Presence of Non-dynamical Fluctuations in the Higher ... · Prakhar Garg: CPOD 2017 4 Several...

ìPresence of Non-dynamical Fluctuations in the Higher Moments of Net-proton Measurements

Prakhar Garg Department of Physics and Astronomy

Stony Brook University

OUTLINE

z BriefIntroduc.onz SourcesofNon-dynamicalFluctua.ons

z MCstudiesforstoppedprotonsandpile-upcontribu.ons

z Conclusion

2PrakharGarg:CPOD2017

BESMotivation:CEP

BaryonChemicalPoten.al(μB)

Tempe

rature

NuclearMaLerHadronGas

QuarkGluonPlasma

LHC

RHIC

CBM

 The temperature driven transi.on at zeroµB indicate a rapid crossover from thehadronicphasetotheQGPphase.

 TheµBdriventransi.onatfiniteTisafirst

orderphasetransi.on. Afirstorderlineorigina.ngatzeroT must

end somewhere in themidst of the phasediagram where the phase transi.on is acrossover

This end point of a first order phase transition line is a critical end point (CEP)

Limitedtheore.calguidance,needdata!!

3

?

PrakharGarg:CPOD2017

Fluctua(ons:TheorytoExperimentalobservablesareperformedusingcumulants

¤  Cumulantsoffluctua.onsofconservedquan..esarerelatedtothermodynamicsuscep.bili.es(La$ceQCDandHadronResonanceGas(HRG)model)

Cumulantra.osareIndependentofVolume

M.Chengetal,Phys.Rev.D79,074505(2009)F.KarschandK.Redlich,Phys.LeB.B695,136(2011)

v 1stmoment:meanµ=<x>v 2ndcumulant:varianceκ2=σ2=<(x-µ)2>v 3rdcumulant:κ3=μ3=<(x-µ)3>v 3rdstandardizedcumulant:skewness=S=κ3/κ2

3/2=<(x- µ)3>/σ3

v 4thcumulant:κ4=<(x-µ)4>-3κ22

v 4thstandardizedcumulant:kurtosis=κ=κ4 /κ2

2={<(x- µ)4>/σ4}-3

Calculate moments from theevent-by-event net-mul(plicitydistribu(onΔN=N+-N-

κ2κ1

=σµ

2

=χ2χ1

κ4κ2

=κσ 2 =χ4χ2

κ3κ2

= Sσ =χ3χ2


SeveralMeasurements

5

Net-Proton Fourth-Order Fluctuation

Ø Non-monotonic energy dependence is observed for4th order net-proton, protonfluctuations in most centralAu+Au collisions.

Ø UrQMD results showmonotonic decrease withdecreasing collision energy.

STARPreliminary

aB5 = -2-5

Roli Esha (UCLA)August7,2017 11

RAPID COMMUNICATIONS

MEASUREMENT OF HIGHER CUMULANTS OF NET-CHARGE . . . PHYSICAL REVIEW C 93, 011901(R) (2016)

collisions at different collision energies. These !Nch distri-butions are not corrected for reconstruction efficiency. Thecentrality classes associated with the average number ofparticipants, ⟨Npart⟩, are defined for each 5% centrality bin.These classes are determined using a Monte-Carlo simulationbased on Glauber model calculations with the BBC, RXNP,and EMCal detector responses taken into account [22,23].

The !Nch distributions are characterized by cumulants andrelated quantities, such as µ, σ , S, and κ , which are calculatedfrom the distributions. The statistical uncertainties for thecumulants are calculated using the bootstrap method [24].Corrections are then made for the reconstruction efficiency,which is estimated for each centrality and energy using theHIJING1.37 event generator [25] and then processed througha GEANT simulation with the PHENIX detector setup. Forall collision energies, the average efficiency for detectingthe particles within the acceptance varies between 65%–72%and 76%–85% for central (0%–5%) and peripheral (55%–60%) events, respectively, with a 4%–5% variation as afunction of energy. The efficiency correction applied to thecumulants is based on a binomial probability distribution forthe reconstruction efficiency [26]. The efficiency correctedµ, σ , S, and κ as a function of ⟨Npart⟩ are shown inFigs. 1(c)–1(f).

The µ and σ for net-charge distributions increase withincreasing ⟨Npart⟩, while S and κ decrease with increasing⟨Npart⟩ for all collision energies. At a given ⟨Npart⟩ value, µ,S, and κ of net-charge distributions decrease with increasingcollision energy. However, the width σ of net-charge distribu-tions increases with increasing collision energy indicating theincrease of fluctuations in the system at higher

√s

NN.

The systematic uncertainties are estimated by: (1) varyingthe Zvertex cut to less than ±10 cm; (2) varying the matchingparameters of PC3 hits and EMCal clusters with the projectedtracks to study the effect of background tracks originatingfrom secondary interactions or from ghost tracks; (3) varyingthe centrality bin width to study nondynamical contributionsto the net-charge fluctuations due to the finite width of thecentrality bins [27–29]; and (4) varying the lower cut. The totalsystematic uncertainties estimated for various cumulants forall energies are: 10%–24% for µ, 5%–10% for σ , 25%–30%for S, and 12%–19% for κ . The systematic uncertainties aresimilar for all centralities at a given energy and are treated asuncorrelated as a function of

√s

NN. For clarity of presentation,

the systematic uncertainties are only shown for central (0%–5%) collisions.

Figure 2 shows the ⟨Npart⟩ dependence of µ/σ 2, Sσ ,κσ 2, and Sσ 3/µ[= (Sσ )/(µ/σ 2)] extracted from the net-charge distributions in Au + Au collisions at different

√s

NN.

The results are corrected for the reconstruction efficiencies.Statistical uncertainties are shown along with the data points.The systematic uncertainties are constant fractional errorsfor all centralities at a particular energy; hence they arepresented for the central (0%–5%) collision data point only.The systematic uncertainties on these ratios across differentenergies varies as follows: 20%–30% for µ/σ 2, 15%–34%for Sσ , 12%–22% for κσ 2, and 17%–32% for Sσ 3/µ. It isobserved in Fig. 2 that the ratios of the cumulants are weaklydependent on ⟨Npart⟩ for each collision energy; the values of

2 σ/ µ

0.01

0.1

1 Net-charge Au+Au| < 0.35η|

(a)

σS

0.0

0.2

0.4

0.67.7 GeV19.6 GeV27 GeV

39 GeV62.4 GeV200 GeV

(b)

⟩ part

N⟨100 200 300

2 σ κ

0.5

1.0

1.5

2.0(c)

PHENIX

⟩ part

N⟨100 200 300

µ/3 σS

0.5

1.0

1.5

2.0(d)

FIG. 2. ⟨Npart⟩ dependence of efficiency corrected (a) µ/σ 2, (b)Sσ , (c) κσ 2, and (d) Sσ 3/µ of net-charge distributions for Au + Aucollisions at different collision energies. Statistical errors are shownalong with the data points while systematic uncertainties are shownfor (0%–5%) collisions.

µ/σ 2 and Sσ decrease from lower to higher collision energies,while the κσ 2 and Sσ 3/µ values are constant as a function of√

sNN

within systematic uncertainties.The collision energy dependence of µ/σ 2, Sσ , κσ 2 and

Sσ 3/µ of the net-charge distributions for central (0%–5%)Au + Au collisions are shown in Fig. 3. The statistical andsystematic uncertainties are shown along with the data points.The experimental data are compared with negative-binomial-distribution (NBD) expectations, which are calculated bycomputing the efficiency corrected cumulants for the measuredN+ and N− distributions fit with NBD’s respectively, whichalso describe total charge (N+ + N−) distributions very well

2 σ/µ

0.01

0.1

1 Net-chargeAu+Au (0-5)%

| < 0.35η|

(a)

σS

0.0

0.2

0.4

0.6PHENIX(b)

Data

NBD

(GeV)NNs10 100

2 σ κ

0.5

1.0

1.5

2.0(c)

(GeV)NNs10 100

µ/3 σS

0.5

1.0

1.5

2.0(d)

FIG. 3. The energy dependence of efficiency corrected (a) µ/σ 2,(b) Sσ , (c) κσ 2, and (d) Sσ 3/µ of net-charge distributions forcentral (0%–5%) Au + Au collisions. The error bars are statisticaland caps are systematic uncertainties. The triangle symbol shows thecorresponding efficiency corrected cumulant ratios for net charge,from NBD fits to the individual N+ and N− distributions.

011901-5

RoliEshatalkinCPOD2017(STAR)

Phys.Rev.LeB.112,032302(2014)(STAR)

Phys.Rev.C93,011901(R)(2016)(PHENIX)

values for the Poisson baselines are always unity. Forperipheral collisions the κσ2 values show almost novariation as a function of beam energy and lie above thePoisson baseline and below the NBD baseline. For centralcollisions, within the statistical and systematic errors of thedata, the κσ2 values at all energies are consistent with eachother, except for

ffiffiffiffiffiffiffiffisNN

p ¼ 7.7 GeV. The weighted mean ofκσ2 calculated for central collisions at all energies is2.4" 1.2. For central collisions, both of the baselinecalculations follow the data points except for the one atthe lowest energy. Deviations of the data points withrespect to the baseline calculations have been quantifiedin terms of the significance of deviation, defined as

ðjData − BaselinejÞ=ðffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffierr2stat þ err2sys

qÞ, where errstat and

errsys are the statistical and systematic errors, respectively.These deviations remain within 2 in the case of Sσ and κσ2

with respect to the corresponding Poisson and NBD base-lines. This implies that the products of moments do notshow nonmonotonic behavior as a function of beam energy.The fluctuations of conserved quantities can be used to

extract the thermodynamic information on chemical freeze-out by comparing experimentally measured highermoments with those from first-principle lattice QCDcalculations [23]. Traditionally, by using the integrated

hadron yields, the first moment of the fluctuations, thechemical freeze-out have been extracted from hadronresonance gas (HRG) models [25,41]. However, higher-order correlation functions should allow stricter tests on thethermal equilibrium in heavy-ion collisions. Calculations offreeze-out parameters based on preliminary experimentaldata on moments of net-charge distributions have beenobtained [42,43]. From the latest lattice [44] and HRGanalyses [45] using the STAR net-charge and net-protonresults for central Auþ Au collisions at 7.7 to 200 GeV, theextracted freeze-out temperatures range from 135 to151 MeV and μB values range from 326 to 23 MeV. Theerrors in these calculations increase from 2% to 10% as afunction of decreasing beam energy, which is mostly due tothe statistical uncertainty in the experimental measure-ments. More details can be found in Refs. [44,45]. Note thatthis is the first time that the experimentally measured highermoments have been used to determine the chemical freeze-out conditions in high-energy nuclear collisions. Thefreeze-out temperatures obtained from the higher momentsanalysis are lower with respect to the traditional method[25,46]. This difference could indicate a higher sensitivityto freeze-out in the higher moments, which warrants furtherinvestigation.In summary, the first results of the moments of net-

charge multiplicity distributions for jηj < 0.5 as a functionof centrality for Auþ Au collisions at seven collisionenergies from

ffiffiffiffiffiffiffiffisNN

p ¼ 7.7 to 200 GeV are presented.These data can be used to explore the nature of theQCD phase transition and to locate the QCD critical point.We observe that the σ2=M values increase monotonicallywith increasing beam energy. Weak centrality dependenceis observed for both Sσ and κσ2 at all energies. The Sσvalues increase with decreasing beam energy, whereas κσ2

values are uniform except at the lowest beam energy. Mostof the data points show deviations from the Poissonbaselines. The NBD baselines are closer to the data thanthe Poisson baselines, but do not quantitatively reproducethe data, implying the importance of intraevent correlationsof the multiplicities of positive and negative particles in thedata. Within the present uncertainties, no nonmonotonicbehavior has been observed in the products of moments as afunction of collision energy. The measured moments of net-charge multiplicity distributions provide unique informa-tion about the freeze-out parameters by directly comparingwith theoretical model calculations. Future measurementswith high statistics data will be needed for a precisedetermination of the freeze-out conditions and to makedefinitive conclusions regarding the critical point.

We thank M. Asakawa, R. Gavai, S. Gupta, F. Karsch,V. Koch, S. Mukherjee, K. Rajagopal, K. Redlich, andM. A. Stephanov for discussions related to this work. Wethank the RHIC Operations Group and RCF at BNL, theNERSC Center at LBNL, the KISTI Center in Korea, andthe Open Science Grid consortium for providing resources

M2 σ

10

210Net-charge

Au+Au| < 0.5η|

(a)

σS

0

0.2

0.4

0.6 (b)

(GeV)NNs√5 6 10 20 30 100 200

2 σκ

-15

-10

-5

0

5(c)

0-5%70-80%0-5% NBD70-80% NBD0-5% Poisson70-80% Poisson

FIG. 4 (color online). Beam-energy dependence of (a) σ2=M,(b) Sσ, and (c) κσ2, after all corrections, for most central(0%–5%) and peripheral (70–80%) bins. The error bars arestatistical and the caps represent systematic errors. Results fromthe Poisson and NBD baselines are superimposed. The values ofκσ2 for the Poisson baseline are always unity.

PRL 113, 092301 (2014) P HY S I CA L R EV I EW LE T T ER Sweek ending

29 AUGUST 2014

092301-6

Phys.Rev.LeB.113,092301(2014)(STAR)

Helen Caines - RHIC&AGS Users Meeting 17

Presence of Critical Point?

11

M. Stephanov. PRL 107:052301(2011)

Correlation lengths diverge → Net-p κσ2 diverge

Hints of Critical fluctuations

HADES data + upcoming FXT testing if mapping correct

New HADES data causing some tension

Comparison with STAR BES-I

red/black = unfolding (preferred method) + vol. flucs. corr.

green = evt-by-evt eff correction of factorial moments + vol. flucs. corr.

HADES preliminary

HADES preliminary

STAR analysis: Xiaofeng Luo et al., PoS (CPOD2014) 019 arXiv:1503.02558v2

QM2017 February 6 - 11, 2017 Chicago IL 20

3

and δ = 5, which are within few percent of their exactvalues in three dimensions. The result of Eq. (9) can thenbe simplified to

κ4(t,H) = −1281− 783θ2 + 105θ4 − 5θ6 + 2θ8

R14/3(3− θ2)3(3 + 2θ2)5. (10)

We represent κ4(t,H) graphically as a density plot inFig. 1. We see that the 4-th cumulant (and kurtosis)is negative in the sector bounded by two curved raysH/tβδ = ±const (corresponding to θ ≈ ±0.32).

(a)

!0.4 !0.2 0.0 0.2 0.4 0.6!20

020406080

100120

t

Κ4

(b)

FIG. 1: (color online) (a) – the density plot of the functionκ4(t,H) given by Eq. (10) obtained using Eq. (9) for the linearparametric model Eqs. (6), (7), (8) and β = 1/3, δ = 5. Theκ4 < 0 region is red, the κ4 > 0 – is blue. (b) – the dependenceof κ4 on t along the vertical dashed green line on the densityplot above. This line is the simplest example of a possiblemapping of the freezeout curve (see Fig. 2). The units of t,H and κ4 are arbitrary.

Also in Fig. 1 we show the dependence of κ4 along aline which could be thought of as representing a possiblemapping of the freezeout trajectory (Fig. 2) onto the tHplane. Although the absolute value of the peak in κ4

depends on the proximity of the freezeout curve to thecritical point, the ratio of the maximum to minimumalong such an H = const curve is a universal number,approximately equal to −28 from Eq. (10).

µB, GeV

, GeV

0

0.1

T

t

1

H

criticalpoint

freezeoutcurve

nuclearmatter

QGP

hadron gas

FIG. 2: A sketch of the phase diagram of QCD with the freeze-out curve and a possible mapping of the Ising coordinates tand H .

The negative minimum is small relative to the positivepeak, but given the large size of the latter, Ref.[7, 15],the negative contribution to kurtosis may be significant.In addition, the mapping of the freezeout curve certainlyneed not be H = const, and the relative size of the posi-tive and negative peaks depends sensitively on that.The trend described above appears to show in the re-

cent lattice data, Ref.[10], obtained using Pade resum-mation of the truncated Taylor expansion in µB. As thechemical potential is increased along the freezeout curve,the 4-th moment of the baryon number fluctuations be-gins to decrease, possibly turning negative, as the criticalpoint is approached (see Fig.2 in Ref.[10]).Another observation, which we shall return to at the

end of the next section, is that −κ4 grows as we approachthe crossover line, corresponding to H = 0, t > 0 on thediagram in Fig. 1(a). On the QCD phase diagram thefreezeout point will move in this direction if one reducesthe size of the colliding nuclei or selects more peripheralcollisions (the freezeout occurs earlier, i.e., at higher T ,in a smaller system).

EXPERIMENTAL OBSERVABLES

In this section we wish to connect the results for thefluctuations of the order parameter field σ to the fluctua-tions of the observable quantities. As an example we con-sider the fluctuations of the multiplicity of given chargedparticles, such as pions or protons.For completeness we shall briefly rederive the results of

Ref.[7] using a simple model of fluctuations. The modelcaptures the most singular term in the contribution of thecritical point to the fluctuation observables. Consider agiven species of particle interacting with fluctuating crit-ical mode field σ. The infinitesimal change of the field δσleads to a change of the effective mass of the particle bythe amount δm = gδσ. This could be considered a def-inition of the coupling g. For example, the coupling ofprotons in the sigma model is gσp̄p. The fluctuations δfp

NB: Different y and pT ranges R. Holzmann QM2017

N.B. non-monotonic behavior not observed by PHENIX - due to different acceptances? (PRC 93, 011901 (2016))

Nor in pp or light nuclei by NA61(PRC 93, 011901 (2016))

HelenCainestalkinRHIC&AGSUsersMeeUng-2017

10 210

10

20

30

40

0-5% STAR 70-80% STAR 0-5% Poisson

70-80% Poisson 0-5% UrQMD

0-5% NBD70-80% NBD

<1.6(GeV/c),|y|<0.5T

0.2<pNet-kaonAu+Au Collisions at RHIC(a)

10 210

0

1

2(b)

STAR Preliminary

7 8 910 20 30 40 100 200

2−

0

2(c)

(GeV)NNs2

σκ

/M2σ

/Ske

llam

σS

Figure 4. Energy dependence of cumulant ratios (�2/M, S�/Skellam, �

2) of net-kaonmultiplicity distributions for top 0-5% central and 70-80% peripheral collisions at Au+Aucollisions at

psNN = 7.7, 11.5, 14.5, 19.6, 27, 39, 62.4, and 200GeV. The Poisson and NBD

expectations are denoted as dotted and solid lines, UrQMD calculations are shown as bluebands. The error bars are statistical errors and the caps represent systematic errors.

phase-space to enhance the search for the QCD critical point in the high net-baryon densityregion 420 < µB < 250 MeV (7.7 <

psNN < 19.6 GeV) .

Acknowledgments

The work was supported in part by the MoST of China 973-Project No.2015CB856901, NSFCunder grant No. 11575069, 11221504.

References

[1] M. A. Stephanov, Phys. Rev. Lett. 102, 032301 (2009).[2] M. Asakawa et al., Phys. Rev. Lett. 103 262301 (2009).[3] M. A. Stephanov, Phys. Rev. Lett. 107 052301 (2011).[4] R. V. Gavai and S. Gupta, Phys. Rev. D 78, 114503 (2008).[5] M. Cheng et al., Phys. Rev. D 79, 074505 (2009); A. Bazavov et al., arXiv:1203.0784.[6] S. Borsanyi et al., JHEP01, 138 (2012).[7] F. Karsch and K. Redlich, Phys. Lett. B 695, 136 (2011).[8] P. Garg et al., Phys. Lett. B 726, 691 (2013).[9] Marlene Nahrgang et al., arXiv: 1402.1238.

[10] J. Fu, Phys. Lett. B 722, 144 (2013).[11] S. Gupta, X. Luo, B. Mohanty, H. G. Ritter and N. Xu, Science 332, 1525 (2011).[12] Aggarwal M M et al. (STAR Collaboration) 2010 Phys. Rev. Lett. 105 022302[13] X. Luo (STAR Collaboration), Nucl. Phys. A 904 911c (2013).[14] X. Luo, arXiv:1512.09215[15] X. Luo, J. Phys. G: Nucl. Part. Phys. 39 025008 (2012).[16] X. Luo, Phys. Rev. C 91, 034907 (2015).[17] L. Adamczyk et al., (STAR Collaboration), Phys. Rev. Lett.113, 092301 (2014).

4

JiXutalkinsQM-2016


SourcesofNon-dynamicalFluctuations

6

¤  Effectofphase-spaceacceptance:P.Garg,D.K.Mishraetal.(Phys.LeB.B726(2013)691-696)FrithjofKarschelal.Phys.Rev.C93(2016),034907¤  Effectofe-by-eeficiencycorrec.ons:P.Garg,D.K.Mishraetal.(J.Phys.G40(2013)055103)A.BzdakandV.Koch,Phys.Rev.C86(2012),044904A.BzdakandV.Koch,Phys.Rev.C91(2015)027901¤  Effectofnon-extensivesta.s.cs:D.K.Mishra,P.Gargetal.(J.Phys.G42(2015),105105)¤  Ensembledependence:P.Garg,D.K.Mishraetal.(Eur.Phys.J.A52(2016),27)¤  Effectofcorrela.onsoncumulants:P.Garg,D.K.Mishraetal.(Phys.Rev.C93(2016),024918)¤  EffectofResonanceDecay:D.K.Mishra,P.Gargetal.(Phys.Rev.C94(2016),014905)MarleneNahrgangetal.Eur.Phys.J.C(2015)75:573¤  EffectofPar.cipantFluctua.ons:P.Braun-Munzingeretal.(NPA960(2017)114)¤  Globalbaryonnumberconserva.on:P.Braun-Munzingeretal.(PLB747(2015)292)¤  ........ANDSOON

z  EffectofstoppedprotonFluctua.ons->D.K.Mishra&P.GargarXiv:1706.04012andD.Thakur,S.Jakhar,P.Gargetal.(Phys.Rev.C95(2017),044903)z  EffectofeventPile-up->P.Garg&D.K.MishraarXiv:1705.01256

Inthistalk(fornet-protonfluctua.onmeasurements)


BaryonStopping

Ionsabouttocollide Ioncollision Quarks,gluonsfreed Plasmacreated

v Largeamountofenergyisdepositedin a small region of space in a shortdura.onof.me.

v Occurrenceofhighenergydensityregions:->BaryonrichQuarkGluonPlasma(@low√sNN)->BaryonfreeQuarkGluonPlasma(@high√sNN)

AtRHICBES-IEnergies:Inclusiveprotonscontainproducedprotonsandstoppedprotons

Numberofstoppedprotonsfluctuatee-by-eleadingtoaddi.onalfluctua.ons

Needtodisentanglethecontribu.onofstoppedprotonsandproducedprotonsExperimentallydifficulttotagstoppedprotonandproducedproton

PartI:


Getprotonandanti-protondistributionsbytuningwithSTARcumulantsdataforAu+Aucollisions

8

p

5

10

15

20 1C

Expt. dataBinomial

Au + Au (0-5)%

p

0

1

2

3

4 1C

(GeV) NNs6 10 20 100200

pp

-

05

101520 1C

2C

2C

(GeV) NNs6 10 20 100 200

2C

3C

3C

(GeV) NNs6 10 20 100 200

3C

4C

4C

(GeV) NNs6 10 20 100 200

4C1

/C 2C

0.6

0.8

1.0

1.2 p

Expt. dataBinomial

Au + Au (0-5)%

2/C 3C

0.6

0.8

1.0

1.2 p

2/C 4C 0.5

1.0p

1/C 2C

0.8

1.0

1.2 p

2/C 3C

0.8

1.0

1.2 p

2/C 4C

0.8

1.0

1.2 p

(GeV) NNs6 10 20 100200

1/C 2C

2

4

6 pp -

(GeV) NNs6 10 20 100200

2/C 3C 0.5

1.0 pp -

(GeV) NNs6 10 20 100200

2/C 4C

0.5

1.0pp -

p

TheBinomialexpecta(onsaretunedforprotonandan(-protoncumulantsdataateach√sNN

Thecumulantsindataarealreadycorrectedforefficiencyandfinitebinwidtheffects

arXiv:1706.04012STARnet-protonDATA

MCPoints

hTps://drupal.star.bnl.gov/STAR/files/starpublica(ons/205/data.html


ComparisonofStoppedProtonswith

STARresults

9

v  Alargecontribu(onofstoppedprotonsatBESenergies.v  AZer subtrac(ng the stopped protons from themean of STAR protons distribu(on, remaining

producedprotonsareconsistentwithmeanofan(-protondistribu(onmeasuredbySTAR.

Phys.Rev.C95(2017),044903

STARDATA:hTps://drupal.star.bnl.gov/STAR/files/starpublica(ons/205/data.html

Phys.LeB.B690,358(2010)


Method:Extracttheweightfactors

10

C1ofpstop_____________=Frac(onofStoppedProtonsC1ofpinclu

Phys.Rev.C95(2017),044903

Now,“assuming”thatthisfrac(onisalsodistributedaccordingtothe

Binomialdistribu(on

Wegetacorrecteddistribu(onforproducedprotons


Cumulantsandtheirratiosforindividuals

11

(GeV) NNs6 10 2030 100 200

1C

0

5

10

15

20 inclpprodpstopp

p

(GeV) NNs6 10 2030 100 200

2C0

5

10

15

20

(GeV) NNs6 10 2030 100 200

3C

0

5

10

15

20

(GeV) NNs6 10 2030 100 200

4C

0

5

10

15

20

21C

0.00.51.01.52.0 inclp

prodpstopp

p

32C

0.00.51.01.52.0

(GeV) NNs6 10 2030 100 200

42C

-0.50.00.51.01.52.0

arXiv:1706.04012

Atlowercollisionenergies,thepinclfluctua(onsaredominatedbypstopandathigherenergiestheyaredominatedbyproducedprotonfluctua(ons.


Cumulantsandtheirratiosfornet-protons

12

(GeV) NNs6 10 2030 100 200

1C

0

5

10

15

20 p- inclpp- prodp

(GeV) NNs6 10 2030 100 200

2C

0

5

10

15

20

(GeV) NNs6 10 2030 100 200

3C

0

5

10

15

20

(GeV) NNs6 10 2030 100 200

4C

0

5

10

15

20

32C

-1.0

-0.5

0.0

0.5

1.0 p- inclp

p- prodp

(GeV) NNs67810 20 3040 100 200

42C

0.4

0.6

0.8

1.0

1.2

arXiv:1706.04012

Ø  Correc.onsforstoppedprotonfluctua.onmayenhancethesignalascanbeseenforC32PrakharGarg:CPOD2017

EventPile-upEffects

13

PartII:

Ref:HarnarineIan,”AStudyofPile-upin200GeVAu+AuCollisionsatRHIC”,DoctoraldissertaOon,UniversityofIllinoisatChicago,2005.andreferencestherein.

Inhighluminosityheavy-ioncollisions,theremaybefollowingsourcesofthebackgroundeventsduringacollisionØ  In-(mepile-up:Ifmorethanonecollisionsareoccurringinthesamebunch-crossingina

collisionofinterest;

Ø  Out-of-(mepile-up:Ifaddi(onalcollisionsareoccurringinabunch-crossingbeforeandaZerthecollision.

Ø  Cavernbackground:Mainlylowenergyneutronsandphotons

Ø  Beamhaloevents:Thedispersioninthebeam

Ø  Beamgasevents:Collisionsbetweenthebunchandtheresidualgasinsidethebeam-pipe.


SimpleMCforeventpile-upstudy

14

Cou

nts

110

210

310410

510

610

710 p19.6 GeV

w/o pile-upw (0.05%) pile-up

pN0 10 20 30 40

Cou

nts

110

210310410510610 p

200 GeV

p19.6 GeV

pN0 5 10 15 20

p200 GeV

pp - 19.6 GeV

pp-N-10 0 10 20 30 40

pp - 200 GeV

arXiv:1705.01256

GeneratethePoissonorNBDDistribu.onforprotonsandan.-

protonsusingtheMeanvaluesfromSTARdata

Addextraprotonsandan.-protonscomingfrompile-upevent

Randomlyselecttheprotonmul.plicityfromMBprotonsampleandaddittotheoriginaldistribu.on

Studytheeffectoncumulantswithdifferentfrac.onofmixedevents

Ø  Theprotonandan(-protonmul(plici(esfromminimumbiasevents as pile-up are added with the individual p and p ̄distribu(onsassumingeachofthedistribu(onasNBD.


Central+MinimumBiaseventaspile-up

15

Individual cumulants for Central + min.bias assuming PoissonSimilar to Fig.2 of the draft.

Individual cumulants for Central + min.bias assuming NBDSimilar to Fig.5 of the draft

arXiv:1705.01256PoissonAssump(on NBDAssump(on

Ø  Moreimportantforhighercumulants!!PrakharGarg:CPOD2017

Central+MinimumBiaseventaspile-up

16

(GeV) NNs6 10 20 100 200

21C

2

4

6% of pileup

0.00.010.050.100.501.002.00

(a)

NBD

(GeV) NNs6 10 20 100200

32C

0

1

2

3 (b)

(GeV) NNs6 10 20 100 200

42C

1

10

210(c)

(GeV) NNs6 10 20 100200

31C

0

1

2

3

4 (d)



MostExtremeSituation(Central+Centraleventasapile-up)

17

(GeV) NNs6 10 20 100200

21C

2

4

6% of pileup

0.00.010.050.100.501.002.00

(a)

Poisson

(GeV) NNs6 10 20 100200

32C

02

4

6

8 (b)

(GeV) NNs6 10 20 100200

42C

1

10

210(c)

(GeV) NNs6 10 20 100200

31C

02468

10 (d)

(GeV) NNs6 10 20 100 200

21C

2

4

6% of pileup

0.00.010.050.100.501.002.00

(a)

NBD

(GeV) NNs6 10 20 100200

32C

0

2

4

6

8 (b)

(GeV) NNs6 10 20 100 200

42C

1

10

210(c)

(GeV) NNs6 10 20 100200

31C

02468

10 (d)



Conclusion

18

Ø StoppedProtonFluctua(onsmayhavesignificanteffecton the net-proton measurements which needs to beaddressedcarefully.

Ø Event-pile up can also influence the Fluctua(onMeasurements and should be studied in eachexperimentalset-upforcumulantsobservable.


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