Introduction

1. Neutral pion number fluctuations at high multiplicity in pp-interactions at 50 GeV(SVD-2 Collaboration, exp. Е-190) • 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) SVD-2 Collaboration (IHEP, JINR, SINP MSU)

2. 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 Ntotrelative values are used n0=N0/Ntotandr0=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 Ntotfor any N0 FRITIOF7.02 Fig. 2. The dependence of the photons number detected in ECal <N > on N0in MC events. SVD-2 Collaboration (IHEP, JINR, SINP MSU) To define N0 in event it is impossible, but there is a linear correlation between average <N> and N0 Fig. 1. Distributions r0 for normalized multiplicity of neutral pions in QCD model and when the system approaches to BEC.

3. 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 ррХinelastic interactions at 50 GeV. Only the events with Nch4 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. For events with Nch4: 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). SVD-2 Collaboration (IHEP, JINR, SINP MSU) Fig. 3. а) Average <n0> , <n>; b) standard deviation and c) scaled variance  = 2Ntot/<n> dependence onNtotfor MC events. Ntot=Nch+N0 for 0 and Ntot=Nch+N for photons

4. Photon and charged particles reconstruction 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 956919experimental events Photon 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. 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. SVD-2 Collaboration (IHEP, JINR, SINP MSU) Fig. 5. Multiplicity distributions : a) Nchbefore and after corrections; b) of corrected Nch, Nand Ntot=Nch+N After corrections: <Nch>= 6.7 < N >= 2.3 Fig. 4. a) Photon multiplicity distribution; b) photon energy distribution.

5. Neutral pion fluctuation measurements Table 1 SVD-2 Collaboration (IHEP, JINR, SINP MSU)

6. Neutral pion fluctuation measurements 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=N0and 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)=cijNev(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 N10 and Nch14 only because of limitation of the MC events statistics. Regularities of factors cijare 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 cijfor 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. SVD-2 Collaboration (IHEP, JINR, SINP MSU) 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. Fig. 6. The dependence of cij factors on N0 for various Nand Nch

7. Neutral pion fluctuation measurements 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. SVD-2 Collaboration (IHEP, JINR, SINP MSU) Fig. 8. Scaled neutral pions number n0distributionsfor various Ntot(are specified by number)

8. Neutral pion fluctuation measurements 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. SVD-2 Collaboration (IHEP, JINR, SINP MSU) 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.

9. Neutral pion fluctuation measurements The theoretical prediction of scaled variance  behavior (in our case =D(N0)/<N0>=2Ntot/<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. SVD-2 Collaboration (IHEP, JINR, SINP MSU) 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+N0for neutral pions, Ntot=Nch+Nfor photons.

10. 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/Ntotandr0=Nev(N0,Ntot)/Nev(Ntot) with interval n0 is equal to 01. • 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. This work was supported by the Russian Foundation for Basic Research (projects no. 08-02-90028 Bel_a, 09-02-92424KE_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. References : V. V. Avdeichikov et al., Proposal “Termalization” (in Russian), JINR-P1-2004-190 (2005). V. V. Ammosov et al., Phys. Lett. B 42, 519 (1972). V.V. Begun and M.I. Gorenstein, Phys. Lett. B 653, 190 (2007). V.V. Begun and M.I. Gorenstein, Phys. Rev. C 77, 064903 (2008). 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 E. S. Kokoulina, AIP Conf. Proc. 828, 81 (2006). SVD-2 Collaboration (IHEP, JINR, SINP MSU)