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