Convolutions, factorial cumulants and intermittency

Tannenbaum, M. J.

doi:10.1016/0370-2693(95)00200-5

Cited by 9 publications

(4 citation statements)

References 72 publications

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“…In section 4 we justify this choice by simulating and analysing data sets consisting of a mixture of critical protons generated by the Critical Monte-Carlo (CMC) code [7,12] and randomly distributed protons. We searched for an intermittency effect ∆F (e) 2 (M ) ∼ (M 2 ) φ2 for M 2 ≫ 1 [22,31]. The intermittency index φ 2 can be determined by a power-law fit (PF) to ∆F (e) 2 (M ) in the region of sufficiently large M 2 .…”

Section: Data and Methods Of Analysismentioning

confidence: 99%

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Critical fluctuations of the proton density in A+A collisions at 158A GeV

Antičić¹,

Baatar²,

Bartke³

et al. 2015

Eur. Phys. J. C

108

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We look for fluctuations expected for the QCD critical point using an intermittency analysis in the transverse momentum phase space of protons produced around midrapidity in the 12.5% most central C+C, Si+Si and Pb+Pb collisions at the maximum SPS energy of 158A GeV. We find evidence of power-law fluctuations for the Si+Si data. The fitted power-law exponent φ2 = 0.96 +0.38 −0.25 (stat.) ±0.16 (syst.) is consistent with the value expected for critical fluctuations. Power-law fluctuations had previously also been observed in low-mass π + π − pairs in the same Si+Si collisions.

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Section: Data and Methods Of Analysismentioning

confidence: 99%

“…) ∼ (M 2 ) φ2 for M 2 ≫ 1[22,31]. The intermittency index φ 2 can be determined by a power-law fit (PF) to ∆F(e) 2 (M ) in the region of sufficiently large M 2 .…”

mentioning

confidence: 99%

Critical fluctuations of the proton density in A+A collisions at 158A GeV

Antičić¹,

Baatar²,

Bartke³

et al. 2015

Eur. Phys. J. C

108

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“…This property is known (see, e.g., Ref. [36] and references therein), but for completeness and to provide a better intuitive understanding we derive it for k ≤ 4 in Appendix A.…”

Section: Acceptance Dependence Of Cumulantsmentioning

confidence: 99%

Acceptance dependence of fluctuation measures near the QCD critical point

2016

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We argue that a crucial determinant of the acceptance dependence of fluctuation measures in heavy-ion collisions is the range of correlations in the momentum space, e.g., in rapidity, ∆ycorr. The value of ∆ycorr ∼ 1 for critical thermal fluctuations is determined by the thermal rapidity spread of the particles at freezeout, and has little to do with position space correlations, even near the critical point where the spatial correlation length ξ becomes as large as 2−3 fm (this is in contrast to the magnitudes of the cumulants, which are sensitive to ξ). When the acceptance window is large, ∆y ∆ycorr, the cumulants of a given particle multiplicity, κ k , scale linearly with ∆y, or mean multiplicity in acceptance, N , and cumulant ratios are acceptance independent. In the opposite regime, ∆y ∆ycorr, the factorial cumulants,κ k , scale as (∆y) k , or N k . We demonstrate this general behavior quantitatively in a model for critical point fluctuations, which also shows that the dependence on transverse momentum acceptance is very significant. We conclude that extension of rapidity coverage proposed by STAR should significantly increase the magnitude of the critical point fluctuation signatures.

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“…This is in contradiction to the results obtained in nuclear collisions [38], where the Γ-distribution was found to be significantly inconsistent to reproduce the measurements: it underestimates the low-multiplicity parts of the experimental multiplicity distributions in different rapidity bins, while overestimates the high-multiplicity tails. Again in contrast to e + e − data, the NB regularity is found to be the best one to describe small fluctuations in the multiplicity distribution in nuclear data, and large fluctuations are well reproduced by two-particle correlations [38,[40][41][42][43]…”

Section: Normalized Factorial Moments and Cumulants From Various Paramentioning

confidence: 99%

Description of local multiplicity fluctuations and genuine multiparticle correlations

Sarkisyan

2000

Physics Letters B

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Various parametrizations of the multiplicity distribution are studied using the recently published large statistics OPAL results on multidimensional local fluctuations and genuine correlations in e + e − → Z 0 → hadrons. The measured normalized factorial and cumulant moments are compared to the predictions of the negative binomial distribution, the modified and generalized versions of it, the log-normal distribution and the model of the generalized birth process with immigration. This is the first study which uses the multiplicity distribution parametrizations to describe high-order genuine correlations. Although the parametrizations fit well the measured fluctuations and correlations for low orders, they do show certain deviations at high orders. We have shown that it is necessary to incorporate the multiparticle character of the correlations along with the property of self-similarity to attain a good description of the measurements. * Email address: edward@lep1.tau.ac.il 1 Earlier, using correlation (strip) integrals to reduce statistical errors, multiparticle genuine correlations have been searched for in hadron-hadron [9,10] and lepton-hadron [11] interactions. It is worth to note that except for problems arising due to various possibilities in defining of a proper topology of particles and a distance between them (see e.g. [2]), a rather important difficulty in interpreting results could come from a translation invariance breaking of the many-particle distributions [12]. This will lead to different results on moments/cumulants according to a variable used because different variables are sensitive to different hadroproduction mechanisms [12,13]. For example, in the high-order genuine correlations obtained in Ref. [9,11] the study is performed in four-momentum difference squared, Q 2 , dependent on Bose-Einstein correlations, whereas in the pseudorapidity analysis [10] no correlations higher than two-particle ones were found, since (pseudo)rapidity seems [13] to be more "natural" variable to search for jet formation than e.g. for Bose-Einstein correlations.

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Convolutions, factorial cumulants and intermittency

Cited by 9 publications

References 72 publications

Critical fluctuations of the proton density in A+A collisions at 158A GeV

Critical fluctuations of the proton density in A+A collisions at 158A GeV

Acceptance dependence of fluctuation measures near the QCD critical point

Description of local multiplicity fluctuations and genuine multiparticle correlations

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