Measurement of cumulants of conserved charge multiplicity distributions in Au+Au collisions from the STAR experiment
Ashish Pandav
nucl-ex



























XXVIIIth International Conference on Ultrarelativistic Nucleus-Nucleus Collisions
 (Quark Matter 2019)













School of Physical Sciences, National Institute of Science Education and Research, HBNI, Jatni-752050, INDIA




 We report the collision-centrality dependence of cumulants  of event-by-event net-proton, net-charge and net-kaon distributions in Au+Au collisions for center-of-mass energy √(s_NN) = 54.4 GeV from the STAR experiment. Strong collision-centrality dependence is observed for cumulants (C_n, n ≤ 4) of the net-particle distributions. The cumulant ratios C_3/C_2, C_4/C_2 and C_6/C_2 exhibit a weak collision-centrality dependence. The C_6/C_2 of net-proton and net-charge distributions for most central gold nuclei collisions at √(s_NN) = 54.4 GeV show positive sign while they remain negative  at 200 GeV for the same collision system. To understand effects of acceptance and baryon number conservation, the measurements are compared to expectations from the UrQMD and HIJING models calculated within the STAR detector acceptance.




QCD phase diagram, QCD critical point, conserved charge fluctuations, cumulants
















§ INTRODUCTION


One of the major goals of heavy-ion collision experiments is to explore the Quantum Chromodynamics (QCD) phase diagram and search for the QCD critical point. Lattice QCD calculations have shown that for vanishing baryonic chemical potential (μ_B), the nature of phase transition between quark-gluon plasma (QGP) and hadronic matter is a smooth crossover <cit.> whereas QCD-based models suggest this phase transition to be of first order for finite  μ_B <cit.>. The cumulants of conserved quantities in strong interactions are proposed to be sensitive observables for the search of the QCD critical point and the phase transition between quark-gluon plasma (QGP) and hadronic matter <cit.>. The cumulants and their ratios are related to the correlation length of the hot and dense medium formed in the heavy ion collisions and the thermodynamic susceptibilities that are calculable via various QCD-based models and lattice QCD <cit.>.

 Cumulants quantify the traits of a distribution, for example, the first- and second-order cumulant (C_1 and C_2) are the mean and variance of a distribution whereas the third- and fourth-order cumulants (C_3 and C_4) reflect the skewness and kurtosis of a distribution, respectively. Cumulants and their ratios for event-by-event distributions of net-charge, net-kaon and net-proton in collision of gold nuclei were measured by the STAR detector in the phase I of Beam Energy Scan (BES) program at the Relativistic Heavy Ion Collider (RHIC) <cit.>. Non-monotonic dependence on beam energy is observed for the cumulant ratios C_3/C_2 and C_4/C_2 of net-proton distribution in the most central (0-5%) collisions, which may hint at existence of a possible critical point. The sixth-order cumulants (C_6) could also provide insights into the nature of phase transition. Negative C_6/C_2 of net-baryon and net-charge distributions are predicted from a QCD-based model for crossover phase transitions, if the chemical freeze-out is close to the chiral phase transition <cit.>.
 
 

§ ANALYSIS TECHNIQUES

 About ∼ 550 million events are analysed for obtaining cumulants of net-particle distributions in Au+Au collisions at √(s_NN) = 54.4 GeV. Time Projection Chamber (TPC) and Time-of-Flight (TOF) detectors <cit.> are used to select protons (antiprotons) within p_T range 0.4 – 2.0 GeV/c, and charged pions and kaons within p_T range 0.2 – 1.6 GeV/c. The rapidity coverage |y|< 0.5 is used to select charged particles for measuring net-proton and net-kaon cumulants while psuedorapidity coverage |η|< 0.5 is considered for charged particle selection for net-charge fluctuation measurements. The collision centrality is determined from the charged particle multiplicity excluding the particles of interest to avoid the autocorrelation effect <cit.>. In order to suppress the volume fluctuation effects, centrality bin width correction is applied to the measurement of the cumulants <cit.>. Cumulants are correction for finite efficiency and acceptance effects of the detector with the assumption that the distribution of the detector response is binomial <cit.>. For estimation of statistical uncertainties of cumulants and their ratios, delta theorem method and a resampling method called the bootstrap are used <cit.>. Systematic uncertainties of the C_n's are estimated varying tracking efficiency, track selection and particle identification criteria. 
 
 

§ RESULTS

 

 §.§ Cumulants of net-particle distributions

 Cumulants up to the 4^th order of the event-by-event net-proton, net-charge and net-kaon distributions for Au+Au collisions at √(s_NN) = 54.4 GeV as a function of collision centrality (given by the average number of participant nucleons, <Npart>) are presented in Fig. 1. The statistical and systematic uncertainties on the measurements are shown by red bars and black brackets, respectively. Cumulants of the net-partcle distributions increase from peripheral to central collisions. Cumulants of the net-charge distribution have the largest statistical uncertainties for a given centrality which can be attributed to the larger width of net-charge distributions among all net-particle distributions for a given centrality.








 


 §.§ Cumulant ratios of net-particle distributions

Figure 2 shows collision-centrality dependence of cumulant ratios C_2/C_1, C_3/C_2 and C_4/C_2 (σ^2/M, Sσ and κσ^2 respectively) of net-particle distributions constructed from the measured cumulant values. While C_2/C_1 decreases with collision centrality, the cumulant ratios C_3/C_2 and C_4/C_2 exhibit a weak dependence on collision centrality for net-proton, net-charge and net-kaon distributions. The expectations from the UrQMD and HIJING models are also compared to the measurements <cit.>. The model expectations are inconsistent with the measurements and only qualitatively reproduce the measured centrality dependence of the cumulant ratios. The Skellam baseline for C_4/C_2, which is the expected value of C_4/C_2 under the assumption that protons and antiprotons follow Poisson distribution independently, fails to describe the measured values.
 


 §.§ Beam energy dependence of C_4/C_2 of net-particle distributions

Beam-energy dependence of the cumulant ratio C_4/C_2 of net-particle distributions for peripheral (70-80%) and most central (0-5%) collisions with inclusion of the results from the current measurement (open and solid red markers respectively) are shown in the Fig. 3. Non-monotonic beam energy dependence of C_4/C_2 is observed for net-proton distribution while  C_4/C_2 of net-charge and net-kaon distributions show monotonic variation as a function of beam energy. The new C_4/C_2 measurements of net-particle distributions at √(s_NN) = 54.4 GeV are consistent with the trends established for the other BES energies.

 


 §.§ The sixth-order cumulant 

The collision-centrality dependence of the ratio of the sixth- to second-order cumulants (C_6/C_2)  of net-proton and net-charge distribution for Au+Au collisions are shown in Fig 4. The C_6/C_2 of net-proton distributions for central collisions (0-40%) at √(s_NN) = 54.4 GeV is positive while C_6/C_2 measured at √(s_NN) = 200 GeV is negative for the same collision centrality <cit.>. A negative  C_6/C_2 is predicted for the crossover phase transition between hadronic matter and quark-gluon plasma in QCD-based calculations <cit.>. The UrQMD model expectations for Au+Au collisions at √(s_NN) = 200 GeV and √(s_NN) = 54.4 GeV are found to be positive and consistent with the Skellam baseline across all collision centralities. The C_6/C_2 of net-charge distribution for Au+Au collisions at √(s_NN) = 54.4 GeV for two most central collision classes (0-5% and 5-10% ) show positive sign. 
 
















§ SUMMARY

We presented the collision-centrality dependence of cumulants and cumulant ratios of net-particle distributions from high statistics Au+Au collisions at √(s_NN) = 54.4 GeV. The cumulants (C_n, n ≤ 4) of net-particle distributions increase with average number of participant nucleons whereas the cumulant ratios C_3/C_2, C_4/C_2 and C_6/C_2 exhibit a weak collision-centrality dependence. The C_4/C_2 (κσ^2) measurement of net-particle distributions at √(s_NN) = 54.4 GeV are consistent with the existing beam energy trend of C_4/C_2 from the BES-I program. Furthurmore, the C_6/C_2 of net-proton distribution for Au+Au collisions at √(s_NN) = 200 GeV for most central collisions (0-40%) is negative, and this could be an experimental evidence of crossover phase transition. The new measurements at √(s_NN) = 54.4 GeV serve precise baselines for the critical fluctuation studies which are expected at lower center-of-mass energies. 


§ ACKNOWLEDGMENTS

We acknowledge the financial support by Department of Atomic Energy, Govt. of India.

















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Aoki:2006we 
Y. Aoki, G. Endrodi, Z. Fodor, S. D. Katz and K. K. Szabo, Nature 443, 675 (2006).
Ejiri:2008xt 
S. Ejiri, Phys. Rev.  D78, 074507 (2008).
Stephanov:2008qz
M. A. Stephanov, Phys. Rev. Lett.  102, 032301 (2009).


Gavai:2010zn
R. V. Gavai and S. Gupta, Phys. Lett. B 696, 459 (2011).
Gupta:2011wh
S. Gupta, X. Luo, B. Mohanty, H. G. Ritter and N. Xu, Science 332, 1525 (2011).
starNC L. Adamczyk et al. [STAR Collaboration], Phys. Rev. Lett.  113, 092301 (2014). 
starNK L. Adamczyk et al. [STAR Collaboration], Phys. Lett.  B785, 551 (2018).
starNP_old M. M. Aggarwal et al. [STAR Collaboration], Phys. Rev. Lett.  105, 022302 (2010).
starNP L. Adamczyk et al. [STAR Collaboration], Phys. Rev. Lett.  112, 032302 (2014).
shor_nature J. Adam et al., [STAR Collaboration], arXiv:2001.02852.
negc6:friman B. Friman et al., Eur. 346 Phys. J. C71, 1694 (2011).
Shao:2005iu 
M. Shao et al., Nucl. Instrum. Meth.  A558, 419 (2006).
arghya_auto A. Chatterjee, Y. Zhang, J. Zeng, N. R. Sahoo, X. Luo, arXiv:1910.08004.
bin_width X. Luo, J. Xu, B. Mohanty and N. Xu, J. Phys.  G40, 105104 (2013).
efcor_luo X. Luo, Phys. Rev.  C91, 034907 (2015).
Nonaka:2017kko T. Nonaka, M. Kitazawa and S. Esumi, Phys. Rev. C95, no. 6, 064912 (2017).
Luo:2011tp X. Luo, J. Phys.  G39, 025008 (2012).
bootstrap A. Pandav, D. Mallick and B. Mohanty, Nucl. Phys. A991 (2019) 121608.
urqmdS. A. Bass et al., Prog. Part. Nucl. Phys. 41, 255 (1998).
hijing M. Gyulassy et al., Comput. Phys. Commun.  83, 307 (1994).
tnonaka T. Nonaka, [STAR collaboration], contribution to these proceedings. 




















