E.Andronov , 13/05/14, SPbSU ALICE/NA61

1)LRC in the model of independent sources of two types. 2) Small step to the finite strings in NA61 data. E.Andronov, 13/05/14, SPbSU ALICE/NA61

MIS of two types Not fused Fused [1] E.Andronov, V.VecherninPoS(QFTHEP 2013)054

Basic formulae for MC simulations

MIS of two types Limit to one type case Presence of covariation term is important

MIS of two types One can not perform analytical calculations further for pT-n correlations

Connection between N1 and N2 Toy model Number of pomerons R

Connection between N1 and N2 Toy model

MIS of two types Analytical result for b_{nn} and simple MC calculations with an approximation for b_{pTn} were obtained in [1] for FIXED r. Only negative pT-n correlations in this case! [1] E.Andronov, V.VecherninPoS(QFTHEP 2013)054

MIS of two types Introduce in the probability of fusion “r” dependence on the number of primary strings N with following logic: Less strings-smaller probability to fuse More strings-bigger probability to fuse Candidate:

MIS of two types Candidate: Only MC simulations could help us calculate needed average values with this r(N) function.Except one case – when number of primary strings N does not fluctuate from event to event!

MIS of two types Nonfluctuating number of strings N MC simulation script for nonfluctuating number of strings N can be checked by this analytical formula

MIS of two types Nonfluctuating number of strings N Shift=15 Analytical MC

MIS of two types Nonfluctuating number of strings N Shift=100 Analytical MC

MIS of two types Fluctuating number of strings N, w[N]=2 Shift=100 MC

MIS of two types Fluctuating number of strings N, w[N]=2 Shift=100 MC MC Numerator of b_{nn}

MIS of two types Fluctuating number of strings N, w[N]=2 Shift=100 MC MC Denominator of b_{nn}

MIS of two types MC Fluctuating number of strings N, w[N]=2 Shift=100 Numerator of b_{nn} <nF>

MIS of two types MC Fluctuating number of strings N, w[N]=2 Shift=100 b_{nn}

MIS of two types MC Nonfluctuating number of strings N Shift=100

MIS of two types MC Fluctuating number of strings N, w[N]=2 Shift=100

Conclusions for part1 • MC generator with string fusion was developed and tested for fluctuating and nonfluctuating number of primary strings • Analytical calculations and MC generator results are the same in nn case for fixed N • Shark fin behavior of b_{nn} was found in the not total fusion region • Only negative pT-n correlations for fixed N • As positive, as negative pT-n correlations for fluctuating N P.S. Test of approximation of b_{pTn} from bachelor thesis was performed. Results are not shown here, but it turns out that approximation works quite well.

Part2String length in NA61

String length in NA61 Let us consider only right slope of dN/dy distribution Let N be total number of strings in event Let: strings For fixed backward window on the top of the hill – p=0

String length in NA61 In order to calculate b_{nn} or Sigma we should know correlation between NB and NF, i.e. we should know P_N (NB,NF)

String length in NA61 Linearity of <nF> with eta implies linearity of q, and, consequently, omega[nF]

String length in NA61 Linearity of <nF> with eta implies linearity of q, and, consequently, omega[nF] 0.5 eta windows <n>

String length in NA61 Linearity of <nF> with eta implies linearity of q, and, consequently, omega[nF] 0.5 eta windows <n> Big chi-squared! Not so good

String length in NA61 Linearity of <nF> with eta implies linearity of q, and, consequently, omega[nF] 0.5 eta windows w[N]

String length in NA61 Linearity of <nF> with eta implies linearity of q, and, consequently, omega[nF] 0.5 eta windows w[N] Decent chi-squared

String length in NA61 Linearity of <nF> with eta implies linearity of q, and, consequently, omega[nF] Fit results: In the range of fittinf (4;5) there is configuration of B-F windows (4;4.5)-(4.5;5) For these windows delta=0.850±0.012

String length in NA61 More realistic: Complicated to fit data

Backup

Definitions [1] M.I. Gorenstein, M. Gazdzicki, Phys. Rev. C 84, 014904 (2011)

Normalization factors IPM and Independent Emitters [2] M.Gazdzicki, M.I.Gorenstein, M.Mackowiak-Pawlowska, Phys.Rev.C 88, 024907 (2013)

Long-range fluctuations

IPM and Independent Emitters Long-range fluctuations

Long-range fluctuations Uncertainty in Delta for symmetric windows (mu_B=mu_F) ? No uncertainty for these lambdas

E.Andronov , 13/05/14, SPbSU ALICE/NA61