Study of in-medium ω meson properties in Ap, pA and AA collisions
aa r X i v : . [ nu c l - e x ] M a r Study of in-medium ω meson propertiesin Ap, pA and AA collisions S.Belogurov, M.Chumakov, S.Kiselev, Yu.Kiselev ∗ , V.SheinkmanNovember 21, 2018 Institute for Theoretical and Experimental PhysicsMoscow, Russia
Abstract
We propose to investigate the in-medium properties of vector ω mesonsat the normal nuclear density in Ap(pA) collisions and at higher densityin AA collisions at the ITEP accelerator facility TWAC. Using of the in-verse Ap kinematics will permit us to study the ω meson production ina wide momentum interval included the not yet explored range of smallmeson momenta relative to the projectile nuclei where the mass modifica-tion effect in nuclear matter is expected to be the strongest. Momentumdependence of the in-medium ω meson width will be studied in the tra-ditional pA kinematics. We intend to use the electromagnetic calorimeterfor reconstruction of the ω meson invariant mass by detecting photonsfrom the ω → π γ → γ decay. The model calculations and simulationswith RQMD generator show feasibility of the proposed experiment. Avail-able now intensity of the ion beams provides a possibility to collect largestatistics and make decisive conclusion about the ω meson properties atdensity of normal nuclei. At the second stage of the investigation the ω meson properties will be studied in AA collisions at higher density. Inter-pretation of these measurements will be based on the results obtained inAp(pA) interactions. Further investigation of the in-medium properties oflight unflavored and charmed mesons can be performed at ITEP and atGSI(FAIR) where higher ion energies will be accessible in near future. ∗ e-mail address: [email protected] ontents ω meson in nuclear matter 8 ω meson mass . . . . . . . . . . . . . . . . . . . . . . 86.2 In-medium ω meson width . . . . . . . . . . . . . . . . . . . . . . 11 Physics motivaion
Modification of the hadron properties in baryon environment is one of the im-portant topics of contemporary strong interaction physics. This phenomenon hasbeen predicted within various theoretical approaches such as QCD sum rules [1],chiral dynamics [2], relativistic mean-field [3] and quark-meson coupling model [4].A recent review can be found in the Ref. [5]. A hadron can change its propertiessuch as mass and width once it is embedded into a baryon matter. This change isconnected to the many body interactions of a hadron with surrounding nucleons.Whether a hadron is - in addition - also affected by QCD condensates and theirin-medium change [1], [2], [6] is still a matter of debate. Nevertheless, the greatinterest in study of in-medium hadron properties is caused by the expectation tofind the evidences of the chiral symmetry restoration. Investigation of the vectormesons is of special interest in this context. Theoretically, the possibility of thedecrease in the mass of light vector mesons in matter was first pointed in [7] andlater in [2]. According to [2] the masses of the vector mesons scale with quarkcondensate, i.e. drop with rising of baryonic density. This effect can be a precur-sor phenomenon of the transition of strongly interacting matter to the chirallysymmetric phase. First experimental signal of this phenomenon was recently ob-served in [8]. Nambu and Jona-Lasino proposed the spontaneous breaking ofthe chiral symmetry as the fundamental mechanism for the creation of a mass ofhadrons [9]. Recently, the in-medium change of the ω mesons spectral functionwas proposed as a probe of higher order QCD four-quark condensate [10].An evidence for a decrease of the ρ meson mass in heavy-ion collisions wasobtained by the CERES collaboration at CERN [11] and later by the STARcollaboration at RHIC [12]. Since heavy-ion interaction is very complicated pro-cess in which the temperature and baryon density varies dramatically with timedue to the formation and expansion of the ”fireball”, the interpretation of exper-imental data on nucleus-nucleus collisions is far from being simple. The aboveresults have been found an explanation in terms of shifting a ρ meson spectralfunction to a lower mass, as expected from the theory. However, even the cal-culations that just used the free radiation rates with their - often quite large -experimental uncertainties are compatible with the observation.Therefore, it is useful to explore the reactions with elementary probes ( γ , π ,p) since sizeable - about 20% - medium effects were predicted already at thedensity of ordinary nuclei [2], [13], [14]. The advantage of the investigations ofthe reactions on nuclei is related to the fact that they proceed in the nearly coldstatic nuclear matter and thus the colliding system is much better under control.Indeed, the first signals for lowering of the ω meson mass at normal nuclear matterdensity were recently observed in the γA [15] and pA [16] reactions. However,the critical analysis [17] shows that data of the experiment [15] are compatiblewith normal ω mass and an enlarged width. In contrast to the conclusion [16] thepreliminary results of the CLAS collaboration (JLAB) on the photoproduction3f ρ and ω mesons [18] also evidence for no shift in the mass. Now there are onlyfirst estimates of the ω meson width in matter [15], [19]. Thus, the availablenow experimental information does not allow to draw the final conclusion aboutthe change of the ω meson properties even in nuclear matter of normal density. Itshould be stressed that the indications for decreasing of the ω meson mass in bothexperiments [15], [16] have been found for the mesons with low momenta relativeto the surrounding nuclear matter. Therefore, next generation of experimentsneed to addresses the issue of momentum dependence of medium effects. Wesuggest to explore the momentum dependence of the in-medium mass and widthof the ω meson using the ion and proton beams of the ITEP accelerator facilityTWAC [20].The investigation of in-medium meson modification addresses the fundamen-tal problems of strong interaction physics and is one of the hot current topicsnowadays. The experiments with photon, pion, proton and ion projectiles areplanned in wide collision energy range from a few GeV (GSI, JLAB, JINR, COSY,SPring-8, ITEP) till TeV (RHIC, LHC). The goal of the proposed experiment is the investigation of the vector ω mesonproperties at normal nuclear density ρ = 0 . f m − in nucleus-proton (proton-nucleus) collisions and at higher density in nucleus-nucleus collisions. The ex-periment aims at the study of the mesons with low momentum relative to thebaryonic environment where the in-medium mass modification is expected to bemost strong as well as at the study of high momentum range which is sensitiveto the in-medium ω meson width. All information about the intrinsic properties of a meson is encoded in its spectralfunction S(M) which can be written in non-relativistic Breit-Wigner form. In freespace: S ( M ) = (Γ / / [( M − M ) + (Γ / ] , (1)where Γ and M stand for a meson width and pole mass, correspondingly.Due to the interaction with surrounding nuclear medium the meson acquiresa selfenergy Σ which is related to the nuclear optical potential U as [21]:Σ / E = U = ReU + i ImU, (2)where E is the total meson energy.The meson spectral function in nuclear medium is read: S ( M ) = [(Γ /
2) + (Γ ∗ / / [ M − ( M + M ∗ )] + [(Γ /
2) + (Γ ∗ / . (3)4wo extra terms, M ∗ and Γ ∗ /
2, which describe the shift of the meson pole massand the increase of its width in matter, are related to the nuclear optical potential U as follows [21]: M ∗ = ReU ; Γ ∗ / − ImU ; (4)The pole mass and width of the ω meson in free space (vacuum) are M = 782MeV and 8.4 MeV, correspondingly. Most theoretical investigations predict thedropping of the in-medium ω meson mass by 20-140 MeV [22] at normal nucleardensity. However, there have also been suggestions for a rising mass [23] oreven a structure with several peaks [24]. At the same time there seems to bea general agreement that in-medium ω width is within the range from 20 MeVto 60 MeV [25] at the density ρ = ρ . Thus, it is expected that the ω mesonin matter survives as a quasiparticle and can be observed as a structure in the ω mass spectrum. In principle, both dilepton and π γ invariant mass spectracan be used for the study of modification effects. The advantage of the dileptondecay channel is related to the fact that leptons are almost undistorted by thefinal state interactions. However, the ω signal in the dilepton mode is rather weak( BR ( ω → e + e − ) ≈ . × − ) and is always accompanied by a comparativelylarge background from ρ → e + e − decays. The ω → π γ decay has a branchingratio 8 . × − what is 3 orders of magnitude higher. Furthermore, the competing ρ → π γ channel has a branching ratio which is a factor 10 smaller. By thesereasons the ω → π γ decay mode can be considered as an exclusive probe to studythe ω meson properties in matter. The disadvantage of this channel is a possiblerescattering of the π within the nuclear medium which would distort the deduced ω invariant mass distribution. However, as it was shown in Refs. [26], [27] theabove distortion effect can be significantly decreased by applying an appropriatecut on the pion kinetic energy. The ω meson invariant mass spectrum has two components which correspond tothe decay ’inside’ and ’outside’ the nucleus. Only vector mesons decaying ’inside’nuclei can be used for an identification of the in-medium ω mass. This imposesthe kinematical condition that the decay length of the vector meson should beless than nucleus size. It implies that the ω meson should be produced with smallmomentum (velocity) relative to the nuclear matter rest frame. The study of lowmomentum ω mesons production in the inverse Ap kinematics [28] has severalimportant advantages over the study in the direct pA kinematics. First, as itfollows from the Lorentz transformation, slow particles in a projectile nucleussystem appear to be fast in the laboratory (in the target proton rest frame) andbecome convenient for the detection. At beam energy of 4 AGeV all the ω ’sproduced in full solid angle with momenta less than 0.3 GeV/c relative to theprojectile nucleus rest frame will be concentrated in the laboratory inside narrow5one of less than ± and the momentum range from 2.8 till 5.9 GeV/c. The pro-duced mesons which are almost at rest inside the incident nucleus (”comovers”)have the laboratory momenta around of 4 GeV/c. Due to the decrease of theproduction cross section with laboratory ω meson momentum the main contribu-tion to the ω yield comes from the momentum interval of 2.8 - 4.0 GeV/c. Theseevents will be observed in small phase space dP dcosθ in the laboratory resultingin significant increase in forward production cross section as compared to one inpA reactions. That can be easily understood because experimentally observed non-invariant double differential cross sections measured in the direct (pA) andinverse (Ap) kinematics are related as: Ap ( d σ/dP dcosθ ) = Ap ( P /E ) pA ( E/P ) pA ( d σ/dP dcosθ ) . (5)One can see that the factor pA ( E/P ) grows strongly with lowering of the ω mesonmomentum while the factor Ap ( P /E ) changes rather smoothly.The photons from the decay ω → π γ → γ are distributed inside more widecone as compared to parent mesons, however the coverage of the angular interval5 − - which corresponds to the solid angle of less than 9% of 4 π - permits tocollect significant part of the useful events.Second, the mean free pass of the proton in nuclear matter is as small as 2fm and therefore the ω mesons are predominantly created inside the front layersof a projectile nucleus. Since the forward produced ω ’s in the momentum range2.8-4.0 GeV/c have the laboratory velocities which are less than ones of thesurrounding nucleons, the produced mesons move in the direction opposite to theion beam direction and then decay in more dense inner layers of a nucleus. Thatis of great importance because the strength of the medium effects increases withnuclear density.Third advantage of the inverse kinematics is an increase in the energies ofthe detected photons because they are emitted by relativistic ω and π . Forexample, the π γ decay in transverse direction of the ω carrying the momentumof 4 GeV/c results in emission of the photon of energy 2 GeV and π of energy2.1 GeV followed by the pion decay to two photons of 1 GeV energy. The aboveenergies exceed the photon energies from the ω → π γ decay at rest (0.38 GeVfor the γ from ω and 0.19 GeV for the γ ’s from π ) by a factor of about 5. Thatresults in more precise measurement of the photon energy leading to more narrowwidth of the signal in the invariant mass spectrum and hence improved signal tobackground ratio. At last, only moderate momentum resolution in the laboratoryis required for the rather precise determination of the ω momentum relative tothe projectile nucleus because the momentum range of interest 2.8-4 GeV/c inthe laboratory corresponds to the interval 0-0.3 GeV/c in the nucleus frame ofreference.In contrast with in-medium ω meson mass the value of its width is expectedto be deduced from the analysis of the production of fast mesons relative to the6 (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) CPVEMCALLH target Beam
Figure 1: Sketch of the experimental set-upbaryonic matter. It is well known that high momentum mesons can be abundantlyproduced in the pA interactions. Thus, the combination of the Ap and pAmeasurements provides the possibility to study both ω meson mass and width innuclear matter. We intend to carry out the proposed measurements using the ion and protonbeams extracted in the inner hall of the accelerator. Expected extraction effi-ciency is of 50%. Two dipole and two pairs of quadrupole magnets serve for thedeflection and focusing the beams onto the target. The sketch of the experimen-tal set-up is shown in Fig. 1. The ions (or protons) which do not interact inthe target pass through the central hole of the electromagnetic calorimeter (EM-CAL) and then directed to the downstream beam-dump located in the inner hallor thick concrete wall of the accelerator. That prevents the environment fromthe radiation pollution. 7 .2 Projectiles and targets
The projectile Ta, Cu, Al and C ions will be used for the investigations of the in-medium ω meson mass while the projectile protons will be used for the explorationof the ω width in the nuclear matter. The proton runs will permit us to study theEMCAL performance and calibrate the invariant mass scale by measurements ofthe reactions p + A → π +X, p + A → η +X and p + A → ω +X.We plan to use the liquid hydrogen ( LH ) target of 2% interaction length (12cm) for Ap measurements and simple foil targets (Be, Al, Cu, Ag and Ta) for thepA and AA measurements. The ring-like electromagnetic calorimeter with total area of 0.64 m will be lo-cated at the distance of 1 m downstream of the target. We intend to use theEMCAL based on the PbWO cells 20 × mm size with avalanche photodiodeor photomultiplier readout. The energy and spatial resolution of the cell are σ /E=2% √ E +1% and σ x = σ y = 6 mm , respectively [29]. The total number ofcells is 1400. In front of a group of cells the 5 mm thick plastic scintillator withphotodiode readout will be mounted for the detection of charged particles. Dueto the moderate charge ejectile multiplicity (see section 7) the number of CPV(Charged Particle Veto) counters is less than about 100. This array can be alsoused as a multiplicity detector offering the possibility to apply the cuts on theimpact parameter of the collision. ω meson in nuclear matter ω meson mass For the evaluation of the expected signal of in-medium ω meson mass and widthmodification the calculations of the ω meson production were performed in theframework of the folding model. The model takes properly into account bothincoherent direct proton-nucleon and secondary pion-nucleon ω meson produc-tion processes as well as internal nucleon momentum distribution (see for exam-ple [30]). The folding model describes the production, propagation and decay ofthe ω meson inside a nucleus taking into account its four-momentum and localnuclear density. The calculations were performed for Ta, Cu, Al and C nuclei atinitial energy of 4 AGeV.In our approach the ω meson mass shift was introduced according to the localnuclear density ρ ( r ): M ∗ = ReU = δM ρ/ρ , (6)8 ,MeV
680 700 720 740 760 780 N Cu Q All P and
M,MeV
680 700 720 740 760 780 N Cu P<0.3 GeV/c
M,MeV
680 700 720 740 760 780 N P<0.3, b 12 - in accordance with the theoretical predictions and the experimentalobservations [15], [16] - means that the ω meson feels a strong attraction insidenuclear matter which is of about 90 MeV at nuclear saturation density ρ . In ourcalculations the nuclear density distributions were taken in two-parameter Fermiform.We primarily focus at study of the ω mesons with low momentum in theprojectile nucleus rest frame by two reasons. First, the strength of the ’inside’component of the ω decay - which carries the information on the in-mediummeson mass - obviously increases with lowering of a meson momentum. Second,the in-medium ω mass shift can depend on the meson velocity with respect tothe surrounding nuclear matter (see discussion in [26]). The most strong effect ispredicted to be manifest itself in the low momentum range. One can also expectthat the low momentum ω mesons can be captured by the nucleus which leadsto the formation of the ω - nucleus bound state [31], [5].The mass distributions of the ω mesons from Cu+p collisions at 4 AGeVcalculated within the frame of the folding model are presented in Fig. 2. Inthe left panel we show the mass spectrum of all produced ω ’s. The right peakcorresponds to the decays ’outside’ the nucleus and hence to the vacuum ω mesonmass while the left part of the distribution corresponds to the decays ’inside’the nucleus and contains the events with reduced meson masses . The relativeamount of events where the ω mesons decay at finite nuclear matter density isvanishingly small. The fraction of the ’inside’ decays increases up to 1/3 for the ω mesons of momentum ≤ We refer a decay to the ’inside’ component provided the local density ρ/ρ > r / r Cu ) r / r decay point w at Density ( Figure 3: Nuclear density at the ω meson decay point for P < . GeV /c and b < R Cu / ω ’s produced in the central collisions with the impact parameter b < R Cu / ω momentum and theimpact parameter is shown in Fig. 3. It is seen that significant part of lowmomentum mesons produced in the central collisions decays in dense layers ofthe nucleus. Note that the calculations within the folding model provide thepossibility to estimate average nuclear density for the ’inside’ decay component. Itshould be mentioned that inelastic ω -nucleus collisions, i.e., the processes ωN → ωX result in slowing down of the ω mesons and an enhancement of low momentumpart of the spectrum. Moreover, one can think that the range of low ω momentawould be even further enhanced due to decrease of the absorption effect. Thevalue of σ ωN in nuclear matter is expected to be less than one in the free spacesince Pauli blocking prevents the low energy ω -nucleon interactions.Thus, we conclude that the prospective signal of the ω meson mass shift isstrong enough to be observed experimentally. The proposed detector layout willpermit us to collect a large amount of the ω mesons with low momenta relativeto the surrounding nuclear matter (see section 10) and study the momentumdependence of the predicted effect. 10 .2 In-medium ω meson width The straightforward determination of the in-medium ω meson width from theshape of the observed mass spectrum is hardly possible because the rescatteringof the pion would changes its kinematical parameters which results in distortionof the observed invariant mass peak. The authors of Ref. [21] have proposedthe alternative method to study the φ -meson width in the nuclear medium - byan attenuation measurements of the φ meson flux in photonuclear reactions ondifferent nuclear targets. This method is based on the well known connectionbetween the particle absorption in nucleus and the imaginary part of the respec-tive nuclear optical potential (see Eq.4). The method proposed in Ref. [21] wasapplied by Muehlich and Mosel to the ω photo-production [32]. The flux of π γ pairs which escape a nucleus had been calculated within the Boltzmann-Uehling-Uhlenback (BUU) coupled-channel transport approach. As a measure of the ω width in nuclei the authors of Ref. [32] used the so-called nuclear transparencyratio: T A = σ γA → V X /Aσ γN → V X , (7)i.e. the ratio of the inclusive ω photo-production cross section on nucleus dividedby A times the same quantity on a free nucleon. It can be interpreted as theprobability of the ω meson to get out of the nucleus. It was shown that theA-dependence of the production cross sections significantly differs from that ex-pected in the case when there are no medium effects on the ω width. Similarly, thevaluable information about the ω width in the matter can be obtained from theanalysis of A-dependence of ω meson production cross section in proton-inducedreactions.Although a proton initial state interaction is rather strong, the ω absorption isessential. For small angle ω production the last effect can be taken into accountby the Glauber eikonal factor which explicitly depends on the ω meson widthΓ ∗ [33]: P = exp [ − ∞ Z dl Γ ∗ ( p ω , ρ ( r ′ )) /β ω ] , (8)where ~r ′ = ~r + l~p ω / | ~p ω | with ~r ′ the ω production point, p ω and β ω are themomentum and velocity of the ω in the target nucleus frame, while ρ ( r ′ ) standsfor the local nuclear density. Eq. 8 shows that the survival probability P of the ω meson in its way out of a nucleus decreases with increasing of the ω width Γ ∗ .The ω width in nuclear matter is defined by Eq.3, where Γ is free mesonwidth and the additional width Γ ∗ can be expressed according to Ref. [34] as:Γ ∗ = γ { βσ ∗ ωN } ρ ( r ) . (9)Here β is the the relative velocity of nucleon and ω meson, γ denotes theLorentz factor for the transformation from nuclear rest frame to the ω rest frame,11 ( r ) stands for the local nuclear density. It is seen that in-medium ω mesonwidth depends on its velocity (momentum) relative to the nucleus rest frame. Toevaluate the sensitivity of the A-dependence to the magnitude of in-medium σ ∗ ωN we use the total ωN cross section in the free space adopted from the model [35]: σ el = [5 . exp ( − . | ~q | )] mb, (10) σ in = [20 + 4 / | ~q | ] mb, (11)where q is ω meson momentum. The brackets in Eq.9 indicate an average overthe Fermi motion of the nucleons. In Ref. [32] the ω collision width was estimatedas 37 MeV at nuclear saturation density for vanishing meson momentum.The momentum averaged atomic mass dependence of the transparency ob-tained within the folding model is shown by solid curve in Fig. 4. The dash AT H C Al Cu Ta20 MeV40 MeV80 MeV G Figure 4: Transparency as a function of atomic mass numberand dash-dotted lines - which correspond to the calculations with the value of Γ ∗ ∗ . The difference between the curves is largeenough to be detected in the experiment. Since the shape of the A-dependence,and not so much the absolute value, is important to learn about the ω width, thecross section for middle and heavy nuclei can be normalized to the cross sectionfor light nucleus. The A-dependence of the transparency normalized to the crosssection for the ω production on carbon target is presented in Fig. 5. In spite A T A / T C C Al Cu Ta20 MeV40 MeV80 MeV G Figure 5: Transparency ratio as a function of target mass numberof some less difference between the curves the measurement of the ratios has anadvantage to cancel out most of systematic uncertainties. Thus, the calculationsclearly show that the proton induced ω meson production in nuclei can indeedbe used to get information on the ω width in the medium.Obviously, the discussed above ω width calculated according the Eq. 9 withtotal ω -nucleon cross section in the free space is only the estimate. The real total ω N cross section in the medium can differ from that in the free space. Indeed,13he experiment on incoherent φ photoproduction on Be, C, Al and Cu targetsrecently performed at SPring8 (LEPS) [36] has found an unexpectedly strongdependence of the loss of K + K − flux from the φ decay on target mass number.The total in-medium φN cross section has been estimated by the authors as 35 +17 − mb using the Glauber-type multiple scattering theory. This value significantlydiffers from σ totφN in the free space which is equal to 9-11 mb. One can expectsimilar effect for the ω mesons.Note that the investigation of the ω meson width and its momentum depen-dence in pA reactions has several important advantages as compared with one inAp reactions. First, the proton beams are usually much more intensive than theion ones. Second, the simple solid targets can be used instead of the hydrogentarget. Third, in the pA collisions the momentum dependence of the ω mesonwidth can be studied in wide momentum range from 0.5 to 4 GeV/c. It is worthto note, that the possible effect of density dependent ω meson mass shift is ofminor importance in high momentum range. For the simulations we use Relativistic Quantum Molecular Dynamics (RQMD) [37]event generator, version 4.12. RQMD produces hadrons through the excitationof baryonic and mesonic resonances. Heavy resonances (more than 2 GeV forbaryons and more than 1 GeV for mesons) are treated in the string picturefollowing the Lund model [38] and all particles are allowed to reinteract (baryon-baryon, baryon-meson and meson-meson). The model provides a complete time-dependent description of the evolution of each event. The probabilities for ex-citation of specific channels are governed by experimental cross sections to theextent possible. The formation points of hadrons are taken from the propertiesof resonance decay and string fragmentation.About 3 × minimum bias Cu+p events have been generated. The followingsimulation was performed for the ring-like electromagnetic calorimeter coveringthe range of the polar angles θ = 5 − and full azimuthal angle of 0 < φ < . At projectile energy of 4 AGeV the mean total multiplicity is equal to12 for Cu+p and 3.4 for C+p collisions. Multiplicities of different species arepresented in Table 1. Since the charged component (protons and pions) amountsto one half of the total multiplicity one can estimate the impact parameter of thecollision by detecting the charged ejectiles by CPV counters.The angular dependence of the secondaries in the laboratory is shown in Fig. 6.It is seen that the multiplicity drops rapidly with the production angle. Due to thering-like geometry of the EMCAL the first angular bin 0 − is out of the detectoracceptance. Assuming the target-detector distance of 1 meter and granularity ofthe EMCAL of 2 × cm one gets for the interval of 5 − maximum celloccupancy of about 0.006 for minimum bias events and approximately two times14pecies n p π o π + π − η γ multiplicity 4.7 4.6 1.47 0.74 0.66 0.037 0.0026Table 1: Mean multiplicities of particles predicted by the RQMD code for theminimum bias Cu+p events at 4 AGeVmore for most of central collisions.The two-dimensional plot for the ω mesons produced in Cu+p collisions ation beam energy of 4 AGeV is presented in the left upper panel of Fig. 7. Itis seen that fast mesons in the laboratory (the target proton frame of reference)are predominantly concentrated in the range of small angles. The momentumspectrum of all produced ω ’s (right upper panel of Fig. 7) extends up to 5 GeV/c.In the right upper panel of Fig. 8 we present the same laboratory spectrum withcut on the ω meson momentum p < p < ω momentum, respectively. Onecan see the sizeable number of events with small p t in the vicinity of the projectilenucleus rapidity Y =2.34 in the laboratory system. The most of ω ’s have therapidities Y < Y < p t and very small rapiditiesis accessible for the investigation in Ap kinematics. As was above mentioned the ω meson mass shift probably depends on the ω momentum relative to the nuclearmedium. The strongest effect is expected for the momenta of less than 0.3 GeV/c.The study of the ω meson invariant mass distributions reconstructed for differentmomentum bins in the range of P ω < ω mesons mass shift in the medium.For the selection of useful events the EMCAL should be able to detect effi-ciently three photons from the ω → π γ → γ decay. The performed simulationsshow that the geometrical efficiency for the detection of the photons from the ω decay is near 40 % for the range of small production angles ( θ < . ) and high ω momentum ( p > . GeV /c ) in the laboratory which corresponds to the rangeof p ω < E γ > ω mesons relative to the projectile nucleusturns out approximately by an order of magnitude higher than that averaged overall meson momenta. 15 (deg.) q q ) d N / d S ( / d m -4 -3 -2 -1 n, p - p , + p g --> 2 o p from g RQMD, Cu+p at T/A=4.0 GeV, plane at 1 m from the target Figure 6: Density of particles in a plane at 1 m from the targetAs was explained in section 6.2 the in-medium ω meson width can be de-duced from the analysis of the A-dependence of the production cross sections ofrelatively fast ω ’s, which are mostly decay outside the nucleus. Obviously, thatthe photons from the decay of high momentum mesons produced in traditionalpA kinematics will also be detected with high efficiency because the efficiencydepends on photon energy relative to the detector.Thus, the momentum dependencies of both in-medium ω meson mass andwidth can be investigated in the inverse and direct kinematics – i.e. using the ionand proton beams – without the change of the detector position and its layout. The feasibility of the experiment depends on the signal to background ratio.RQMD simulations show that the main source of the background is the π π (deg.) q p ( G e V / c ) hOmegaPvsTheta Entries 3486Mean x 11.52Mean y 2.196RMS x 7.416RMS y 0.986 020406080100 hOmegaPvsTheta Entries 3486Mean x 11.52Mean y 2.196RMS x 7.416RMS y 0.986 w RQMD, Cu+p at T/A=4.0 GeV, p (GeV/c)0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 hOmegaP Entries 3486Mean 2.179RMS 0.9932 p (GeV/c)0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 N ( / b i n ) hOmegaP Entries 3486Mean 2.179RMS 0.9932 w RQMD, Cu+p at T/A=4.0 GeV, (deg.) q q N ( / b i n ) w RQMD, Cu+p at T/A=4.0 GeV, y-1 -0.5 0 0.5 1 1.5 2 2.5 3 ( G e V / c ) t p hOmegaPTvsYEntries 3486Mean x 1.541Mean y 0.3638RMS x 0.4651RMS y 0.1756 hOmegaPTvsYEntries 3486Mean x 1.541Mean y 0.3638RMS x 0.4651RMS y 0.1756 w RQMD, Cu+p at T/A=4.0 GeV, Figure 7: ω spectrum in the laboratory frame17 (deg.) q p ( G e V / c ) hOmegaCutPvsTheta Entries 796Mean x 4.476Mean y 3.372RMS x 1.508RMS y 0.6092 hOmegaCutPvsTheta Entries 796Mean x 4.476Mean y 3.372RMS x 1.508RMS y 0.6092 <0.5 GeV/c w Cu , p w RQMD, Cu+p at T/A=4.0 GeV, p (GeV/c)0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 hOmegaCutP Entries 796Mean 3.372RMS 0.6092p (GeV/c)0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 N ( / b i n ) hOmegaCutP Entries 796Mean 3.372RMS 0.6092 <0.5 GeV/c w Cu , p w RQMD, Cu+p at T/A=4.0 GeV, (deg.) q hOmegaCutTheta Entries 796Mean 4.429RMS 1.512 (deg.) q N ( / b i n ) hOmegaCutTheta Entries 796Mean 4.429RMS 1.512<0.5 GeV/c w Cu , p w RQMD, Cu+p at T/A=4.0 GeV, y-1 -0.5 0 0.5 1 1.5 2 2.5 3 ( G e V / c ) t p hOmegaCutPTvsY Entries 796Mean x 2.107Mean y 0.2617RMS x 0.181RMS y 0.09509 010203040506070 hOmegaCutPTvsY Entries 796Mean x 2.107Mean y 0.2617RMS x 0.181RMS y 0.09509 <0.5 GeV/c w Cu , p w RQMD, Cu+p at T/A=4.0 GeV, Figure 8: The same as for Fig. 7 but for ω with p < . (deg.) q p ( G e V / c ) hOmegaCMAPvsTheta Entries 3486Mean x 32.92Mean y 0.8747RMS x 22.51RMS y 0.4323 0102030405060708090 hOmegaCMAPvsTheta Entries 3486Mean x 32.92Mean y 0.8747RMS x 22.51RMS y 0.4323 in c.m. of Cu w RQMD, Cu+p at T/A=4.0 GeV, p (GeV/c)0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 hOmegaCMAP Entries 3486Mean 0.8747RMS 0.4323 p (GeV/c)0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 N ( / b i n ) hOmegaCMAP Entries 3486Mean 0.8747RMS 0.4323 in c.m. of Cu w RQMD, Cu+p at T/A=4.0 GeV, (deg.) q hOmegaCMATheta Entries 3486Mean 31.1RMS 22.49 (deg.) q N ( / b i n ) hOmegaCMATheta Entries 3486Mean 31.1RMS 22.49 in c.m. of Cu w RQMD, Cu+p at T/A=4.0 GeV, y-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 ( G e V / c ) t p hOmegaCMAPTvsY Entries 3486Mean x -0.7995Mean y 0.3642RMS x 0.4596RMS y 0.1758 020406080100 hOmegaCMAPTvsY Entries 3486Mean x -0.7995Mean y 0.3642RMS x 0.4596RMS y 0.1758 w RQMD, Cu+p at T/A=4.0 GeV, Figure 9: ω spectrum in the projectile nucleus frameproduction. Such events can lead to the misidentification due to a finite geome-try of the detector if one of the four photons is out of the EMCAL acceptance.The contribution from other sources of the background like ηπ , η ′ , ∆ → nγ etc.is relatively small in the invariant mass range of interest 0.65 - 0.85 GeV sincethe invariant masses reconstructed from kinematical parameters of three uncor-related photons are spread over wide mass range from 0.1 to 1.0 GeV. Therefore,the useful events from the ω → π γ → γ decay will be detected on the topof smooth continuum steming mainly from the π π production process. TheSignal/(Signal+Background) ratio R = S/ ( S + B ) for the minimum bias eventsis less than approximately one per cent. However, this value can be significantlyimproved by applying the appropriate kinematical cuts. RQMD simulations in-dicate that the spectrum of the photons originating from the π decay dropssteeper than that from the ω decay. By this reason the cut on photon energyshould lead to the background suppression. The histograms in Fig. 10 demon-19 InvMassSignalEntries 327Mean 0.7814RMS 0.01019 g o p M0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 N ( / b i n ) -1 hInvMassSignalEntries 327Mean 0.7814RMS 0.01019 origin: g g o p --> w from g --> 2 o p from ’, ...) h from other ( - 25 =5 q set-up: hInvMassSignalRes Entries 327Mean 0.7695RMS 0.02797 g o p M0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 N ( / b i n ) -1 hInvMassSignalRes Entries 327Mean 0.7695RMS 0.02797 =6 mm y s = x s +1 (%) + E=2/ E s + hInvMassSignal Entries 149Mean 0.7808RMS 0.009075 g o p M0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 N ( / b i n ) -1 hInvMassSignal Entries 149Mean 0.7808RMS 0.009075 >0.5 GeV/c g + p hInvMassSignalRes Entries 149Mean 0.7721RMS 0.02341 g o p M0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 N ( / b i n ) -1 hInvMassSignalRes Entries 149Mean 0.7721RMS 0.02341hInvMassSignal Entries 18Mean 0.7887RMS 0.006833 g o p M0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 N ( / b i n ) -1 hInvMassSignal Entries 18Mean 0.7887RMS 0.006833 >1 GeV/c g + p hInvMassSignalRes Entries 18Mean 0.7837RMS 0.01207 g o p M0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 N ( / b i n ) -1 hInvMassSignalRes Entries 18Mean 0.7837RMS 0.01207 Figure 10: Invariant mass spectra with and without cuts on the photon energiesfor RQMD Cu+p events at 4 AGeV 20MCAL info all E γ > . GeV E γ > GeV without S/(S+B) 9.5% 10.5% 21%resol. RMS(S) MeV 10 9 7PbWO S/(S+B) 1.8% 5.9% 21%resol. RMS(S) MeV 28 23 12Table 2: Parameters of signal (S) and background (B) π o γ pairs for RQMD Cu+pevents at 4 AGeVstrate this effect . Invariant mass distributions of π γ system without the cut onphoton energies are shown in the upper row, while the middle and bottom rowsrepresent the distributions obtained with cuts on E γ > E γ > E γ > E γ > π and γ which are, in fact, from the ω decay are strongly correlated while the photons steming from the π π or othersources will not show such a correlation. Due to two-body nature of the ω → π γ decay the pion should be emitted in the plane which is formed by the projectilemomentum and the momentum of the photon originated from the ω decay. Insuch a case the difference in the azimuthal angles of the π and γ should be closeto 180 degrees. The cut φ π − φ γ > results in additional increase of R bya factor of 2. Thus, we conclude that the applying of the appropriate cuts willpermit to reduce the background to the level acceptable for the measurements. The events of interest detected by EMCAL are accompanied by the deposit of en-ergy in three or more groups of cells. For the selection of such events a multileveltrigger could be used. A first level should be provided by the signals selected theevents with energy deposit of more than 0.5 GeV for the suppression of back-ground from low momentum π production and their rescattering. The secondlevel of the trigger would include the requirement the energy deposit of morethan 1 GeV in one of the cell group which correspond to the photon energy from The medium effects are not included in the RQMD simulations ω meson decay. The third level would select the events with large az-imuthal separation corresponding to actual two-body ω decays. One can estimatea contribution of background events using the experimental counting statisticsof the inclusive trigger and the trigger of delayed coincidence. The informationfrom CPV counters will be used as an off-line trigger for the reduction of chargedbackground and for the estimation of the collision centrality. 10 Event rate estimate Let us first estimate the expected number of events for the production of lowmomentum mesons with respect to a projectile nucleus. Assuming a moderateion beam intensity of 1 × ions/cycle, the extraction efficiency of 50% andtarget efficiency of 2% one gets the number of the ion interactions inside thetarget of 1 × per one accelerator cycle. The normalization factor N - which isthe ratio of the number of interactions during one accelerator cycle to the numberof simulated collisions - is equal to 0.33. The momentum intervals of less than0.3 GeV/c and 0.5 GeV/c contain 225 and 796 events, respectively (see right tophistogram in Fig. 9).Assuming the cycle repetition of 10 min − and taking into account the detec-tor efficiency of 15% (after applying the cut on E γ > P ω < P ω < P ω < × events/dayN( P ω < . × events/dayThe number of events in the lowest momentum interval P ω < ω meson mass shift in the nuclear mattercan be performed with high statistical accuracy.It should be noted that the above estimates are based on the RQMD simula-tions which disregard any medium effects on the ω . If the ω meson mass reallydrops in nuclear matter by 80-100 MeV the production cross section would in-crease due to the downward shift of the reaction threshold. Moreover, one canexpect that the produced mesons will be decelerated during their way out ofthe nucleus due to the action of the attractive nuclear ω meson potential. Thisslowing down would lead to the increase in number of events in low momentum22ange. Note also that the energy loss of a meson in the elastic and quasielastic ωN scattering inside a nucleus results in the same effect.The usage of more intensive proton beam provides the possibility to collectlarge amount of data on high momentum ω meson production and perform thedetail investigation of the momentum dependence of the ω meson width in thenuclear matter. Data on the ω meson production in the momentum range around1.5 GeV/c can be obtained in both inverse and direct kinematics. These datawill be used for the cross check and mutual normalization of the Ap and pA mea-surements. The statistics which can be obtained in AA interactions is obviouslyhigher than that in Ap collisions. 11 Conclusion The modification of the properties of the vector mesons in baryon environmentcontinue to be one of the most interesting topics in hadron physics today.We suggest to investigate the in-medium properties of the ω mesons at normalnuclear density in nucleus-proton and proton-nucleus collisions as well as at higherdensity in nucleus-nucleus collisions at ITEP accelerator facility TWAC.Study of the Ap and pA reactions is the effective tool to get the informationon the in-medium ω meson properties at normal nuclear density. The using of theinverse Ap kinematics and ω → π γ decay mode permits to collect large statisticsfor production of the ω mesons with low momenta relative to the nuclear matter.Estimated high event rate offers the possibility to split the statistics into severalmomentum bins and study the ω meson mass shift in wide momentum interval including not yet explored range of momentum less than 0.3 GeV/c which isexpected to be most sensitive to the mass change effect . The detail informationon in-medium ω meson width in wide momentum interval will be obtained inpA collisions. The goal of the first stage of the experiment is to make decisiveconclusion about the in-medium ω meson mass and width at normal nucleardensity.On the second stage of the suggested study we shall obtain the information onthe ω meson production in nucleus-nucleus collisions which will be used for theinvestigation of the in-medium ω meson properties at higher density compared tothat accessible in nucleus-proton interactions. The results obtained at the firststage of the investigation at normal nuclear density will provide the reliable basisfor the selection and interpretation of specific nucleus-nucleus phenomena.Ap, pA and AA measurements will be performed in quite identical conditionsusing the same experimental set-up. 23 One of the possible extension of the proposed studies in a few GeV energy range isthe investigation of the in-medium change of unflavored mesons. The performedRQMD simulations of the Ap collisions show the significant yield of the η and η ′ mesons for which the modification effects had also been theoretically predicted[39], [5]. The branching ratios of the η → γγ and η ′ → π π γγ decays are ashigh as 39% and 21%, correspondingly. The properties of these mesons can beinvestigated at TWAC using the same experimental set-up.The in-medium properties of the charmed mesons and charmonium can be ex-plored at significantly higher ion energy which will be accessible at the new FAIRfacility (GSI). In particular, the mass splitting of DD mesons at high baryonicdensity [40] will be investigated by CBM experiment in heavy-ion collisions. Asa masses of charmonia are large, only little sensitivity to changes in the quarkcondensate is expected. Consequently, the in-medium mass of the charmoniumstates would be affected primary by a modification of the gluon condensate. Largeattractive mass shifts are predicted for exited charmonium states [41]. Using theinverse and direct kinematics provides the possibility to study the production andpropagation of both low and high momentum heavy quark systems in baryonicmatter. 13 Acknowledgments The authors gratefully acknowledge N.O.Agasian, B.L.Ioffe, L.A.Kondratuyk forfruitful discussions. This work was partially supported by Federal agency ofRussia for atomic energy (Rosatom).— The suggested investigation is open for the cooperation with theexperimentalists and theorists who are interested in the above dis-cussed physics and in the performing of the proposed experiment. References [1] T. Hatsuda and S.H. Lee, Phys. Rev. C46 , R34 (1992).[2] G.E. Brown and M. Rho, Phys. Rev. Lett. , 2720 (1991).[3] P.S. Reinhard, Rep. Prog. Phys. , 439 (1989).[4] K. Tsushima et al., Phys. Lett. B429 , 239 (1998).[5] K. Saito et al., Prog. Part. Nucl. Phys. , 1 (2007).[6] S. Leupold, Nucl. Phys. A628 , 311 (1998).247] V. Bernard and U.-G. Meissner, Nucl. Phys. A489 ,647 (1988)[8] K. Suzuki et al., Phys. Rev. Lett. , 072302 (2004).[9] Y. Nambu and G. Jona-Lasino, Phys. Rev. , 345 (1961).[10] S. Zschocke et al., Phys. Lett. B562 , 57 (2003); R. Tomas et al., Phys. Rev. Lett. , 232301 (2005).[11] G. Agakichiev et al., Phys. Lett. B422 , 405 (1998).[12] J. Adams et al., Phys. Rev. Lett. , 092301 (2004).[13] W. Weise, Nucl. Phys. A610 , 35c (1996).[14] U. Mosel, Pramana , 709 (2006).[15] D. Trnka et al., Phys. Rev. Lett. , 192303 (2005).[16] M. Naruki et al., Phys. Rev. Lett. , 092301 (2006).[17] M. Kaskulov et al., Eur. Phys. J. A31 , 245 (2007), arXiv:nucl-th/0610067.[18] C. Djalali for the CLAS Collaboration, Proceedings of the QM’2006 Confer-ence, China, November 2006.[19] M. Kotulla, arXiv: nucl-ex/0609012.[20] B. Yu. Sharkov et al., Nucl. Instr. Meth. A415 , 20 (1998).[21] D. Cabrera et al., Nucl. Phys. A733 , 130 (2004).[22] K. Tsushima et al., Phys. Lett. B443 , 26 (1998); F. Klingl et al., Nucl. Phys. A624 , 527 (1997); B. Friman, Acta Phys. Pol. B29 , 3115 (1998); K. Saito et al., Phys. Lett. B433 , 243 (1998); K. Saito et al., Phys. Rev. C59 , 1203(1999); F. Klingl et al., Nucl. Phys. A650 , 299 (1999);[23] A.K. Dutt-Mazumder et al., Phys. Rev. C63 , 015204 (2001); M. Post andU. Mosel Nucl. Phys. A669 , 169 (2002); B. Stainmueller and S. LeupoldNucl. Phys. A778 , 195 (2006);[24] M. F. M. Lutz et al., Nucl. Phys. A706 , 431 (2002); P. Muehlich et al., Nucl. Phys. A780 , 187 (2006);[25] F. Klingl et al., Nucl. Phys. A624 , 527 (1997); B. Friman, Acta Phys. Pol. B29 , 3115 (1998);[26] P. Muehlich et al., Eur. Phys. J. A20 , 499 (2004).2527] J. G. Messchendorp et al., Eur. Phys. J. A11 , 95 (2001).[28] Yu. Kiselev and V. Sheinkman, JETP Lett. , 528 (2003).[29] R. Novotny et al., Radiation Measurements , 615 (2001).[30] A.V. Akindinov et al., JETP Lett. , 100 (2000).[31] R. S. Hayano et al., Eur. Phys. J. A6 , 99 (1999); F. Klingl et al., Nucl. Phys. A650 , 299 (1999);[32] P. Muehlich and U. Mosel Nucl. Phys. A773 , 156 (2006).[33] V. K. Magas et al., Phys. Rev. C71 , 065202 (2005).[34] P. Muehlich et al., Phys. Rev. C67 , 024605 (2003).[35] G. I. Lykasov et al., Eur. Phys. J. A6 , 71 (1999).[36] T. Ishikawa et al., Phys. Lett. B608 , 215 (2005).[37] H. Sorge, H. St¨ocker and W. Greiner, Ann. Phys. (NY) , 266 (1989);Nucl. Phys. A498 , 567c (1989); Z.Phys. C47 , 629 (1990); H. Sorge, Phys.Rev. C52 , 3291 (1995).[38] B. Nilsson-Almqvist and E. Stenlund, Computer Phys. Comm. , 387(1987); B. Andersson, G. Gustafson and B Nilsson-Almqvist, Nucl. Phys. B281 , 289 (1987).[39] H. Nagahiro et al., Phys. Rev. C74 , 045203 (2006).[40] K. Tsushima et al., Phys. Rev. C59 , 2824 (1999); A. Sibirtsev et al., Eur. Phys. J. A6 ,351 (1999); A.Hayashigaki Phys. Lett. B487 , 96 (2000);L. Tolos et al., Phys. Rev. B635 , 85 (2006).[41] S. Lee and C. Ko Phys. Rev. C67 , 038202 (2003).26 tudy of in-medium ! meson propertiesin Ap, pA and AA
ollisionsS.Belogurov, M.Chumakov, S.Kiselev, Yu.Kiselev(cid:3), V.SheinkmanFebruary 27, 2008Institute for Theoreti
al and Experimental Physi
sMos
ow, RussiaAbstra
tWe propose to investigate the in-medium properties of ve
tor ! mesonsat the normal nu
lear density in Ap(pA)
ollisions and at higher densityin AA
ollisions at the ITEP a
elerator fa
ility TWAC. Using of the in-verse Ap kinemati
s will permit us to study the ! meson produ
tion ina wide momentum interval in
luded the not yet explored range of smallmeson momenta relative to the proje
tile nu
lei where the mass modi(cid:12)
a-tion e(cid:11)e
t in nu
lear matter is expe
ted to be the strongest. Momentumdependen
e of the in-medium ! meson width will be studied in the tra-ditional pA kinemati
s. We intend to use the ele
tromagneti
alorimeterfor re
onstru
tion of the ! meson invariant mass by dete
ting photonsfrom the ! ! (cid:25)0(cid:13) ! 3(cid:13) de
ay. The model
al
ulations and simulationswith RQMD generator show feasibility of the proposed experiment. Avail-able now intensity of the ion beams provides a possibility to
olle
t largestatisti
s and make de
isive
on
lusion about the ! meson properties atdensity of normal nu
lei. At the se
ond stage of the investigation the !meson properties will be studied in AA
ollisions at higher density. Inter-pretation of these measurements will be based on the results obtained inAp(pA) intera
tions. Further investigation of the in-medium properties oflight un(cid:13)avored and
harmed mesons
an be performed at ITEP and atGSI(FAIR) where higher ion energies will be a
essible in near future.(cid:3)e-mail address: yurikisitep.ru 1ontents1 Physi
s motivaion 32 Goal of the experiment 43 Theoreti
al predi
tions 44 Inverse and dire
t kinemati
s 55 Experimental arrangement 75.1 Extra
ted ion and proton beams . . . . . . . . . . . . . . . . . . . 75.2 Proje
tiles and targets . . . . . . . . . . . . . . . . . . . . . . . . 85.3 Photon dete
tor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Study of the ! meson in nu
lear matter 86.1 In-medium ! meson mass . . . . . . . . . . . . . . . . . . . . . . 86.2 In-medium ! meson width . . . . . . . . . . . . . . . . . . . . . . 117 Simulations with RQMD event generator 148 Ba
kground and its suppression 169 Event trigger 2110 Event rate estimate 2211 Con
lusion 2312 Further investigations at ITEP and GSI 2413 A
knowledgments 242 Physi
s motivaionModi(cid:12)
ation of the hadron properties in baryon environment is one of the im-portant topi
s of
ontemporary strong intera
tion physi
s. This phenomenon hasbeen predi
ted within various theoreti
al approa
hes su
h as QCD sum rules [1℄,
hiral dynami
s [2℄, relativisti
mean-(cid:12)eld [3℄ and quark-meson
oupling model [4℄.A re
ent review
an be found in the Ref. [5℄. A hadron
an
hange its propertiessu
h as mass and width on
e it is embedded into a baryon matter. This
hange is
onne
ted to the many body intera
tions of a hadron with surrounding nu
leons.Whether a hadron is - in addition - also a(cid:11)e
ted by QCD
ondensates and theirin-medium
hange [1℄, [2℄, [6℄ is still a matter of debate. Nevertheless, the greatinterest in study of in-medium hadron properties is
aused by the expe
tation to(cid:12)nd the eviden
es of the
hiral symmetry restoration. Investigation of the ve
tormesons is of spe
ial interest in this
ontext. Theoreti
ally, the possibility of thede
rease in the mass of light ve
tor mesons in matter was (cid:12)rst pointed by Brownand Rho [2℄. In their approa
h the masses of the ve
tor mesons s
ale with quark
ondensate, i.e. drop with rising of baryoni
density. This e(cid:11)e
t
an be a pre
ur-sor phenomenon of the transition of strongly intera
ting matter to the
hirallysymmetri
phase. First experimental signal of this phenomenon was re
ently ob-served in [7℄. Nambu and Jona-Lasino proposed the spontaneous breaking ofthe
hiral symmetry as the fundamental me
hanism for the
reation of a mass ofhadrons [8℄. Re
ently, the in-medium
hange of the ! mesons spe
tral fun
tionwas proposed as a probe of higher order QCD four-quark
ondensate [9℄.An eviden
e for a de
rease of the (cid:26) meson mass in heavy-ion
ollisions wasobtained by the CERES
ollaboration at CERN [10℄ and later by the STAR
ollaboration at RHIC [11℄. Sin
e heavy-ion intera
tion is very
ompli
ated pro-
ess in whi
h the temperature and baryon density varies dramati
ally with timedue to the formation and expansion of the "(cid:12)reball", the interpretation of exper-imental data on nu
leus-nu
leus
ollisions is far from being simple. The aboveresults have been found an explanation in terms of shifting a (cid:26) meson spe
tralfun
tion to a lower mass, as expe
ted from the theory. However, even the
al-
ulations that just used the free radiation rates with their - often quite large -experimental un
ertainties are
ompatible with the observation.Therefore, it is useful to explore the rea
tions with elementary probes ((cid:13), (cid:25),p) sin
e sizeable - about 20% - medium e(cid:11)e
ts were predi
ted already at thedensity of ordinary nu
lei [2℄, [12℄, [13℄. The advantage of the investigations ofthe rea
tions on nu
lei is related to the fa
t that they pro
eed in the nearly
oldstati
nu
lear matter and thus the
olliding system is mu
h better under
ontrol.Indeed, the (cid:12)rst signals for lowering of the ! meson mass at normal nu
lear matterdensity were re
ently observed in the (cid:13)A [14℄ and pA [15℄ rea
tions. However,the
riti
al analysis [16℄ shows that data of the experiment [14℄ are
ompatiblewith normal ! mass and an enlarged width. In
ontrast to the
on
lusion [15℄ thepreliminary results of the CLAS
ollaboration (JLAB) on the photoprodu
tion3f (cid:26) and ! mesons [17℄ also eviden
e for no shift in the mass. Now there are only(cid:12)rst estimates of the ! meson width in matter [14℄, [18℄. Thus, the availablenow experimental information does not allow to draw the (cid:12)nal
on
lusion aboutthe
hange of the ! meson properties even in nu
lear matter of normal density. Itshould be stressed that the indi
ations for de
reasing of the ! meson mass in bothexperiments [14℄, [15℄ have been found for the mesons with low momenta relativeto the surrounding nu
lear matter. Therefore, next generation of experimentsneed to addresses the issue of momentum dependen
e of medium e(cid:11)e
ts. Wesuggest to explore the momentum dependen
e of the in-medium mass and widthof the ! meson using the ion and proton beams of the ITEP a
elerator fa
ilityTWAC [19℄.The investigation of in-medium meson modi(cid:12)
ation addresses the fundamen-tal problems of strong intera
tion physi
s and is one of the hot
urrent topi
snowadays. The experiments with photon, pion, proton and ion proje
tiles areplanned in wide
ollision energy range from a few GeV (GSI, JLAB, JINR, COSY,SPring-8, ITEP) till TeV (RHIC, LHC).2 Goal of the experimentThe goal of the proposed experiment is the investigation of the ve
tor ! mesonproperties at normal nu
lear density (cid:26)0 = 0:17f m(cid:0)3 in nu
leus-proton (proton-nu
leus)
ollisions and at higher density in nu
leus-nu
leus
ollisions. The ex-periment aims at the study of the mesons with low momentum relative to thebaryoni
environment where the in-medium mass modi(cid:12)
ation is expe
ted to bemost strong as well as at the study of high momentum range whi
h is sensitiveto the in-medium ! meson width.3 Theoreti
al predi
tionsAll information about the intrinsi
properties of a meson is en
oded in its spe
tralfun
tion S(M) whi
h
an be written in non-relativisti
Breit-Wigner form. In freespa
e: S(M ) = ((cid:0)0=2)2=[(M (cid:0) M0)2 + ((cid:0)0=2)2℄; (1)where (cid:0)0 and M0 stand for a meson width and pole mass,
orrespondingly.Due to the intera
tion with surrounding nu
lear medium the meson a
quiresa selfenergy (cid:6) whi
h is related to the nu
lear opti
al potential U as [20℄:(cid:6)=2E = U = ReU + i ImU; (2)where E is the total meson energy.The meson spe
tral fun
tion in nu
lear medium is read:S(M ) = [((cid:0)0=2) + ((cid:0)(cid:3)=2)℄2=[M (cid:0) (M0 + M (cid:3))℄2 + [((cid:0)0=2) + ((cid:0)(cid:3)=2)℄2: (3)4wo extra terms, M (cid:3) and (cid:0)(cid:3)=2, whi
h des
ribe the shift of the meson pole massand the in
rease of its width in matter, are related to the nu
lear opti
al potentialU as follows [20℄: M (cid:3) = ReU ; (cid:0)(cid:3)=2 = (cid:0)ImU ; (4)The pole mass and width of the ! meson in free spa
e (va
uum) are M = 782MeV and 8.4 MeV,
orrespondingly. Most theoreti
al investigations predi
t thedropping of the in-medium ! meson mass by 20-140 MeV [21℄ at normal nu
leardensity. However, there have also been suggestions for a rising mass [22℄ oreven a stru
ture with several peaks [23℄. At the same time there seems to bea general agreement that in-medium ! width is within the range from 20 MeVto 60 MeV [24℄ at the density (cid:26) = (cid:26)0. Thus, it is expe
ted that the ! mesonin matter survives as a quasiparti
le and
an be observed as a stru
ture in the! mass spe
trum. In prin
iple, both dilepton and (cid:25)0(cid:13) invariant mass spe
tra
an be used for the study of modi(cid:12)
ation e(cid:11)e
ts. The advantage of the dileptonde
ay
hannel is related to the fa
t that leptons are almost undistorted by the(cid:12)nal state intera
tions. However, the ! signal in the dilepton mode is rather weak(BR(! ! e+e(cid:0)) (cid:25) 7:1 (cid:2) 10(cid:0)5) and is always a
ompanied by a
omparativelylarge ba
kground from (cid:26)0 ! e+e(cid:0) de
ays. The ! ! (cid:25)0(cid:13) de
ay has a bran
hingratio 8:9(cid:2)10(cid:0)2 what is 3 orders of magnitude higher. Furthermore, the
ompeting(cid:26) ! (cid:25)0(cid:13)
hannel has a bran
hing ratio whi
h is a fa
tor 102 smaller. By thesereasons the ! ! (cid:25)0(cid:13) de
ay mode
an be
onsidered as an ex
lusive probe to studythe ! meson properties in matter. The disadvantage of this
hannel is a possibleres
attering of the (cid:25)0 within the nu
lear medium whi
h would distort the dedu
ed! invariant mass distribution. However, as it was shown in Refs. [25℄, [26℄ theabove distortion e(cid:11)e
t
an be signi(cid:12)
antly de
reased by applying an appropriate
ut on the pion kineti
energy.4 Inverse and dire
t kinemati
sThe ! meson invariant mass spe
trum has two
omponents whi
h
orrespond tothe de
ay 'inside' and 'outside' the nu
leus. Only ve
tor mesons de
aying 'inside'nu
lei
an be used for an identi(cid:12)
ation of the in-medium ! mass. This imposesthe kinemati
al
ondition that the de
ay length of the ve
tor meson should beless than nu
leus size. It implies that the ! meson should be produ
ed with smallmomentum (velo
ity) relative to the nu
lear matter rest frame. The study of lowmomentum ! mesons produ
tion in the inverse Ap kinemati
s [27℄ has severalimportant advantages over the study in the dire
t pA kinemati
s. First, as itfollows from the Lorentz transformation, slow parti
les in a proje
tile nu
leussystem appear to be fast in the laboratory (in the target proton rest frame) andbe
ome
onvenient for the dete
tion. At beam energy of 4 AGeV all the !'sprodu
ed in full solid angle with momenta less than 0.3 GeV/
relative to theproje
tile nu
leus rest frame will be
on
entrated in the laboratory inside narrow5one of less than (cid:6)50 and the momentum range from 2.8 till 5.9 GeV/
. The pro-du
ed mesons whi
h are almost at rest inside the in
ident nu
leus ("
omovers")have the laboratory momenta around of 4 GeV/
. Due to the de
rease of theprodu
tion
ross se
tion with laboratory ! meson momentum the main
ontribu-tion to the ! yield
omes from the momentum interval of 2.8 - 4.0 GeV/
. Theseevents will be observed in small phase spa
e dP d
os(cid:18) in the laboratory resultingin signi(cid:12)
ant in
rease in forward produ
tion
ross se
tion as
ompared to one inpA rea
tions. That
an be easily understood be
ause experimentally observednon-invariant double di(cid:11)erential
ross se
tions measured in the dire
t (pA) andinverse (Ap) kinemati
s are related as:Ap(d2(cid:27)=dP d
os(cid:18)) =Ap (P 2=E)pA(E=P 2)pA(d2(cid:27)=dP d
os(cid:18)): (5)One
an see that the fa
tor pA(E=P 2) grows strongly with lowering of the ! mesonmomentum while the fa
tor Ap(P 2=E)
hanges rather smoothly.The photons from the de
ay ! ! (cid:25)0(cid:13) ! 3(cid:13) are distributed inside more wide
one as
ompared to parent mesons, however the
overage of the angular interval50 (cid:0) 250 - whi
h
orresponds to the solid angle of less than 9% of 4(cid:25) - permits to
olle
t signi(cid:12)
ant part of the useful events.Se
ond, the mean free pass of the proton in nu
lear matter is as small as 2fm and therefore the ! mesons are predominantly
reated inside the front layersof a proje
tile nu
leus. Sin
e the forward produ
ed !'s in the momentum range2.8-4.0 GeV/
have the laboratory velo
ities whi
h are less than ones of thesurrounding nu
leons, the produ
ed mesons move in the dire
tion opposite to theion beam dire
tion and then de
ay in more dense inner layers of a nu
leus. Thatis of great importan
e be
ause the strength of the medium e(cid:11)e
ts in
reases withnu
lear density.Third advantage of the inverse kinemati
s is an in
rease in the energies ofthe dete
ted photons be
ause they are emitted by relativisti
! and (cid:25)0. Forexample, the (cid:25)0(cid:13) de
ay in transverse dire
tion of the !
arrying the momentumof 4 GeV/
results in emission of the photon of energy 2 GeV and (cid:25)0 of energy2.1 GeV followed by the pion de
ay to two photons of 1 GeV energy. The aboveenergies ex
eed the photon energies from the ! ! (cid:25)0(cid:13) de
ay at rest (0.38 GeVfor the (cid:13) from ! and 0.19 GeV for the (cid:13)'s from (cid:25)0) by a fa
tor of about 5. Thatresults in more pre
ise measurement of the photon energy leading to more narrowwidth of the signal in the invariant mass spe
trum and hen
e improved signal toba
kground ratio. At last, only moderate momentum resolution in the laboratoryis required for the rather pre
ise determination of the ! momentum relative tothe proje
tile nu
leus be
ause the momentum range of interest 2.8-4 GeV/
inthe laboratory
orresponds to the interval 0-0.3 GeV/
in the nu
leus frame ofreferen
e.In
ontrast with in-medium ! meson mass the value of its width is expe
tedto be dedu
ed from the analysis of the produ
tion of fast mesons relative to the6 (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) CPVEMCALLH target Beam Figure 1: Sket
h of the experimental set-upbaryoni
matter. It is well known that high momentum mesons
an be abundantlyprodu
ed in the pA intera
tions. Thus, the
ombination of the Ap and pAmeasurements provides the possibility to study both ! meson mass and width innu
lear matter.5 Experimental arrangement5.1 Extra
ted ion and proton beamsWe intend to
arry out the proposed measurements using the ion and protonbeams extra
ted in the inner hall of the a
elerator. Expe
ted extra
tion eÆ-
ien
y is of 50%. Two dipole and two pairs of quadrupole magnets serve for thede(cid:13)e
tion and fo
using the beams onto the target. The sket
h of the experimen-tal set-up is shown in Fig. 1. The ions (or protons) whi
h do not intera
t inthe target pass through the
entral hole of the ele
tromagneti
alorimeter (EM-CAL) and then dire
ted to the downstream beam-dump lo
ated in the inner hallor thi
k
on
rete wall of the a
elerator. That prevents the environment fromthe radiation pollution. 7.2 Proje
tiles and targetsThe proje
tile Ta, Cu, Al and C ions will be used for the investigations of the in-medium ! meson mass while the proje
tile protons will be used for the explorationof the ! width in the nu
lear matter. The proton runs will permit us to study theEMCAL performan
e and
alibrate the invariant mass s
ale by measurements ofthe rea
tions p + A ! (cid:25)0+X, p + A ! (cid:17)+X and p + A ! !+X.We plan to use the liquid hydrogen (LH2) target of 2% intera
tion length (12
m) for Ap measurements and simple foil targets (Be, Al, Cu, Ag and Ta) for thepA and AA measurements.5.3 Photon dete
torThe ring-like ele
tromagneti
alorimeter with total area of 0.64 m2 will be lo-
ated at the distan
e of 1 m downstream of the target. We intend to use theEMCAL based on the PbWO
ells 20 (cid:2) 20mm2 size with avalan
he photodiodeor photomultiplier readout. The energy and spatial resolution of the
ell are(cid:27)/E=2%pE+1% and (cid:27)x = (cid:27)y = 6mm, respe
tively [28℄. The total number of
ells is 1400. In front of a group of
ells the 5 mm thi
k plasti
s
intillator withphotodiode readout will be mounted for the dete
tion of
harged parti
les. Dueto the moderate
harge eje
tile multipli
ity (see se
tion 7) the number of CPV(Charged Parti
le Veto)
ounters is less than about 100. This array
an be alsoused as a multipli
ity dete
tor o(cid:11)ering the possibility to apply the
uts on theimpa
t parameter of the
ollision.6 Study of the ! meson in nu
lear matter6.1 In-medium ! meson massFor the evaluation of the expe
ted signal of in-medium ! meson mass and widthmodi(cid:12)
ation the
al
ulations of the ! meson produ
tion were performed in theframework of the folding model. The model takes properly into a
ount bothin
oherent dire
t proton-nu
leon and se
ondary pion-nu
leon ! meson produ
-tion pro
esses as well as internal nu
leon momentum distribution (see for exam-ple [29℄). The folding model des
ribes the produ
tion, propagation and de
ay ofthe ! meson inside a nu
leus taking into a
ount its four-momentum and lo
alnu
lear density. The
al
ulations were performed for Ta, Cu, Al and C nu
lei atinitial energy of 4 AGeV.In our approa
h the ! meson mass shift was introdu
ed a
ording to the lo
alnu
lear density (cid:26)(r): M (cid:3) = ReU = ÆM0(cid:26)=(cid:26)0; (6)8 ,MeV 680 700 720 740 760 780 N Cu Q All P and M,MeV 680 700 720 740 760 780 N Cu P<0.3 GeV/c M,MeV 680 700 720 740 760 780 N P<0.3, b Figure 6: Density of parti
les in a plane at 1 m from the targetAs was explained in se
tion 6.2 the in-medium ! meson width
an be de-du
ed from the analysis of the A-dependen
e of the produ
tion
ross se
tions ofrelatively fast !'s, whi
h are mostly de
ay outside the nu
leus. Obviously, thatthe photons from the de
ay of high momentum mesons produ
ed in traditionalpA kinemati
s will also be dete
ted with high eÆ
ien
y be
ause the eÆ
ien
ydepends on photon energy relative to the dete
tor.Thus, the momentum dependen
ies of both in-medium ! meson mass andwidth
an be investigated in the inverse and dire
t kinemati
s { i.e. using the ionand proton beams { without the
hange of the dete
tor position and its layout.8 Ba
kground and its suppressionThe feasibility of the experiment depends on the signal to ba
kground ratio.RQMD simulations show that the main sour
e of the ba
kground is the (cid:25)0(cid:25)016 (deg.) q p ( G e V / c ) hOmegaPvsTheta Entries 3486Mean x 11.52Mean y 2.196RMS x 7.416RMS y 0.986 020406080100 hOmegaPvsTheta Entries 3486Mean x 11.52Mean y 2.196RMS x 7.416RMS y 0.986 w RQMD, Cu+p at T/A=4.0 GeV, p (GeV/c)0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 hOmegaP Entries 3486Mean 2.179RMS 0.9932 p (GeV/c)0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 N ( / b i n ) hOmegaP Entries 3486Mean 2.179RMS 0.9932 w RQMD, Cu+p at T/A=4.0 GeV, (deg.) q q N ( / b i n ) w RQMD, Cu+p at T/A=4.0 GeV, y-1 -0.5 0 0.5 1 1.5 2 2.5 3 ( G e V / c ) t p hOmegaPTvsYEntries 3486Mean x 1.541Mean y 0.3638RMS x 0.4651RMS y 0.1756 hOmegaPTvsYEntries 3486Mean x 1.541Mean y 0.3638RMS x 0.4651RMS y 0.1756 w RQMD, Cu+p at T/A=4.0 GeV, Figure 7: ! spe
trum in the laboratory frame17 (deg.) q p ( G e V / c ) hOmegaCutPvsTheta Entries 796Mean x 4.476Mean y 3.372RMS x 1.508RMS y 0.6092 hOmegaCutPvsTheta Entries 796Mean x 4.476Mean y 3.372RMS x 1.508RMS y 0.6092 <0.5 GeV/c w Cu , p w RQMD, Cu+p at T/A=4.0 GeV, p (GeV/c)0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 hOmegaCutP Entries 796Mean 3.372RMS 0.6092p (GeV/c)0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 N ( / b i n ) hOmegaCutP Entries 796Mean 3.372RMS 0.6092 <0.5 GeV/c w Cu , p w RQMD, Cu+p at T/A=4.0 GeV, (deg.) q hOmegaCutTheta Entries 796Mean 4.429RMS 1.512 (deg.) q N ( / b i n ) hOmegaCutTheta Entries 796Mean 4.429RMS 1.512<0.5 GeV/c w Cu , p w RQMD, Cu+p at T/A=4.0 GeV, y-1 -0.5 0 0.5 1 1.5 2 2.5 3 ( G e V / c ) t p hOmegaCutPTvsY Entries 796Mean x 2.107Mean y 0.2617RMS x 0.181RMS y 0.09509 010203040506070 hOmegaCutPTvsY Entries 796Mean x 2.107Mean y 0.2617RMS x 0.181RMS y 0.09509 <0.5 GeV/c w Cu , p w RQMD, Cu+p at T/A=4.0 GeV, Figure 8: The same as for Fig. 7 but for ! with p < 0:5 GeV/
in the proje
tilenu
leus frame 18 (deg.) q p ( G e V / c ) hOmegaCMAPvsTheta Entries 3486Mean x 32.92Mean y 0.8747RMS x 22.51RMS y 0.4323 0102030405060708090 hOmegaCMAPvsTheta Entries 3486Mean x 32.92Mean y 0.8747RMS x 22.51RMS y 0.4323 in c.m. of Cu w RQMD, Cu+p at T/A=4.0 GeV, p (GeV/c)0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 hOmegaCMAP Entries 3486Mean 0.8747RMS 0.4323 p (GeV/c)0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 N ( / b i n ) hOmegaCMAP Entries 3486Mean 0.8747RMS 0.4323 in c.m. of Cu w RQMD, Cu+p at T/A=4.0 GeV, (deg.) q hOmegaCMATheta Entries 3486Mean 31.1RMS 22.49 (deg.) q N ( / b i n ) hOmegaCMATheta Entries 3486Mean 31.1RMS 22.49 in c.m. of Cu w RQMD, Cu+p at T/A=4.0 GeV, y-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 ( G e V / c ) t p hOmegaCMAPTvsY Entries 3486Mean x -0.7995Mean y 0.3642RMS x 0.4596RMS y 0.1758 020406080100 hOmegaCMAPTvsY Entries 3486Mean x -0.7995Mean y 0.3642RMS x 0.4596RMS y 0.1758 w RQMD, Cu+p at T/A=4.0 GeV, Figure 9: ! spe
trum in the proje
tile nu
leus frameprodu
tion. Su
h events
an lead to the misidenti(cid:12)
ation due to a (cid:12)nite geome-try of the dete
tor if one of the four photons is out of the EMCAL a
eptan
e.The
ontribution from other sour
es of the ba
kground like (cid:17)(cid:25)0, (cid:17)0, (cid:1)0 ! n(cid:13) et
.is relatively small in the invariant mass range of interest 0.65 - 0.85 GeV sin
ethe invariant masses re
onstru
ted from kinemati
al parameters of three un
or-related photons are spread over wide mass range from 0.1 to 1.0 GeV. Therefore,the useful events from the ! ! (cid:25)0(cid:13) ! 3(cid:13) de
ay will be dete
ted on the topof smooth
ontinuum steming mainly from the (cid:25)0(cid:25)0 produ
tion pro
ess. TheSignal/(Signal+Ba
kground) ratio R = S=(S + B) for the minimum bias eventsis less than approximately one per
ent. However, this value
an be signi(cid:12)
antlyimproved by applying the appropriate kinemati
al
uts. RQMD simulations in-di
ate that the spe
trum of the photons originating from the (cid:25)0 de
ay dropssteeper than that from the ! de
ay. By this reason the
ut on photon energyshould lead to the ba
kground suppression. The histograms in Fig. 10 demon-19 InvMassSignalEntries 327Mean 0.7814RMS 0.01019 g o p M0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 N ( / b i n ) -1 hInvMassSignalEntries 327Mean 0.7814RMS 0.01019 origin: g g o p --> w from g --> 2 o p from ’, ...) h from other ( - 25 =5 q set-up: hInvMassSignalRes Entries 327Mean 0.7695RMS 0.02797 g o p M0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 N ( / b i n ) -1 hInvMassSignalRes Entries 327Mean 0.7695RMS 0.02797 =6 mm y s = x s +1 (%) + E=2/ E s + hInvMassSignal Entries 149Mean 0.7808RMS 0.009075 g o p M0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 N ( / b i n ) -1 hInvMassSignal Entries 149Mean 0.7808RMS 0.009075 >0.5 GeV/c g + p hInvMassSignalRes Entries 149Mean 0.7721RMS 0.02341 g o p M0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 N ( / b i n ) -1 hInvMassSignalRes Entries 149Mean 0.7721RMS 0.02341hInvMassSignal