Multiplicity and net-charge fluctuations in ion+ion collisions at theSPS energies
Agnieszka Borucka
for the NA61/SHINE Collaboration

Agnieszka Borucka (WUT)

August 24, 2021

1 / 10NA61/SHINE – fixed target experiment at SPS CERN
The ion programme aims to search for the critical point (CP) of strongly interacting matterand study the onset of deconfinement.

colliding nuclei

Energy and system size scan
Pb+Pb

2022-2024

Pb+Pb

2016/18

Xe+La

2017

Ar+Sc

2015

Be+Be

2011/12/13

p+Pb

2012/14/16/17

p+p

2009/10/11

1320304075

http://shine.web.cern.ch/150

beam momentum [A GeV/ c ]http://shine.web.cern.ch/Large (up to 50%) acceptance and precise forward
energy measurements makes NA61/SHINE asuitable experiment for fluctuations measurements.
*Setup corresponds to analysed data.

Agnieszka Borucka (WUT)

August 24, 2021

2 / 10Motivation
Multiplicity and net-charge fluctuations of higher order moments are tools to search for criticalpoint of strongly interacting matter. 2D system size and energy scan gives an ideal
opportunity to search for it at SPS energies.
Theoretical
calculation of phasetransition with valuesof normalized kurtosis
for nuclear matterdescribed with vander Waals equations.
Vovchenko et al. Acta Phys.Polon. Supp. 10,75

CP → increase of the correlation length (ξ → ∞)hN 2 i ∼ ξ 2 hN 4 i ∼ ξ 7
Stephanov, J.Phys.G 38,124147
arXiv:1901.04482v1 [hep-ex] 14 Jan 2019
Agnieszka Borucka (WUT)

August 24, 2021

3 / 10Definitions of intensive quantities
Multiplicity

Net-charge

Normalized kurtosis

K σ 2 = µµ42 − 3µ2 = κκ42

κ4 +−
κ2 [h − h ]Normalized skewness

Sσ = µµ32 = κκ32κ3 +−κ1 [h − h ]Scaled varianceω(N) = µµ21 = κκ21

κ2 [h+ −h− ]κ1 [h+ ]+κ1 [h− ]µi and κi – central moment and cumulant of i-th order
Reference values:
01Multiplicity
without fluctuations
for Poisson distribution

Net-charge
without fluctuationsfor Skellam distribution

Begun and MMP, arxiv:1705.01110[nucl-th]
Agnieszka Borucka (WUT)

August 24, 2021

4 / 10

3.5
32.5

κ4/ κ2

κ4/ κ2

System size and energy dependence-hNA61/SHINE preliminary
p+p
1% Be+Be
1% Ar+Sc-65241.53120.5

100−0.5−14681012141618sNN (GeV)

4h+-hNA61/SHINE preliminaryp+p
1% Be+Be
1% Ar+Sc

681012141618sNN (GeV)

Statistical uncertainties – black bars.
Estimated systematic uncertainties – solid line of the same color as marker with arrows.
For A+A collisions only 1% of the most central ones.
A.Seryakov, CPOD 2016
Agnieszka Borucka (WUT)

August 24, 2021

5 / 10System size and energy dependence
Acceptance of NA61/SHINE:

κ4/ κ210-h+-h50−5p+p−10arXiv:1401.4699v1 [physics.ins-det] 19 Jan 2014−151% Be+Be
1% Ar+Sc
STAR Au+Au 0-5% |η|<0.510102sNN (GeV)
Acceptance of STAR: |η| <0.5

Agnieszka Borucka (WUT)

Comparison with STAR: Phys. Rev. Lett. 113, 092301 (2014)

August 24, 2021

6 / 10Rapidity dependence – constant bin
Constant bin – sensitivity for different
measurements conditions.

 EPOS1.99 qualitatively agrees withdata the strongest signal for yπ < 1.5
Dashed green line – value in full analysis acceptanceDashed blue line – value in full analysis acceptanceTop x axis – ratio of haccepted to htotal
Statistical uncertainties – black bars (hidden behind markers).
Estimated systematic uncertainties – colorband.

Dashed violet line – 1 (reference for Poisson distribution)
Agnieszka Borucka (WUT)

August 24, 2021

7 / 10Rapidity dependence – expanding bin
Expanding bin - comparision of shortand long-range correlations.

 data present strong dependence on
rapidity acceptance EPOS1.99 predicts similar
dependence

Top x axis – ratio of haccepted to htotal
Statistical uncertainties – black bars (hidden behind markers).

Dashed green line – value in full analysis acceptanceDashed blue line – value in full analysis acceptanceDashed violet line – 1 (reference for Poisson distribution)
Agnieszka Borucka (WUT)

Estimated systematic uncertainties – colorband.
August 24, 2021

8 / 10Summary

 System size and energy dependence κ4 /κ2 of multiplicity and net-charge fluctuations for p+p, Be+Be and Ar+Sc were
measured in energy dependence
 comparison with STAR’s results Au+Au interaction
 no indication of CP Radpidity dependence in p+p interactions κ4 /κ2 of multiplicity and net-charge fluctuations for p+p interactions at 158GeV/cwere measured in rapididity dependence
 data present strong dependence on rapidity acceptance EPOS1.99 qualitatively describes the data

Agnieszka Borucka (WUT)

August 24, 2021

9 / 10Thank you
Have a shiny day! ;)This work was supported by the Polish National Science Centre grant 2016/21/D/ST2/01983
and by WUT ID-UB.
Agnieszka Borucka (WUT)

August 24, 2021

10 / 10

Backup

Agnieszka Borucka (WUT)

August 24, 202111 / 10

Fluctuations – p+p interactions as a reference measure
Known for decades property of multiplicity in full rapidity range in p+pinteractions is the KNO-G scalling:

For full range:(a) – multiplicity distributions measured at different energies P(n)(b) – represented as a function of ratio n/hni have pick at the same place(c) – represented as a function of ratio n/hni and multiplied by hni areadditionaly normalised

A. I. Golokhvastov,Phys. Atom. Nucl.64, 84, 2001
Agnieszka Borucka (WUT)

arXiv:nucl-th/0003046v5 3 May 2001
August 24, 2021

12 / 10

Fluctuations – acceptance dependence
In modern experiments we usually do not measure everything.
∆Ytotal – range of the total measured distribution∆Yaccept – range of the accepted charged particles∆Ycorr – charge correlation length∆Ykick – rapidity shift blurring acceptance boundaries
arXiv:0810.2520v1 [nucl-th] 14 Oct 2008
total charge

Extream cases: full range – everything is detected, eg. there is no net-charge
fluctuation

net-charge

 infinitesimally small range – only single particles are measured
Searching for CP requires ∆Ycorr << ∆Yaccept << ∆YtotalarXiv:nucl-th/0003046v5 3 May 2001

arXiv:1512.05038v2 [nucl-th] 15 May 2016
Agnieszka Borucka (WUT)

August 24, 2021

13 / 10

1% Be+Be
p+pNA61/SHINE preliminary-h+-h

1% Ar+Sc

21κ4/ κ21.2

κ3/ κ1-κ2[h+-h ]+〈h 〉+〈h 〉System size and energy dependence – net-charge

NA61/SHINE preliminary
p+p
1% Be+Be
1% Ar+Sc

540.8h+-hNA61/SHINE preliminary
p+p
1% Be+Be
1% Ar+Sc310.6-620.4

100.2

04−1−106810 12 14 16 18

468sNN (GeV)

1012141618sNN (GeV)

4681012141618sNN (GeV)

 p+p≈Be+Be≈Ar+Sc except for κ3 /κ1Agnieszka Borucka (WUT)

August 24, 2021

14 / 10

1.6
1.4-h

1.6

NA61/SHINE preliminary

p+p
1% Be+Be
1% Ar+Sc

1.4
1.2

1.2

κ4/ κ2

1.8

κ3/ κ2κ2/ κ1

System size and energy dependence – negative charge

3.5-hNA61/SHINE preliminary

p+p
1% Be+Be
1% Ar+Sc

2.51.50.8

0.8

0.6

0.6

0.4

0.4

00.2

0.2

−0.5

4681012141618

sNN (GeV)

04-hNA61/SHINE preliminary
p+p1% Be+Be
1% Ar+Sc

211310.5681012141618

sNN (GeV)

4681012141618

sNN (GeV)

 p+p6≈Ar+Sc in case of κ2 /κ1 but not for higher-order ratios

Agnieszka Borucka (WUT)

August 24, 2021

15 / 10

Rapidity dependence – negative charge
Constant bin – sensitivity for different
measurements conditions.

 EPOS1.99 qualitatively agrees withdata the strongest signal for yπ < 1.5
Dashed blue line – value in full analysis acceptanceDashed violet line – 1 (reference for Poisson distribution)
Agnieszka Borucka (WUT)

August 24, 2021

16 / 10

Rapidity dependence – net-charge
Constant bin – sensitivity for different
measurements conditions.

 EPOS1.99 qualitatively agrees withdata the strongest signal for yπ < 1.5
Dashed green line – value in full analysis acceptanceDashed violet line – 1 (reference for Poisson distribution)
Agnieszka Borucka (WUT)

August 24, 2021

17 / 10

Rapidity dependence – negative charge

Expanding bin - comparision of shortand long-range correlations.

 EPOS1.99 doesn’t agree with data
Dashed blue line – value in full analysis acceptanceDashed violet line – 1 (reference for Poisson distribution)

Agnieszka Borucka (WUT)

August 24, 2021

18 / 10

Rapidity dependence – net-charge

Expanding bin - comparision of shortand long-range correlations.

 EPOS1.99 is comparable with data
Dashed green line – value in full analysis acceptanceDashed violet line – 1 (reference for Poisson distribution)

Agnieszka Borucka (WUT)

August 24, 2021

19 / 10