SUBTHRESHOLD ρ0 PHOTOPRODUCTION ON 2H,3He and 12C 1 G.J. LOLOS Department of Physics, University of Regina, Regina, SK, S4S 0A2, Canada 1 0 Abstract 0 2 Theρ0 hasbeenphotoproducedusingtaggedphotonenergiesinthe700- n 1120 MeV region on 2H,3He and 12C by utilizing the Fermi momentum a J oftheboundnucleonstoproducetheρ0. Theseenergiesliemostlybelow 9 the production threshold on the free proton. Large mass modifications 1 are indicated from the analysis, together with large polarizations of the 1 produced ρ0 mesons with helicity zero, unlike the case of coherent ρ0 v production on nuclei. 5 0 0 1 Introduction 1 0 1 The effects of hadron density and/or temperature on the mass and lifetimes of 0 vector mesons have been the subject of numerous investigations, experimental / x as well as theoretical [1]. Under conditions of chiral symmetry restoration, the e quark condensate vanishes, < q¯q >→ 0. The condensate is not, however, an - l c observable but it is related to the meson mass, which is. Thus, the behaviour u of vector meson masses under high hadron densities and/or temparatures has n : become a testbed of our understanding of hadron or quark dynamics in nuclear v i matter. A renormalization of vector meson masses in hot and dense matter is X of significant importance to the pursuit of quark gluon plasma research, has r a relevance to the equation of state for nuclear matter in supernovae explosions, and could affect lower energy nuclear physics, as well. It has been argued that the mass modification of vector mesons should be measurable even at normal nuclear matter densities [2]. Even though a reduction of vector meson mass in hadronic matter is sup- portedby most ofthemorerecent theoreticalmodels, thespectralshape (man- ifested in the width) is more of an open question. If there is substantial broad- ening as reported in [3], then extracting meaningful mass change information from ρ production and decay experiments becomes problematic, especially so 1Proceedings of the International Workshop XXVIII on Gross Properties of Nuclei and Nuclear Excitations, Hirschegg, Austria, January 16-22,2000, p. 203. for massive nuclei. In this respect, production of either the ω in massive nuclei or the ρ from light nuclei may be a better solution. In any case, production of vector mesons, by whatever method, is not enough to probe medium mod- ifications. The production of mesons must be accompanied by a substantial decay fraction within the nuclear volume, a fact which favours either low beam energies or restricted phase space in which the vector mesons are essentially at rest with respect to the recoiling nuclear system. 2 The TAGX Results from A(γ ,π+π−)X Reactions t 2.1 The Subtreshold Energy Regime Photo- or lepto-production of vector mesons from nuclei has been and is being explored at many facilities. Given the quantum numbers of the vector mesons and those of the photon (real or virtual), the primary interaction of the latter proceeds via the interaction of the former with the nucleons in nuclei, the well established VMD model of γ-N interactions. At incident photon energies of approximately 1.2 GeV and higher, the diffractive mechanism dominates, in which the photon flactuates into a ρ0 or ω, which then scatters off the nucleon field with sufficient four-momentum transfer to bring the meson on the mass shell. In the case of nuclei, the single γ-N amplitudes add coherently and large production cross sections result. Since the momentum transfer t is less than 0.1 GeV2/c2, coherent or diffractive cross sections are very forward peaked. As a result, they also conserve helicity and the reaction is characterized by a large impact parameter of approximately 10 fm or more. While coherent photoproduction produces vector mesons prolifically, the probability of the vector mesons penetrating the nuclear interior and decaying within it is rather small. The observation, then, of medium modifications in such reactions is diminished by “geometry” (including trajectory of the produced meson with respect to the nucleus) and the large Lorentz boost of the meson with respect to the nucleus. This is particularly severe for the ω due to its long cτ compared to that of the ρ0. One is thus forced to depend on the large number of mesons produced to observe the small fraction that penetrates and decays within the nuclear volume, and which is perharps overwhelmed in the invariant mass signature from the low tail of the unmodified mesons decaying freely. Where the fraction is larger, like in the ρ-meson case, the free ρ0 width is also large, thus effectively masking the modified mass. In the case of the ω, the narrow width makes it easier to separate the modified from the unmodified masses, but the fraction of the former to the latter is very small. An alternative is to produce the ρ0 below the free γ + N → ρ0 nominal threshold of 1083 MeV. In this case, the reaction is characterized by large t and the Fermi four-momentum of the struck nucleon is utilized to bring the ρ0 on the mass shell. A penalty one pays for such subthreshold ρ0 production is the small cross section compared to coherent production. There are numerous advantages, however. First, the ρ0 production vertex is forced to be within the nuclear volume (small impact parameter) by the interaction of the photon with a bound nucleon. The reaction then is quasi-free γ-N interaction in nature. Second, the ρ0 is produced with small relative momentum and Lorentz boost with respect to the struck nucleon or the nucleus, thus maximizing the probability of decay within the hadronic volume. Third, the large opening angle (of 180o in the ρ0 rest frame) is essentially preserved in the lab frame due to the small Lorentz boost and this provides a characteristic signature of the ρ0 decay, which can be used effectively in the suppression of competing processes. 2.2 The TAGX Results on 3He The choice of 3He was made based on several reasons. (a): Its core nuclear density is near saturation density for heavier nuclei, while the small number of nucleons reduces final state interactions (FSI) between the pions and the recoiling nucleus or nucleons. (b): The kinematical analysis is much simpler due to the small number of spectator nucleons and the Monte Carlo (MC) simulations carry more confidence. And, (c): extrapolations of cross sections for background processes on proton and 2H are more accurate for 3He than more complex nuclei. Thus, it was felt that any mass modification, even if small, could carry higher confidence due to the simplicity of the probe-target system. The analysis was based on a detailed and kinematically constrained fit to several distributions simultaneously for all processes that can lead to a π+π− final state. Details arepublished in [4], [5], and [6]. The results were consistent with a large mass modification for the ρ0, which was also found to depend on incident photonenergy. At photonenergies aslow as660±40MeV, the best fit was obtained for a m∗ = 490±40 MeV/c2, while for 840±40 MeV the mass of ρ0 the ρ0 was m∗ = 640±40 MeV/c2. For the highest energy bin available to the ρ0 experiment (which was centered around 1080MeV), the data were shown to be insensitive to any ρ0 mass modification. The conclusions survived a number of different analyses, and even the data sets for two of the analyses were different and independent of each other. The analysis was based on the simultaneous fitting of a number of “key” variables, such as missing momentum (p ), missing mass (m ), invari- miss miss ant mass (m ), pion opening angle (θ ), and emission angle of the di-pion ππ ππ system (θ ). All these are kinematical observables and follow phase space IM distributions, applicable to each individual reaction assumed. For the 80 MeV wide photon energy bins in the analysis, the assumption was made that the matrix element is constant. The yield then is the product of several factors: ∗ 2 Y = |M (s,t)| ·Φ (p)·Ψ(s,I,J)·[MBPS ∗F(m,Γ)] (1) 3He ∗ where Y = Yield, |M | = invariant matrix element for the reaction, Φ = the single nucleon momentum distribution, Ψ = function of spin, isospin, and total angular momentum, and [MBPS ∗F] = the multi-body phase space for this reaction with the mass and width of any resonances folded in. Therefore, ∗ even though a variation of |M | within the 80 MeV bin is not taken explicitly into account, the width Γ of the states involved has a large part of this energy dependence foldedin. Eachbackgroundandforegroundreactionwassimulated using Monte Carlo (MC) generators, which incorporated equation 1. Cross sections for known processes, such as ∆π,N∗π,∆∆ and π+π−π0, were extracted and compared to established measurements in the literature, if such existed. The cross sections for ρ0 production with modified masses were quite small (a few µb), while that of competing processes are of the order of 200 µb [5]. The small ρ0 signal could be extracted due to the features of the TAGX acceptance. The trigger requirement of left-right (with respect to the photon beam) π+ − π− coincidences, and the small out of plane acceptance of the spectrometer, result in substantially larger acceptance for the ρ0 → π+π− decay than the other competing two-step processes leading to two-pion emission. Furthermore, the requirement of simultaneous fitting of so many different kinematical variables provided severe contraints to the strength of these background reactions in different regions of the various distributions. One of the difficulties of the above analysis is the model dependency and the smallness of the ρ0 production cross sections compared to all the other competing processes. The analysis, however, has been shown to be insensitive toreasonablevariationsinassumedcrosssectionsforthedominantbackground processes because the ρ0 events occupy quite distinct regions of phase space. Thus, variations in∆π production cross sections, for example, affected ∆∆ fits ∗ and resulting cross sections, but they did not affect the value of m . Another ρ0 conclusion was that m is not a very sensitive parameter and good fits can ππ be obtained for large differences in the input parameters. On the other hand, θ and p are difficult (and sensitive) distributions to fit. ππ miss In the case of coherent ρ0 production and at very small angles of emission ∗ in the helicity frame of reference, the angular distribution for θ of one pion π with respect to the di-pion center of mass momentum in the helicity frame, has ∗ a sinθ -like distribution for unpolarized photons. This is a result of s-channel π helicity conservation. In the case of helicity non-conservation, for example at large angles of ρ0 emission due to large t exchange, a random distribution of ∗ polarization would result in an isotropic distribution for θ . When, however, π such a θ∗ distribution was formed, an enhancement in the regions of 0o and π+ 180o was observed in the “raw” event sample. This has been interpreted as a substantial polarization component in the ρ0 event sample which corresponds to the l = 1, m = 0 substate. Such a Y0 -like distribution was most prominent 1 in the same m bins where the independent kinematical analysis placed the ππ mean of the modified ρ0 mass. 2.3 The TAGX Results on 2H, 12C The analysis of the 2H and 12C results is still ongoing and a final value for the modified masses has not been extracted yet. The philosophy and method- ology is quite different than the analysis of the 3He data. The simpler 2H nucleus, coupled with photoabsorption cross sections in the literature for most of the channels leading to di-pion emission, allow the use of experimental am- plitudes and cross sections and a likelyhood method of fitting the kinematical observables. Unlike the analysis of the 3He data, in this analysis the θ∗ dis- π+ tributions are explicitly involved among the kinematical variables fitted. The ∗ cross section results are not yet final, however, the analysis based on the θ π+ ∗ distribution is quite interesting. In Figure 1, the cosθ distributions are π+ shown for 12C +2 H data, (a) without any restrictions on the data, and (b) with a θ ≥ 120o cut. Several observations can be drawn: ππ • In the M bin of 300-400 MeV/c2, the shape of the distribution and ππ the small number of events near the -1 and +1 limits is characteristic of acceptance effects due to trigger and geometry of TAGX. As such, the populationin these two regions for the invariant mass bins inthe 500-600 MeV/c2 regions, signify substantial ρ0 → π+π− -like production. • The application of the opening angle (θ ) cut, removes events form the ππ central regions of the distribution, but leaves the population around the two limits unchanged. ∗ The cosθ distributions for all three nuclei exhibite the same overall be- π+ haviour. The preliminary results from the cross section fitting of the 2H data 600 500 400 no θππ cut 300 200 100 s ent 6000 v e 500 400 θ >120º ππ 300 200 100 0 -1 0 -11 0 -11 0 1 cosθ* π+ 300 ≤ m ≤ 400 500 ≤ m ≤ 600 700 ≤ m ≤ 800 ππ ππ ππ Figure 1: Selected invariant mass bins for data from the 2H,12C(γ,π+π−)X experiment obtained with TAGX. The top panels have no θ cut, whereas ππ the bottom panels have been subjected to a θ ≥ 120o cut. The invariant ππ mass bins for 400-500 and 600-700 MeV/c2 also exhibit a p-wave signature, but it’s neither as strong nor as symmetric as that in the 500-600 MeV/c2 bin; they are not shown here for the sake of clarity. are consistent with a few µb cross section for polarized ρ0 production in the l = 1, m = 0 substate and no strength in the l = 1, m = 1 substate. This is qualitatively inagreement with the 3He data which also showed no statistically significant population in the small angle regions in plots such as shown in Fig- ure 1. This was verified by successively applying increasingly tighter opening ∗ angle cuts and comparing the behaviour as a function of cosθ values. π+ 2.4 The Effects of θ Cuts ππ The l = 1, m = 0 signature is model independent and difficult to argue away. Nevertheless, there have been a number of possible explanations, other than a modified and polarized ρ0. One is that there may be other reactions which lead to two-pion emission in a relative p-state and with a m = 0 substate. However, no such specific reaction has ever been identified or proposed as θππ >0 θππ >60 θππ >80 θππ >100 θππ >120 π ∆ π ↑∆ ∆ ∆ ↑∆ ↑∆ ρ ↑ρ cosθ H Figure 2: Deuterium distributions of the cosine of the pion angle in the helicity frame. The columns indicate the effect of progressively larger opening angle cut. The rows portray the different MC-generated channels, with the verticle arrow indicating that the particle in question is produced in a polarized state. a candidate; in any case, if there is indeed one, this by itself is a new and interesting result. Another concern put forward is that the application of ever tighter θ requirements mayartificially produce such l = 1, m = 0 signatures. ππ In order to address this valid concern, a detailed investigation of the behaviour of two of the most prolific background processes has been made as a function of θ cuts. MC simulations of three production reactions have been made ππ and analyzed in the same fashion as the real data are analyzed in the TAGX detector. These are shown in Figure 2 for 2H, plotted as a function of cosθ H in the helicity frame. The ∆π and ∆∆ background channels are the two strongest channels lead- ingtoπ+π− production. AscanbeseeninFigure2, whether the∆isproduced polarized (indicated by the arrow) or not, the application of successively more demanding θ cuts does not alter the shape of the distributions. In the case ππ of unpolarized ρ0 production, the distribution is essentially flat with a slight enhancement at the limits due to detector acceptance. Only in the case of polarized ρ0 production do the MC simulations in Figure 2 agree with the observed behaviour of the data in Figure 1. 3 Conclusions The analyses of 3He data using MC and model dependent, as well as model independent variables, agree on a substantial mass modification of the ρ0. The preliminary results on 2H and 12C, using primarily the model independent θ∗ π+ analysis, agree with the earlier results and strongly support the production of longitudinally polarized (zero helicity) and mass modified ρ0 -mesons. The similarities among the results for these three different nuclei is suggestive of a ρ0-N based interaction effect rather than a nuclear effect. Since the relative ρ0- N momenta at such low incident photon energies are also very low, the mean decay length of the ρ0 from its production vertex is less than the nucleon radius. Hadronic densities at the interior of a nucleon are very high, thus qualitatively accounting for the large mass modifications reported so far from TAGX results. The excellent agreement on the θ dependence for data and ππ MC simulations conclusively shows that only a l = 1, m = 0 substate of the ρ0 is present in the data. 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