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A Student’s Guide to Hard Scattering at RHIC. Thomas K Hemmick Stony Brook University. Helmut Satz. A Defining Moment for Me. In 1988, Brookhaven National Lab held a school for the students in the fledgling field of Relativistic Heavy Ions.

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a student s guide to hard scattering at rhic

A Student’s Guide to Hard Scattering at RHIC

Thomas K Hemmick

Stony Brook University

a defining moment for me

Helmut Satz

A Defining Moment for Me.
  • In 1988, Brookhaven National Lab held a school for the students in the fledgling field of Relativistic Heavy Ions.
  • I was one of the attendees and am still grateful for this school nearly 20 years later (I still have the Xeroxed notes)
  • One of my colleagues recently dug up the “class photo”.
  • It is simply amazing that most of the people in that photo are still in the field today…I credit the school and its teachers:
  • BTW: The most popular teacher at that school…
goals of this presentation
Goals of this Presentation
  • Quark Matter is one of the most exciting, current, and results-filled conferences.
  • Necessarily, the talks use jargon heavily and assume knowledge of the history of the field.
  • I hope to give a self-contained (and somewhat whirl-wind) tour over the concepts, previous measurements, and present issues in hard scattering measurements.
  • My goal is to help you attain something of the necessary background to fully enjoy this conference.
nuclear collision terminology
Nuclear Collision Terminology
  • Centrality and Reaction Plane determined on an Event-by-Event basis.
  • Npart= # of Participants
    • 2  394
  • Nbinary=# of Collisions

Peripheral Collision

Semi-Central Collision

Central Collision

100% Centrality 0%


Reaction Plane

  • Fourier decompose azimuthal yield:
the paradigm
The Paradigm
  • We accelerate nuclei to high energies with the hope and intent of utilizing the beam energy to drive a phase transition to QGP.
  • The created system lasts for only ~10 fm/c
  • The collision must not only utilize the energy effectively, but generate the signatures of the new phase for us.
  • I will make an artificial distinction as follows:
    • Medium: The bulk of the particles; dominantly soft production and possibly exhibiting some phase.
    • Probe: Particles whose production is calculable, measurable, and thermally incompatible with (distinct from) the medium.
the probes gallery hard scattering
The Probes Gallery (Hard Scattering):

Jet Suppression

charm/bottom dynamics

J/Y & U

direct photonsCONTROL

The importance of the control measurement(s) cannot be overstated!

calibrating the probe s

Thermally-shaped Soft Production

“Well Calibrated”



Calibrating the Probe(s)
  • Measurement from elementary collisions matches calculations.
  • Question: What goes into these calculations?

p+p->p0 + X

hep-ex/0305013 S.S. Adler et al.

factorization theorem

NOTE: Only the pQCD cross sections are fundamental. PDF and Fragmentation are

based upon measurement

Factorization Theorem:
  • Nucleon is a collection of partons described by PDF.
  • Pair-wise interactions of partons at high Q2 can described by pQCD.
  • Scattered partons materialize as jets via the fragmentation function.

Collins, Soper, Sterman, Nucl. Phys. B263 (1986) 37

parton distribution functions
Parton Distribution Functions
  • Parton Distribution Functions are well measured and universal (at least under the factorization theorem).
  • Calculations (PYTHIA) use theoretical form guided by the data:
    • CTEQ 5M
    • others…
  • Parton distributions in nuclei are modified as compared to nucleons.


fragmentation function
Fragmentation Function
  • The fragmentation function, D(z) describes the process of by which a scattered parton materializes as a jet of particles.
  • A medium might be expected to modify D(z).
  • When the full jet is difficult to identify, z is replaced by zT referencing the leading or “trigger” particle of the jet.
q g jets as probe of hot medium

schematic view of jet production







leading particle

q/g jets as probe of hot medium

Jets from hard scattered

quarks observed via fast

leading particles or

azimuthal correlations

between the leading


  • However, before they create jets, the scattered quarks radiate energy (~ GeV/fm) in the colored medium
  • decreases their momentum (fewer high pT particles)
  • “kills” jet partner on other side

Jet Quenching

r aa normalization



If no “effects”:

RAA < 1 in regime of soft physics

RAA = 1 at high-pT where hard

scattering dominates


RAA < 1 at high-pT


RAA Normalization

1. Compare Au+Au to nucleon-nucleon cross sections

2. Compare Au+Au central/peripheral





cross section



Au-Au s = 200 GeV: high pT suppression!

PRL91, 072301(2003)

Effect is real…seen by ALL 4 experiments…Final or Initial State Effect?

more than just a bunch of nucleons

An example of gluon shadowing prediction

gluons in Pb / gluons in p





More than just a bunch of nucleons
  • The parton distributionsin a nucleus differ fromthose of the nucleon.
  • Depletion at low xis called shadowing andexcess at intermediate xis called anti-shadowing.
  • Shadowing calculations are theoretical calculations “inspired” by experimental measurements (not fundamental).

probe rest frame



  • Color Glass Condensate
  • Gluon fusion reduces number of scattering centers in initial state.
  • Theoretically attractive; limits DGLAP evolution/restores unitarity
control experiment







Control Experiment
  • Collisions of small with large nuclei quantify all cold nuclear effects.
  • Small + Large distinguishes all initial and final state effects.


No Medium!

no suppression in d au
NO suppression in d+Au!





centrality dependence
Centrality Dependence

Au + Au Experiment

d + Au Control Experiment

  • Dramatically different and opposite centrality evolution of Au+Au experiment from d+Au control.
  • Jet Suppression is clearly a final state effect.

Final Data

Preliminary Data

second control experiment



Second Control Experiment
  • The medium should be transparent to photons.
  • These thereby probe the initial rate of pQCD production and provide independent normalization of hard collision rates.
direct photons in au au
Direct Photons in Au+Au

PRL 94, 232301

p0 suppression caused by medium created in Au+Au collisions

Expectation for Ncoll scaling of direct photons

holds for all centrality classes

so opaque even a 20 gev p 0 is stopped
So opaque, even a 20 GeV p0 is stopped.
  • Suppression is very strong (RAA=0.2!) and flat up to 20 GeV/c
  • Common suppression for p0 and h; it is at partonic level
  • e > 15 GeV/fm3; dNg/dy > 1100

RAA data vs GLV model

Empirical energy loss from data

Fractional energy loss

Quantify the Energy Loss

  • Medium induced energy loss is the only currently known physical mechanism that can consistently explain the high pT suppression.
  • From GLV model, initial gluon density dng/dy~1000 is obtained. This corresponds to an initial energy density e~15 GeV/fm3.
how about a heavy probe charm quark


0.906 <  < 1.042



dN/dy = A (Ncoll)



How about a heavy probe: Charm Quark
  • Electon spectrum used to infer charm yield.
  • “Photonic” electrons measured with convertor and subtracted.
  • Yield scales with Nbinary
  • Mass alone makes for valid pQCD regime.
modification of charm
Modification of Charm

M. Djordjevic, et. al. nucl-th/0507019

  • Electrons from heavy quark decay have nearly same RAA as pions!
  • Electrons from heavy quark decay flow (“stopped in medium”)?
  • But how do you stop a b-quark?
  • Data imply small diffusion coefficient for charm.
jet tomography

Escaping Jet

“Near Side”


Lost Jet

“Far Side”


Jet Tomography
  • Jets are produced as back-to-back pairs.
  • If one jet escapes, is the other shadowed?
  • Map the dynamics of Near-Side and Away-Side jets.
    • Vary the reaction plane vs. jet orientation.
    • Study the composition of the jets
    • Reconstruct the WHOLE jet
      • Find “suppressed” momentum & energy.

X-ray pictures areshadows of bones

Can Jet Absorption be Used to“Take an X-ray” of our Medium?

back to back jets
Back-to-back jets

STAR PRL 90, 082302 (2003)

Peripheral Au + Au

near side

Central Au + Au

away side



d + Au


0 3 Df (radians)

back to back wrt reaction plane





Back-to-Back wrt Reaction Plane
  • Suppression stronger in the out-of-plane direction.
  • Indicates suppression depends upon length of medium traversed.
  • Dilemma: How to quantify “completely opaque”.
    • Get something to punch through.
    • Find the lost energy and momentum
many sides of r aa
Many sides of RAA
  • Can examine suppression at differing centrality but same medium length (via emission angle)


search for the scaling variable

Au+Au collisions at 200GeV




Search for the Scaling Variable
  • SHOCK-1! The data do not scale with rL, differing from the naïve energy loss picture.
  • SHOCK-2! The data do scale with L alone and show no suppression for L<2 fm
away jet cannot disappear

1 < pT (assoc) < 2.5 GeV/c

Away Jet cannot “Disappear”
  • Energy and momentum conservation require that the “lost” jet must be found somewhere.
  • “Loss” was seen for partner momenta just below the trigger particle…Search low in momentum for the remnants.



correlation of soft 1 2 gev c jet partners
Correlation of soft ~1-2 GeV/c jet partners

Emergence of a Volcano Shape

PHENIX (nuclex/0507004)

“split” of away side jet!

peripheral: normal jet pattern

explanations for splitting
Explanations for splitting
  • Mach cone
    • Sonic (or displacement) shock wave propagating through strongly interacting medium.
  • Cherenkov Radiation
    • Color charge equivalent to high velocity electric chg
  • Bent Jet
    • Jet scatters through medium and is deflected from back-to-back

Explaining Modification of Jet Topology

Wake Effect or “sonic boom”

Cherenkov Gluon Radiation

hep-ph/0411315 Casalderrey-Solana,Shuryak,Teaney

nucl-th/0406018 Stoecker

hep-ph/0503158 Muller,Ruppert

nucl-th/0503028A. K. Chaudhuri

Renk & Ruppert Phys. Rev. C73 011901 (2006)

nucl-th/0507063 Koch, Majumder, X.-N. Wang

Transport Theory

nucl-th/0601012 Ma, Zhang, Ma, Huang, Cai, Chen, He, Long, Shen, Shi

Mult. Scat.

nucl-th/0605054 Chiu & Hwa

Jets and Flow couple

hep-ph/0411341 Armesto,Salgado,Wiedemann

mach cones common in em plasma
Mach cones common in EM plasma

Experimental Handle:3-particle correlations

conical flow vs deflected jets















deflected jets

mach cone

Conical Flow vs Deflected Jets
three particle correlations
signal obtained by subtraction of dominant backgrounds

flow components, jet-related two-particle correlation

clear elongation (jet deflection)

off-diagonal signal related to mach cone?

Three-Particle Correlations

Au+Au Central 0-12% Triggered





Raw – Jet x Bkgd – Bkgd x Bkgd


(Soft-Soft incl. Flow)


Some of both patterns

3 particle correlations in phenix

Hi pT

Assoc. pTs



3-Particle Correlations in PHENIX

(3 particles from di-jet) + (2 from dijet + 1 other)

Same Side

Away Side

PHENIX Preliminary

correlation topologies

triples/trigger (A.U.)

PHENIX Preliminary

Renk&Ruppert: Some of both OK

Correlation Topologies

Normal Jet


Azimuthal Section:

Deflected Jet

PHENIX Simulation

(scattered jet axis)

Cone Jet

(medium excitation)

Some of both patterns

near side long range correlation the ridge

Au+Au 20-30%






Near-Side Long-Range  Correlation: the Ridge

Near-side jet-like corrl.+ ridge-like corrl. + v2 modulated bkg.

Ridge-like corrl. + v2 modulated bkg.

Away-side corrl.+ v2 modulated bkg.

centrality dependence of the ridge
yield of associated particles can be separated into a jet-like yield and a ridge yield

jet-like yield consistent in  and  and independent of centrality

ridge yield increases with centrality

3 < pt,trigger < 4 GeV and pt,assoc. > 2 GeV

(J+R) method

(J) method

(J) method


STAR preliminary




Centrality Dependence of the Ridge
ridge particle spectrum
jet-like spectra harder than inclusive

flatter for higher trigger pT

ridge spectra similar to inclusive

slightly larger slope

approximately independent of trigger pT

“Ridge” Particle Spectrum

STAR preliminary




anomalous composition
Anomalous Composition
  • Large (anti)baryon to pion
  • Bifurcation of Rcp
    • One curve for mesons
    • One curve for baryons.
  • f meson proves not mass effect.
  • Recombination:
    • Coalescing constituent quarks lifts baryon “disadvantage”.
recombination models
Recombination Models
  • Recombination models assume particles are formed by the coalescence of “constituent” quarks.
  • Explain baryon excess by simple counting of valence quark content.
  • Baryon vs meson scaling becomes natural consequence
some lore and my charge to you
Some Lore and My Charge to You
  • When Rutherford lead the Cavendish Laboratory, the scientists were thrown out and the doors padlocked promptly at 6:00 PM.
    • Charge to the scientists: Go Home and THINK!
  • When the Professor and two students shared the three wishes from the Genie of the Lamp:
    • Student 1: I wish to be the RICH and powerful ruler of a nation.
    • Student 2: I wish to live on a tropical isle with beautiful people and no cares in the world.
    • Professor: I want them back in the lab by nightfall.
  • My charges to you:
    • STAY OFF COMPUTER; Listen to talksand THINK.
    • I want you back in the lab next week.
emergence of dijets w increasing p t assoc

8 < pT(trig) < 15 GeV/c

Emergence of dijets w/ increasing pT(assoc)

pT(assoc) > 2 GeV/c

pT(assoc) > 3 GeV/c

pT(assoc) > 4 GeV/c

pT(assoc) > 5 GeV/c

pT(assoc) > 6 GeV/c

pT(assoc) > 7 GeV/c

pT(assoc) > 8 GeV/c

  • Narrow peak emerges cleanly.
  • Open question: Punch-through or Tangential?


j y enigma wrapped in mystery




200 GeV



200 GeV



200 GeV



200 GeV



200 GeV



62 GeV

J/Y:Enigma wrapped in Mystery.
  • c-cbar produced together.
  • Dissolve in plasma.
  • Unlikely(?) to find appropriate mate.
  • 3X Suppression(~same as CERN)
  • Models:
    • Dissolution and recombination?
    • Cronin broadening?
    • Feed-down?
enough of this probe business
Enough of this Probe Business…


  • What does the medium itself have to say?
pressure elliptic flow barometer








Pressure? “elliptic flow” barometer

Almond shape overlap region incoordinate space

Origin:spatial anisotropy of the system when created, followed by multiple scattering of particles in the evolving system

spatial anisotropy  momentum anisotropy

v2:2nd harmonic Fourier coefficient in azimuthal distribution of particles with respect to the reaction plane

large v 2
Hydrodynamic limit exhausted at RHIC for low pT particles.

Can microscopic models work as well?

Flow is sensitive to thermalization time since expanding system loses spatial asymmetry over time.

Hydro models require thermalization in less than t=1 fm/c

Large v2

Adler et al., nucl-ex/0206006

hints of recombination in v 2

STAR preliminary

200 GeV Au+Au

Hints of Recombination in v2
  • Species dependence of v2 well accounted for (except p) by scaling v2 and pT by n quarks.

Theory I: Hydro-models Score Board

  • The hydro-models which include both hadronic and QGP phases reproduce the qualitative features of the measured v2(pT) of pions, kaons, and protons.
  • These hydro-models require an early thermalization (ttherm<1fm/c) and high initial energy density e > 10 GeV/fm3
  • Several of the hydro-models fail to reproduce the v2 and spectra simultaneously.
  • HBT source parameters are not reproduced by any hydrodynamic calculations.
hot result charm flows

Greco,Ko,Rapp: PLB595(2004)202

Hot Result: Charm Flows!!
  • Charm flows, but not as strong as light mesons.
  • Drop of the flow strength at high pT. Is this due to b-quark contribution?
  • The data favors the model that charm quark itself flows at low pT.
  • Charm flow supports high parton density and strong coupling in the matter. It is not a weakly coupled gas.


v2(D)=0.6 v2(p)

v2(D)=0.3 v2(p)

hot result low momentum photons shine

PHENIX preliminary

Hot Result: Low momentum photons shine.
  • The first promising result of direct photon measurement at low pT from low-mass electron pair analysis.
  • Are these thermal photons? The rate is above pQCD calculation. The method can be used in p+p collisions.
  • If it is due to thermal radiation, the data can provide the first direct measurement of the initial temperature of the matter.
  • T0max ~ 500-600 MeV !?

T0ave ~ 300-400 MeV !?

  • The matter formed at RHIC is a nearly “perfect” (zero viscosity) fluid that is strongly coupled.
  • Continued measurements of the fluid promise to elucidate many of its most fundamental properties:
    • Viscosity.
    • Opacity.
    • Number of degrees of freedom.
  • RHIC program more wildly successful than best hopes.
  • I hope I have sparked your interest and I cordially invite you to learn more in the parallel sessions on RHIC physics.
the medium i initial energy density
The Medium I: Initial Energy density
  • Bjorken estimate of energy density:
  • dET/dy(t0) > dET/dyfinal= 760 GeV
  • Three values of t0
    • tmin = 2R/g = 0.13 fm/c (RHIC)
    • = 1.6 fm/c (SPS)
    • tform=ħ/<mT>(tform)

≤ħ/<mT>final = 0.35 fm/c

    • ttherm≤ 1 fm/c (hydro-model)

≤ 2 fm/c (conservative)

  • Conservative lower limits on the energy density:

e(form) > 15 GeV/fm3 (0.35 fm/c)

e(therm) > 2.8 GeV/fm3 (2.0 fm/c)

  • These values are well in excess of ~1 GeV/fm3 obtained in lattice QCD as the energy density needed to form a deconfined phase.
emergence of dijets with increasing p t trig



pT(assoc) > 2 GeV/c

Emergence of dijets with increasing pT(trig)
  •  correlations (not background subtracted)

Au+Au, 0-5%

  • Hint of narrow back-to-back peak for higher pT(trig)
    • Higher pT(trig) reflects higher-Q2 hard scattering


medium ii thermalization
Medium II: Thermalization

Stat. model fit:Tch~ 160MeV, gs~1.0

Strangeness saturation at RHIC?

  • Hadron yields and spectra are consistent with thermal emission from a strongly expanding source.
  • The observed strangeness production is consistent with complete chemical equilibrium

p/K/p measurement in a

Broad pt range

Chemical freezeout

Thermal freezeout

stronger radial flow at RHIC?


Expansion velocity

Tkin ~ 100 MeV

<vT/c> ~ 0.5