nucleus−nucleus
0.15 nucleon−nucleon
0.1
0.05
0 protons M3
−0.05 Ca+Au
−0.1
−0.15
Au+Ca
−1
−0.5
0
0.5
1 Y
0
Figure 1: Mean transverse momentum of protons projected into the reaction plane as function of scaled rapidity. The data from non-central collisions (multiplicity bin M3) shown in Fig. 1 appear to cross the zero line in between the values of rapidity indicated by the vertical lines, which means that there is a sizeable interaction of the reaction zone with the nominal spectators. The symmetry
4
Warsaw University - for the FOPI collaboration
condition between the two reaction kinematics with respect to the point of origin is fulfilled satisfactorily. Squeeze-out is investigated by analyzing the complete azimuthal distributions of the emitted particles. As an example, Fig. 2 shows the azimuthal angular distributions for protons from semicentral collisions (M4). These distributions are fitted with a Fourier function up to second order. The emission perpendicular to the reaction plane is measured by the expansion coefficient v2 . A rapidity window of 0.3Y 0 around the effective c.o.m. rapidity is selected, where the effective c.o.m. rapidity is taken from the sidewards flow analysis, the lower limit in p⊥ /m is 0.4. The vertical lines indicate an angle of ±90◦ relative to the reaction plane. protons, semicentral collisions
dN/d φ
1
4500
7000
4000
6000
3500 Ca+Au
0
−100
Au+Ca
0
100
0 φ [°]
−100
0
100
φ [°]
Figure 2: Azimuthal angular distributions of protons at effective c.o.m. rapidity. The distributions in Fig. 2 show a clear squeeze-out signal at ±90◦ . The distributions still have a sizeable v1 component which reflects the different collision geometries. The spectator nucleons are distributed quite asymmetrically around the azimuth. At effective c.o.m. rapidity the yield in Ca+Au has its maximum at 0◦ and becomes minimal at ±180◦, where the symmetric collision shows the maximum at ±90◦ and equal yields at 0 and ±180◦ [3, 1]. By varying the position of the rapidity window a situation with a vanishing v1 is found. Note that for the asymmetric systems the magnitude of v2 is larger than in the symmetric reaction Au+Au [3], which points also to a spectator contribution rather than to a pure expansion effect. Comparing the results with the microscopic transport calculation IQMD [4], the model gives a somewhat larger signal if it is used with its standard parameters. As the following table shows, the data prefer a nuclear equation of state with smaller compression module (soft EOS). The sum of protons, deuterons and tritons is less affected by the model problems concerning the clusterization (the model gives a smaller number of fragments) and therefore is used for quantitative comparisions.
particles protons p,d,t
v2 (data) -0.096±0.011 -0.128±0.010
IQMD (hard) -0.151±0.009 -0.154±0.009
IQMD (soft) -0.129±0.008 -0.134±0.008
- 53 2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2
10
3
10
2
10
Au+Ca
10
3
10
2
of the filter which takes into account the acceptance of the detector (dashed line). In the Ca+Au case the acceptance is more complete than in the Au+Ca case. The general tendency of the model to overpredict the proton yield is obvious. To derive quantitative information on the degree of stopping the nucleon-nucleon cross section is varied in the calculation. The standard value is the free one (as used in Fig 4), to simulate a larger stopping power the cross section is artificially increased (doubled), for a smaller stopping power it is decreased, respectively. A completely stopped scenario is reached when the shape of the rapidity distribution does not change any more even if the nucleon-nucleon cross section is increased further.
10 protons+deuterons+tritons, central collisions
-1.5
-1
-0.5
0
0.5
1
1.5
2
0
-2
0
Z=1 p⊥/m(Y )
Figure 3: Phase space distributions of Z = 1 particles.
dN/N ev dY
1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0
Ca+Au
20
Ca+Au
17.5 data
15
Nuclear Stopping
2σ
free NN
Rapidity distributions of asymmetric reactions reveal an unambigous signal of the degree of stopping. The phase space distributions for the two kinematics are shown in Fig. 3. The fact that one distribution is not a perfect mirror image of the other is due to the detector acceptance and slightly different efficiencies. The different phase space populations in the asymmetric collisions can easily be seen, the lines show constant c.o.m.-energies in the N N -system. Thus, the rapidity distributions are less difficult to interprete compared to symmetric reactions where a longitudinal expansion scenario cannot be ruled out.
12.5 IQMD
0.5 σ
10 σ
7.5
free NN
free NN
5 2.5 0
protons (central collisions)
−2
−1.5
−1
−0.5
0
0.5
1
1.5 Y
0
dN/N ev dY
2
12
IQMD hm IQMD hm + filter Data
10 8 6 4
Figure 5: p,d,t rapidity distributions, data and transport calculation
Ca+Au
2
IQMD hm IQMD hm + filter Data
10 8 6 4
Au+Ca
2 0
−2
−1.5
−1
−0.5
0
0.5
1
0
1.5
2 Y
In Fig. 5 the comparison of the rapidity distributions is shown for protons, deuterons and tritons from central Ca+Au collisions. The data are not described by the plotted model calculations. The free nucleon-nucleon cross section (full line) still overestimates the degree of stopping, and the doubled cross section (dashed line) can be ruled out. Hence, the data do not show a complete stopping of the projectile nucleus, they rather describe a partially transparent scenario. In a continuation of these experiments the FOPI collaboration has investigated in 2003 the system 58 Ni and 208 Pb at 400A, 800A and 1160A MeV, again in normal and inverse kinematics.
0
Figure 4: Proton rapidity distributions for central events. Fig. 4 shows the rapidity distributions for central collisions (M5, corresponding to 2% of the reaction cross section) in the two kinematics. The prediction of the IQMD calculation (full line) is shown, and also the effect
References [1] [2] [3] [4]
Hartmann, O., Dissertation, TU Darmstadt 2003 Eskola, K.J., Nucl. Phys. B 323 (1989) 37 Kreß, T., Dissertation, TU Darmstadt 2002 Hartnack, C., EPJ A1 (1998) 151
- 54 -
Excitation function of elliptic flow in Au+Au collisions A. Andronic1 , Y.-J. Kim1 , M. Kirejczyk1 , T. Kress1 , P. Koczon1 , Y. Leifels1 , O.N. Hartmann1 , N. Herrmann2 , K.D. Hildenbrand1 , W. Reisdorf1 , A. Sch¨ uttauf1 , Z. Tyminski1 , Z.-G. Xiao1 (for the FOPI Collaboration) 1 GSI Darmstadt, 2 Universit¨ at Heidelberg
0.1
M2 M3 M4
0.05
energy of 0.4 AGeV, which is more pronounced towards more peripheral collisions, followed by a decrease towards larger energies. This behaviour is a complex interplay between the magnitude of the fireball expansion (determined in turn by the equation of state, but also by stopping) and spectator shadowing. Comparisons with transport models will establish the importance of these data in the long quest for unraveling the nuclear EoS. The v2 pattern is very similar to that of observables related to directed flow and stopping in the same energy range, recently completed by our collaboration [2]. The excitation function shows subtle differences in case (0) of high-pt particles (Fig. 1, lower panel), which may originate from their different participation in the expansion.
v2
v2
We present a complete excitation function of elliptic flow in Au+Au collisions at beam energies from 0.09 to 1.49·A GeV, measured with the FOPI detector. To characterize the elliptic flow we study the second order Fourier coefficient v2 = cos(2φ), where φ is the angle with respect to the reaction plane. The results are for midrapidity (|y (0) | < 0.1), which can be covered at all beam energies for particles identified in Z or for light particles (0) selected by mass (A) with the momentum cut pt > 0.8 (0) (0) (pt = (pt /A)/(pcm = (y/yP )cm , where the subP /AP ), y script P denotes the projectile).
(0)
Au+Au M3 |y | 0.8
0
-0.05
-0.1
-0.1
10
-1
1
10
10
2
Ebeam /A (GeV)
-0.2
10
-1
1
Figure 2: Excitation function of the elliptic flow for the M3 centrality bin. The FOPI data are compared to all existing measurements at fixed target experiments (protons).
Ebeam /A (GeV) Figure 1: Excitation function of elliptic flow for three centrality bins. Upper panel: Z=1 particles, integrated for all momentum values. Lower panel: particles with A≤4 (0) weighted with their mass, for pt > 0.8. In Fig. 1 we present the v2 excitation function for three centrality bins, M2, M3 and M4, corresponding in a geometrical approximation to impact parameter ranges 7.510.0, 5.5-7.5, and 2-5.5 fm, respectively. The elliptic flow shows a transition from in-plane (v2 > 0) to out-of-plane (v2 < 0, also called squeeze-out) at low energies, which depends on centrality. This transition was already studied by our collaboration in great detail [1]. For data inte(0) grated on pt , a maximum of v2 is seen around the beam
In Fig. 2 we present a compilation of the elliptic flow values measured up to SPS energy. FOPI data for Z=1 particles in the M3 centrality bin are compared to values for protons measured by the experiments E895 [3], E877 [4], and CERES [5]. FOPI data for protons integrated on pt are included for energies above 0.4 AGeV.
References [1] [2] [3] [4]
A. Andronic et al., Nucl. Phys. A 679 (2001) 765. W. Reisdorf et al., submitted to PRL. C. Pinkenburg et al., Phys. Rev. Lett. 83 (1999) 1295. P. Braun-Munzinger and J. Stachel, Nucl. Phys. A6383 (1998) 3c. [5] K. Filimonov, nucl-ex/0109017.
- 55 -
Nuclear Collective Flow from the Method of Lee-Yang Zeroes N. Bastid1 , V. Barret1 , P. Crochet1 , P. Dupieux1 , X. Lopez1 , N. Borghini2 , J.Y. Ollitrault2 , and FOPI Collaboration LPC Clermont-Ferrand, France;
CEA-Saclay, France
tion that, like at SPS and RHIC energies [3, 4] for elliptic flow, the four-particle correlation analyses can reliably separate flow and non-flow effects. Similar conclusions are also valid for the proton elliptic flow. One can also mention that statistical errors, which are the main limitation of the method, are not a problem here: the resolution parameter χ, measuring the relative strength of flow compared to finite multiplicity fluctuations, is well above one (χ = 1.7). The method of Lee-Yang zeroes will be applied to pion flow studies. It should provide more reliable results than standard methods by eliminating correlations, like the decay of ∆ resonances which is a typical non-flow effect. |Gθ(ir)|
This report presents the first analysis of collective flow with the new method of Lee-Yang zeroes [1]. So far in the SIS energy range all directed and elliptic flow analyses were performed using standard procedures. In these methods, based either on the reaction plane reconstruction or on two-particle correlations one assumes that correlations between particles are only due to flow. This shortcoming motivated the development of alternative procedures where other correlations due to quantum statistics, resonance decays, final state interactions,... are not neglected. The method based on a cumulant expansion of multiparticle (typically, four-particle) correlations [2] eliminates most of non-flow effects. It is intensively exploited at SPS and RHIC energies [3, 4] and the results differ significantly from those obtained with conventional methods, showing the importance of non-flow effects. More recently, the theory of Lee-Yang zeroes [1] has been proposed to extract for the first time the genuine flow directly from the correlation between a large number of particles. This latter is expected to provide the cleanest separation between collective flow and non-flow effects. Here both the cumulant method (applied for the first time at SIS energies) and Lee-Yang zeroes are used to extract flow in semi-central (< bgeo > = 3.8 fm) Ru + Ru reactions at 1.69 AGeV measured with the FOPI detector at GSI. The theory of Lee-Yang zeroes, applied for the first time to experimental data, is explained in the following. The procedure is based on the projection of the event flow vector on a fixed, arbitrary direction under an angle nθ relative to the x-axis. This projection is Qθ = M j=1 ωj cos(n(ϕj − θ)) (ωj is a weight to optimize the statistical errors, n is the Fourier harmonic, ϕj is the azimuthal angle). The probability distribution of Qθ is fully characterized by the moθ ment generating function Gθ (z) = < ezQ >, with z = ir. Figure 1 displays the amplitude of Gθ (ir) versus r for θ = 0 and n = 1 (results are comparable for other θ values). One clearly observes two minima which correspond to the zeroes of Gθ (ir). This is a clear indication of collective flow effects in this system [1]. Furthermore, the position of the first minimum, rθ0 , directly yields an estimate for the integrated directed flow, v1θ (rθ0 scales as 1/v1θ ) used afterwards to analyze differential flow. In practice one performs the analysis for several equally spaced values of θ and the results are averaged over θ. The proton differential directed flow calculated with the Lee-Yang theory (circles) is shown in Fig. 2. The values are compared to the ones obtained from the standard flow analysis (squares). Also shown are the two (stars) and fourth (crosses) particle cumulant values. The (small) differences between the standard method and the second order cumulant could be partially explained by momentum conservation effects not taken into account with twoparticle cumulant. The Lee-Yang zeroes and the fourth order cumulant give same values for v1 . This is an indica-
2
1
θ=0 n=1
0.8
0.6
0.4
0.2
0
0
0.1
0.2
0.3
0.4
0.5
r
Figure 1: |Gθ (ir)| versus r for semi-central Ru (1.69 AGeV) + Ru reactions. v1
1
-0.1
(0)
y from -1.25 to -0.65 Protons
-0.15 Standard method Cumulants 2nd order Cumulants 4th order Lee-Yang zeroes
-0.2 -0.25 -0.3 -0.35 -0.4 -0.45
0
0.2
0.4
0.6
0.8
1
1.2
Pt (GeV/c)
Figure 2: Proton differential directed flow in semi-central Ru (1.69 AGeV) + Ru reactions in a rapidity window of backward hemisphere.
References [1] R.S. Bhalerao et al., Nucl. Phys. A 727 (2003) 373 and Phys. Lett. B 580 (2004) 157; N. Borghini et al., nucl-th/0402053 (2004) [2] N. Borghini et al., Phys. Rev. C 64 (2001) 054901 [3] C. Alt et al., Phys. Rev. C 68 (2003) 034903 [4] C. Adler et al., Phys. Rev. C 66 (2002) 034904
- 56 -
Azimuthal emission pattern of K+ and of K− in Heavy Ion Collisions at SIS energies F.Uhlig1 , A.F¨orster1 , I.B¨ottcher4 , E.Grosse6,7 , P.Koczo´ n2 , B.Kohlmeyer4 , S.Lang1 , M.Menzel4 , L.Naumann6 , H.Oeschler1 , M.Plosko´ n2 , W.Scheinast6 , A.Schmah1 , T.Schuck3 , E.Schwab2 , P.Senger2 , 3 Y.Shin , H.Str¨obele3 , C.Sturm1 , A.Wagner6 , and W.Walu´s5 TU Darmstadt;
2
GSI;
3
Univ. Frankfurt;
4
Univ. Marburg;
Relativistic heavy ion collisions provide a unique opportunity to study both the behavior of nuclear matter at high densities as well as the properties of hadrons within this dense nuclear medium. In particullar strange mesons are considered to be sensitive to these in-medium effects. The behavior of K + and K − is expected to be different due to two characteristic properties: (i) Their interaction with nuclear matter: K + are hardly absorbed in nuclear matter due to strangeness conservation. They contain an s¯-quark and the probability that a K + encounters a Λ or Σ is negligible. K − on the contrary, can easily be absorbed on a nucleon converting it into a Λ or Σ and a pion. Consequently, the propagation of K + and of K − in nuclear matter is very different and should lead to different emission patterns for K + and for K − . The strangeness-exchange channel (πY ↔ K − N, Y = Λ, Σ) can cause the absorption of K − as well as an enhanced K − production as suggested in [1, 2] and found in [3, 4]. (ii) K + and K − experience different potentials in nuclear matter: While the scalar potential acts attractively on both kaon species, the vector potential repels K + and attracts K − . For K + these two contributions mainly cancel each other leading to a small repulsive K + N interaction. The superposition of both attractive interactions results in an strong attractive potential for K − [5]. Our goal is to study the azimuthal distributions of K + and K − in nucleus nucleus collisions which are expected to be a sensitive observable for in-medium properties. Indeed, the azimuthal distribution of K + and K − turn out to be very different. For K + we have already reported an unexpected out-of-plane enhancement in Au+Au collisions at 1.0 A·GeV [6]. This result is confirmed by new measurements presented here. In addition we show first data on the azimuthal distribution of K − . Two new measurements have been performed with the KaoS spectrometer: Ni+Ni at 1.93 A·GeV(both for K + and for K − ) and Au+Au at 1.5 A·GeV(K + only). For comparison also the emission patterns of π + are presented. The measurements were performed using an Au beam of 1.5 A·GeV impinging on an Au target (0.96 g/cm2 ) and a Ni beam of 1.93 A·GeV on a Ni target (0.68 g/cm2 ). The phase-space coverage is shown in Fig. 1 for K + in Au+Au reactions at 1.5 A·GeV. The particles were identified using the magnetic spectrometer KaoS and two hodoscopes were used for event characterization [7, 8]. The orientation of the event plane was reconstructed from the azimuthal emission angle of the charged projectile spectators with the transverse momentum method [9]. These particles were identified (up to Z = 8) by their energy loss and their time of flight as measured with the small-angle hodoscope which is about 7 m
5
6
Univ. Cracow;
pt [GeV/c]
1
1
K+
FZ Rossendorf;
60
o
0.8
72
o
40
o
32
0.6
TU Dresden
Au+Au, 1.5 AGeV 48
o
7
o
0.4 0.2 0
0
0.2 0.4 0.6 0.8
1
y/ybeam Figure 1: Phase-space coverage of K + for the measurements of Au+Au reactions at 1.5 A·GeV. Shown are the different laboratory angles measured.
downstream from the target covering polar angles between 0.5◦ and 11◦ . Figure 2 shows the azimuthal distribution of K + and + π for semi-central Au+Au collisions at 1.5 A·GeV. The distribution is corrected for the angular resolution of the reaction plane determination [8], which is ∆Φ2 1/2 = 37◦ for the Au-system and ∆Φ2 1/2 = 61◦ for the Ni-system. The data are fitted using the function dN ∼ 2 v1 cos(φ) + 2 v2 cos(2φ) dΦ
(1)
resulting in values for v1 and v2 , as given in the figures. The coefficent v1 is subject to a systematical error of 0.04. Both π + and K + exhibit a pronounced out-of-plane enhancement. For π + this can easily be interpreted as rescattering and absorption in agreement with previous observations [8]. This explanation cannot hold easily for K + as their mean free path is rather long and one might expect only a moderate out-of-plane enhancement [10]. This experimental result is rather suggestive for a repulsive inmedium K + N interaction [10, 11]. The study of Ni+Ni collisions has been performed at a higher incident energy of 1.93 A·GeV. The resulting higher production cross section for K − provides an opportunity to study both kaon species. The data are shown in Fig. 3 along with π + for semi-central Ni+Ni collisions. Both π + and K + follow the same trend already observed in Au+Au collisions. The values for v2 are smaller than in Au+Au as one might expect for the smaller system. In contrast to the π + and K + , the K − show an in-plane enhancement. This “positive” (in-plane) elliptic flow of particles is observed for the first time in heavy-ion collisions at SIS energies. In contrast to this observation, one would expect
cor
π
+
(1/N dN/dφ)
(1/N dN/dφ)
cor
- 57 -
0.1
0.05
v1=0.01±0.01 v2=-0.15±0.01
π
0.1 0.05
v1=-0.02±0.01 v2=-0.04±0.01
0
0
+
K
+
K
0.1
0.1
0.05
+
0.05 v1=0.04±0.01 v2=-0.08±0.02
0 -90
o
0
o
v1=-0.01±0.01 v2=-0.04±0.02
0 90
-
K
o
φ
Figure 2: Azimuthal distribution of π + and K + for semicentral Au+Au collisions at 1.5 A·GeV. The data are corrected for the resolution of the reaction plane and correspond to impact parameters of 5.9 fm < b < 10.2 fm, rapidities of 0.3 < y/ybeam < 0.7 and momenta of 0.2 GeV/c < pt < 0.8 GeV/c. The lines are fits with function (1) resulting in the values for v1 and v2 as given in the figure.
a preferential out-of-plane emission (negative elliptic flow) of K − mesons due to their large absorption cross section in spectator matter. However, as shown recently, the K − are produced predominantly via strangeness-exchange reaction Λπ → K − N and consequently, the K − are emitted later than the K + which are produced together with the Λ. Therefore, the shadowing spectator might have moved away when the K − emission occurs which would lead to a flat azimuthal distribution. Nevertheless, a late emission of K − mesons cannot explain their elliptic in-plane flow pattern. Recent transport calculations find such an effect if an attractive in-medium K − potential is taken into account [12]. A quantitative comparison of our data to transport calculations is presently beeing performed. Recently, a new high-statistics measurement of the azimuthal distribution of K − in Au+Au collisions at 1.5 A·GeV has been performed. These data are presently beeing analyzed.
References [1] C. M. Ko, Phys. Lett. B 138 (1984) 361. [2] C. Hartnack, H. Oeschler and J. Aichelin, Phys. Rev. Lett. 90 (2003) 102302. [3] H. Oeschler, J. Phys. G 27 (2001) 1. [4] A. F¨ orster, F. Uhlig et al., (KaoS Collaboration), Phys. Rev. Lett. 91 (2003) 152301. [5] J. Schaffner et al., Nucl. Phys. A 625 (1997) 325.
0.1 0.05
v1=-0.02±0.02 v2=0.08±0.06
0 -90
o
o
0
90
o
φ
Figure 3: Azimuthal distribution of π + , K + and K − for semi-central Ni+Ni collisions at 1.93 A·GeV. The data are corrected for the resolution of the reaction plane and correspond to impact parameters of 3.8 fm< b < 6.5 fm, rapidities of 0.3 < y/ybeam < 0.7 and momenta of 0.2 GeV/c < pt < 0.8 GeV/c. The lines are fits with function (1) resulting in the values for v1 and v2 as given in the figure.
[6] Y. Shin et al., (KaoS Collaboration), Phys. Rev. Lett. 81 (1998) 1576. [7] P. Senger et al., (KaoS Collaboration), Nucl. Instr. Meth. A327 (1993) 393. [8] D. Brill et al., (KaoS Collaboration), Phys. Rev. Lett. 71 (1993) 336; D. Brill et al., (KaoS Collaboration), Z. Phys. A 355 (1996) 61; D. Brill et al., (KaoS Collaboration), Z. Phys. A 357 (1997) 207. [9] P.Danielewicz and G.Odyniec, Phys. Lett. 157B (1984) 147 [10] Li et al., Phys. Lett. B. 381 (1996) 17. [11] Z.S. Wang et al., Eur. Phys. J. A 5 (1999) 275. [12] A. Mishra et al., nucl-th/0402062
- 58 -
Hadron and Dielectron Production in C+C Collisions at 2 A·GeV The HADES collaboration 1
Introduction
In summer 2003 all components of the HADES spectrometer have been installed except for two of the 24 Multiwire Drift Chambers (MDC) delivery of which is scheduled for 2004/2005. In this configuration the tracking system of HADES is completed in four out of six HADES sectors and ready to perform high-resolution measurement with an anticipated ∆M/M = 1.5% mass resolution. Therefore a series of proton-proton experiments have been scheduled in fall of 2003 and beginning of 2004. The goal of these experiments is to establish high resolution tracking and to measure calibration reactions like pp elastic scattering, as well exclusive meson production channels i.e π 0 , η. The latter ones are extremely important for the full understanding of the HADES dielectron reconstruction efficiency and second level trigger performance. In September 2003 we have installed for the first time the LH2 target for proton and pion experiments. The target, first trigger settings and background situation were commissioned in October 2003. A maximum beam intensity of 2 × 107 protons/sec and trigger rates of 5kHz have been achieved. Careful design of the target area allowed to obtain a very good ratio of full/empty target trigger rates of 10 : 1. The production physics run took place in February 2004. In parallel the data obtained from C+C reaction at 2 A·GeV have been extensively studied. The recent two experimental runs in 2001 and 2002 with a total collected statistics of around 5 ∗ 107 (LVL1) and 20 ∗ 107 (56%LVL1 + 44% LVL2) events are analyzed. In the second run we used for the first time a second level trigger (LVL2) to select LVL1 events with electron candidate tracks. Selected preliminary results from these experiments are presented below.
2
Particle Production in C+C at 2 A·GeV
Particle identification in the HADES detector starts with track reconstruction in the Multiwire Drift Chambers (MDC). The inner MDC track segments are correlated with hits in the Time-of-Flight (TOF) wall and the PreShower placed behind the magnetic field to form particle trajectories (no MDIII/IV information was used in the analysis presented here). Particle momenta are derived from the measured deflection in the magnetic field. Particle identification in HADES is performed using a probabilistic approach. The basis of the method is a test of the hypothesis that the reconstructed track belongs to a certain type of particle (e.g., proton, charged pion, electron etc.). In the test the information from several measured variables and sub-detectors (i.e time of flight, energy deposition) is combined using probability density functions (PDF) that are determined by simulations for each variable and for all possible particle types. The particle identification (PID) probabilities are calculated taking into account the measured abundances of the different particles and the specific PDFs of measured variables. The identifi-
cation efficiency and selectivity achieved with this method is then evaluated in detailed simulations. Hadron identification is performed on the basis of momentum as measured by the magnetic deflection, the velocity and energy loss as measured by the TOF detector. For the lepton identification, data from the RICH (Ring Imaging Cherenkov) and the Pre-Shower detectors are used in addition.
: Left Correlation between velocity and signed(charge) momentum for all reconstructed tracks from C+C collisions at 2 A·GeV. Pion and proton branches are clearly resolved. Right: same as on the left but with the additional condition that an electron was identified. The intensity scale is logarithmic.
Figure 1:
The principle of the particle identification is illustrated in Figure 1. Particles with different mass fill different region in the velocity vs momentum distribution shown on the left hand side. The pronounced maxima correspond to positive/negative pions and protons. The analysis shows that pions can be separated from protons up to momenta of p < 1000M eV /c with purity better then 80%. Electron identification can be achieved only if the RICH electron condition is switched on, as shown on the right side of Figure 1. Detailed investigations of measured electron distributions and dedicated Monte Carlo simulations using the URQMD event generator, reveal that the residual contamination of hadronic background is less than 2% and the purity of electron reconstruction is around 90%. The remaining 10% is electron misidentification that can be attributed, in addition to the mentioned hadron contribution, to fake combinations of inner MDC track segments with the hits in the TOF/Shower detectors. This fake contribution is expected to be significantly reduced once the MDCIII/IV information is included in the analysis of the November 2002 data. Absolute proton and pion yields were extracted from the data. The correction factors accounting for the geometrical acceptance and the efficiency of detectors and the tracking method were obtained via simulations. As an example of our hadron analysis results we show on Figure 2 the transverse mass distribution of positively charged pions measured at midrapidity, dσ/dmt · 1/m2T . The solid
- 59 line shows a thermal fit with two slopes (T1 = 41 ± 3 and T2 = 87±3 MeV) which describe our data better than a fit with one component only. Similar conclusions can also be derived from the analysis of negative pion distributions, in agreement with previous data on pion production for the same system and similar energy [1]. The average number of participants in the events selected by the 1st level trigger (LVL1) was estimated from URQMD simulations to be Apart = 8.6. The preliminary pion yield per participant extrapolated to 4π is Np /Apart = 0.148±0.015, where Np /Apart is the average of the yields of positively and negatively charged pions. This value is in a good agreement with the previous result measured by the TAPS detector for neutral pions as 0.138 ± 0.014 [2].
larger than Θ > 9◦ . Furthermore, a powerful Close Pair Rejection (CPR) method [3] has been applied to identify and reject those leptons which originate from (close) pairs that produce only one ring, only one cluster in the inner MDCs and have only one associated hit in the downstream TOF/Pre-Shower detectors (because the second low energy partner of the pair is deflected out of the detection system). The CPR uses information from the inner MDC system, like cluster size and number of contributed wires, and allows for efficient rejection of pairs with very small opening angle.
Figure 2: : Transverse mass distribution of positively charged pions in C+C collisions at 2 A·GeV. The solid line is a thermal fit with the two slope parameters 41 and 84 MeV.
The yields and shapes of the momentum spectra of electrons and positrons (not shown) are very similar with average multiplicities of 2 ∗ 10−2 per LVL1 event. The measured spectra agree in shape with the ones obtained from simulation but their integral is by ∼ 25% lower. The simulation is based on URQMD events with realistic trigger conditions the particles of which are tracked through the HADES detectors leading to digitized raw data. These simulated events were then reconstructed by the standard analysis software chain. This finding and studies of single electron identification capabilities indicate that with the current analysis procedure the inefficiency amounts to 20%.
3
Dielectron Production in C+C at 2 A·GeV
From the identified electrons and positrons we have constructed unlike (e+ e− ) and like sign (e+ e+ , e− e− ) pairs. Most of these pairs are uncorrelated and due to leptons from (different) photon conversions (∼ 60%) and Dalitz decays of π 0 mesons (∼ 20%). For the further analysis we have used only pairs that contain lepton tracks producing well separated hits in all detectors with opening angles
Figure 3: Top: Dielectron invariant mass distribution and Combinatorial Background (CB), calculated as described in the text. The distributions have been normalized to the number of LVL1 events. Bottom: Signal-to-background ratio after CB subtraction. These distributions are preliminary and subject to further corrections due to detector inefficiencies.
In order to evaluate the combinatorial background NCB we have used like-sign pairs N++ , N−− and the formula NCB = 2 N++ ∗ N−− . Figure 3 (top) shows unlike sign invariant mass distributions together with the corresponding combinatorial background. The expected most dominant sources of dielectron signal pairs are π 0 , and to a much smaller extent, η Dalitz decays. We observe indeed that the dominant signal (with signal to background ratio of S/B ∼ 5) is in the invariant mass region up to 150 MeV/c2 . In the higher mass region we also observe a systematic excess of dielectron yield over the combinatorial background with an average S/B ∼ 1 : 3. The total pair statistics, after subtraction of combinatorial background
- 60 ment of exclusive π 0 and η production in pp scattering is scheduled for February 2004. Analysis of the high statistics C+C data set from Nov02 will provide insight into lepton identification.
4
Figure 4: : Measured (black squares) and simulated (red dots) dielectron invariant mass distributions after CB subtraction normalized to the average number of charged pions. The error bars indicate statistical uncertainty. The systematic errors in this early analysis stage are estimated to be around 40%. These distributions are preliminary and subject to further corrections due to detector inefficiencies.
Preliminary
Nov 2002 -4
dNe+edM[1/MeV]
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invariant mass (MeV/c )
Figure 5: Comparison of dielectron invariant mass distributions (CB subtracted) normalized to the number of LVL1 events (November 2001) and the LVL2 events (November 2002 data).These distributions are preliminary and subject to further corrections due to detector inefficiencies.
and analysis cuts described above, amounts to ∼ 2.5k. Figure 4 shows dielectron invariant mass distributions for data and simulation normalized to the average number of charged pions, 0.5(Nπ+ + Nπ− ), determined from the same data set. It can be seen that in the low mass region (π 0 Dalitz) simulation overestimate data by a factor of ∼ 2 but in higher mass region simulation and data agree rather well. A significant part of this discrepancy can be traced back to the already mentioned differences in the single electron yields. However, detailed studies of dielectron analysis show additional differences in reconstruction efficiencies for very close tracks that need further investigations. On the other hand, both the HADES measurement of charged pions and the neutral pion yields from TAPS indicate that URQMD overestimates pion production by 20 − 30% at this energy. In order to disentangle the different sources of the discrepancy (elementary cross sections and electron identification efficiency) a dedicated calibration measure-
Second level Trigger Performance
The HADES second level trigger was fully operational during the beam-time of November 2002 where C+C reactions were measured at 2 A·GeV. Events which contain at least one electron candidate, i.e. a correlation between a RICH ring and a hit in the Pre-Shower or TOF within a broad azimuthal window were positively triggered, with an event reduction by a factor 12. It has been estimated that higher reductions, up to a factor 20 are achievable without further loss of efficiency. A preliminary analysis of the collected data allows an estimation of the second level trigger performance. Due to a more restrictive implementation of the ring recognition algorithm, a single electron efficiency of 62% was calculated, while 84% efficiency was estimated for dielectrons with opening angle larger than 4◦ , and 92% for opening angle larger than 8◦ . No physical bias was introduced in the data, since agreement between electron and dielectron spectra for triggered and untriggered events is observed. In the triggered events an enhancement by a factor 7.5 is found in the electron yield, and by a factor 11 in the (lepton) pair yield, with respect to the untriggered ones. In Figure 5 the signal distributions after the combinatorial background subtraction are plotted for November 2001 and November 2002 data. The the former distributions (stars) is normalized to the number of LVL1 events. The dielectron invariant mass distribution obtained from the November 2002 data is normalized to the number of those events in which both electron candidates identified by the trigger can be associated to a a charged particle trajectory found in the MDCs (LVL3). Otherwise the analysis procedures were the same as explained above with exception of the CPR method (not applied) and a pair opening angle cut of Θ > 4◦ (note different dielectron production probabilities). The higher statistics (factor of 10) was achieved thanks to the second level trigger. It allows to investigate dielectron production up to and beyond the ρ, ω mass. This work has been supported by GA CR 2002/00/1668 and GA AS CR IAA1048304 (Czech Republic), KBN 5p03B 140 20 (Poland), BMBF (Germany), INFN (Italy), CNRS/N2P3 (France), MCYT FPA2000-2041-C02-02 and XUGA PGIDT02PXIC20605PN (Spain), INTAS.
References [1] A. Kugler et al., (HADES collaboration) Nucl.Phys. A734c(2004)78-81 and the contributions of P. Tlusty, R. Holzmann, and J. Otwinowski (for the HADES collaboration) in Proceedings of the XLII International Winter Meeting on Nuclear Physics, Bormio, Italy, 2004, to be published. [2] R. Averbeck PRC 68,024903(2003) [3] J. Bielcik Phd Thesis, Darmstadt; T. Eberl Phd Thesis, M¨ unchen; J. Otwinowski Phd Thesis, Cracow.
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Two pion correlations in central Pb+Pb collisions at SPS energies C.Alt1 , C. Blume1 , P. Dinkelaker1 , D. Flierl1 , V. Friese2 , M. Ga´zdzicki1 , S.Kniege1 , I. Kraus2 , M. Kliemant1 , B. Lungwitz1 , C. Meurer2 , M. Mitrovski1 , R. Renford1 , A. Richard1 , A. Sandoval2 , R. Stock1 , H. Str¨obele1 Fachbereich Physik der Universit¨ at Frankfurt
References [1] R. Hanburry Brown and R.Q. Twiss, Nature 177, (1956) 27 [2] U. Heinz and U. Wiedemann, Phys. Rep. 319, (1999) 145
2
E895
GSI Darmstadt
E866
NA49
STAR
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Rout [fm]
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10 s NN [GeV]
Figure 1: From AGS to RHIC: Energy dependence of HBT parameters in central heavy ion collisions in the central rapidity bin at kt ∼ 0.15GeV /c.
20 AGeV
160 AGeV
8
Rout [fm]
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Rside [fm]
Momenta of identical particles produced in heavy ion collisions are correlated due to basic principles of quantum theory. Especially, an interference pattern in the pair production probability for identical bosons is found. The observed enhancement of the correlation function at low relative momenta is referred to as Bose Einstein enhancement and originates from this interference. The width of the Bose Einstein peak is correlated with the spatial distribution of the emission points of the particles. Hence it is possible to derive information about the space time structure of the particle source by measuring the correlation function. After the pioneering work of Hanbury Brown and Twiss [1] the technique is often called HBT and the widths of the correlation function are often referred to as HBT radii. The momentum difference is usually decomposed in ’out’, ’side’ and ’long’ directions, where qlong corresponds to the momentum difference along the beam [2]. qout and qside are measured in the transverse plane and correspond to the momentum difference parallel and perpendicular to the transverse momentum of the pair. A fit to the 3 dimensional correlation function thus yields values for the the parameters Rout , Rside and Rlong . Hydrodynamical inspired models show that an expanding particle source causes the HBT radii to depend on the transverse momentum kt of the particle pair [2]. Therefore, the parameters are usually determined in bins of kt in order to quantify the strength of the collective motion. The energy scan programme at CERN SPS allowed the NA49 collaboration to measure the HBT parameters at 20, 30, 40, 80, and 160 AGeV beam energy. In figure 1 the HBT parameters are shown as function of the center of mass energy of central heavy ion collisions. From the lowest AGS energies to the top RHIC energy and at all SPS energies the radii change only very little. Compared to the strong change in other observables - the number of particles per unit of rapidity grows two orders of magnitude the saturation of the HBT radii is rather astonishing. Since the initial energy density is higher at higher beam energies one would expect a stronger expansion. But also the kt dependence of the HBT radii varies only little with energy. Figure 2 shows the kt dependence for 20 and 160 AGeV. Currently there is no satisfying explanation for this observation, but ongoing discussion about the theoretical fundations of HBT and measurements at even higher energies at the LHC might help to solve this puzzle.
4 2 8 6
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Figure 2: kt dependence in central Pb+Pb collisions at 20 and 160 AGeV measured by the NA49 experiment.
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Multistrange Particles in Nuclear Collisions at SPS energies C. Alt1 , L. Betev1 , C. Blume1,2 , R. Bramm1 , P. Bunˇci´c1 , P. Dinkelaker1 , D. Flierl1 , V. Friese2 , M. Ga´zdzicki1 , S. Kniege1 , M. Kliemant1 , I. Kraus2 , B. Lungwitz1 , C. Meurer2 , M. Mitrovski1 , R. Renfordt1 , A. Richard1 , A. Sandoval2 , R. Stock1 , H. Str¨obele1 , and A. Wetzler1 1
Universit¨ at Frankfurt;
2
Ξ-
40 AGeV
+
Ω -+Ω (x4)
GSI Darmstadt
factors and systematic error estimates. Preliminary rapidity spectra of Ξ− and Ω− are presented in Figs. 1 and 2. At the lower energy the sum of Ω− ¯ + is shown. Filled symbols denote measured points and Ω and open ones are reflected at midrapidity. The rapidity spectra of Ω at both energies and of Ξ− at 40 A·GeV are parametrised by Gaussians as indicated by the full lines. The spectrum of Ξs at 158 A·GeV is parametrised by the sum of two Gaussians displaced symmetrically with respect to midrapidity. We observe an increase of the width of the rapidity distributions with beam energy for Ξs (FWHM from 2.3 to 2.5) and Ωs (FWHM from 1.4 to 2.5). But we see no indication for a change of the shape. The measured rapidity spectra have been integrated to obtain the mean multiplicities in full phase space. For Ξ we observe < Ξ− >= 2.41 ± 0.15 at 40 A·GeV and 4.12 ± 0.2 at 158 ¯ + >= 0.20 ± 0.03 are found A·GeV. For Omegas < Ω− + Ω − at 40 A·GeV and for < Ω > 0.47±0.07 at 158 A·GeV (errors are statistical only; systematic errors are of the order of 10%).
dN/dy
dN/dy
The NA49 collaboration has taken high statistics data of Pb+Pb collisions at the CERN SPS in the energy range from 20 to 158 A·GeV. This contribution covers the production of the multistrange baryons Ξ and Ω at 40 and 158 A·GeV[1, 2]. Identification of these multistrange baryons proceeds via their weak decays into a Λ hyperon and a negatively charged pion (kaon) for the Ξ− (Ω− ). In a first step the characteristic V0 topology of the Λ-decay into proton and π − is searched for. The momentum vector of the resulting Λ-candidates is derived from those of the assumed decay particles. The straight trajectory of Λ-candidates is paired with all negatively charged particles to locate the Ξ− or Ω− decay vertex. For anti-particles the oppositely charged particles are used. Combinatorial background is reduced by geometrical cuts and particle mass selection based on energy loss measurements in the Time Projection Chambers. For details see [1, 2] . This procedure is not 100% efficient. Its losses and shortcomings are quantified by Monte Carlo simulation of the hyperon decays in the experimental setup and embedding of the resulting raw information into raw data of original events. Reconstruction of these special events with the standard analysis software is compared to the “hyperon input” to obtain corrections
2
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¯+ Figure 1: Rapidity distributions of Ξ− (circles) and Ω− + Ω
Figure 2: :Rapidity distributions of Ξ− (circles) and Ω−
(squares) at 40 A·GeV.
(squares) at 158 A·GeV.
0.2 AGS NA49
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- 63 -
10
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s NN (GeV) Figure 3: Energy dependence of < Λ > / < π − >, < Ξ− > / < ¯ + > / < π − > compared to a prediction π − > and < Ω− + Ω of the Hadron Gas model[6]. For clarity the < Ξ− > / < π − > and Ω data are scaled by factors of 6 and 15, respectively The mean 4π multiplicities of Ξ− and Ω− are plotted as a function of the centre-of-mass energy in the corresponding nucleon-nucleon collision system in Fig. 3. For comparison we here include the corresponding distribution of Λ-hyperons[4]. All yields are divided by the mean multiplicity of the negatively charged pions at the same energy. The relative yield of Λ-hyperons which contain one strange and two light quarks -the latter stem mostly from the incident nucleons- exhibits a pronounced maximum around a beam energy of 30 A·GeV. In the distribution of the relative yields of Ξ− -hyperons (which contain two strange and and only one light quark) the maximum is still visible but to a much lesser extend. The energy dependence of ¯ + > / < π − > ratio shows a monotonous the < Ω− + Ω increase. This systematic behavior is also seen in hadrongas model calculations [5] as indicated by the dashed lines. The model includes the variation of the baryo-chemical potential and of the temperature with beam energy [5]. The quantitative agreement between model and experimental data is good for Λ- and Ω− hyperons, whereas the < Ξ− > / < π − > ratio is generally lower in the data than in the model. The significance of this difference still needs to be evaluated. However, the role of the maximum relative strangeness content in heavy ion collisions around 30 A·GeV in the hyperon to pion ratio[5] is clearly born out in the data. In Fig. 4 the midrapidity multiplicity density of Ξ− hyperons is studied as function of centrality at 40 A·GeV. A pronounced increase from peripheral to mid-central collisions is followed by a saturation towards central reactions.
100
200
300 400
Figure 4: Centrality dependence of Ξ− production in Pb+Pb collisions at 40 A·GeV at mid-rapidity. The squares show the measurement of NA49 compared to a measurement of NA57 (circle)[3]. All values are normalised to the number of wounded nucleons derived from a Glauber approach.[7] Also shown is a single Ξ− measurement from the experiment NA57 [3] which was obtained from the 40% most central collisions (filled circle). The NA49 data on the centrality dependence of Ξ− production suggest that strangeness saturation occurs already in peripheral collisons (less than 160 wounded nucleons) as was already seen earlier in kaon and Λ production.
References [1] C. Meurer, Diplomarbeit Frankfurt, 2003 [2] M. Mitrovski, Diplomarbeit Frankfurt, 2004 [3] D. Elia (NA57 collaboration), Nucl. Phys. A 715(2003)514 and private communication [4] C. Alt et al, NA49 collaboration, nucl-ex/0311024, submitted for publication in PRL [5] P. Braun-Munzinger, J. Cleymans, H. schler and K. Redlich, Nucl. Phys. A697 (2002) 902 [6] K. Redlich, private communication [7] RJ. Glauber and G. Matthiae, Nucl. Phys.B21(1970)135
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Radiator Production and Development of Test Equipment for the ALICE TRD * C. Baumann 1, D. Bucher 1, R. Glasow 1, H. Gottschlag 1, N. Heine 1, H.W. Orthjohann 1, K. Reygers 1, R. Santo 1, W. Verhoeven 1, J.P. Wessels 1, A. Wilk 1 for the ALICE-TRD collaboration Institut für Kernphysik, Universität Münster; Germany The Transition Radiation Detector (TRD) of the ALICE ex- In addition to the work on the radiators, a test equipment for periment will be used to measure high momentum electrons the TRD readout chambers has been developed. One imporabove 1 GeV/c where the TPC no longer allows to separate tant aspect during production of the readout chambers is electrons from pions. Through the addition of the TRD the monitoring of the wire tension. The wire tension needs to be sensitivity of ALICE to measure hard processes, in particu- kept within certain limits to ensure gain uniformity of gas lar charm and beauty production, is much improved. More- amplification. To this end, a tool has been developed that over, the TRD gives the possibility to trigger on jets or elec- allows for an automatic measurement of the position and tension of each wire on the chamber following a similar detrons with high transverse energy [1]. sign used by the PHENIX experiment [3]. The main component of the device is an optical head (HBCS 1100) with a light source (at about 700 nm wavelength). The focus is at 5 mm in front of its lens. A photo sensor inside the head returns a voltage corresponding to the intensity of the light reflected by the wire when the head is properly positioned. A puff of compressed air is used to excite the wire. The resulting oscillation of the wire causes a modulation of the output voltage of the optical sensor. The signal is read out with an ADC connected to a PC running LabView®. A fast Fourier transform algorithm is used to calculate the resonance frequency of the wire. In conjunction with known Figure 1: Radiators during production at the IKP material constants the wire tension can be determined. The Each of the 540 TRD modules consists of a radiator, which optical head is mounted on a carrier attached to a KANYA® produces transition radiation, and a drift chamber for its dealuminum profile. It is moved across the wires by a precitection and for recording the inclination of traversing sion spindle and a PC-controlled stepper motor. The position charged particles. After a series of tests at Münster, GSI, and of each wire is determined by finding the maximum of the CERN the design of the TRD radiator was finalized. It conreflected light and referencing it to the reading of a magnetic sists of a main radiator material, which is a polypropylene tape measure. The device is able to scan up to 1.45 m with a fiber material and a supporting structure built from carbon position resolution of about 30 µm over the entire range. fiber reinforced foam (ROHACELL HF71). This foam forms the front and rear panel of the radiator and is con30 50 nected by a shelf like structure of foam without backing. The 25 resulting cells are filled with the fiber material. 40 20 30 Mass production of the radiators takes place at the “Institut 15 für Kernhysik”. Here, a production site has been prepared 20 10 with gluing tables and storage areas. The tables are glass 10 5 ® tables mounted on KANYA profiles to ensure flatness of 0 0 the produced radiators. With three of these tables a maxi0.85 0.9 0.95 1 2400 2500 2600 Tension (N) Separation (µm) mum number of six radiators can be produced simultaneously. Fig. 1 shows the radiators during production. The Figure 2: Wire tension and separation measured on a performance of the radiator hinges on two factors: the prosmall prototype chamber duction probability for transition radiation and the probabil- Fig. 2 shows a measurement of the dispersion of wire tenity for reabsorption in the material. This needs to be mini- sion on a small prototype grid which was wound about 3 mized. Therefore, an automated X-ray measurement system years prior to measurement. has been designed and constructed for quality assurance during mass production. The device consists of a stabilized X- * Supported by BMBF and GSI ray source [2], a setup for handling the radiator material, a ® thick Si(Li)-detector, and a LabView -based data acquisi- [1] ALICE TRD Technical Design Report, CERN/LHCC tion system. With this setup, it is possible to measure X-ray 2001-021. absorption in the energy range from 2 to 10 keV. Prior to [2] X-ray source developed by V. Yurevich et al., JINRproduction of the radiators each sheet of carbon fiber lamiDubna. nated Rohacell is measured. In addition, after production [3] A. Franz, E. O'Brien, private communication. each radiator is checked at several points for production uniformity. 1
Mean RMS
0.9197 0.3268E-01
Mean RMS
2507. 46.83
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Estimation of the radiation level in the ALICE TPC electronics G.Tsiledakis1 , A.Fass`o12 , P.Foka1 , A.Morsch2 , and A.Sandoval1 GSI,Darmstadt;
The CERN LHC experiment ALICE, will study central Pb–Pb collisions at 5.5 TeV per nucleon pair which result in very high particle multiplicities. The inaccessibility of the ALICE experiment during the entire year of LHC running makes stringent quality tests of the readout electronics mandatory before installation. Here we analyze and present the contributions to the radiation background in the region where the ALICE TPC front-end electronics is situated. The simulations were based on the FLUKA [1] interaction and transport Monte Carlo code. The Time Projection Chamber (TPC) [2] surrounds the Inner Tracking System (ITS) and is the main tracking detector of the central barrel and together with the ITS, TRD and TOF will provide charged particle momentum measurement, particle identification and vertex determination with sufficient momentum resolution, two track separation and dE/dx resolution for studies of hadronic and leptonic signals in the region Pt 10 MeV in both sides of TPC are summarized in Table 1. The aforementioned results of this study concerning the particle rates, fluences and fluxes should be taken into account for evaluating the radiation tolerance of the TPC electronics.
References [1] http://www.fluka.org [2] ”Time Projection Chamber” ALICE Technical Design Report, CERN/LHCC/2000-001 (2000).
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Neural Networks for Electron-Pion Separation in the ALICE TRD* C. Baumann 1, D. Bucher 1, R. Glasow 1, H. Gottschlag 1, N. Heine 1, H.W. Orthjohann 1, K. Reygers 1, R. Santo 1, W. Verhoeven 1, J.P. Wessels 1, A. Wilk 1 for the ALICE TRD collaboration Institut für Kernphysik, Universität Münster; Germany The Transition Radiation Detector (TRD) of the ALICE ex- runs with no pion scaledown were available. The results for periment consists of TR producing radiators followed by 1,2,3 and 4 combined chambers for an energy of 2 GeV/c drift chambers with a Xe/CO2 mixture [1]. This drift cham- are shown in Fig. 1. Also plotted is a fit used for the extrapobers provide information about the amount and spatial loca- lation to six chambers, which is the final number of layers tion of charge deposited by charged particle traversing the used in ALICE. chambers. Classical analysis methods for electron-pion sepa- In Fig. 2 a comparison between the results for six layers obration don’t make use of the entire available information. tained for the neural network and for the classical LQX Widely used are likelihood cuts on the total measured method is plotted. The neural network shows a significant charge, and on the spatial position of the largest found clus- improvement of the pion rejection capabilities of a factor of ter (LQX method). This neglects a lot of information, which 3-5 over the whole energy range compared to the classical is contained in the detailed charge distribution along the track. Efficiency NN+LQX (INV6) (extrapolated) To utilize all available information electron-pion separation 0.03 based on neural networks were. The Stuttgart Neural Net+ Neural Net work Simulator (SNNS) [2] was used as a framework to test x LQX 0.025 different network configurations. The most successful setup for a single chamber was a feed forward network with two 0.02 hidden layers. The input neurons corresponded to the readout pad with the highest charge deposit and the two sur0.015 rounding ones for each time bin and 15 time bins, so a total of 15*3 input neurons were used. The 2 hidden layers con0.01 sists of 16 and 7 neurons and the output layer of 2. These tow output neurons represent the likelihood for an electron 0.005 and a pion, respectively. The experimental setup consisted of 4 chambers, each represented by a separate neural net0 work. The output of these networks was fed into an addi0 1 2 3 4 5 6 7 tional feed forward network without hidden layers. The reMomentum (GeV/c) Pion Efficiency
1
Pion Efficiency
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Figure 2: Comparison of the pion efficiency obtained for a neural network and for the LQX method method.
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[1] ALICE TRD Technical Design Report, CERN/LHCC 2001-021. [2] SNNS – Stuttgart Neural Network Simulator, http://www-ra.informatik.uni-tuebingen.de/SNNS/
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Supported by BMBF and GSI
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Figure 1: Pion efficiency vs. number of chambers and extrapolation fit sulting probabilities were then also used in likelihood cuts to extract the pion rejection at 90% electron efficiency (called “pion efficiency”). This was done similar as in the classical methods. The network was trained and tested with data from the CERN PS test beamtime in 2002. For training we used data from 2 to 6 GeV/c with an similar content of electrons and pions. For the tests the same energies were used, but only
