Bratkovskaya, E. L.

Kämpfer, Burkhard

Titov, A. I.

English

Qucosa – Hemholtz-Zentrum Dresden-Rossendorf

FORSCHUNGSZENTRUM ROSSENDORF e.v. FZR FZR Preprint 92 - 04 September 1992 B. Kampfer, A.1. Titov, E.L. Bratkovskaya Estimat es of dielectron production in pp and pd reactions at 1 - 2 GeV Estimates of dielectron production in pp and pd reactions at 1 - 2 GeV B. Kämpfer1, A.I. Titov2 Forschungszentrum Rossendorf, Institut für Kern- und Hadronenphysik, 0-8051 Dresden, PF 19, Germany E.L. Bratkovskaya Far Eastern State University, Vladivostok, Russia Abstract: Estimates of elementary Cross sections for dielectron prsduction in pN and pd reactions are presented. We use the vector dominance model for a11 hadron-hadrsn- photon vertices. Dynamical suppression mechanisms (off-shdl behavior of two-body T- matrix, mass dependent A production rate) bring the elementary rate near to previoua estimates which did not use vector meson dominance. Hswever, near t s  p mass a characteristic shoulder appears in our approach. We consider A, 7 BaPitz decays and bremsstrahlung at 1- 2 GeV as dominant sourees of dielectrsns. At higher energies the bremsstrahlung contribution is only a subclass sf direct vecitsr meson decays. Relying on a realistic deuteron wave function we predict the ratio s f  dielectron production in pd to pp reactions 'ako: Institute for ThesreticaP Physics (KAI e.V.1, Technical Unniversity, o\Iomrrnsenstr. 13, anY JINZE Dubna, Lab. 'IYneoe. Phys., 16PIOOO hI<-~scow, Plead Post P.0.13. 79, Rusaia 1. Introduction Dielectrons represent one of the promising Signals [I] which can probe directly dense and hot nuclear matter produced in heavy-ion collisions at intermediate energies. The electron pairs are created in various elementary reactions of hadrons. The reliable des,cription of these elementary reaction channels serve as input in theoretical models and event generators for simulating heavy-ion collisions [2,3,4, 5, 61. Such simulations are needed to unfold dielectron spectra and to get the wanted Signal of compressed and heatted nuclear matter. There are several calculations of the elementary production mechanisms of dielec- trons in pN reactions [2, 3, 4, 5, 6, 7, 81. The corresponding available experimental data [9] is yet rare and with low statistics. New data with high statistics is expected in near future. Then the theoretical estimates can be tested, since they depend on some model parameters, which are difficult to fix without experimental data. In particular the off-shell behavior of the strong interaction part is probed in a wider kinematical regime than in case of real photon bremsstrahlung or elastic scattering. The aim of the present note is to re-estimate dielectron production cross sections in dementary nucleon-nucleon subprocesses and apply them in pp and pd reactions at 1 anid 2 GeV. These reactions and energies serve just as the needed input for theoret- ical models of heavy-ion collisions at Bevalac and CIS energies. We rely here on the vector dominante model (VDM), which has been proven as useful guding principle for hadron-photon interactions [10]. The VDM form factor has been implemented, e-g., in Ref. [3] within a traditional approach. However, a strong overestimate of the rate near p mass has been found, and consequently VDM has been-disregarded. Here we present a. catreful improvement of the underlying microscopy and find indeed reasonable results within VDM. 2. Elementary processes At energies considered and for invariant dielectron mass M 5 1 GeV, we include A, 7 alitz decays and bremsstrahlung as main contributions [ll]. Their gross features are described as follows. (Detailed formlae are too complex to display here. They will be pubJished elsewhere.) Dalitz decays IVe use a folding of tbe t integrated A production cross section anrnT+allr(s7 Ma) = dt with A psopagator squared, D, gsing into the A decay vertex which is described Ea turn by total width Fa(m&) and differential width d I ' A ' e - e ' / d ~ ~  [3, 41. The final expression for dielectron cross section via A Dalitz decays reads (s and t are the Mandelstam variables). Observe the MA dependence of the A produc- tion cross section which is usullay not included. It follows directly within a one-boson exchange model. Our cross section a~N,aw is normalized so that the total A pro- duction cross section [12] is reproduced. The one-pion exchange model parameters are fitted to the experimental angular distribution d ~ ~ ~ + ~ ~ / d t  of .A's. In the AN7 vertex [13] we include the electromagnetic form factor from VDM 2.2 77 Dalitz decays The contribution of 17 Dalitz decay takes the form We calculate the 71 production cross section C,, in pN reactions as in Ref. [14]. When calculating the 7 production in pd scattering we use a realistic deuteron wave function S>d obtained within the Paris potential model [15] where P' is the relative nucleon momentum in the deuteron, and R denotes the flux factor. The internal nucleon motion in the deuteron is important near and below the 77 threshold. We also include short range correlations which describe simultaneous interaction sf the proton with a correlated two-nucleon cluster in the deuteron wave function with a 5% probability as in Ref. [16]. 2.3 Bremsstrahlung The bremsstrablung contribution in pp collisions is strongly suppressed beeause of destructive interference of exchange diagrams [Y]. In Refs. &7, S] the bremsstrahlun was estimated by diagrammatic caiculation within a one-boson exchan without VDM form factor. It was found that tbe result depends an the ttw-bsdy T- matrix parameters which cannot be fixed only by fitting pn eiastic scattering. To avoid these uncertainties we use here a model which resembles the soft-photon approximation, however, we use exact kinematical relations. The net result reads and P'" = - 8(gfiv q2 - qfiqU) as projector, and daab'alb'/dt denotes the elastic ab -t a'b' scattering cross section. The factor g;(&) with & = (P; - a;q)2/mS controls the off-shell corrections. In the one-boson exchange model g; corresponds to an additional off-shell dependence of the nucleon-nucleon-boson vertex. We use a simple symmetric ansatz for g(t), namely g(t)  = K ((1 - E)2 + X ) - ' .  The parameter x = 6 is found by a fit of the electromagnetic form factor which was calculated in a relativistic oscillator quark model of baryons [17]. I For the pd interaction we assume that both pn and pp bremsstrahlung contribute. Due to the deuteron wave function the usual destructive exchange interference, which suppresses the pp contribution, is not operative here. Details of the lengthy derivation will be given elsewhere. This effect is to be included also in A and 7 production. 3. Results In Figs. 1 and 2 we display our results. For orientation we also display in Fig. 1 the results of the DLS collaboration (11 for p 'Be interaction (scaled by a factor A;;?), which can be considered as dilepton production in p - isoscalar nucleon interaction. (Please note that we do not apply the experimental filter which is important below 250 MeV.) In calculating the A Dalitz decay in pd reactions we also take into account the internal motion of nucleons in the deuteron as in eq. (4). The integrations in eqs. (1, 3 , 4 )  are performed with a Monte Carlo method. At 1 GeV we find the bremsstrahlung contribution nearly as strong as the A Dalitz decay. There is no significant contribution of the 7 decay. To check this point we also employ the 7 production cross section from Ref. [I$] and do not find noticeable changes. Subthreshold effects are responsible for the larger invariant mass tails of the A and bremsstrahlung contributions in pd reactions. The vector dominance effects (i.e., the form factor) are not important; off- shelP effects also not. Contrary, at 2.1 GeV these latter effects are important. However, the strong en- hancement of the brenasstrahlung cofitribution at the p peak is reduced by strong ofi-shell effects. The net reault is a sho&&r in the sum of all contributions. This is not so clearPy seen in pp reactions due t s  the kinematical lirnit. However in pd reactions, due to subt hreshold effects it can be observed. Our net results are in the order of mag- nitude as those obtained in Ref. [3], but in Ref. [3] there is not the shoulder behavior in the p region. Note that at higher energies (not displayed here) at p position even a peak appears. In the low-mass region the q contribution dominates at 2.1 GeV and above. The ratio (See Fig. 2) shows an energy dependence which is in agreement with preliminary data [9]. Most significant is the levelling-off due to the subthreshold production at kinematic limits. Our calculations predict that R increases with decreasing energy because of in- creasing importance of bremsstrahlung at lower energies. At energies above 2.1 GeV more processes must be considered. In particular, direct vector meson decays must be included (cf. [5, 111 for some estimates) which introduce considerable more complex- ity. Double counting problems become important, because bremsstrahlung with form factor represents only a subclass of other processes. 4. Summary In Summary we re-estimate the dielectron production in pp and pd reactions at 1 and 2.1 GeV. We base our calculations on the VDM and find gosd agreement with avail- able data when considering A, Dalitz decays and bremsstrahlung with appropriate off-shell effects in the two-body T-matrix and mass dependent A production. The model for the off-shell T-matrix used here can be checked in independent prsceasea, e.g., by real photon bremsstrahlung. Work in this line is in Progress. Acknowledgements: Useful discussions with W. Cassing, B. Frirnan, U. Mosel, V.D. Toneev, and G. Wolf are acknowledged. We thank A. MolockPiov for assistance in cdcdat-  ing the A production. A.I.T. wish to thank the nuclear theory greup in Research Center Rossendorf for the warm hospitalitity. This work is supported by BMFT under grant No. DR 107. References [I] G. Roche et al., Phys. Rev. Lett., 62 (1989) 2652, Phys. Lett. 226B (1989) 228 [2] C. Gale, J. Kapusta, Phys. Rev. C35 (1987) 2107, C40 (1989) 2397 [3] G. Wolf, G. Batko, W. Cassing, U. Mosel, K. Niita, M. Schäfer, Nucl. Phys. A517 (1990) 615 [4] L. Xiong, Z.G. Wu, C.M. Ko, J.Q. Wu, Nucl. Phys. A512 (199Q) 772 151 K.K. Gudima, V.D. Toneev, A.I. Titov, Phys. Lett. B287 (1992) 302 [6] A. Winkelmann, Proc. Third Workshop on a Dilepton/Real Photon program at SIS, Rauischholzhausen, Nov. 21 - 22, 1991, p, 253 [7] K. Haglin, J. Kapusta, C. Gale, Phys. Lett. 224B (1989) 433 K. Haglin, Ann. Phys. (N.Y.) 212 (1991) 84 [SI M. Schäfer, T.S. Biro, W. Cassing, U. Mosel, Phys. Lett. 221B (1989) 1 [9] G. Roche, preprint PCCF RI 9208, B. Pascal University Clermont-Ferrand L.S. Schroeder, Nucl. Phys. A538 (1992) 177c [lO] J.J. Sakurai, Currents and Mesons, University of Chicago Press 1969 [ll] B. Kämpfer, A.I. Titov, V.D. Toneev, preprint ZFK-753 (1991) [12] B.J. VerWest, R.A. Arndt, Phys. Rev. C25 (1982) 1979 1131 H.F. Jones, M.D. Scadron, Ann. Phys. 81 (1973) 1 1141 T. Vetter, A. Engel, T. Biro. U. MoseP, Phys. Lett. B263 (1091) 153 [l5] M. Lacombe et al., Phys. Rev. C21 (1980) 861 [16] V.V. Burov et aP., L. Phys. A306 (1982) 149 [If] E.L. Bratkovskaya, A.I. Titov, B. Resnik, preprint Dubna JINR, P2-92-151 (1992) [IS] J.M. Laget, F. Wellers, J.F. Lecolley, Phys. Lett. B257 (1991) 254 Fig. 2: Tbe ratio (6) as function of the invariant dielectron mass for different energes. The preiiminary experimental data for 4.9 GeV (dots) are from Ref. 191. 

Estimates of dielectron production in pp and pd reactions at 1 - 2 GeV

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Estimates of dielectron production in pp and pd reactions at 1 - 2 GeV

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