zeromissing mass are related to single η -production, the con-tribution at large positive missing mass, which is only vis-ible at higher incident photon energies, originates from ηπ final states and secondary production processes like γN → πN , πN → ηN . The experimental results are com-pared to a simulation of the detector response based on theshape of the missing mass distributions for single quasi-free η -production predicted by a BUU model (see sec. 6).The indicated cut was used for the analysis of single η -production. This cut does not allow a perfect separation ofsingle η -production from the other contributions since thetails of the different distributions are overlapping. How-ever, since the same cut was used for the model results(see sec. 8), the comparison between data and model isnot affected. T. Mertens et al.: Photoproduction of η -mesons off nuclei The absolute normalization of the measured yields was ob-tained from the target densities, the incident photon flux,the η → π → γ decay branching ratio ( b η → γ =31.35%), and the detection efficiency of the calorimeter. Themeasurement of the photon flux is based on the count-ing of the deflected electrons in the focal plane detectorsof the tagging spectrometer (see. fig. 1). The fraction ofcorrelated photons, passing the collimator and impingingon the target, was determined roughly once per day in amode where the trigger is derived from the tagger and thephoton flux (at reduced beam intensity) is measured bya photon counter placed downstream of the calorimeter.The detector dead-time of approximately 60 % was deter-mined with scalers gated by life-time of the experimentand spill-time of the accelerator, respectively. Q h [ d e g ] T h [ M e V ] c oun t s -4 -3 -2 -1 Q h [ d e g ] T h [ M e V ] eh Fig. 6.
Left hand side: laboratory angle and kinetic energydistribution of measured η -mesons. Right hand side: detectionefficiency as function of the same parameters (regions clearlyoutside kinematically possible combinations have not been sim-ulated). The detection efficiency of the Crystal Barrel/TAPScalorimeter has been determined by Monte Carlo simu-lations using the GEANT3 package [46]. The simulationincludes all relevant properties of the experimental setuplike geometrical acceptance, trigger efficiency, detectionefficiency, and analysis cuts. The branching ratio for the η → γ decay is not included in the efficiency. The η mesons are produced in many different final states andreaction types: single η , ηπ , re-scattered η mesons, and η mesons from secondary reactions in the nucleus. All pro-cesses are additionally complicated by the momentum dis-tribution of the bound nucleons. Consequently, the cor-relation between momentum and emission angle of themesons is a priori not known. Therefore, a reliable modelis not available for an event generator for the Monte Carlosimulations. Instead, the detection efficiency has been de-termined from the simulations as a function of the lab-oratory polar angle and laboratory kinetic energy of the η -mesons, which are measured quantities. It was then ap-plied on an event-by-event basis to the data. The methodis described in more detail in [6] for inclusive π produc-tion off nuclei. In this way, a model independent detectionefficiency correction is achieved as long as the efficiency does not vanish for any kinematically possible combina-tion of η polar angle and kinetic energy. This is demon-strated in fig. 6 where the correlation between angles andenergies of the measured η mesons is compared to thesimulated detection efficiency. The absolute values of thedetection efficiency are not large since the first level trig-ger was only sensitive to photons in the TAPS forwardwall (see sec. 2). Even for the six-photon decay of the η the efficiency of this trigger condition is small, in partic-ular for η mesons emitted at large polar angles. However,it is obvious from the figure, that the entire phase spaceof kinematically possible combinations is covered by non-vanishing detection efficiency, so that for the determina-tion of cross sections no extrapolations had to be done. The main sources for systematic uncertainties are relatedto the background level in the η -invariant mass spectra,the simulation of the detection efficiency, and the deter-mination of the incident photon flux. Other uncertaintieslike e.g. the surface thickness of the solid targets (betterthan 1 %) are comparably negligible. s / A / [ m b ] E g [ MeV ] Ds / s [ % ] Fig. 7.
Typical systematic effects (carbon data). Main plot:total cross section from detection efficiency with 10 o binningin θ η (filled (red) circles) compared to 2 o binning (open (black)circles). Bottom insert: ratio of cross sections. Top insert: typ-ical systematic uncertainty related to background shape in η -invariant mass spectra (see text). As discussed in sec. 3, the background level beneaththe η signal has been determind by fitting the amplitudeof the simulated shape of the invariant mass peak andthe three parameters of a background polynomial. The . Mertens et al.: Photoproduction of η -mesons off nuclei 7 Kinoshita et al. ( C)Yorita et al. ( C)Roebig-Landau et al. ( C)this work. ( C) s / A / [ m b ] E g [ MeV ] Kinoshita et al. ( Cu)F.Bloch et al. ( Ca)Roebig-Landau et al. ( Ca)this work ( Ca)this work ( Nb) s / A / [ m b ] E g [ MeV ] Fig. 8.
Comparison with earlier results. Upper part: C fromMainz [5], Tohoku [37] and this work. Bottom part: Ca fromMainz [45], Cu from Tohoku [37], and Ca and Nb thiswork. The error bars of the present data include only the statis-tical errors, the shaded bands at the bottom indicate the totalsystematic uncertainties for C (top) and Ca (bottom). resulting background subtracted signal, shown in fig 4,agrees well with the simulated line shape. The systematicuncertainty of this procedure was studied by a variationof the fitted range in the spectra, giving rise to systematicdeviations in the background shape. Typical systematicvariations of the fitted peak amplitude (see fig. 7, upperinsert) range from 2% at low incident photon energies to8% at the highest incident photon energies.Since the detection efficiency could be simulated with-out any assumptions about the angular and energy dis-tributions of the mesons, the corresponding uncertaintiesare small, estimated at the 5 % level. They are mainly due to the exact representation of thresholds, shower develop-ment, absorbing inactive material in the detector, and theexact target and beam positions in the GEANT simula-tions. The stability of the detection efficiency correctionhas been checked by a variation of the bin size of thesimulated efficiency by a factor of five (Fig. 6 shows thecoarsest binning in angle). Figure 7 shows a comparisonof the total cross section for carbon constructed with binsizes of 10 o and 2 o . Most data points from the two anal-yses agree within ± η production extracted from the two runs agreedwithin ±
10 %, taken as the typical systematic uncertainty.The flux uncertainty is identical for all nuclei (samesettings of incident photon energy, beam intensity, andparameters of the tagging system for all nuclei) and thusdoes not influence A -dependent properties. It must only beaccounted for in the comparison to model results or datafrom other experiments. For this case, all three systematiceffects have been added in quadrature. The systematic un-certainties of the detection efficiency and the backgroundsubtraction are also not completely independent for thefour nuclei. However, for an estimate of systematic uncer-tainties of scaling properties we have made the most pes-simistic assumption that this effects vary independently.The total cross section data for inclusive η productionare compared in fig. 8 to previous results below 1.2 GeV.Carbon and Calcium data are available from Mainz below0.8 GeV [5,45], Carbon data from KEK [36] and Carbonand Copper data from Tohoku [37] below 1.2 GeV. Inthe Carbon case, the KEK and Tohoku data are system-atically higher by roughly 10 %. For the heavier nuclei,a direct comparison between the Tohoku results and thepresent data is not possible, since different target nucleihave been investigated. At incident photon energies below800 MeV, all data scale like A / . At higher incident pho-ton energies, the A / scaling does not hold anymore, thepresent Calcium data are clearly lower than the presentNiobium data (see also fig. 9). From this behavior, oneexpects that the scaled cross section for Copper lies inbetween the Calcium and Niobium results. However, theTohoku Copper results fall on top of our Niobium data,indicating that also for the heavier nuclei the Tohoku re- T. Mertens et al.: Photoproduction of η -mesons off nuclei sults are systematically higher by roughly 10 %. However,the energy dependence of the excitation functions for thepresent data and the KEK and Tohoku results is verysimilar. Rather good agreement is found when all dataare re-scaled by 10 %, which is within their systematicuncertainty. The detailed interpretation of the experimental resultsis only possible via a comparison to model calculationswhich incorporate effects like nuclear Fermi motion, Pauli-blocking of final states, and in particular the propagationand absorption of mesons and nucleon resonances in nu-clear matter. Results obtained in the framework of theBUU transport model for photon induced reactions as dis-cussed in detail in [47,48,11] have been used. The modelis based on the BUU equation: (cid:18) ∂∂t + ∇ p H · ∇ r − ∇ r H · ∇ p (cid:19) F i ( r , p , µ ; t ) == I coll [ F N , F π , F η , F N ⋆ , F ∆ , ... ] (5)which describes the space-time evolution ( r : space coor-dinate, p : momentum) of the spectral phases space density F i of an ensemble of interacting particles i = N, N ⋆ , ∆, π, η, ... in nuclear matter from the moment of their creation totheir absorption or escape through the outer boundariesof the nucleus. The left hand side of the equation - theVlasov term - describes the propagation of the particlesunder the influence of a Hamilton function H . It containsinformation about energy, mass, self-energy (mean field)of the particle and a term that drives back an off-shellparticle to its mass shell. Explicitly, it can be written as H = p ( µ + S ) + p (6)with the particle mass µ and a scalar potential S forbaryons [11]. The right hand side of the BUU equation- the collision integral - describes particle production andabsorption. It consists of a gain and a loss term for thephase space density F i , accounting for interactions be-tween the particles beyond the mean-field potential.The constituents of the nucleus are defined as ‘testnucleons’ and follow a Woods-Saxon density distribution ρ ( r ) = ρ o e ( r − R ) /a , (7)where the nuclear radius is related to the nucleus massvia R = 1 . A / fm and a = (0 . A / + 0 . f m .The momentum distribution is described within the Fermigas approach. p F ( r ) = (cid:18) π ρ ( r ) (cid:19) / . (8)The elementary η cross sections off protons and neu-trons are included in this model. The produced resonancesand mesons propagate in the nucleus and can be scattered, absorbed or decay. The different reaction probabilities areeither fitted to experimental data or calculated. They areincorporated into the model by the collision term and mayinteract according to the geometrical condition that thedistance between the two particles is smaller than the im-pact parameter b c = p σ/π where σ is the reaction crosssection. The total inclusive η production cross sections (i.a. forthe reaction γA → ηX , without any condition for X ) aresummarized in fig. 9. At incident photon energies below ≈
800 MeV the cross sections scale with A / ( A atomicmass number) for the heavier nuclei and agree with the av-erage nucleon cross section (deuteron cross section scaledby a factor of 2). In the following A eff means A =2 forthe deuteron and A / for all other nuclei. This behavior,which indicates strong absorption of the mesons, was al-ready found in [6] for η , π , and double π photoproductionin the same energy range. However, at higher energies, thecross sections behave completely differently and scale al-most with the mass number.This is shown more quantitatively in fig. 9 (bottom)where the scaling coefficient α obtained from a fit of σ ( A ) ∝ A α (9)is plotted versus the incident photon energy. It would betempting to argue that the rise of the scaling coefficientsimply reflects a decrease of the absorption cross sectionwith increasing kinetic η -energy, since the most efficientabsorption process is s-wave excitation of the S (1535)resonance. However, the situation is not that simple. Forthe further discussion, we must keep in mind, that thescaling is not only influenced by the absorption cross sec-tion of the η -mesons, but may also reflect A -dependentdifferences of their production. In the most simple case ofquasi-free single-meson production, the production beforeFSI will scale with A and then a scaling of the observedmeson rates with α =2/3 indicates strong FSI, while a scal-ing with A indicates transparent nuclear matter. In thiscase, the scaling coefficient will only depend on the ki-netic energy T of the mesons (energy dependent absorp-tion cross section).However, the data show a different behavior. As shownin Fig. 10 for fixed values of T the scaling is dependenton the incident photon energy E γ . Furthermore for fixedincident photon energy the coefficients drop from valuesclose to unity for small T to roughly 2/3 for the largest T possible at that incident photon energy. This is exactlythe opposite of what one would expect when the behav-ior of the scaling coefficients would be dominated by thes-wave absorption into the S . However, the observed be-havior can arise when the production rates of the mesonsbefore absorption do not scale with A . Problematic in thisrespect are side-feeding contributions from secondary pro-duction processes like γN → πN , πN → ηN , and FSIprocesses that modify the observed energy distribution of . Mertens et al.: Photoproduction of η -mesons off nuclei 9 deuteriumcarboncalcium niobium lead s / A e ff [ m b ] E g [ MeV ] a E g [ MeV ]
10 10 E g =780-860 MeV s [ m b ] mass number A
10 10 E g =1800-1950 MeV Fig. 9.
Upper part: Total fully inclusive η cross section nor-malized by A eff = A / for A = 12 , , ,
208 and A eff = 2for the deuteron. Error bars are statistical, the shaded bandsat the bottom show the systematic uncertainties for carbon(lower double shaded band) and lead (upper band) excludingthe 10% flux normalization uncertainty. Bottom part: Scalingcoefficient α (see text) as function of incident photon energy.Black circles: results if only statistical uncertainties are con-sidered. Slightly displaced open symbols: including systematicuncertainties except 10% overall normalization. Curve: resultfrom BUU model. The two inserts show the scaling with massnumber for two typical ranges of incident photon energy. the η mesons. They may completely obscure the effectsrelated to η -absorption, since they may strongly increasewith mass number. The BUU-model simulations predict,that both contributions are substantial (see sec. 8).However, due to energy and momentum conservation,secondary production processes (as well as ηπ final states)cannot contribute at the kinematical limit (i.e. at maxi-mum T for given E γ ), but will produce η mesons withsmaller kinetic energies (some energy is carried away bythe additional nucleon(s) involved in the secondary reac- tions). Therefore, it is possible to extract the ηN -absorptioncross section from the scaling behavior in this regime. Forthis purpose, the scaling factors α have been fitted forthe high energy end of the T distributions for differentincident photon energies using the condition T > ( E γ − m η ) / E γ is the incident photon energy and m η the massof the η mesons. The result as function of η kinetic energyis compared in fig. 11 to the previous results for low-energy η mesons [5] and for π mesons [6]. The somewhat surpris-ing result is that for η mesons the scaling coefficient α isalmost constant at 2/3 over a large range of η kinetic en-ergy, indicating strong absorption independent of kineticenergy. In the case of pions, the absorption is expectedlyvery weak for kinetic energies, which are too low to ex-cite the ∆ resonance. The pions escape from the nucleusand α (pions) is one. The scaling factor reaches 2/3 inthe ∆ regime and then seems to slowly increase again.The large absorption cross section for η mesons at smallkinetic energies was expected since this is the excitationregion of the S resonance with a strong coupling to the N η channel. Unexpectedly, a decrease of the absorptioncross section is not observed, even at kinetic energies farabove this range. The corresponding ηN absorption crosssection σ absηN can be deduced from the results of a Glaubermodel calculation discussed in [5]. The model is based onthe assumption, that secondary production processes playno role, which has been assured, as discussed above, by thechoice of the kinematical conditions. The dependence ofthe scaling coefficient α on σ absηN is shown in fig. 12. It yields a T [ MeV ] E g =1550-2200 MeVE g =1050-1550 MeVE g =835-1050 MeVE g =650-835 MeV Fig. 10.
Evolution of the scaling factor α with the kineticenergy for different ranges of incident photon energies. Theopen, slightly displaced symbols show for the highest incidentphoton energy the result when systematic uncertainties exceptthe 10% flux normalization are included.0 T. Mertens et al.: Photoproduction of η -mesons off nuclei a p o h , Roebig Landau et al. h , this work T [ MeV ] Fig. 11.
Evolution of the scaling factor α with the kineticenergy for π [6] and η mesons (low energy η data from [5]. s h N [ mb ] a abs [ mb ] a Glauber-theoryexp. value
Fig. 12.
Dependence of the scaling coefficient α on the ηN absorption cross section [5]. σ absηN ≈
30 mb for the average value of α ≈ .
66. In a sim-ilar analysis, recently Kotulla et al. [49] have investigatedthe scaling behavior of the photoproduction of ω -mesonsoff nuclei. They found typical absorption cross sections inthe range of 50 mb, corresponding to inelastic in-mediumwidths of the mesons around 150 - 200 MeV. Here, we donot folluw-up this analysis quantitatively, however, it isevident that also the extracted η absorption cross sectionmust correspond to inelastic widths at least in the few tenMeV range.Due to the contribution from ηπ final states and sec-ondary production processes, the inclusive reaction can-not be used to extract an in-medium line shape of theS (1535) resonance. A separation of quasi-free single η production can only be achieved by cuts on the reac-tion kinematics. A cut on the missing mass (see fig. 5)at ∆m <
140 MeV is motivated by a comparison of themissing mass spectra to the simulated line shape of the re- E g [ MeV ] s / A e ff [ m b ] C Ca Nb Nat Pb H Fig. 13.
Total η cross section with missing mass cut at 140MeV. Errors are statistical, the shaded band shows the sys-tematic uncertainty (excluding the 10% flux normalization) forCalcium. sponse for quasi-free single η production. The total crosssections after the cut are summarized in fig. 13.The shape (position and width) of the S -resonancestructure is very similar for carbon, calcium, niobium, andlead. A clear systematic evolution with mass number is notobserved. The shape is different for the deuteron data butthis effect can mostly be explained by the different mo-mentum distributions of nucleons bound in the deuteronor a heavy nucleus.With the exception of the deuteron target, the separa-tion of single quasi-free η production from other processeswith the missing mass cut is only an approximation, dueto the overlapping tails of the distributions from differentprocesses. However, it gives already an indication, thatno strong in-medium effects on the shape of the S res-onance occur. A more detailed discussion is possible by acomparison to the results of the BUU-model subjected tothe same kinematical cuts. The distributions of kinetic energy and cm-angle (cm sys-tem of the incident photon and a nucleon at rest) for theinclusive data are compared in Fig. 14 to the results ofthe BUU model. The overall agreement between data andmodel is quite good. The most significant disagreement isobserved for the differential cross sections at small kineticenergies of the η -mesons. In this regime, the model cal-culations are closer to the simple A / scaling and under-estimate the observed cross sections for the heavy nuclei.As discussed below, these discrepancy can be traced back . Mertens et al.: Photoproduction of η -mesons off nuclei 11 -2 CarbonCalciumNiobiumLead d s / d T / A / [ m b / M e V ] T [ MeV ] E g (650-835) E g (835-1050)E g (1050-1550) E g (1550-2200) -2 CarbonCalciumLead -3 -2 -3 -2 d s / d W / A e ff [ m b / s r ] cos( Q h ) H C Ca Nb nat Pb E g (650-835) E g (835-1050) E g (1050-1550) E g (1550-2200) -1 0 1 -1 0 1 -1 0 1 -1 0 1 Fig. 14.
Upper part: energy distributions for different inci-dent photon beam energy ranges. Bottom part: angular dis-tributions. Curves are BUU model calculations. Uncertaintiesinclude systematic effects except the 10% flux normalization. to the contribution from ηπ final states and/or secondaryproduction processes of η -mesons. At low incident photonenergies the angular distributions are similar to the mea-sured deuteron distributions (i.e. to the average nucleoncoss section) and agree quite well with the model results.At the highest incident photon energies, the angular dis-tribution for the deuteron peaks at forward angles, sincefor the free nucleon t -channel processes become impor-tant. This effect is not seen for the heaviest nuclei, wherethe distributions peak at backward angles. The model re- s / A / [ m b ] C Ca Nb E g [ MeV ] nat Pb s / A / [ m b ] C Ca Nb E g [ MeV ] nat Pb Fig. 15.
Upper part: Comparison of the total exclusive sin-gle η production cross (missing mass cut at 140 MeV) toBUU results. Shaded bands: total systematic uncertainty. Bot-tom part: filled symbols: inclusive cross sections (solid curves:BUU results). Open symbols: difference of inclusive and exclu-sive single η production (dashed curves: BUU-results). Shadedbands: total systematic uncertainty of the open symbols. sults show the same tendency and in the model the back-ward peaking contribution arises mainly from secondaryproduction processes. This behavior is easily understoodsince η -mesons from secondary production processes onaverage have small kinetic energies and therefore appear η -mesons off nuclei at backward angles in the fast forward moving photon -nucleon cm-system.The total cross sections for the inclusive reaction, forquasi-free single η production and for the contributionfrom ηπ final states and secondary production processesare summarized and compared to the model results in Fig.15. The shape of the total inclusive cross section is reason-ably well reproduced for the lighter nuclei, but disagreessignificantly for lead, where the model shows still the peakof the S resonance, which is absent in the data. How-ever, this systematic shape change from light to heavynuclei is not related to an in-medium modification of theS resonance. This is clearly demonstrated by the sepa-ration of the inclusive cross section into quasi-free single η -production and the other components. The separationhas been done by the missing mass cut at ∆m <
140 MeV,which has been applied to data and model calculations (tothe latter after folding them with the experimental resolu-tion). Although, as discussed above, this separation is notperfect, the result for the line-shape of the S dominat-ing quasi-free single η production is clear. Position, width,and peak cross section of the S agree for all nuclei quitewell with the model results. Only the peak cross sectionshows a little systematic evolution from carbon (slightlyoverestimated) to lead (slightly underestimated), which ishowever within the systematic uncertainty introduced bythe missing mass cut. The shape is fully explained by the‘trivial’ in-medium effects included in the BUU model,in particular the momentum distribution of the nucleonsbound in heavy nuclei.The agreement is less good in the energy range abovethe S resonance, where the model overestimates the mea-sured cross sections. However, one must keep in mind,that here the separation by the missing mass cut becomesstrongly dependent on the exact shape of the missingmass distributions for the different components. Indeedthe main effect at higher incident photon energies seemsto be a strong underestimation of the contribution from ηπ final states and/or secondary processes (see Fig. 15, bot-tom part). In particular for lead around 1 GeV incidentphoton energy, this component rises much more rapidly inthe data than in the model.This mismatch is most clearly seen in the missing massspectra in this energy range which are compared in fig.16 to the BUU calculation. The contribution from single,quasi-free η production is overestimated while the contri-bution from ηπ final states seems to be underestimated inthe model. Part of this discrepancy is probably due to theuncertainty in the elementary cross sections for ηπ pro-duction reactions. There are recent precise data for the γp → pηπ o reaction [50], however, much less is known forthe channels with charged pions in the final state or aneutron in the initial state. In this range of incident pho-ton energy, the modeled missing mass plots seem to indi-cate that the quasi-free single η -peak has already signifi-cant contamination from the tails of the ‘background’ pro-cesses, in particular, from secondary η -production. How-ever, it is not possible to obtain a reasonable fit of the mea-sured missing mass distributions by a variation of the ar- d s / d ( D m ) / A / [ m b / G e V ] C, E g =1.2 - 1.4 GeV C, E g =1.4 - 1.6 GeV Pb, E g =1.2 - 1.4 GeV -200 0 200 400 D m [ MeV ] Pb, E g =1.4 - 1.6 GeV Fig. 16.
Missing mass spectra for carbon and lead for tworanges of incident photon energies. Curves: BUU-results forfull model (full curves), single, quasi-free η -production (dot-ted), ηπ final states (dash-dotted) and secondary η -production(dashed). eas of the three model contributions, keeping their shape.Fitting the part of large missing mass with the ηπ andsecondary η production contributions leads to unreason-able contributions of their tails in the quasi-free regionaround zero missing mass. Therefore not only the magni-tude but also the shape of this contributions seems to bepartly in conflict with the data. On the other hand, themissing mass shape of the quasi-free single η productionseems to be in better agreement with the data (see Fig.5), it certainly agrees with it below the ηπ threshold. The investigation of inclusive and exclusive η productioncross sections for heavy nuclei from threshold to 2 GeVcan be summarized as follows. In the excitation region ofthe S (1535) resonance, contributions from ηπ final statesand secondary production processes to inclusive η pro-duction are already significant. At higher energies thesecontributions even become dominant. A discussion of in-medium properties of the S resonance or of absorptionproperties of η mesons in nuclear matter requires a carefultreatment of these effects.An analysis of the scaling of the cross sections withatomic mass number has been performed for η mesons pro-duced closely to the kinematical limit where only quasi-free single η production can contribute. Combined withprevious low energy results [5], it is found that the scalingcoefficient α is almost constant at a value of 2/3 for η ki-netic energies from 20 MeV up to 1 GeV. Using a simple . Mertens et al.: Photoproduction of η -mesons off nuclei 13 Glauber model approximation, this corresponds to a con-stant ηN absorption cross section of ≈
30 mb. A decreaseof the absorption probability for η -mesons with kineticenergies much above the S range is not observed.An analysis of the line shape of the S resonance canbe achieved with the results for single, quasi-free η pro-duction after cuts on the reaction kinematics. The ob-served excitation functions for heavy nuclei have almostidentical shape from carbon to lead. The results in theS range are in good agreement with BUU model calcu-lations which include the ‘trivial’ in-medium effects likeFermi smearing, Pauli blocking of final states, and contri-butions from secondary processes. Thus, an indication ofa shift or broadening of the resonance has not been found.At higher incident photon energies, the agreement be-tween BUU calculations and experiment is less good. Therelative contribution of single, undisturbed η photopro-duction is overestimated in the model and the contribu-tion of secondary processes and/or ηπ final states is sig-nificantly underestimated. This indicates a need for betterinput for the semi-inclusive ηX channels in the BUU cal-culations.
10 Acknowledgments
We wish to acknowledge the outstanding support of theaccelerator group and operators of ELSA. This work wassupported by Schweizerischer Nationalfonds and DeutscheForschungsgemeinschaft (SFB/TR-16.)