24 B

24 B093348 25 3 6

RHIC (BNL) 10 18 Gauss LHC (CERN) 10 19 Gauss 2 spectators ALICE s NN = 2.76T ev ALICE spectators ZDC-ZN ZDC ZDC 61.17 +0.34 0.40 1

1 6 1.1 (QGP)....................... 6 1.2................................ 7 1.2.1.............................. 7 1.2.2 Landau Bjorken.......................... 8 1.2.3 Collective Flow................................. 9 1.2.4..................................... 10 1.3..................... 11 1.3.1........................... 12 1.4......................................... 13 2 14 2.1 LHC....................................... 14 2.2 ALICE (A Large Ion Collider Experiment)..................... 14 2.2.1 VZERO detector................................ 16 2.2.2 Zero Degree Calorimeter(ZDC)........................ 16 2.3...................... 17 3 19 3.1..................................... 19 3.1.1 Full stopping.................. 19 3.1.2 Stopping power.................... 20 3.2..................................... 22 3.2.1 Full stopping................... 22 3.2.2 Stopping power.................... 22 3.3........................................... 24 3.3.1............................. 24 3.3.2................................. 24 3.4................................ 25 4 27 4.1..................................... 27 4.2......................... 28 4.2.1 rapidity v1........................... 28 4.3 spectators.................... 30 4.3.1 ZDC (ZDCcentroid Q)................ 30 4.3.2 Recentering................................... 31 4.3.3 Event Selection................................. 33 4.3.4 ZDCcentroid........................ 35 2

5 36 5.1..................... 36 5.2................ 37 6 39 6.1.................... 39 6.1.1 rapidity v1.................... 39 6.1.2 v1.............................. 40 6.2.................... 40 6.2.1................... 40 6.3 (360 )............................... 42 7 46 47 49 50 3

1.1 [2]...................................... 6 1.2 [4].................. 7 1.3................................. 7 1.4 Landou Bjorken ( ) net proton rapidity ( )[7]....... 8 1.5 Collective Flow............................. 9 1.6 [2]....................... 10 1.7 [2]............................ 11 1.8 [2]............... 12 2.1 LHC [2] [3].............................. 14 2.2 ALICE [1].................................... 15 2.3 ZDC [5]................................ 16 2.4 ZDC ZN ZP [5]........................... 17 3.1 net proton.............................. 21 3.2 paritipant proton.......................... 21 3.3 Full stopping........................... 22 3.4 net proton participant proton R NN.................... 23 3.5 stopping power.......................... 23 3.6 b=6............................ 24 3.7....................... 25 4.1..................................... 27 4.2 participants...................... 28 4.3................. 29 4.4 spectators........................... 30 4.5 ZDC................................... 31 4.6 ZDC................................... 31 4.7 ZDC (ZDCcentroid).................. 31 4.8 Multiplicty................................... 32 4.9 Vertex x..................................... 32 4.10 Vertex y..................................... 32 4.11 Recentering Multiplicity Vertex x y ZDCcentroid. 34 4.12 Recentering Multiplicity Vertex x y ZDCcentroid 34 4.13 Recentering ZDC-ZN (ZDCcentroid)...... 34 5.1 rapidity v1....................... 36 5.2 2.............................. 37 5.3.................... 38 6.1 b 5 10 v1 rapidity................... 39 4

6.2 participants...................... 40 6.3 Aside ϕ A Cside ϕ C ϕ A ϕ C................ 42 6.4....................... 43 6.5............. 44 6.6 ( ) ( ). 44 5

1 1.1 (QGP) (Quark-Gluon Plasma, QGP) (Quantum Chromo-Dynamics QCD) ( ) QGP 137 t = 10 37 t = 10 6 10 5 QGP 1.1: [2] 6

1.2 QGP QGP RHIC LHC QGP 1.2: [4] QGP 1.2.1 1.3: participants spectators 2 7

(impactparameter) 2 b[fm] R b 0 (central collision) 0 < b < R ( peripheral collision) (participant) (spectator) spectators participants Binary Collision Binary Collision participants spectators centrality (Reaction Plane) z x ( ) y 1.2.2 Landau Bjorken participants GeV (Stopping power) rapidity stopping Fermi-Landau 100GeV 1fm rapidity rapidity scaling Bjorken-McLerran gluon QGP 1.4: Landou Bjorken ( ) net proton rapidity ( )[7] (1.4)( ) net proton dn/dη rapidity net proton 8

rapidity net proton rapidity net proton dn/dη 0 stopping power RHIC LHC 100GeV bjorken 1.2.3 Collective Flow collective flow( ) λ λ ( ) v n v n θ dn d(θ Φ) = N 0 + 2v 1 cos(θ Φ) + 2v 2 cos[2(θ Φ)] + (1.1) v n = < cos(n[θ Φ]) > (1.2) v n v 1 v 2 v 3 1.5: Collective Flow v1 v2 v3 9

QGP 1.2.4 Bjorken 1.6: [2] 1. Initial state and Pre-equilibrium 1/γ ( ) 2 2. QGP and Hydrodinamic expansion 3. Mixed phase 5 10 23 4. Hadronization and Freeze-out 2 (chemical freeze-out) ( Thermal freeze-out) 10

1.7: [2] QGP Hadronization Bjorken 1.3 30 BNL-RHIC 10 18 [T ] CERN-LHC 10 19 [T ] Magnetar 10 3 t r Lienard- Wiechert Potential 1.3 B(r, t) = eµ 0 4π v R (1 v 2 /c 2 ) R 3 [1 (v/c) 2 (1.3) sinϕ Rv ] 3/2 R = r r µ 0 ϕ Rv R v r (1.3) r r 10fm spectators participants spectators z (x ) spectators (y ) spectators spectators participants y 11

1.8: [4] fm participants y spectators QGP QGP spectators participant [6] 1.3.1 [10] QGP QGP ( ) [11] [8] [9] 12

1 [12] schwinger 1.4 ( (3.4) ) [6] update 13

2 2.1 LHC LHC CERN 100m 26.7km LHC 14TeV 5.5TeV 2009 900GeV 2.36TeV 2010-7TeV 11 - (2.76 TeV ) LHC ALICE ATLAS CMS LHC-b TOTEM LHC-f LHC QGP 2.1: LHC [2] [3] LHC m km LHC 6 2.2 ALICE (A Large Ion Collider Experiment) ALICE(A Large Ion Colider Experiment) LHC LHC 100,000 QGP ALICE QGP ALICE 14

QGP LHC QGP ALICE LHC 16m 16m 26m ALICE (1) Central Barrel( 0.9 < η < 0.9) (2) Muon Spectrometer( 4 < η < 2.5) (3) (3.4 < η ) Central Barrel (0.5 Tesla) Central Barrel ITS,TPC,TRD TPC,TRD,TOF Time offlight,hmpid High Momentum PID (TPC) (TRD) TOF HMPID Central Barrel Central Barrel PHOS,EMCal,DCal FMD,V0,T0 PMD ZDC 36 132 2.2: ALICE [1] 17 QGP 15

2.2.1 VZERO detector V0 A (A-side) C (C-side) A VZERO-A z = 3.3m 2.8 < η < 5.1 C VZERO-C z = 0.9m 3.7 < η < 1.7 ZER 2.2.2 Zero Degree Calorimeter(ZDC) participant spectators ALICE spectators Zero-Degree Calorimeters(ZDC) ZDC spectators ZN spectators ZP ZEM ZN ZP 115m ZEM Muon Spectrometer 7m ZDC PMD L1 ZDC 2.3: ZDC [5] ZN ZP ZEM spectators LHC ZN 0 ZP Aside Cside ZDC (ZN, ZP) ZDC 4 2 1 4 PMT PMT 16

2.1: ZDC [5] ZN ZP ZEM dimensions(cm 3 ) 7.04 7.04 100 12 22.4 150 7 7 20.4 Absorber tungsten alloy brass lead ρ absorber (gcm 3 ) 17.6 8.5 11.3 Fibre core diameter(µm) 365 550 550 Fibre spacing(mm) 1.6 4 not applicable Filling ratio 1/22 1/65 1/11 Length(in X 0 units) 251 100 35.4 Length(in λ 1 units) 8.7 8.2 1.1 Number of PMTs 5 5 1 2.4: ZDC ZN ZP [5] spectators 2.3 PYTHIA PYTHIA PYTHIA QCD 17

HIJING Heavy Ion Jet INteraction Generator) HIJING PYTHIA QCD soft excitation PDF nuclear shadowing PYTHIA PYTHIA QCD ALIROOT AliRoot ALICE LHC ALICE ROOT ALICE PYTHIA,HIJING, Geant ALICE ALIROOT QGP QGP 18

3 [6] stopping power RHIC LHC 3.1 Glauber t = 0 participant proton Glauber 3.1.1 Full stopping rapidity( 2) Full stopping Landau 1. (b/2, 0, 0) 1 (-b/2, 0, 0) ρ(r) = ρ(0) 1 + exp( r R a ) (3.1) R = 1.21 A 1/2 [fm] A a = 0.54[fm] diffusenessparameter r z x +x 1 +z z 1/γ 19

2. Glauber participant spectator - σ 2 σ 3.1: σ [6] (sqrts NN ) σ[mb] Au + Au@200GeV 42 P b + P b@2.76t ev 84 P b + P b@5.5t ev 94 1 2 r 12 R 12 = sqrt(σ/π) > r 12 [fm] (3.2) 1 2 1 participant spectator 3. participant proton participant proton 1.3 1 participant proton participant proton participant proton v c 4. event gauss fitting mean Full stopping 3.1.2 Stopping power Full stopping rapidity y RHIC LHC Bjorken ( 1.2.2) Stopping power rapidity spectators (1.4) stopping power rapidity spectators stopping power participant proton rapidity Full stopping rapidity net proton participant proton 20

net proton proton net proton HIJING net proton 1. HIJING b 0.5 < b < b + 0.5 2. rapidity 1 < η < 1 proton anti proton event by event net proton 3. event net proton event gaus fitting mean net proton P b + P b S NN = 2.76T ev net proton (3.1) net proton rapidity Stopping power 1 < η < 1 rapidity proton stopping power participant proton net proton event by event participant proton event gaus fitting mean participant participant proton (3.2) net proton participant proton(full stopping proton) R NN = N net p /N fs p Full stopping B fs stopping power B sp B s p = N net p N fs p B fs = R NN B fs (3.3) 3.1: HIJING net proton 3.2: participant proton 21

3.2 3.2.1 Full stopping Full stopping b 6 11[fm] RHIC 10 14 [T ] LHC 10 16 [T ] [6]( 3 1) 4 3.3: Full stopping 3.2.2 Stopping power stopping power (3.4) R NN R NN stopping power b > 12fm participant proton 22

3.4: net proton participant proton R NN R NN (3.3) stopping power 3.5 Full stopping b 6 10[fm] R NN 0.04 0.08 Stopping power Full stopping 4 8 RHIC 10 14 [T ] LHC 10 15 [T ] 3.5: stopping power 23

3.3 3.3.1 Full stopping 3 4 z participant z z 1/γ γ z 0 participant z 3 4 3.3.2 participant (3.3) 3.6: b=6 (3.6) b=6 Full stopping 4 (3.3) 10 17 [T ] 24

participant participant 3.4 q E B v F F = q(e + v B) (3.4) 3.7: RHIC 10 14 [T ] LHC 10 15 [T ] QGP 25

p B R p[gev ] = 0.3 B R[T m] (3.5) GeV B = 10 14 [T ] R 1 3 10 13 [m] 3 10 13 1fm 1.5 QGP QGP 10fm (1.3) π/2 < ϕ < π/2 26

4 4.1 (Reaction Plane) z x y z y θ x y ϕ π/2 < ϕ < π/2 (projectile) (target) 4.1 x projectile +x target x projectile x target +x 2 projectile (+x -x ) 2 projectile 4.1: projectile 27

4.2 participants +z -z participants projectile +z target -z rapidity projectile rapidity target participants +z -z rapidity rapidity 4.2: participnat projectile +z target -z rapidity rapidity v1 4.2.1 rapidity v1 (3+1) ( 1) QGP ( ) z x projectile x +b/2 target -b/2 projectile +x target -x LHC ( s NN = 2.76T ev ) ALICE rapidity(vzero-a 2.8 < η < 5.1) rapidity(vzero-c 3.7 < η < 1.7) 28

4.3: v1 v1 x +x -x +x v1 -x v1 1. Pb+Pb s NN = 2.76T ev MC-KLN 0 16[fm] 2. v1 rapidity rapidity (4.1) η = log(tan( θ )) (4.1) 2 px θ = arctan 2 + py 2 pz 3. rapidity 2.8 < η < 5.1 x px rapidity v1 rapidity 3.7 < η < 1.7 x px rapidty v1 4. rapidity v1 1fm gaus fitting mean v1 RMS rapidity v1 29

4.3 spectators spectators spectators spectators spectators fm spectators 4.4: spectators ZDC-ZN ALICE s NN = 2.76T ev ALICE spectators ZDC-ZN ( 2.2.2) ZDC-ZN Aside( ) Cside( ) ZDC-ZN (ZN ) spectators ZDCcentroid spectators AsideZDC-ZN ( Cside) ϕ ZDC-ZN π < ϕ < π ZDC-ZN ZDC 4.3.1 ZDC (ZDCcentroid Q) spectators (centroid) ZDC 4 Tower ZDC spectators Aside Cside Tower r k E k (4.2) Q(X, Y ) = 4 r k E k k=1 (4.2) 4 E k k=1 30

4.5: ZDC 4 Tower spectators 4.6: ZDC Aside Cside ZDC ZDCcentroid Q(X,Y) 1 Tower ZDCcentroid Tower ZDCcentroid side Qx < 1.5 Qy < 1.5 ZDC Aside Cside Qx Qy Aside Cside ZDCcentroid 4.3.2 Recentering 4.7: ZDC (centroid) (4.7) Aside Cside ZDCcentroid 31

Aside Cside ZDC run z ZDCcentroid Aside Cside Recentering ZDCcentroid vertex vertex x y z vertex ZDCcentroid 4.8: Multiplicty 4.9: Vertex x 4.10: Vertex y vertex x vertex y multiplicity Multiplicity spectators ZDCcentroid (4.8) multiplicity multiplicity multiplicity 0 3500 spectators ZDCcentroid 32

0 < multiplicity < 2500 Vertex x Vertex y 0.03 < V x < 0.01 0.15 < V y < 0.19 Recentering Y X ( ) 1 X RMS multiplicity X ZDCcentroid Y 1 multiplicity ZDCcentroid (4.11) Multiplicity Vertex x Vertex y side ZDCcentroid 2 side 0.1 3 Recentering 3 Recentering multiplicity Vertex x Vertex y ZDCcentroid 3 (1 3 RMS ) ZDCcentroid 3 Recentering Recentering (4.11) (4.12) 3 Recentering (4.13) Recentering Aside Cside ZDCcentroid Recentering 4.3.3 Event Selection (4.1) 4.1: spectators event selection Pb+Pb s NN = 2.76T ev LHC10h Qx Qx < 1.5 Qy Qy < 1.5 Vertex x 0.03 < V x < 0.01 Vertex y 0.15 < V y < 0.19 Vertex z 20 < V z < 20 33

4.11: Recentering Multiplicity Vertex x y 4.12: Recentering Multiplicity Vertex x y 4.13: Recentering ZDC-ZN (centroid) 34

4.3.4 ZDCcentroid ZDCcentroid ZDCcentroid Aside Cside spectators AsideZDCcentroid CsideZDCcentroid AsideQx CsideQx QxA,QxC AsideQx CsideQy QxA,QyC AsideQy CsideQx QyA,QxC AsideQy CsideQy QyA,QyC X,Y X,Y (4.3) < X, Y >= n (x i x)(y i y) i=i (4.3) n n (x i x) 2 (y i y) 2 i=1 i=1 Aside Cside 0 35

5 5.1 (5.1) rapidity v1 5.1: rapidity v1 rapidity rapidity 5 11[fm] v1 10 3 rapidity rapidity 0 rapidity rapidity v1 rapidity 36

5.2 (5.2) ALICE s NN = 2.76T ev ZDC Aside Cside ZDCcentroid 5.2: 2 0 multiplicity 2500 QxA,QxC QxA,QyC QyA,QxC QyA,QyC QxA,QyC QyA,QxC QxA,QxC QyA,QyC 37

(5.3) multiplicity multiplicity 5.3: QxA,QyC QyA,QxC QxA,QxC QyA,QyC 0 ZDCcentroid spectators ALICE ZDC ZDCcentroid AsideZDCcentroid projectile CsideZDCcentroid target spectators ZDCcentroid 360 38

6 6.1 6.1.1 rapidity v1 v1 rapidity rapidty (5.1) v1 rapidity rapidity 6.1: b 5 10 v1 rapidity (6.1) b=5 10 rapidity v1 v1 rapidity rapidity 0 < rapidity < 5 v1 5 < rapidity < 10 rapidity 5 < rapidity < 0 v1 10 < rapidity < 5 participant rapidity (6.2) participant rapidity loss rapidity rapidity loss rapidity rapidity (6.2) (6.1) 39

6.2: participnat rapidity rapidity rapidity rapidity ALICE VZERO-A(2.8 < η < 5.1) VZERO-C( 3.7 < η < 1.7) rapidity v1 rapidity v1 6.1.2 v1 (5.1) v1 v1 v1 participant paritipant projectile +z target -z v1 6.2 6.2.1 (5.3) QxA,QxC QyA,QyC multiplicity multiplicity 750 1000 multiplicity multiplicity multiplicity (5.3) spectators 1 1 spectators ZDCcentroid 40

spectators multiplicity spectators spectators participant spectators QxA,QyC QyA,QxC AsideZDCcentroidtoCsideZDCcentroid 41

6.3 (360 ) (4.3) π < ϕ < π Aside Cside ZDCcentroidQ(X,Y) ϕ = arctan( Qy Qx ) (6.1) Aside ZDCcentroid Cside ZDCcentroid AsideZDCcentroid (Aside ) CsideZDCcentroid (Cside ) Aside Cside Aside+Cside ) 3 Aside Cside Aside+Cside Aside Cside ZDCcentroid Aside Cside 2 Aside -Cside /2 Aside+Cside 6.3: Aside ϕ A Cside ϕ C ϕ A ϕ C (6.3) Aside ϕ A Cside ϕ C ϕ A ϕ C -0.01 ϕ A ϕ C 0 ϕ ϕ A ϕ C π π < ϕ A ϕ C < π π ϕ π 42

6.4: π 5 5π (6.2) f(x) = C(e x2 2σ 2 + e (2π x)2 2σ 2 + e (2π+x)2 2σ 2 + e (4π+x)2 2σ 2 + e (4π x)2 2σ 2 ) (6.2) C f(x) 1. C C C C = f(0) C = C(C(1 + 2 e 2π2 σ 2 C = C 1 + 2 e 2π2 σ 2 + 2 e 4π2 σ 2 ) + 2 e 4π2 σ 2 (6.3) C (6.3) -1 1 C =286 2. x x i f(x i ) yi (6.4) i [ f(x i) y i δy i ] 2 (6.4) δy i 3. σ σ σ 43

6.5: 6.6: ( ) ( ) 44

(6.5) σ σ = 2.141 +0.012 0.013 σ σ = 2.141 (6.6) σ = 2.141 Aside+Cside σ/2 = 1.071 +0.006 0.007 = 61.17+0.34 0.40 90 ZDCccentroid (6.2.1) multiplicity Aside Cside multiplicity ZDCcentroid ZDCcentroid ZDC ZDCcentroid ZDCcentroid π < ϕ < π pi/2 < ϕ < π/2 1.081/(π/2) = 0.6882 70 ALICE VZERO Aside Cside VZERO Aside Cside VZERO 50 π < ϕ < π VZERO 45

7 RHIC LHC full stopping stopping power RHIC 10 14 [T ] LHC 10 15 [T ] v1 v1 2 spectators ALICE s NN = 2.76T ev ALICE spectators ZDC-ZN ZDC ZDC spectators 360 61.17 +0.34 0.40 46

1. [13] (3+1) RHIC LHC (Au + Au200GeV P b + P b2.76t ev ) Kharzeev-Levin-Nardi model(mc-kln) Glauber model(mc-glauber) 2 [14] 1. MC-KLN, MC-Glauber[14] (x, y, s ) binary 2. 1 T sw = 155MeV dat 3. JAM JAM(Jet AA Microscopic Transport Model)[15] QCD phasespace.dat 47

2. rapidity rapidity Rapidity y longitudinal rapidity y = 1 ( ) E + P 2 ln E P ( ) E + P = ln PT 2 + m2 (7.1) y Phase Space rapidity y rapidity E max = s/2 ( y max = 1 s 2 ln 2 + s s 4 m2 ) 2 s 4 (( m2 s 2 = 1/2ln + s 4 m2) ) 2 m 2 ( ) s = ln m (7.2) (7.3) (7.4) y kinematical limit rapidity(pseudorapidity)η y m = 0 η = 1 ( ) E + E cos θ 2 ln E E cos θ ( ) = 1 2 ln 1 tan ( ) θ 2 2 ( ( ) ) θ = ln tan (7.5) 2 θ θ θ = 2arctan(e η ) (7.6) 48

Ilya Selyuzhenkov ZDC 2 ALICE 1 49

[1] http://aliceinfo.cern.ch/public/welcome.html [2] LHC ALICE http://alice-j.org/ [3] cern homepage http://public.web.cern.ch/public/welcome.html [4] RHIC homepage http://www.bnl.gov/rhic/ [5] 2008 JINST 3 S08002 http://jinst.sissa.it/lhc/ [6] [7] [8] K. Hattori and K. Itakura, in print in Ann. Phys., [hep-ph/1209.2663]. Vacuum birefringence in strong magnetic fields: (I) Photon polarization tensor with all the Landau levels [9] K. Hattori and K. Itakura, [hep-ph/1212.1897]. Vacuum birefringence in strong magnetic fields: (II) Complex refractive index from the lowest Landau level [10] K.Tuchin, Phys Rev C 82,034904(2010) [11] K.Tuchin,Phys Rev C 83,017901(2011) [12] K.Fukushima, D.E.Kharzeev, H.J.Warringa, Phys.Rev.D 78, 074033(2008) [13] T. Hirano, P. Huovinen, K. Murase and Y. Nara, arxiv:1204.5814 [nucl-th]. Integrated Dynamical Approach to Relativistic Heavy Ion Collisions, [14] H. -J. Drescher and Y. Nara, Phys. Rev. C 75, 034905 (2007) [nucl-th/0611017]. Effects of fluctuations on the initial eccentricity from the ColorGlass Condensate in heavy ion collisions, [15] Y. Nara, N. Otuka, A. Ohnishi, K. Niita and S. Chiba, Phys. Rev. C 61, 024901 (2000) [nucl-th/9904059]. Study of relativistic nuclear collisions at AGS energies from p + Be to Au + Au with hadronic cascade model, 50