Jets in Nuclear Collisions l Why jets in
- Slides: 56
Jets in Nuclear Collisions l Why jets in nuclear collisions? l How do we find jets in nuclear collisions? l Is hard scattering different in nuclear collisions than in e+e- or pp collisions? l What happens in the nuclear medium? Is jet transport & fragmentation changed? l What do we still want to know? Barbara Jacak Stony Brook University June 29, 2004 1
Why collide nuclei at s=200 Ge. V/A? high energy nuclear collisions should create quark gluon plasma Attractive potential Confinement at large distance At high temperature and density: T~170 Me. V and/or r~5 r 0 Debye screening by produced color-charges expect transition to “free” gas of quarks and gluons 2
how to probe the plasma? e, pressure builds up Hard scattered or heavy q, g probes of plasma formed , * e+e-, m+m. Real and virtual photons emitted as thermal radiation. System expands & cools , K, p, n, f, L, D, X, W, d, Hadrons reflect (thermal) properties when inelastic collisions stop (chemical freeze-out). 3
Hard quarks & gluons jets Hard scattering happens early affected by initial state nucleus Hard partons propagate fast quarks, gluons traverse the interesting stuff radiate gluons interact with QGP partons Fragmentation is last step - outside the medium 4
Plasma physics of the quark gluon plasma? l Want to know pressure, viscosity, energy gradients, equation of state, thermalization time & extent determine from collective behavior l Other plasma parameters radiation rate, collision frequency, conductivity, opacity, Debye screening length? what is interaction s of q, g in the medum? need short wavelength strongly interacting probe l high momentum q, g provide just this! 5
What is the effect of the medium? schematic view of jet production hadrons leading particle q q before they create jets, the scattered quarks radiate energy (~ Ge. V/fm) in the colored medium hadrons leading particle decreases their momentum fewer high momentum particles beam “jet quenching” Approach: calculate jet rate, test in pp, compare jets in A+A to p+p 6
QCD and EM Radiation EM EM Radiation by scattering: Interference between initial and final state radiation QCD gluon BUT radiated gluons also interact with gluons in the medium! Energy loss depends on gluon density along the path. quark Radiation interferes too 7
Energy Loss in Dense QCD Matter Ivan Vitev, ISU • Elastic energy loss J. D. Bjorken, SLAC preprint (1982) unpublished • Inelastic (radiative) energy loss QCD is very different from QED in the ability of the gluon to reinteract 8
Energy loss expected Since QCD is non-abelian, even 1 scattering in final state is sufficient to generate energy loss Remember that radiated gluon couples to medium! formation length of max E gluon: l. F ~ 2 E/m 2 ( m = p. T kick ) So: E ~ E x L/l x L m 2/2 E ~ m 2 L 2 /2 l formation time of radiated gluon standard radiation with no interference ( gluon interaction probability) In normal, cold nuclei d. E/dx ~ 0. 5 Ge. V/fm Prediction for RHIC: 10 x DE of cold nuclei 9
A closer look at the calculation M. Gyulassy, P. Levai, I. V. , Nucl. Phys. B 594, (2001); Phys. Rev. Lett. 85, (2000) • Radiative energy loss • Significantly larger than the elastic for static nuclear matter • Can be related to the density of gluons/quarks in the system or T • Takes into account geometry, the small number of scatterings, finite kinematics But medium is not static! Expands density drops 10
How do we find jets in nuclear collisions? Central Au+Au collision In p+p can look for hadrons in the characteristic “cone” pattern How to find the jet? s=200 Ge. V energy is modest; jet s not large 11
3 Ways to “Skin a Cat Jet” 1) Single Particle Spectra: High p. T dominantly from jets d /dp. T RAA, Rd. A nuclear modification factor 2) 2 -Particle Correlations: d. N/d( ) “Trigger” =0 Adler et al. , PRL 90: 082302 (2003), STAR 3) Jet Reconstruction: d /d. ET, Fragmentation function Nice work if you can get it! trigger near-side away-side 12
opposing j et 0° Jet physics in Au+Au Trigger: hadron with p. T > 2. 5 Ge. V/c Biased, low energy, high z jets! of associated partners Count associated lower p. T particles for each trigger 13 “conditional yield” Near side yield: number of jet associated particles from same jet in specified p. T bin Away side yield: jet fragments from opposing jet
Subtract the underlying event includes ALL triggers (even those with no associated particles in the event) combinatorial background large in Au+Au CARTOON 1 d. N flow+jet Ntrig d flow jet associated particles with non-flow angular correlations -> jets! Treat as 2 Gaussians Underlying event is big! Collective flow causes another correlation in them: B(1+2 v 2(p. Ttrig)v 2(p. Tassoc)cos(2 )) 14
Benchmark calculation of probe rate on a simple system: p+p collisions p-p PRL 91 (2003) 241803 0 Good agreement with NLO p. QCD 0 rates: d. N/dp. T 2 dy 1 dy 2 ~ dxa dxb dzc dzd fa/N(xa, Q 2). fb/N(xb, Q 2). Dh 1(zc, Q 2). Dh 2(zd, Q 2). dsab /d. Q 2 dy Parton distribution functions Fragmentation functions To generalize for nuclei: fa/N(xa, Q 2, r) fa/N(xa, Q 2). Nuclear modification to Sa/A(xa, r). structure function t. A(r) (shadowing, saturation, etc. ) Nuclear thickness 15 function
Now check that it works in Au+Au l Not so easy – cannot use anything that should be affected by the medium! l Try QCD direct photons 16
p. QCD in Au+Au? direct photons Probe calculation works! Au+Au 200 Ge. V/A: 10% most central collisions ( p. QCD x Ncoll) / background Vogelsang/CTEQ 6 Preliminary ( p. QCD x Ncoll) / ( background x Ncoll) [w/ the real suppression] [if there were no suppression] [ ]measured / [ ]background = p. T (Ge. V/c) measured/ background 17
Is the message in the medium? l Is there “jet quenching” as predicted from energy loss? count high p. T particles (AA vs. pp) look at back-to-back jets l How much energy do fast partons lose? What does it tell us about the medium? l Where does the “lost” energy go? l What does the presence of q and q in the QGP do to jet fragmentation? 18
Technique to search for jet quenching l Compare to baseline: nucleon-nucleon collisions at the same energy l To 0’th order: Au + Au collisions start with collisions of quarks & gluons in the individual N-N reactions (+ effects of nuclear binding and collective excitations) nucleons l Hard scattering (p transfer > few Ge. V) processes scale as the number of N-N binary collisions <Nbinary> so for p. T> 2 Ge. V/c expect: Yield. A-A = Yield. N-N. <Nbinary> 19
Nuclear Modification of Hadron Spectra? 1. Compare Au+Au to nucleon-nucleon cross sections 2. Compare Au+Au central/peripheral Nuclear Modification Factor: nucleon-nucleon cross section <Nbinary>/sinelp+p AA AA AA If no medium effect: RAA < 1 in regime of soft physics RAA = 1 at high-p. T where hard scattering dominates Jet quenching: RAA < 1 at high-p. T 20
Au-Au s = 200 Ge. V: high p. T suppressed! PRL 91, 072301(2003) 21
look for the jet on the other side Peripheral Au + Au STAR PRL 90, 082302 (2003) near side Central Au + Au away side peripheral central Medium is opaque! Trigger 4 -6 Ge. V/c p. T 22
Path Length Dependence di-hadron, 20 -60% Central STAR Preliminary Background Subtracted See J. Bielcikova et al. , (nucl-ex/0311007) for background derivation Out-of-plane Measured Reflected In-plane Suppression larger out-of-plane 23
Suppression: a final state effect? Hadron gas l Hadronic absorption of fragments: Gallmeister, et al. PRC 67, 044905(2003) Fragments formed inside hadronic medium l Hadron source is soft, after all Recombination of flowing partons Fries, Muller, Nonaka, Bass nucl-th/0301078 Lin & Ko, PRL 89, 202302(2002), Hwa, et al. l Energy loss of partons in dense matter Gyulassy, Wang, Vitev, Baier, Wiedemann… But absent in d+Au collisions! d+Au is the “control” experiment 24
Suppression: an initial state effect? l Gluon Saturation probe rest frame (color glass condensate) Wavefunction of low x gluons overlap; the selfcoupling gluons fuse, saturating the density of gluons in the initial state. (gets Nch right!) Levin, Ryshkin, Mueller, Qiu, Kharzeev, Mc. Lerran, Venugopalan, Balitsky, Kovchegov, Kovner, Iancu … • Multiple elastic scatterings gg g r/ Rd. Au~ 0. 5 D. Kharzeev et al. , hep-ph/0210033 Broaden p. T : (Cronin effect) Wang, Kopeliovich, Levai, Accardi 25
Experiments show NO suppression in d+Au! PHENIX Preliminary 0 STAR Preliminary 26 PHOBOS Preliminary
Centrality Dependence Au + Au Experiment d + Au Control PHENIX preliminary l Dramatically different and opposite centrality evolution of Au. Au experiment from d. Au control. l Jet Suppression is clearly a final state effect. 27
Are back-to-back jets there in d+Au? Yes! Pedestal&flow subtracted leading particle suppressed hadrons So this is the right picture for Au+Au q q ? 28
Property probed: density Agreement with data: Vitev, Gyulassy, Wang, others say d. E/dx ~ 7. 5 Ge. V/fm get d. Au right too! initial gluon density= d. Ng/dy ~ 1100 e ~ 15 Ge. V/fm 3 d. Au d-Au hydro initial state same e 5 -10 x ecritical NB: Lowest energy radiation sensitive to infrared cutoff. Au-Au 29
Recap l Hard partons are excellent probes of QGP l Can calculate their production rate with p. QCD in Au+Au l (surprisingly) Can do jet physics in heavy ion collision l See jet quenching in single particles & back-to-back correlations Infer: d. E/dx ~ 7. 5 Ge. V/fm d. Ng/dy ~ 1100 e ~ 15 Ge. V/fm 3 30
Turn to the fragmentation function Standard picture If true: fragmentation independent of medium Baryon/meson at high p. T same in Au+Au and p+p 31
Formation time of fragmentation hadrons l Uncertainty principle relates hadron formation time to hadron size, Rh and mass, mh In laboratory frame: tf ~ Rh (Eh /mh) consider 2. 5 Ge. V p. T hadrons tf ~ 9 -18 fm/c for pions; Rh~0. 5 -1 fm tf ~ 2. 7 fm/c for baryons (Rh~1 fm) l Alternatively, consider color singlet dipoles from combination of q & q from gluon splitting Using gluon formation time, can estimate tf ~ 2 Eh (1 -z)/(k. T 2+mh 2) for z = 0. 6 -0. 8 and k. T ~ LQCD (tf baryons) ~ 1 -2 fm/c R(Au nucleus) ~ 7 fm Baryon formation is NOT outside the medium! 32
We observe a puzzle h/ 0 ratio shows that p is enhanced only < 5 Ge. V/c 33
Are extras from the (soft) underlying event? Hydro. expansion at low p. T + jet quenching at high p. T. R. Fries, et al p. QCD spectrum shifted by 2. 2 Ge. V Coalesce (recombine) boosted quarks hadrons enhances mid p. T hadrons baryons especially Teff = 350 Me. V 34
Phase space filled with partons: coalesce into hadrons Use lowest Fock state, i. e. valence quarks l Re. Co of hadrons: convolution of Wigner functions Wab(1; 2) = wa(1)wb(2) l Where does Re. Co win? Exponential: Power law: fragmenting parton: ph = z p, z<1 recombining partons: p 1+p 2=ph 35 R. Fries
Coalescence Model results Greco, Ko, Levai: PRC 68 (2003)034904 Fries et al: Phys. Rev. C 68 (2003) 044902 • particle ratios and spectra OK • intermediate p. T hadrons from coalescence of flowing partons NOT from jets, so no jet-like associated particles 36
But baryons show jet-like properties too… Baryons at 2 -4 Ge. V/c p. T scale with Ncoll ! 37
So baryons seem jet-like! Rcp l baryons & antibaryons not suppressed!? parton E depends upon what fragmentation WILL be? ? ? l baryon excess due to fragmentation function modification? Step 1: determine if baryons are from jets do we see hadronic partners from the same jet? Step 2: calculate effect of q, q in surrounding medium upon 38 (soft part of) fragmentation function
Step 1: use 2 particle correlations Select particles with p. T= 2. 5 -4. 0 Ge. V/c Identify them as mesons or baryons via Time-of-flight Find second particle with p. T = 1. 7 -2. 5 Ge. V/c Plot distribution of the pair opening angles 39
Jets in PHENIX l Large multiplicity of charged particles --solution: find jets in a statistical manner using angular correlations of particles mixed events give combinatorial background l 2 x 90 degree acceptance in phi and | |<0. 35 --solution: correct for azimuthal acceptance, PHENIX PRL 91 (2003) 182301 but not for acceptance l Elliptic flow correlations --solutions: use published strength values and subtract (could integrate over 90° to integrate all even 40 harmonics to zero)
Subtracting combinatorial background includes ALL triggers (even those with no associated particles in the event) CARTOON 1 d. N flow+jet Ntrig d flow jet associated particles with non-flow angular correlations -> jets! Treat as 2 Gaussians Associated particles from the underlying event. Collective flow causes another correlation in them: B(1+2 v 2(p. Ttrig)v 2(p. Tassoc)cos(2 )) 41
Identify Trigger: Source of intermediate p. T baryons? • jet partner equally likely for trigger baryons & mesons • Same side: only slight decrease with centrality • Away side: partner rate as in p+p confirms jet source of baryons! • See disappearance of away-side jet for both baryons and mesons 42
partners expected from recombination • Yield of partners per trigger expected from recombination of purely thermal (soft) constituent quarks (dilutes jets) pions only soft protons Allow fast quark to combine with quarks from medium Many baryons ARE from jets, but medium modifies those jets 43
p. T spectra of same jet associated particles Spectra in lab, rather than jet, frame Allows to compare with inclusive spectra 44
Compare slope to inclusive hadron spectra Generally higher Perhaps thermalized in most central collisions? Calculations (step 2) desperately needed! 45
Conclusion about fragmentation function l It’s modified in the medium! Au+Au jets richer in soft hadrons than p+p or d+Au Au+Au jets baryon yield increases with medium volume l Maybe some evidence that jet fragments are beginning to thermalize in the medium 46
What do we still want to know? l Quantitative information on medium modification of jet fragmentation l Where does the energy radiated by fast partons go? Many soft gluons – no (per observed multiplicity) A few semi-hard gluons? … could be l How is the lost energy propagated in the medium? Infer energy, color transport properties of QGP basic plasma physics! Is the lost energy thermalized in the medium? 47
values B (fm) Npart R/R+F p Partner yield p 12 24 0. 45 0. 95 0. 027 0. 0047 0. 0014 0. 0007 7. 5 156 0. 65 0. 97 0. 0172 0. 0030 0. 0008 0. 0004 0 390 0. 8 0. 98 0. 0098 0. 04017 0. 0005 0. 0003 48
k. T, j. T at RHIC from p+p Data Statistical Errors Only di-hadron J. Rak, Wed. J. Rak, DNP 03 near-side away-side Df 49
Moment Analysis of QCD Matter I. Vitev, nucl-th/0308028 § § Induced Gluon Radiation ~collinear gluons in cone “Softened” fragmentation Gyulassy et al. , nucl-th/0302077 50
Collective effects? Pressure: a barometer called “elliptic flow” Origin: spatial anisotropy of the system when created, followed by multiple scattering of particles in the evolving system spatial anisotropy momentum anisotropy v 2: 2 nd harmonic Fourier coefficient in azimuthal distribution of particles with respect to the reaction plane Almond shape overlap region in coordinate space 51
v 2 reproduced by hydrodynamics Hydro. Calculations Huovinen, P. Kolb, U. Heinz STAR PRL 86 (2001) 402 • see large pressure buildup • anisotropy happens fast • early equilibration ! central Hydrodynamics assumes early equilibration Initial energy density is input Equation of state from lattice QCD Solve equations of motion 52
But at forward rapidity reach smaller x y = 3. 2 in deuteron direction x 10 -3 in Au nucleus Strong shadowing, maybe even saturation? d Au 53 Phenix Preliminary
Pions in 3 detectors in PHENIX l Charged pions from TOF l Neutral pions from EMCAL l Charged pions from RICH+EMCAL Cronin effect gone at p. T ~ 8 Ge. V/c 54
Centrality dependence of Cronin effect l Probe response of cold nuclear matter with increased number of collisions. l See larger Cronin effect for baryons than for mesons (as at Fermilab) Qualitative agreement with model by Accardi and Gyulassy. Partonic Glauber-Eikonal approach: sequential multiple partonic collisions. nucl-th/0308029 55
Does Cronin enhancement saturate? l A different approach: l Intrinsic momentum broadening in the excited projectile proton: l hp. A: average number of collisions: X. N. Wang, Phys. Rev. C 61 (2000): no upper limit. Zhang, Fai, Papp, Barnafoldi & Levai, Phys. Rev. C 65 (2002): n=4 due to proton d dissociation. 56
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