Introduction

Neutral pion number fluctuations at high multiplicity in pp-interactions at 50 GeV(SVD-2 Collaboration, exp. Е-190)

MESON 2012, Krakow 1SVD-2 Collaboration (IHEP, JINR, SINP

MSU)

After submission first results of this work in Phys. of Atomic Nuclei and arXiv (http://arxiv.org/abs/1104.3673) were carried out following upgrades:The statistical of data for analysis was increasing by factor 2;More detail modeling with program GEANT was made;Algorithm for photon reconstruction was optimized;Experimental date of neutral pion multiplicity was compared with Mirabelle data at 70 GeV (M. Boratov at al., Nucl. Phys. B111 (1976) 529-547)

Introduction M. I. Gorenstein and V. V. Begun (Phys. Lett. B 653, 190 (2007)) have shown that at the approach of the pion system to Bose-Einstein condensate conditions (BEC) the neutral pion number fluctuations are increasing in accordance with the model based on quantum statistics. These fluctuations can be detected by the scaled variance, ω, which is defined as the ratio of variance D for neutral pion number N0 distribution to average <N0>,

= D / <N0>.The value of rising with increasing of the total particle number, Ntot=Nch+N0 , depends on the temperature and energy density of pion system. For the analysis of the data at different Ntot relative values are used

n0=N0/Ntot and r0=Nev(N0,Ntot)/Nev(Ntot). n0=0÷1, r0(Ntot)=1.

Nev(N0,Ntot)=number of events with N0 and Ntot=Nch+N0

Nev(Ntot)=number of events with Ntot for any N0

Fig. 1. Distributions r0 for normalized multiplicity of neutral pions in QCD model and when the system approaches to BEC.MESON 2012, Krakow 2

SVD-2 Collaboration (IHEP, JINR, SINP MSU)

Fig. 2. The dependence of the photons number detected in ECal <N > on N0 in MC events.

FRITIOF7.02

To define N0 in event it is impossible, butthere is a linear

correlation between average <N> and N0

Simulation of neutral pion detection

Calorimeter ECal at SVD-2 setup detects the events with photons from neutral pions decay. Registration of all 0 in the event is not possible because of limited ECal aperture and the threshold on the photon detection energy. But 0 reconstruction efficiency can be estimated by means of simulation. Using FRITIOF7.02 and GEANT codes 3.5*105 events (MC) are simulated for ррХ inelastic interactions at 50 GeV. Only the events with Nch4 are analyzed. It is clear that there is no unique connection between N and N0. Instead each N is associated with some number of N0 and there is a linear correlation between average <N> and N0 (Fig. 2). So relation between the number of events Nev(N, Nch) and Nev(N0, Nch) can be found from this analysis.

MESON 2012, Krakow 3


Fig. 3. а) Average <n0> , <n>; b) standard deviation and c) scaled variance = 2Ntot/<n> dependence on Ntot for MC events. Ntot=Nch+N0 for 0 and Ntot=Nch+N for

photons

For events with Nch4: 92% events with 0, 95% are the product of 0

<Nch>= 7.9, <N0>=2.9, <N>=5.4 , in ECal <N>=2.5

Values n and r are calculated for MC events. Then parameters <n>, and are defined for distribution r(n).

Photon and charged particles reconstruction



For the charged tracks reconstruction the data only from VD have been used.

Corr. 1 - for the setup acceptance and the particle reconstruction efficiency [5]Corr. 2 – for trigger conditions

The change of the event number for Nch after introduction of corrections also leads to the change of the event number for N.

DEGA = 1344 elements from lead glass

blocks (38х38х505 mm3) with PM. The calibration with 15 GeV electron beam.The cell (3х3) = 98% energy of the e.m.

shower and 77% in central element.The minimum energy of = 100 MeV

956919 experimental eventsPhoton reconstruction consists in the searching for (3х3) signal clusters and analyzing of them

with criteria for the photon.<Е>=2.8 GeV, <N>=1.8 before

corrections.

Fig. 4. a) Photon multiplicity distribution; b) photon energy distribution.

Fig. 5. Multiplicity distributions : a) Nch before and after corrections; b) of corrected Nch, N and Ntot=Nch+N

After corrections:

<Nch>= 6.7< N >= 2.3

Neutral pion fluctuation measurements



Ntot Nch= 4 6 8 10 12 14 16 18 20 22 24 NevN Nev N Nev N Nev N Nev N Nev N Nev N Nev N Nev N Nev N Nev N Nev

4 0 233164 2331645 1 422592 4225926 2 459512 0 193631 6531437 3 360538 1 356215 7167538 4 235720 2 387419 0 117924 7410639 5 131634 3 310509 1 220895 663038

10 6 63900 4 203024 2 240271 0 46371 55356511 7 29252 5 113479 3 195037 1 88136 42590312 8 13348 6 56553 4 127779 2 95925 0 14598 30820213 9 4970 7 25997 5 72079 3 77174 1 27805 20802614 10 2840 8 11869 6 36898 4 50832 2 30726 0 3366 13653015 11 1420 9 4932 7 17125 5 29301 3 24553 1 6468 8380016 12 710 10 2555 8 7767 6 15237 4 16371 2 7170 0 639 5044917 13 426 11 1218 9 3635 7 7224 5 9537 3 5724 1 1227 2899118 14 284 12 629 10 1718 8 3268 6 4997 4 3904 2 1377 0 110 1628719 15 142 13 334 11 781.0 9 1681 7 2438 5 2249 3 1081 1 206 891220 16 142 14 196 12 440 10 758 8 1186 6 1200 4 772 2 240 0 13.3 494821 17 56.8 15 138 13 206 11 351 9 609 7 595 5 437 3 182 1 27.2 260122 18 0.0 16 78.6 14 121 12 189 10 259 8 302 6 247 4 130 2 34.4 0 1.8 136223 19 28.4 17 39.3 15 95.8 13 105 11 141 9 160 7 120 5 76.3 3 26.0 1 4.0 79624 20 0.0 18 19.6 16 59.6 14 49.1 12 75.9 10 80.0 8 69.3 6 45.8 4 18.1 2 4.7 0 0.3 42225 21 0.0 19 15.7 17 29.8 15 49.1 13 40.3 11 39.0 9 38.8 7 20.7 5 11.5 3 3.7 1 0.7 24926 22 28.4 20 0.0 18 25.6 16 28.1 14 18.6 12 22.0 10 19.7 8 13.1 6 7.2 4 2.4 2 0.8 16627 21 0.0 19 6.4 17 13.3 15 20.1 13 9.0 11 9.6 9 7.8 7 3.1 5 1.7 3 0.4 71.628 22 15.7 20 4.3 18 10.2 16 8.1 14 5.5 12 6.0 10 3.8 8 2.5 6 0.9 4 0.4 57.429 21 1.4 19 2.5 17 1.9 15 4.7 13 1.5 11 2.6 9 1.9 7 0.4 5 0.2 17.130 22 6.4 20 6.3 18 2.2 16 1.3 14 0.7 12 1.4 10 1.3 8 0.5 6 0.3 20.331 23 0.0 21 1.8 19 0.8 17 0.7 15 1.2 13 0.4 11 0.4 9 0.2 7 0.1 5.632 24 1.4 22 2.5 20 4.0 18 0.3 16 0.1 14 0.1 12 0.5 10 0.2 8 0.1 9.133 23 0.0 21 0.3 19 1.0 17 0.2 15 0.2 13 0.1 11 0.0 9 0.3 1.834 24 1.8 22 0.3 20 0.8 18 0.0 12 0.1 10 0.7 3.035 23 0.0 19 0.3 0.336 24 0.3 20 0.1 0.4

Nev 1960707 1668866 1042908 416717 133393 31302 6048 1040 147 20.6 3.3

Table 1




Fig. 6. The dependence of cij factors on N0 for various N and Nch

Thus we have corrected event numbers Nev(N, Nch). Then two-dimensional Nev(N, N0) distributions for МC events (see Fig. 2а) are used to recover event numbers Nev(N0, Nch). We have introduced notations i=N, j=N0 and Nev(N, N0)=Nev(i,j). For each Nch matrix of coefficients cij=Nev(i,j)/Nev(i) is calculated, where Nev(i)=jNev(i,j). Event number Nev(N, Nch) is decomposed in sums of events with various N0, Nev(i,j)=cijNev(i) at Nch=const. Normalization condition cij=1 is satisfied. Resulting sum Nev(j)=iNev(i,j) at Nch=fix is the analog of event number Nev(N, Nch), but for pions.The simulation by PYTHIA5.6 allows obtain cij for N10 and Nch14 only because of limitation of the MC events statistics. Regularities of factors cij are used to continue them to N>10 and Nch>14 region.

The form of these distributions slightly depends on N and Nch, but their average <N0> increases with N. After fitting it by linear dependence coefficients cij for N>10 and Nch>14 are calculated and the full sample of Nev(Ntot, Nch, N0) is obtained, which is used then to determine pion fluctuation.

Fig. 7. The dependence of average number of neutral pions <N0> on charge multiplicity.

The average of neutral pions < N0 > after their reconstruction is in agreement with Mirabelle data at 70 GeV. This fact is confirmation that the procedure of this reconstruction is correct.




As mention before we have used scaled variables n0 and r0 (see Introduction):

n0=N0/Ntot and r0(n0)= Nev(N0, Ntot)/Nev(Ntot),

where Ntot=N0+Nch.

Function r0(n0) is shown in Fig. 8 for every Ntot >10.

The data in the intervals (25, 26, 27) are combined due to small statistics.

The dependence of the parameters is presented in Fig. 9.

Fig. 8. Scaled neutral pions number n0 distributions for various Ntot (are specified by number)




Fig. 9. Parameters of neutral pions number and photons number distributions for experimental data and МC events as function of Ntot. For neutral pions Ntot=Nch+N0, for photons Ntot=Nch+N.

One can see that the measured average <n0> (Fig. 9а) is similar with the same values for the neutral pions from MC events. The average <n> is also shown. The measured standard deviations, , (Fig. 9b) have shown the qualitative agreement with MC model only for Ntot<18. The measured values increase at high Ntot.




Fig. 10. a) Scaled variance as function of Ntot [3] and b) the result of the present measured of for neutral pions and photons. Ntot=Nch+N0 for neutral pions, Ntot=Nch+N for photons.

The theoretical prediction of scaled variance behavior (in our case =D(N0)/<N0>=2Ntot/<n0>) is given in [3]. The analysis has been done for three energy densities of the pion system at the approach to the Bose-Einstein condensate condition (pion condensate) (Fig. 10а). Our experimental data (Fig. 10b) have confirmed assumption on the BEC formation in pion system at Ntot>18 in pp-interactions at 50 GeV.

Conclusion



Measurements of the charged and neutral pions number in the events with high multiplicity in pp-interactions at 50 GeV (experiment SERP-Е-190, SVD-2 setup) together with MC analysis led to the following results: The number of neutral pions in the event and the photons number detected in ECal are linearly connected that allows one to extract pion number fluctuations from photon number fluctuations. It is convenient to present the data in the scaled form: n0=N0/Ntot and r0=Nev(N0,Ntot)/Nev(Ntot) with interval n0 is equal to 01. The corrections for the limited aperture VD, trigger action and efficiency of data processing system have been introduced to the data. Pion number fluctuations increase at Ntot>18, that indicates approaching to pion condensate conditions for the high multiplicity pion system according to GCE, CE, MCE models [3, 4]. This effect has been observed for the first time.

References :1.V. V. Avdeichikov et al., Proposal “Termalization” (in Russian), JINR-P1-2004-190 (2005).2.V. V. Ammosov et al., Phys. Lett. B 42, 519 (1972).3.V.V. Begun and M.I. Gorenstein, Phys. Lett. B 653, 190 (2007).4.V.V. Begun and M.I. Gorenstein, Phys. Rev. C 77, 064903 (2008).5.Ardashev Е. et al. Topological cross-sections in pp-interactions at 50 GeV: IHEP Preprint 2011-4 http://web.ihep.su/library/pubs/all-w.htm , http://arxiv.org/PS_cache/arxiv/pdf/1104/1104.0101v1.pdf 6.E. S. Kokoulina, AIP Conf. Proc. 828, 81 (2006).

This work was supported by the Russian Foundation for Basic Research (projects no. 08-02-90028 Bel_a, 09-02-92424 KE_a, 09-02-00445а, 06-02-16954) and was funded by a grant (no. 1456-2008-2) for support of leading scientific schools. Authors are grateful to a management of IHEP for support in carrying out of researches, to the staff of accelerator division and beam department for effective work of U-70 and the channel 22. Authors are appreciated to M. I. Gorenstein and V. V. Begun for stimulation of these studies and useful discussions.

Introduction

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Transcript of Introduction