Charge balancing and the fall off of the ridge Piotr Bo zek and - PowerPoint PPT Presentation

Charge balancing and the fall off of the ridge Piotr Bo˙ zek and Wojtek Broniowski Institute of Nuclear Physics Krak´ ow QM 2012 Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge

Two-particle correlations N pairs phys (∆ η, ∆ φ ) C 2 (∆ η, ∆ φ ) = N pairs mixed (∆ η, ∆ φ ) flow correlations φ Fluctuating IC dN ∆ 13.4 d trigg 13.2 1 N 0.6 13 ∆ρ /√ρ ref 0.4 12.8 12.6 0.2 12.4 0 2 12.2 -3 -2 -1 0 1 2 3 -0.2 ∆ φ (rad) 1 11.6 -0.4 φ dN ∆ Smooth IC d 0 trigg 1 11.5 4 η ∆ N -1 2 11.4 φ ∆ 0 -2 11.3 STAR 11.2 -3 -2 -1 0 1 2 3 (rad) ∆ φ J. Takahashi et al. (2009) Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge

3 + 1-D viscous hydrodynamics Au-Au 200GeV 25 ideal, e-b-e 0-5% central 20 η /s=0.08, e-b-e η /s=0.16, e-b-e PHOBOS c=0-6%,...,45-55% 15 800 BRAHMS c=0-5% visc. hydro 10 ideal fluid 700 5 600 0 10-20% central PS 20 500 h +/- v 3 [%] η 15 dN/d 400 10 5 300 0 30-40% central 200 20 15 100 10 0 5 -6 -4 -2 0 2 4 6 η 0 PS 0 0.5 1 1.5 2 2.5 3 p T [GeV] 3 10 Au-Au 200GeV PHENIX data π + first 3+1D visc. : B.Schenke et al. 10 ] -2 0-5% dy) [GeV lQCD Wuppertal-Budapest -1 10 0.3 c s2 T -3 dp 10 0.2 T p π dN/(2 -5 10 0.1 0 10 -7 0 200 400 600 800 1000 ideal fluid T [ MeV ] visc. hydro 40-50% -9 10 0 0.5 1 1.5 2 2.5 3 lQCD + Hadron Gas p [GeV] T η/ s = 0 . 08(0 . 16) Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge

2-D correlations (0 . 8 < p T < 4 GeV - “unbiased”) Unlike-sign Like-sign 1.01 1.01 1 1 0.99 0.99 0 0 0 0 0.5 0.5 50 50 1 1 100 100 ∆ ∆ 1.5 1.5 φ 150 η φ 150 η (a) (deg) ∆ (b) (deg) ∆ STAR data, 2007 Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge

2-D correlations No balancing 0-5% 0-5% (0 . 8 < p T < 4 GeV - “unbiased”) 1.014 (+-) 1.012 1.01 1.008 2 R 1.006 1.004 1.002 Unlike-sign Like-sign 1 0.998 0.996 0.994 2 1.5 1 0.5 5 0 ∆ 4 -0.5 3 1.01 η -1 2 1 -1.5 0 φ ∆ -2 -1 1.01 1 0-5% 0-5% 1 0.99 0.99 0 0 0 0 (++,--) 0.5 0.5 1.01 50 50 1.008 1 1 100 100 ∆ 1.006 ∆ 1.5 1.5 φ 150 η φ 150 η 1.004 (a) (deg) ∆ (b) (deg) ∆ 2 R 1.002 1 0.998 STAR data, 2007 0.996 0.994 2 1.5 1 0.5 5 0 ∆ 4 -0.5 3 η 2 -1 1 -1.5 0 ∆ φ -2 -1 Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge

Charge balancing local charge conservation charge balance function p 1 + u _ p 2 _ + Bass et al. (2000) Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge

2-D correlations With balancing! N pairs phys (∆ η, ∆ φ ) 0-5% 0-5% R 2 (∆ η, ∆ φ ) = N pairs mixed (∆ η, ∆ φ ) 1.025 (+-) 1.02 (0 . 8 < p T < 4 GeV) 2 1.015 R 1.01 1.005 1 0.995 Unlike-sign Like-sign 2 1.5 1 0.5 5 0 ∆ 4 -0.5 3 η -1 2 1 -1.5 0 φ ∆ -2 -1 1.01 1.01 0-5% 0-5% 1 1 (++,--) 1.015 0.99 0.99 0 0 0 0 1.01 50 0.5 50 0.5 2 1.005 100 1 100 1 R ∆ ∆ φ 1.5 η 1.5 150 φ 150 η 1 (deg) (a) ∆ (b) (deg) ∆ 0.995 2 STAR data 1.5 1 0.5 5 0 ∆ 4 -0.5 3 η 2 -1 1 -1.5 0 ∆ φ -2 -1 Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge

2D balance functions B (∆ η, ∆ φ ) = � N + − − N ++ � + � N − + − N −− � � N + � � N − � c = 0 − 5% B 1.4 1.2 1 0.8 0.6 0.4 0.2 0 ∆ 3 φ 2 1 η ∆ 2 0 1.5 1 -1 0.5 0 -2 -0.5 -1 -1.5 -3 -2 Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge

2D balance functions B (∆ η, ∆ φ ) = � N + − − N ++ � + � N − + − N −− � � N + � � N − � c = 0 − 5% B 0.35 B 1.4 0.3 1.2 0.25 1 0.2 0.8 0.15 0.1 0.6 0.05 0.4 0 0.2 -0.05 0 ∆ ∆ 3 φ 3 φ 2 2 1 1 η ∆ η ∆ 2 0 2 0 1.5 1.5 1 1 -1 0.5 -1 0.5 0 0 -2 -0.5 -2 -0.5 -1 -1 -1.5 -1.5 -3 -3 -2 -2 big (direct balancing) small (resonance decays only) balancing → collimation important non-flow effect, a way to look at the data Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge

Model Summary (a) 30-40%, unbal. (b) 30-40%, unbal. C(++,--) C(+-) 1.015 1.015 1.01 1.01 1.005 1.005 1 1 0.995 0.995 0.99 0.99 2 2 1.5 1.5 1 1 0.5 0.5 5 5 0 0 ∆ 4 ∆ 4 -0.5 -0.5 η 3 η 3 2 2 -1 -1 1 φ 1 φ -1.5 ∆ -1.5 ∆ 0 0 -2 -2 -1 -1 (c) 30-40%, bal. (d) 30-40%, bal. 1.02 1.03 C(++,--) C(+-) 1.025 1.015 1.02 1.01 1.015 1.005 1.01 1.005 1 1 0.995 0.995 0.99 0.99 0.985 2 2 1.5 1.5 1 1 0.5 0.5 5 5 0 0 ∆ 4 ∆ 4 -0.5 3 -0.5 3 η η -1 2 -1 2 1 φ 1 φ -1.5 ∆ -1.5 ∆ 0 0 -2 -1 -2 -1 Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge

Balance functions in relative rapidity Jeon & Pratt 2002, ... charge balance function in ∆ η 0.7 0.7 0.7 ) η (a) 0-5% (b) 30-40% (c) 60-70% ∆ 0.6 0.6 0.6 B( 0.5 0.5 0.5 0.4 0.4 0.4 0.3 0.3 0.3 0.2 0.2 0.2 0.1 0.1 0.1 0 0 0 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 ∆ η ∆ η ∆ η comparison to the STAR data solid: T f = 140 MeV, dashed: T f = 150 MeV Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge

Non-flow effect on v n 0.9 0.14 ] v -3 PHENIX c=0-10% 2 (a) 0-5% [10 a) 0.8 0.12 STAR 0.7 0.1 2 n v 0.6 v 0.08 2 0.5 v + ch. balan. 2 0.06 0.4 0.04 0.3 0.2 0.02 η hydro + ch. balan. /s=0.16 0.1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 p [GeV] ∆ η T × -3 10 7 (LS) 0.22 v PHENIX c=30-40% 2 STAR Data 0.2 6 STAR 2 hydro (CI)-v 0.18 5 0.16 hydro + ch. balan. hydro + ch. bal. 4 0.14 2 η hydro v hydro + ch. balan. /s=0.16 b) 0.12 3 0.1 2 0.08 0.06 1 η hydro + ch. balan. /s=0.16 0.04 0 0.02 -1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 100 200 300 400 500 600 700 800 η dN/d p [GeV] T event-by-event Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge

v 1 - parity violation observable transverse-momentum conservation lowers v 2 1 ≡ � cos( φ 1 − φ 2 ) � 3 O � s140, X � s150, P T � 20, 18, 15, 12, 10, 8, 7, 5 GeV (b) 30-40% O 2.5 5 2 X 4 � cos � a � b � � � 10 � 3 � 1.5 � 1 3 O � 0.5 2 O � 0 � O O 1 X � -0.5 � O O � O � X � -1 O 0 O X O O O X � O X � � � O O � � � � � -1.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 0 10 20 30 40 50 60 70 ∆ η c � � � comparison to the STAR data Pratt, Schlichting (2011), Bzdak, Koch, Liao (2011) Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge

Summary ◮ E-by-e hydro with charge balancing for 2-D correlation function ◮ Charge balancing explains the shape of the same-side ridge - major non-flow effect ◮ Charge balancing increases v 2 n { 2 } by a few % and splits the like-sign and unlike-sign case ◮ Transverse-momentum conservation important for v 2 1 , parity violation obs. semi-quantitative agreement ◮ Substract charge conservation effects to look for early correlations Piotr Bo˙ zek and Wojtek Broniowski Charge balancing and the fall off of the ridge