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

[1] E.Andronov, V.Vechernin PoS(QFTHEP 2013)054

Not fused Fused

Basic formulae for MC simulations

MIS of two types

Presence of covariation term is important

Limit to one type case

MIS of two types

One can not perform analytical calculations further for pT-n correlations

Connection between N1 and N2Toy model

Number of pomerons R

Connection between N1 and N2Toy model

MIS of two types

[1] E.Andronov, V.Vechernin PoS(QFTHEP 2013)054

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!

MIS of two typesIntroduce in the probability of fusion “r” dependence on the number of primary strings N with following logic:

Less strings-smaller probability to fuseMore strings-bigger probability to fuse

Candidate:

MIS of two typesCandidate:

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 typesNonfluctuating number of strings N

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

MIS of two typesNonfluctuating number of strings N

Shift=15

Analytical MC

MIS of two typesNonfluctuating number of strings N

Shift=100

Analytical MC

MIS of two typesFluctuating number of strings N, w[N]=2

Shift=100MC

MIS of two typesFluctuating number of strings N, w[N]=2

Shift=100

MC

MIS of two typesFluctuating number of strings N, w[N]=2

Shift=100MC

MIS of two typesFluctuating number of strings N, w[N]=2

Shift=100MC

MIS of two typesFluctuating number of strings N, w[N]=2

Shift=100MC

MIS of two typesFluctuating number of strings N, w[N]=2

Shift=100MCMC Numerator of b_{nn}

MIS of two typesFluctuating number of strings N, w[N]=2

Shift=100MC MC Denominator of b_{nn}

MIS of two typesFluctuating number of strings N, w[N]=2

Shift=100

MC

Numerator of b_{nn} <nF>

MIS of two typesFluctuating number of strings N, w[N]=2

Shift=100

MC

b_{nn}

MIS of two typesNonfluctuating number of strings N Shift=100

MC

MIS of two typesFluctuating number of strings N, w[N]=2

Shift=100

MC

MIS of two typesFluctuating number of strings N, w[N]=2

Shift=100

MC

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

strings

Let us consider only right slope of dN/dy distribution

Let N be total number of strings in event

Let:

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 NA61Linearity of <nF> with eta implies linearity of q, and, consequently, omega[nF]

<n>

0.5 eta windows

String length in NA61Linearity of <nF> with eta implies linearity of q, and, consequently, omega[nF]

<n>

0.5 eta windows

Big chi-squared! Not so good

String length in NA61Linearity of <nF> with eta implies linearity of q, and, consequently, omega[nF]

w[N]0.5 eta windows

String length in NA61Linearity of <nF> with eta implies linearity of q, and, consequently, omega[nF]

w[N]0.5 eta windows

Decent chi-squared

String length in NA61Linearity 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 NA61More 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