JET QUENCHING IN MEDIUM TOMOGRAPHY IN HEAVY ION COLLISIONS

Transcription

1 JET QUENCHING IN MEDIUM TOMOGRAPHY IN HEAVY ION COLLISIONS Gergely Gábor Barnaföldi RMKI,ELTE in collaboration with: Burkhard Kämpfer FZ Rossendorf; Péter Lévai KFKI RMKI; Gábor Papp ELTE; George Fai ELTE, Kent State University; Forschungszentrum Rossendorf 4. Nov. 2005, TU Dresden Germany

2 Outline of the Seminar 0. Motivation and history Cronin effect motivation as a short experimental summary definition of the nuclear modification factor I. Theoretical description of pp collisions pqcd baseline generalization of the PDFs in phenomenological way applications for the π production in pp II. Nuclear effects in pa collisions nuclear baseline nuclear shadowing modeling nuclear PDFs multiple scattering genealised D PDFs collision geometry improve the Glauber picture III. The AA collisions at RHIC energies application Gyulassy Lévai Vitev (GLV) jet quenching formalism Extracting the opacity (L/λ) in AA collisions

3 0. Experimental Discovery of the Cronin Effect 1975 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 measuring Cronin effect: R AA = 1 N bin dn AA /dy d 2 p T dnpp/dy d 2 p T D. Antreasyan et al. Phys. Rev. D19, 764 (1979) C.N. Brown et al. Phys. Rev C54, 3195 (1996) Y. Zhang et al. Phys. Rev C65, (2002)

4 Short Experimental Motivation Opening Questions R AA and π spectra in AuAu and dau by PHENIX, y = 0 R AA 3 π % central: α s NN = 200 GeV s NN = 130 GeV s NN = 31.0 GeV s NN = 17.3 GeV pt (GeV/c) Suppression in π spectra in AuAu at RHIC = QGP Test: NO Suppression in dau at RHIC = Jet-quenching Suppression in h +, h spectra in dau by BRAHMS, η > 0 R d+au η = 0 + h +h 2 R d+au η = 1 + h +h 2 R d+au η = h R d+au η = h Conventional or new nuclear effect? p T [GeV/c] p T [GeV/c] p T [GeV/c] p T [GeV/c]

5 I. Theoretical Description of pp Collisions with h p f (x, k ;Q) a/p a T,a a X c ~ D (z,q) h/c c p f (x,k ;Q) b/p b T,b b d dσ ab cd t d X X Phenomenological Dimensional PDFs

6 I/1. pqcd Improved Parton Model for pp Collisions dσπ pp E π d 3 f a/p (x a, Q 2 ; k T ) f b/p (x b, Q 2 ; k T ) dσab cd p π dˆt D π/c(z c, Q 2 ). πzc 2 f a/p (x a, Q 2 ; k T ) : 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 p dσ ab cd dˆt : Partonic cross section f (x, k ;Q) a/p a f (x,k ;Q) b/p b T,a T,b a b X d dσ ab cd t X c d ~ D (z,q) h/c c h X

7 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)

8 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 dx f 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

9 Charged π Productions, and π /π + Ratios at Different PS Energies Calculated with Intrinsic-k T INTRINSIC-k T is a good parameter: ± 20 30% agreement with experimental data

10 Charged Hadron Production in p p Collisions at UA1 Experiment at s = 200; 500 and 900 GeV If s increases then the value of kt 2 is getting negligible! Data: D. Albajar et al., Nucl. Phys. B (1990).

11 s Dependence of Intrinsic-kT in Different pp and p p Experiments from CERN to Tevatron Energies both LO and NLO

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

13 The Summary of pp Calculations Why is interesting to fit the pp π with an extra parameter? Generalisation of PDFs into transverse plane, is motivated intrinsic k T is motivated by Heisenberg uncertaintly some parameterised PDF contains this as a constant Generalisation of the PDF is not unique and not trivial the Small-x Collaboration is working strongly on updf other parameterised phenomenological models exist The intrinsic-k T is measurable experimentally k T values are agree with PHENIX jet-jet correlation data π data reproduction at 10 30% in lower and higher p T regions Intrinsic-k T plays interesting role in pa and AA collisions!

14 II. Nuclear Effects in pa (dau) Collisions h p f (x, k ;Q) a/p a T,a a X c ~ D (z,q) h/c c A f (x,k ;Q,b) b T,b d dσ ab cd t b/a b d X X at CERN SPS and RHIC Energies

15 II/1. pqcd Improved Parton Model for pa Collisions dσπ pa E π d 3 p π f a/p (x a, Q 2 ; k T ) f b/a (x b, Q 2 ; k T, b) dσab cd 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

16 II/2. 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 b t 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.

17 The Glauber Picture Nobel Prize 05 One of the Father of the Glauber Gribov formalism... for his contribution to the quantum theory of optical coherence Roy J. Glauber together with: John L. Hall and Theodor W. Hänsch Roy J. Glauber at Quark Matter 05 Conference (Budapest) (in a renaissance restaurant)

18 II/3. 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)

19 II/3. (a) Measured and Phenomenological Shadowing Measured by many different experimental collaborations

20 II/3. (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)

21 II/4. 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!!!

22 II/5. 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

23 Cronin Effect with shadowing and multiscattering in dau collision at PHENIX ( s = 200 AGeV, min. bias) HIJING (b-indep.) shadowing, ν max = 4, C sat = 0.35, y = 0

24 Cronin effect for π 0 at midrapidity in different pa collisions at CERN SPS energies G.G. Barnaföldi et al.: Proc. of. 10 th ICNRM (2003)

25 Cronin effect in different Centralities in dau collision at PHENIX G.G. Barnaföldi et al.: J. Phys. G30, S1125

26 II/6. Testing Shadowing Functions at Larger Rapidity 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= p T = 4 GeV and y = 0 = 5% suppression p T = 4 GeV and y = 3 = 30% suppression x Au

27 BRAHMS data in dau collision at s = 200 AGeV (min. bias) calculation with shadowing + CRONIN (QM 04) HIJING (b-indep.) shad., ν max = 4, C sat = , y = 3

28 Cronin on min. bias dau π 0 at PHOBOS and BRAHMS η > 0 h Au d-side d BRAHMS data: nucl-ex/ and PHOBOS data: nucl-ex/

29 Cronin on min. bias dau π 0 as inverted, η < 0 h Au NO relevant multiscatt. in d. Au-side d

30 Summary of Nuclear Effects Baseline Calculations What have we learnt from the pa and dau results? Multiple Scattering: is the broadening of the intrinsic k T inside the nucleus depends on A, but still question, is saturation can be seen? position of Cronin peak is depend on the value of k 2 T pp height of Cronin peak is depend on the value of C h pa (b) Nuclear Shadowing: based on EMC, NMC, FNAL, etc. experimental data there are different parameterisations: EKRS, HIJING, HKN quark contributions are similar, but for gluons are different analysing R dau (p T ) is a good testbed for testing shadowing Overall: we have nice description for π in pa (dau) collisions

31 III. Jet Tomography Using GLV Jet-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 in AA Collisions at RHIC Energies

32 III/1. π Spectra in AA Collisions at WA98 and PHENIX Proc. of ISMD 02, 145 (2002), APH NS Heavy Ion Phys. 18, 79 (2003)

33 III/2. Discovery of Jet Quenching in Au + Au π R AA Central π 0 (0-10%) Peripheral π 0 (80-92%) p T (GeV/c) The suppression of high-energy particles goes away, while we create less matter PHENIX (nucl-ex/ )

34 III/3. Jet-Jet Correlation in d + Au and Au + Au 0.2 h + +h - d+au FTPC-Au 0-20% d+au min. bias (a) 0.1 1/N trigger dn/d( φ) p+p min. bias Au+Au central 0.1 (b) 0 0 π/2 π φ (radians) Jet-jet back-to-back correlation data from STAR experiment displays strong jet suppression in Au + Au collision (nucl-ex/ )

35 III/4. 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

36 III/5. 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

37 III/6. 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 πz 2 c, where z c = z 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

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

39 Calculated R π0 AA for central AuAu and CuCu collisions In the smaller CuCu system L/λ is less 0.75 than in AuAu. AuAu,dAu and central CuCu data for π 0 by PHENIX, mid-central CuCu by STAR

40 System size dependence (A) of R π0 AA for AuAu and CuCu AuAu,dAu and central CuCu data for π 0 by PHENIX, mid-central CuCu by STAR

41 Comparing π 0 data in AuAu at η = 3.1 and y = 0 AuAu at BRAHMS η = 3.1 and PHENIX y = 0 Larger shadowing in dau at η > 0 Additional (exp.) information: R AuAu (y = 0) R AuAu (y > 0) R CP R AA New BRAHMS results = Shadowing effect is stronger = Travelling length getting smaller as going more forward = Smaller L/λ can be extracted in the forward π production

42 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

43 Summary Playing with (Nuclear) Effects R π AA := dσaa π /d 3 p ( shadowing+multiscattering+ jet-quenching ) dσ AA π /d 3 p ( NO nuclear effect ) pqcd improved parton model for pp π reaction Initial and final state effects in pa and AA collisions Initial nuclear effects: k T -broadening Cronin effect: k T, C sat, ν max,... Nuclear modification factor: R AA Multiple scattering Glauber picture, saturation Shadowing inside the nucleus nuclear properties Final state effect: Non-abelian jet energy loss (quenching) extracting L/λ g

44 BACKUP SLIDES

45 Intrinsic-k T as a Function of p T in Different Experiments Data: D. Antreasyan et al., Phys. Rev. D (1979). C. Kourkoumelis et al., Z. Phys. C5 95 (1980).

46 (average mom. broadening) 2 /coll. Number of eff. NN collisions 4. Nov FZ-Rossendorf G.G. Barnaföldi Comparing pbe, pt i and pw Collisions s = 19.4, 23.8 and 27.4 GeV

47 Results on π + Productions in pbe, pt i and pw Collisions

48 Calculations for π 0 in pbe and pcu collision at FNAL E706 G.G. Barnaföldi et al.: APH NS (2004)

49 R W/Be (p T ) for π + and π at midrapidity at CP and CCOR Weak dependence on shadowing at lower energies

50 Cronin effect with b-independent (left) and b-dependent (right) shadowing in dau collision at PHENIX (Min. Bias) NO quenching is assumed = NO suppression in dau MINIMUM BIAS reproduction = OK See details in: P. Lévai, G. Papp, G.G. Barnaföldi, G. Fai: nucl-th/