Toy-model Subhasis Samanta Jan Kochanowski University, Institute of - PowerPoint PPT Presentation

Toy-model Subhasis Samanta Jan Kochanowski University, Institute of Physics, Kielce, Poland Subhasis Samanta April 15, 2020; Kielce 1 / 7

Generating uncorrelated particles 80 Multiplicity distribution 60 ⋆ Poisson distribution with mean N =30 No. of events 40 p T , φ distributions 20 ⋆ P ( p T ) = p T e − 6 p T 0 0 20 40 60 ⋆ φ = Uniform(- π, + π ) N mult 0.025 0.015 0.02 Total number of ) 0.01 T ) 0.015 φ P(p P( events = 1000 0.01 0.005 0.005 0 0 0 0.5 1 1.5 2 − 4 − 2 0 2 4 p (GeV/c) φ (rad) T Subhasis Samanta April 15, 2020; Kielce 2 / 7

2 1 3 10 − (GeV/c) ( p x , p y ) distribution 0 ⋆ p x = p T cos ( φ ) y p 4 10 − ⋆ p y = p T sin ( φ ) 1 − 5 10 − 2 − 2 1 0 1 2 − − p (GeV/c) x Subhasis Samanta April 15, 2020; Kielce 3 / 7

Second factorial moment � M 2 F 2 ( M ) = � 1 i = 1 n i ( n i − 1 ) � M - number of bins in p x and p y M 2 � M 2 � 1 i = 1 n i � n i - number of particles in i -th M 2 bin Equivalent formula: N - event multiplicity N pp ( M ) - total number of particle F 2 ( M ) = 2 M 2 pairs in M bins in an event � N � 2 � N pp ( M ) � � N pp ( M ) � =? Subhasis Samanta April 15, 2020; Kielce 4 / 7

N pp in a single event n = 34 2 N = 132 pp 0.05 n = 6, # pair = 15 n = 10, # pair = 45 1 0.04 (GeV/c) 0.03 0 y p 0.02 1 − n = 9, # pair = 36 n = 9, # pair = 36 0.01 2 0 − 2 1 0 1 2 − − p (GeV/c) x Subhasis Samanta April 15, 2020; Kielce 5 / 7

N pp in a single event n = 34 2 2 N = 132 N = 123 pp pp 0.05 0.05 n = 6, # pair = 15 n = 10, # pair = 45 1 1 (0,0) (6,15) (9,36) (1,0) 0.04 0.04 (GeV/c) (GeV/c) 0.03 0.03 0 0 y y p p 0.02 0.02 (0,0) (9,36) (9,36) 1 1 − − n = 9, # pair = 36 n = 9, # pair = 36 (0,0) (0,0) 0.01 0.01 2 2 0 0 − − 2 1 0 1 2 2 1 0 1 2 − − − − p (GeV/c) p (GeV/c) x x M = 1 , N pp = 561 ⋆ Particles in different bins are not M = 2 , N pp = 132 uniformly distributed for M ≥ 4 M = 4 , N pp = 123 ⋆ (Binning in φ would give better result) Subhasis Samanta April 15, 2020; Kielce 5 / 7

N pp distributions 80 hNppM1 hNppM2 hNppM4 Entries 1000 Entries 1000 Entries 1000 Mean 452 Mean 113.6 Mean 111.2 15 RMS 163.7 RMS 41.99 RMS 41.13 15 60 No. of events No. of events No. of events 10 10 40 5 5 20 0 0 0 0 200 400 600 800 1000 1200 0 100 200 300 0 100 200 300 N (M =1) N (M =2) N (M =4) pp pp pp M = 1 , < N pp > = 452 M = 2 , < N pp > = 113 M = 4 , < N pp > = 111 Subhasis Samanta April 15, 2020; Kielce 6 / 7

< N pp >, F 2 vs . M 2 20 400 15 (M) > 300 (M) pp 2 F < N 10 200 5 100 0 0 3 5 3 5 2 4 2 4 1 10 10 10 10 10 1 10 10 10 10 10 2 2 M M F 2 ( M ) = 2 M 2 � N � 2 � N pp ( M ) � Subhasis Samanta April 15, 2020; Kielce 7 / 7

Thank you Subhasis Samanta April 15, 2020; Kielce 7 / 7