Does Cronin Peak Disappear at LHC Energies?

Transcription

1 Does Cronin Peak Disappear at LHC Energies? Gergely Gábor Barnaföldi RMKI,CNR in collaboration with: George Fai CNR, Kent State University; Péter Lévai RMKI,CNR; Gábor Papp ELTE; Seminar at Center for Nuclear Research Kent State Univeristy 28 th November 2006

2 OUTLINE 0. Motivation Nuclear Modification Factor and the Cronin effect Historical survey of the Cronin effect from SPS to RHIC Is the R AA boring, flat at high-p T? I. Theoretical Background pqcd improved parton model for pp, pa and AA II. Initial state effects at very high p T Analysing EMC effect in high-energy AA collisions Predictions for LHC at TeV dpb collisions III. What can we learn from HOT Quenching? Jet tomography results at y = 0 for AuAu and CuCu Is there room for COLD Quenching in da collisions? IV. Does the Cronin Peak disappear at LHC?

3 Hunting for Nuclear Effects (Cronin) at High-p T R AA Historically the Cronin effect: increased particle production in 3 GeV < p T < 6 GeV range (1975) increased means more particles are produced in pa than expected from N bin scaled pp collisions Nuclear Modification Factor (NMF) measuring Cronin effect: R AA = 1 N bin dn AA /dy d 2 p T dnpp/dy d 2 p T

4 History of the Experiments for Cronin Effect Experiment p Target snn (GeV) y or η p T (GeV) Hadron CP p d, Be, Ti, W 19.4; 23.7; [0.77; 6.91] π ±, K ±, p ±, d ± ITA p C, W p inc = [0.7; 1.0] [0.2; 2.35] π ±, K ±, p ± FNAL n Be, Al, C, Sn, Pb 27.4 [4.0; 8.0] [0.1; 1.7] h ±, π +, p FNAL p Be, W 19.4; 23.7; [0.2; 4.5] π ±, K ±, p ±, h ± CP π p, Be, Cu, W 19.4; [0.8; 5.78] π ±, K ±, p ± E577/E672 p p, Be, C, Al, Cu, Pb 38.8 [ 0.75; 0.75] [0.6; 11.5] h ± E605/E789 p Be, W [0.5; 11.5] h ± E605 p d, Be, W [0.5; 11.0] π ±, K ±, p ± E706 p Be 31.6; 38.8 [ 0.75; 0.75] [1.0; 12.0] π 0, η E706 p, π Be, Cu 30.7 [ 0.7; 0.7] [3.5; 10.0] π 0, γ WA80 S S, Au 19.4 [2.1; 2.9] [0.3; 3.9] π 0, γ WA98 Pb Pb, Nb 17.3 [2, 3; 4, 4] [0.3; 3.7] π 0, γ CERES Pb Au 17.3 [2, 1; 2, 6] [1.5; 3.3] π ± PHENIX p, Au p, d, Au 130, 200 η 0.35; 2.0 [0.5; 10.0] π 0, h ±, γ BRAHMS p, Au p, d, Au 130, ; 1.0; 2.2; 3.2 [0.5; 6.0] π 0, h ± STAR p, Au p, d, Au 130, 200 η 0.5; 2.0 [0.2; 5.5] π 0, h ±, Λ, K, γ PHOBOS p, Au p, d, Au 62.4; 130; ; 0.8; 1.2 [0.5; 3.5] K ±, p ± π 0, h ±

5 Motivation for LHC low-x physics Suppression in h +,h spectra in dau by BRAHMS, η > 0 η = h +h η = h +h η = h η = h R d+au 1 R d+au 1 R d+au 1 R d+au p T [GeV/c] p T [GeV/c] Testing small-x in heavy-ion collisons via analysing forward (η > 0) PHOBOS and BRAHMS p T [GeV/c] p T [GeV/c]

6 Motivation for LHC high-x and high-p T physics R AA and π spectra in dau and AuAu by PHENIX, y = 0 How will move the high-p T tail in dau at RHIC Suppression in AuAu at RHIC is really flat?

7 I. (SHORT) INTRODUCTION TO THE THEORETICAL BACKGROUND

8 I/1. pqcd Improved Parton Model for pa Collisions dσπ pa E π d 3 f a/p (x a,q 2 ;k T ) f b/a (x b,q 2 ;k T,b) dσab cd p π dˆt D π/c(z c, Q 2 ). πzc 2 f a/a (x a,q 2 ;k T,b) : Nucl. Parton Dist. Function (PDF), at scale Q 2 D π/c (z c, Q 2 ) : Fragmentation Function for π (FF), at scale Q 2 p A dσ ab cd dˆt : Partonic cross section f (x, k ;Q) a/p a b T,a f (x,k ;Q,b) a X d dσ ab cd t b/a b d T,b X c ~ D (z,q) h/c c h X

9 I/2. Longitudinal 1-Dimensional PDFs and FFs in General (a) Parton Distribution Functions (PDF) : (LO case) GRV Glück, Reya, Vogt Z. Phys C (1992) (NLO case) MRST-(c-g) A.D. Martin et al. Eur. Phys J. C4 463 (1998) Eur. Phys J. C23 73 (2002) CTEQ5M H. L. Lai et al. hep-ph/ (1999) (b) Fragmentation Functions (FF) : KKP Kniehl, Kramer, Pötter. Nucl. Phys. B (2000)

10 I/3. Phenomenological introduction of intrinsic k T Introducing intrinsic k T for colliding partons (in pp coll.) Phenomenological assumption: PDFs are modified 1 dimensional PDFs are changed to 1+2 dimensional ones dxf a/p (x,q 2 ) dx d 2 k T g pp ( k T ) f a/p (x,q 2 ) where g( k T ) is a Gauss distribution function : g pp ( k T ) = e kt 2 / k2 T π kt 2 and kt 2 = 4 k T 2 π Baseline kt 2 values for pp: Phys. Rev. C (2002) value agrees with measured values by PHENIX, k 2 T

11 Pion Production in pp Collisions at RHIC Energies P. Lévai, G. Papp, G.G. Barnaföldi, G. Fai nucl-th/

12 I/4. Collision Geometry Glauber Model in pa π Glauber model : an incoming p collides with ALL nucleons along its travelling tube at b impact param. dσπ E pa π d = d 2 bt 3 A (b)...f a/a (x a,q 2 ;...)... p Nuclear thickness function: t A (b) = dz ρ(b,z) normalized as: p z A b d bdz A O A d dσ ab cd t c d ~ D (z,q) h/c A Target c h X A = b max 0 t A (b)d 2 b, where ρ(b,z) is the nuclear density distribution ρ(b,z): for small A: sharp sphere: t A (b) = 2ρ 0 R 2 A b 2, for large A: Wood Saxon-distribution.

13 I/5. Nuclear Effects Shadowing inside the Nucleus Shadowing PDFs are modified inside the nucleus: ( f ) [ a/a x,q 2 Z = S a/a (x,b) A f ( ) ( a/p x,q Z ( )f )] a/n x,q 2 A S a/a (x,b): Shadowing function (ex.: HIJING); A atomic- and Z the proton number S a/a (x) = ln 1/6 A[x 3 1.5(x 0 + x L )x 2 + 3x 0 x L x] [ ] α A 1.08(A1/3 1) x e x2 /x 2 0 ln(a + 1) where: α A = 0.1(A 1/3 1) and x 0 = 1, x L = 0.7. HIJING: Wang and Gyulassy, Phys. Rev D44, 3501 (1991) EKRS: Eskola et al., Eur. Phys. Jour. C9, 61 (1998) HKN: Hirai et al., hep-ph/ (2004)

14 I/6. (a) Measured and Phenomenological Shadowing Measured by many different experimental collaborations

15 I/7. (b) Different Shadowing Parameterizations 2F 2 (C)/12F 2 (D) 12F 2 (Pb)/207F 2 (C) HIJING new HIJING old HKM x 2G(C)/12G(D) 2G(Pb)/207G(D) HIJING new HIJING old HKM EKS x HIJING: Wang and Gyulassy, Phys. Rev D44, 3501 (1991) EKRS: Eskola et al., Eur. Phys. Jour. C9, 61 (1998) HKN: Hirai et al., hep-ph/ (2004)

16 I/8. Nuclear Modification Factor for dau at s =200 GeV PHENIX data at y = 0 Phys. Rev. Lett. 91, (2003) Shadowing inside nucleus is small effect at PHENIX at y = 0 we are at moderate-x region ( x 0.05) Calculations with ONLY nuclear shadowing is NOT enough!!!

17 I/9. From where Comes the Shadowing Contribution Cumulative probability P > (x Au ) = XAu 0 dσ(x )dx 1 0 dσ(x )dx GeV p T =4.25 GeV substantial contribution from higher-x region P > y=3 y=0 y= Can we understand high-x physics well? x Au

18 I/10. Multiple Scattering Cronin Effect Improve Glauber model: assuming saturation in the number of NN collisons p z A b d bdz A O A A Target dσπ pa E π d 3 p = d 2 b t A (b)e π dσ pp π ( k 2 T pa, k 2 T pp) d 3 p k 2 T pa = k 2 T pp + C h pa (b) Total broadening = pp baseline + nuclear broadening See details in PRC (2002) and hep-ph/ h(ν A (b) 1) : number of effective NN collisions ν max = 3 4 C : (average mom. broadening) 2 / coll. C 0.35 GeV 2 t A (b) : nuclear thickness function

19 The Effect of Multiple Scattering in at SPS and RHIC Nuclear Modification Factor (NMF) theoretical def.: R π AA := dσaa π /d 3 p( shadowing+multiscattering ) dσ AA π /d 3 p( NO nuclear effect )

20 II. INITIAL STATE EFFECTS IN h p z A b d bdz A O A d dσ ab cd t c d ~ D (z,q) h/c A Target c X VERY HIGH-p T π 0 PRODUCTION IN dau

21 Cronin effect at very high-p T in central dau collision HIJING: Wang and Gyulassy, Phys. Rev D44, 3501 (1991) EKRS: Eskola et al., Eur. Phys. Jour. C9, 61 (1998) HKN: Hirai et al., hep-ph/ (2004)

22 Extracting the slope of R dau in dau collision at PHENIX Comparing different shadowing parameterisations Fit 8 < p T < 30 GeV/c range Huge errors at peripheral collisions Different parameterisations have the same slope for EMC region Is there any room for nuclear effect in 0 40% centrality region

23 R dpb at in dpb Collision at different energies beyond RHIC CERN Yellow Rep. hep-ph/ Suppression can be strong at high-p T at the LHC energies.

24 Change of multiscattering at higher- s NN in dpb GGB:QM 06 poster M. Zielinski E706 Cronin peak is slightly moving towards higher-p T values.

25 III. FROM HOT TO COLD QUENCHING A a/a A f (x,k ;Q,b) b T,a b T,b a d dσ ab cd t f (x,k ;Q,b) b d b/a X c z c E(p,L) c ~ D h/c(z c*,q) X h X FINAL STATE EFFECTS IN da COLLISIONS?

26 III/1. Non-abelian Jet Energy Loss Jet-Quenching Energy loss of jets in hot, dense non-abelian plasma: energy loss in a THICK plasma - BDMS, LCPI energy loss in a THIN plasma - GLV method Medium induced radiative energy loss - for thin plasma: L λ g Gyulassy Lévai Vitev, Phys. Rev. Lett. 85, 5535; Nucl. Phy s. B594, 371 GLV: time-ordered pqcd (Feynman diagramms) + OPACITY expansion (N = 1, 2, 3,...) + kinematical cuts M J t 0 M J M 0 t 0 t t k,c p M 1,0,0 t 0 t 1 t q 1,a 1 k,c M 1,1,0 p t 0 t 1 M 1,0,1 t q 1,a 1 t 0 t t 1 k,c p q 1,a 1 p k,c M 5,1,10 M ns,m,l where l = 2 n s m 1 t 0 t 1 t t 2 t 3 t 4 t 5 q 1,a 1 q 2,a 2 q 3,a 3 q 4,a 4 q 5,a 5 p k,c

27 III/2. Calculations of Relative Energy Loss Results Energy dependence of GLV jet energy loss = E GLV E (1) GLV C Rα s N(E) L 2 µ 2 λ g log E µ E is E-dependent N(E) is a numerical function, N(E) 4 at E. E-independent E/E in 3 < GeV E < 10 GeV Opacity n = L/λ

28 III/3. π-suppression in AuAu collisions at RHIC energies GLV jet-quenching in thin plasma approximation L λ g : E GLV L2 µ 2 λ g log E µ Energy loss of jet decreases the p c momenta of c before fragmentation: D π/c (z c,q 2 ) πz 2 c z D c π/c (zc,q 2 ) z c, where z z πzc 2 c = c 1 E/p c, A a/a A f (x,k ;Q,b) b T,a b T,b a d dσ ab cd t f (x,k ;Q,b) b d b/a X c z c E(p,L) c ~ D h/c(z c*,q) X h X

29 Jet tomography in AuAu and dau collision at PHENIX Prog. in Part. and Nucl. Phys (2004), Eur. Phys. J. C33 S609 (2004)

30 Jet-tomography at midrapirity in AuAu and CuCu collisions Extracting opacities in all centralities for p T > 4 GeV/c All of these information is summarised =

31 Analysing opacity dependence in midrapidity AA collisions L A 1/3 N 1/3 part ε = E/E L 2 N 2/3 part L/λ will NOT disappear at very peripherical collision = WHAT DOES THIS MEAN?

32 WHAT KIND OF ANIMAL IS THIS? KITTEN?, BUNNY? or something ELSE?

33 IS THERE ROOM FOR COLD QUENCHING A d f (x,k ;Q,b) a/a b T,a f (x,k ;Q) b/d b T,b a b X d dσ ab cd t c d z c E(p,L) c ~ D h/c(z c*,q) X h X IN da COLLISIONS AT RHIC AND LHC?

34 Cold Quenching in dau collision at PHENIX and this effect is stronger at LHC energies...

35 Suppression at LHC? C.M. Energy dependence of GLV jet energy loss E GLV C Rα s N(E) L 2 µ 2 λ g log E µ = C Rα s N(E) 1 A dn dy L log E µ For central AuAu collision at RHIC 1 A dn dy 680 πr 2 AuAu = 5.1 For dau collison at RHIC 1 A dn dy 18 πr 2 dau = 2.54 Without suppression dn dy ln s At LHC this dn dy will be

36 SUMMARY: So, does the Cronin Peak Disapper at LHC? = Strong, 30 40% shadowing effect at intermediate p T = Cronin peak moves towards higher p T = Pheripheral AuAu and CuCu collisons data and dau data need a L/λ 1 quenching at RHIC. = There are strong suppression effects at LHC! Hmmm?!

37 BACKUP SLIDES

38 Jet-tomography in AuAu Collisions at Large η In the forward directions L/λ is smaller, due to less matter. AuAu, dau data for π 0 by PHENIX and h ± and π +,π by BRAHMS

39 Jet-tomography in AuAu Collisions at 62.4 and 200 AGeV Decreasing s the L/λ is smaller, due Getting close to compare geometrical and ε properties snn (GeV) ǫ Bj (GeV/fm 3 ) Reaction S + S 17, 3 1, 3 S + Au 19, Pb + Pb 17, Pb + Au 17, Au + Au Au + Au Au + Au