Feasibility studies of conserved charge fluctuations in Au-Au collisions with CBM Subhasis Samanta (for the CBM Collaboration) National Institute of Science Education and Research, HBNI, Jatni, India Outline ⋆ Introduction ⋆ CBM experiment ⋆ Analysis details ⋆ Results Net-proton cumulants Net-charge cumulants ⋆ Summary S Samanta (For the CBM Collaboration) Quark Matter - 2019, Wuhan, China 1 / 14
QCD phase diagram ⋆ Study QCD phase diagram at high net-baryon density At high net-baryon density and low temperature, first order phase transition is expected which will end at a critical point (CP) CBM program supplements the Beam Energy Scan Program at RHIC, NA61 at SPS, NICA at JINR Ref: CBM: EPJA 53, 60 (2017); PRC 74, 047901 (2006) S Samanta (For the CBM Collaboration) Quark Matter - 2019, Wuhan, China 2 / 14
Observables for CP search Cumulants ( δ N q ) 2 � ( δ N q ) 3 � � � C 1 = � N q � , C 2 = , C 3 = , ( δ N q ) 2 � 2 ( δ N q ) 4 � � � C 4 = − 3 � � N q = N q + − N q − and δ N q = N q − N q q can be any conserved quantum number (net-baryon, net-charge, net-strangeness etc.) Mean, variance, skewness, kurtosis σ 2 = C 2 , S = C 3 κ = C 4 M = C 1 , σ 3 , σ 4 ⋆ Higher moments of conserved quantities are sensitive to correlation length ( δ N q ) 2 � ∼ ζ 2 ( δ N q ) 3 � ∼ ζ 4 . 5 ( δ N q ) 4 � ∼ ζ 7 � � � ⋆ Non-monotonic variations of S σ = C 3 / C 2 , κσ 2 = C 4 / C 2 with beam energy are believed to be good signatures of CP Ref: STAR: PRL 112, 032302 (2014); PRL 102, 032301 (2009) S Samanta (For the CBM Collaboration) Quark Matter - 2019, Wuhan, China 3 / 14
CBM experiment ⋆ Fixed target experiment ⋆ SIS 100: Au + Au collision, √ s NN = 2 . 7 − 4 . 9 GeV ⋆ High interaction rate ⋆ High statistics data ⋆ Density in the center of the fireball expected to exceed few times greater than density of nucleus Challenges of higher moments measurements at CBM ⋆ Particle identification ⋆ Non-trivial variations of efficiency × acceptance with p T and rapidity (proper method of corrections needed) ⋆ Proper vertex identification in multiple collisions Ref: CBM overview talk at QM2019 by Viktor Klochkov; EPJA 53, 60 (2017); The CBM Physics Book, Lect. Notes Phys. 814, Springer 2011; PRC 75 (2007) 034902 S Samanta (For the CBM Collaboration) Quark Matter - 2019, Wuhan, China 4 / 14
Simulation details ⋆ Event generators: UrQMD ⋆ Collision: Au+Au ⋆ Energy: E lab = 10 AGeV ( √ s NN = 4 . 72 GeV) ⋆ Events: 5 M (minimum bias) Detectors used: MVD, STS, RICH, TOF MVD: Vertex information STS: Momentum information RICH: Electron identification sis100 setup TOF: Hadron identification Detector acceptance: 1 . 5 < η < 3 . 8 ( 25 ◦ > θ > 2 . 5 ◦ ) S Samanta (For the CBM Collaboration) Quark Matter - 2019, Wuhan, China 5 / 14
Particle identification using TOF Centrality selection using STS No. of events Au + Au, E = 10 AGeV lab UrQMD + CBM GEANT3 5 10 2 4 m 2 < 0.4 (GeV /c ) 4 10 3 10 2 10 50 - 60 % 40 - 50 % 30 - 40 % 20 - 30 % 10 - 20 % 5 - 10 % 0 - 5 % 10 1 0 20 40 60 80 100 120 140 N ch (Multiplicities are uncorrected for efficiency and acceptance) ⋆ Clean particle identification for bulk properties studies ⋆ To remove auto correlation in net-proton study, charge particles selected excluding p , ¯ p S Samanta (For the CBM Collaboration) Quark Matter - 2019, Wuhan, China 6 / 14
Proton (anti-proton) selection Mass square cut: 1 1 1 Purity Efficiency Efficiency 0 . 6 < m 2 < 1 . 2 GeV 2 /c 4 0.9 0.9 0.9 Au + Au, E = 10 AGeV 0.2 < p < 2.0 (GeV/c) 0.8 0.8 1.08 < y < 2.08 0.8 lab T Rapidity acceptance: 0.7 0.7 0.7 UrQMD + CBM GEANT3 0.6 0.6 0.6 1.08 < y < 2.08 ∆ y = 1 ( y mid = 1 . 58) 0.5 0.5 0.5 0.4 0.4 0.4 p T acceptance: 0.3 0.3 0.3 0.2 0.2 0.2 0 . 2 < p T < 2 GeV/c 0.1 0.1 0.1 0 0 0 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 0 0.5 1 1.5 2 2.5 3 3.5 4 p (GeV/c) p (GeV/c) y T T 4 (GeV/c) Au + Au 3.5 E = 10 AGeV lab UrQMD 3 10 3 ⋆ Purity > 96 % T CBM GEANT3 p 2.5 ⋆ Efficiency decreases at high p T due to the 2 10 2 detector acceptance 1.5 ⋆ Efficiency for 0-5 % and 70 -80 % 1 10 centralities are ≃ 62 % and ≃ 46 % 0.5 0 1 0 0.5 1 1.5 2 2.5 3 3.5 y S Samanta (For the CBM Collaboration) Quark Matter - 2019, Wuhan, China 7 / 14
Proton (anti-proton) multiplicity distributions No. of events No. of events No. of events 6 Au + Au, E = 10 AGeV (0 - 5) % 6 (5 - 10) % 6 (10 -20) % 10 10 10 lab UrQMD + CBM GEANT3 5 5 5 10 10 10 p 4 4 4 10 p 10 10 3 3 3 10 10 10 2 2 2 10 10 10 0.2 < p < 2.0 (GeV/c) 10 10 10 T 1.08 < y < 2.08 1 1 1 0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 80 N (N ) N (N ) N (N ) p p p p p p No. of events No. of events No. of events 6 6 6 (40 - 50) % (20 - 30) % (30 - 40) % 10 10 10 5 5 5 10 10 10 4 4 4 10 10 10 3 3 3 10 10 10 2 2 2 10 10 10 10 10 10 1 1 1 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70 N (N ) N (N ) N (N ) p p p p p p Uncorrected distributions for efficiency and acceptance S Samanta (For the CBM Collaboration) Quark Matter - 2019, Wuhan, China 8 / 14
Proton (anti-proton) multiplicity distributions No. of events No. of events No. of events 6 Au + Au, E = 10 AGeV 6 (60 - 70) % 6 (70 - 80) % 10 p 10 10 lab UrQMD + CBM GEANT3 p 5 5 5 10 10 10 (50 - 60) % 4 4 4 10 10 10 3 3 3 10 10 10 2 2 2 10 10 10 10 10 10 1 1 1 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 N (N ) N (N ) N (N ) p p p p p p (Uncorrected distributions for efficiency and acceptance) ⋆ Proton multiplicities follow negative binomial distribution ⋆ Number of ¯ p is very less compared to p p / p = 7 . 8 × 10 − 5 (0 -5 %), ¯ p / p = 2 . 5 × 10 − 4 (70 - 80 %) from UrQMD) ( ¯ ⋆ Proton distributions are skewed more to the right side of the mean S Samanta (For the CBM Collaboration) Quark Matter - 2019, Wuhan, China 9 / 14
Net-proton multiplicity distributions No. of events Au + Au, E = 10 AGeV (0-5) % 6 lab 10 N ch ( m 2 < 0 . 4 GeV 2 / c 4 ) (5-10) % UrQMD + CBM GEANT3 Centrality (%) (10-20) % 0.2 < p < 2.0 (GeV/c) 5 T 10 N ch ≥ 71 (20-30) % 0-5 1.08 < y < 2.08 (30-40) % 4 5-10 60 ≤ N ch < 71 10 (40-50) % (50-60) % 44 ≤ N ch < 60 10-20 3 (60-70) % 10 (70-80) % 20-30 32 ≤ N ch < 44 2 10 30-40 23 ≤ N ch < 32 10 40-50 16 ≤ N ch < 23 50-60 10 ≤ N ch < 16 1 0 10 20 30 40 50 60 70 80 90 60-70 6 ≤ N ch < 10 ∆ N (N - N ) p p 70-80 4 ≤ N ch < 6 Uncorrected for efficiency and acceptance ⋆ Mean and variance decreases from central towards the peripheral collisions ⋆ Distributions are skewed more to the right side of the mean S Samanta (For the CBM Collaboration) Quark Matter - 2019, Wuhan, China 10/ 14
C n of net-proton vs centrality (%) 1 2 C 40 C Without CBW correction Centrality bin width correction With CBW correction 40 Au + Au, E = 10 AGeV 30 C n = � r w r C n , r lab UrQMD + CBM GEANT3 30 n r w r = 0.2 < p < 2.0 (GeV/c) T 20 � r n r 1.08 < y < 2.08 20 � r w r = 1 10 10 sum is over multiplicity bins Net-proton 0 0 0 20 40 60 80 0 20 40 60 80 Centrality (%) Centrality (%) ⋆ CBWC done to suppress 3 4 C C volume fluctuations 80 200 ⋆ Statistical error 60 100 estimation is done using 40 Delta theorem 0 20 − 100 Ref: Advanced Theory of Statistics: Vol.1, London (1945); 0 0 20 40 60 80 0 20 40 60 80 Asymptotic Theory of Statistics and Probability, Springer Centrality (%) Centrality (%) (2008); JPG 39, 025008 (2012); JPG 40, 105104 (2013) S Samanta (For the CBM Collaboration) Quark Matter - 2019, Wuhan, China 11/ 14
Correction of cumulants of net-proton using Unfolding method Algorithm used: RooUnfoldBayes 1 2 C 100 C Measured Au + Au, E = 10 AGeV 60 lab Relationship between measured and true Corrected UrQMD + CBM GEANT3 80 True 0.2 < p < 2.0 (GeV/c) T distribution: y = Rx 1.08 < y < 2.08 40 60 y = measured, x = true, R = response 40 matrix 20 20 ⋆ 50 % events are used to construct R Net-proton 0 0 0 20 40 60 80 0 20 40 60 80 No. of events Centrality (%) Centrality (%) Au + Au, E = 10 AGeV 5 Measured 10 lab 3 4 0.2 < p < 2.0 (GeV/c) True C C T 150 Corrected 3000 1.08 < y < 2.08 4 10 (0 - 5) % 100 3 2000 10 50 2 0 10 1000 − 50 10 − 100 0 1 0 20 40 60 80 0 20 40 60 80 0 20 40 60 80 100 120 Centrality (%) Centrality (%) N - N p p ⋆ We are able to get back cumulants of ’True’, even if the efficiency is non-binomial and has non-trivial dependence on p T and rapidity Ref: NIMA 362, 487 (1995) S Samanta (For the CBM Collaboration) Quark Matter - 2019, Wuhan, China 12/ 14
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