Title: ENERGY DEPENDENCE OF NET Λ FLUCTUATIONS MEASURED BY THE STAR DETECTOR AT RHIC
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PAs (alphabetically): Rene Bellwied (UH), Nalinda Kulathunga (UH), William J. Llope (WSU)

Targeted Journal : PLB / PRC

Abstract
The measurement of conserved charge distributions have generated considerable interest in understanding the cumulants of conserved quantum numbers in QCD phase diagram, in particular the behavior near a possible critical end point and hadronization near chemical freeze-out line. Net protons and net kaons have been used as proxies for the net baryon and net strangeness, respectively. In this work, we  show the measurement of efficiency corrected and centrality bin width corrected cumulant ratios (C₂/C₁, C₃/C₂) of net Λ, in the context of both strangeness and baryon number conservation, for five beam energies (√s_NN = 19.6, 27, 39, 62.4 and 200 GeV) from Au + Au collisions at STAR as a function of collision energy, centrality and rapidity. We compare our results to the Poisson and negative binomial expectations. Results are presented with UrQMD and HRG model predictions. Both NBD and Poisson baselines agree with data within the statistical and systematic uncertainties. UrQMD show agreement with measured net Λ C₁ and C₃, but deviates from C₂ and deviation increases as a function of increasing collision energy. The ratios of lower cumulants show no features of critical fluctuations. The chemical freeze-out parameters extracted from a specific HRG calculation, which was successfully used to describe the net proton, net kaon and net charge data indicate Λ freeze-out conditions similar to those of kaons, but show large deviations when compared to the temperatures obtained from net proton fluctuations. The net Λ fluctuations show a weak, but finite , dependance on the rapidity coverage in the acceptance of the detector.
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Previous presentations at STAR:

1. STAR collaboration meeting - 2016 - OSU
    drupal.star.bnl.gov/STAR/system/files/NL_update_01.pdf

2. STAR analysis meeting - 2016 - LBNL
    drupal.star.bnl.gov/STAR/system/files/NLambda_Update-02.pdf

3. STAR collaboration meeting - 2017 - BNL
    drupal.star.bnl.gov/STAR/system/files/Net_Lambda_BNL.pdf

4. STAR analysis meeting - 2017 - BNL
    drupal.star.bnl.gov/STAR/system/files/AnalysisMeeting_NetLambda.pdf

5. STAR collaboration meeting - 2018 - LBNL
    drupal.star.bnl.gov/STAR/system/files/Net_Lambda_Update_0.pdf

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Paper proposal presentation:

1. Paper proposal
    www.star.bnl.gov/protected/bulkcorr/nalinda/Presentations/paper/PWG_Preview_Aug15_01.pdf

2. Paper proposal update 02
    www.star.bnl.gov/protected/bulkcorr/nalinda/Presentations/paper/Sep5_PWG.pdf

3. Paper proposal update 03
    www.star.bnl.gov/protected/bulkcorr/nalinda/Presentations/paper/PWG_Paper_Update3_sep19.pdf

4. Paper proposal update 04
  drupal.star.bnl.gov/STAR/system/files/PWG_update_OCT10.pdf

5. Paper proposal update 05
drupal.star.bnl.gov/STAR/system/files/PaperProposalUpdated_Nov19.pdf

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Analysis note:
Initial version,
drupal.star.bnl.gov/STAR/system/files/Analysis_Note_netLambda_Paper_SHORT.pdf
Update 01,
drupal.star.bnl.gov/STAR/system/files/Analysis_Note_netLambda_Paper_Update_01.pdf
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Paper draft versions:
Update 01:
drupal.star.bnl.gov/STAR/system/files/NetLambda_paper_draft_01.pdf
Update 02(PRC):
drupal.star.bnl.gov/STAR/system/files/NetLambda_paper_update_02_PRC.pdf
Update 02(PLB):
https://drupal.star.bnl.gov/STAR/system/files/NetLambda_paper_update_02_PLB.pdf
Update 03 (PRC):
drupal.star.bnl.gov/STAR/system/files/NetLambda_paper_update_03_PRC.pdf
Update 04 (PRC):
drupal.star.bnl.gov/STAR/system/files/NetLambda_paper_update_04_PRC.pdf
Update 05 (PRC)
drupal.star.bnl.gov/STAR/system/files/NetLambda_paper_update_05_PRC.pdf
Update 06 (PRC)
drupal.star.bnl.gov/STAR/system/files/NetLambda_paper_update_06_PRC.pdf
Update 07 (PRC) - After Institutional Reviews
drupal.star.bnl.gov/STAR/system/files/NetLambda_paper_update_07_PRC.pdf
Update 08 (PRC)
drupal.star.bnl.gov/STAR/system/files/NetLambda_paper_update_08_PRC.pdf
Update 09 (PRC)
drupal.star.bnl.gov/STAR/system/files/NetLambda_paper_update_09_PRC.pdf
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Responses to PWGC comments and suggestions:
drupal.star.bnl.gov/STAR/system/files/Responses_to_PWGC_NetLambda.pdf

Responses to Institutional reviews:
drupal.star.bnl.gov/STAR/blog/nalinda/institutional-reviews-net-lambda-paper
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Figure 02: Centrality dependance of net Lambda cumulant ratio, C₂/C₁ at Au + Au collision energies; 19.6, 27, 39, 62.4 and 200 GeV. NBD and Poisson baselines are presented by dashed lines. UrQMD predictions are shown in solid lines. Black vertical lines represent the statistical uncertainties and caps represent systematic uncertainties. Results are corrected using p_T dependent efficiency correction. CBWC is applied.______________________________________________________________________________________________________________________________________________________________ 

Figure 03: Centrality dependence of net Lambda cumulant ratio, C₃/C₂ at Au + Au collision energies; 19.6, 27, 39, 62.4 and 200 GeV. NBD and Poisson baselines are presented by dashed lines. UrQMD predictions are shown in solid lines. Black vertical lines represent the statistical uncertainties and caps represent systematic uncertainties. Results are corrected using p_T dependent efficiency correction. CBWC is applied. ___________________________________________________________________________________________________________________________________

 Figure 04: Beam energy dependance of  net Lambda cumulant ratios, C₂/C₁ and C₃/C₂ in most central (0-5%) and peripheral (50-60%) Au + Au collision. NBD and Poisson baselines are presented by dashed lines. UrQMD predictions are shown in solid lines. Black vertical lines represent the statistical uncertainties and caps represent systematic uncertainties. Results are corrected using p_T dependent efficiency correction. CBWC is applied. 

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Figure 05: Beam energy dependance of  net Lambda (in black), net proton (in red) and net kaon (in blue) cumulant ratios, C₂/C₁ and C₃/C₂ in most central (0-5%) Au + Au collision. NBD and Poisson baselines are presented by dashed lines. The vertical lines represent the statistical uncertainties and caps represent systematic uncertainties. Results are corrected for reconstruction efficiency CBWC is applied. 

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Figure 06: Black markers show the beam energy dependance of measured net Lambda cumulant ratios, (a). C₂/C₁ and (b). C₃/C₂ in most central (0-5%) Au + Au collisions. Magenta lines show the net Lambda cumulant ratios calculated in HRG [1] assuming Lambda freezes-out (FO) at the same freeze-out conditions as for the kaons. Pink lines show the net Lambda cumulant ratios calculated in HRG [1] assuming lambda freezes-out at the same freeze-out conditions as for the charge/proton freeze-out. For the measurement, vertical bars and caps represent statistical and systematic uncertainties, respectively. Uncertainties in HRG calculations are shown by the width of the bands.
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Figure 07: Rapidity dependance of net Lambda cumulant ratios, (a). C₂/C₁ and (b). C₃/C₂ in 0-5% central, 200 GeV Au + Au collisions. Dashed lines show the NBD expectations. Vertical error bars represent the statistical uncertainties and caps represent the systematic uncertainties. Results are corrected for reconstruction efficiency and CBWC is applied.

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SUMMARY:
  
1. We have analyzed first three cumulants; C₁, C₂, C₃ and cumulant ratios C₂/C₁, C₃/C₂ for net Lambda multiplicity distributions as a function of collision energy, centrality and rapidity.

2. Results were corrected for reconstruction efficiency and centrality bin width correction (CBWC) was applied. Feed-down corrections show no effect in the cumulant ratios. 

3. All three single cumulants and their ratios can be described by Poisson and NBD baselines.

4.The variance (C₂) shows significant deviations from UrQMD predictions which increase as a function of centrality and collision energy.

5. The net Lambda cumulant ratios can be described by the latest HRG model [1].

1. Bellwied, R. et. al. Freeze-out temperature form net kaon fluctuations at RHIC. arXiv:1805.0088v1 [hep-ph]
2. P. Braun-Munzinger et. al. Bridging the gap between event-by-event fluctuation measurement and theory predictions in relativistic nuclear collisions.
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