Probing the Properties of the QuarkGluon Plasma and

Probing the Properties of the Quark-Gluon Plasma and Studying Strong-Field QCD in Heavy Ion Collisions @ RHIC and the LHC Prof. Brian A. Cole. Columbia University PHENIX and ATLAS

The “Big Picture” Heavy Ion (Au+Au) collision as seen by the STAR timeprojection chamber. Why? ? ?

Fundamental Interactions Matter usually studied in the lab has properties determined by EM interactions. How would non-Abelian matter be different?

The Big Picture • We have a fundamental theory of strong interactions • exhibits asymptotic freedom at large momentum transfer. • What about other limits of QCD? –High temperature –High field strength

QCD Thermodynamics (on Lattice) Energy Density / T 4 Pressure / T 4 • Rapid cross-over from “hadronic matter” to “Quark. Gluon Plasma” at T 170 Me. V Energy density, ~ 1 Ge. V/fm 3. • Only fundamental “phase transition” that can be studied in the laboratory. – Is the QGP weakly interacting? ?

Relativistic Heavy Ion Collider STAR ØRun 1 (2000): Au-Au SNN = 130 Ge. V ØRun 2 (2001): Au-Au, p-p SNN = 200 Ge. V ØRun 3 (2003): d-Au, p-p SNN = 200 Ge. V ØRun 4 (2004): Au-Au SNN = 200, 64 Ge. V, p-p SNN = 200 Ge. V ØRun 5 (2005): Cu-Cu SNN = 200, 64 Ge. V, p-p SNN = 200 Ge. V

Heavy Ion Collision Time History RHIC collision space-time history in “parton cascade” model Hadronization (interesting but I won’t cover) t “Hydrodynamic” evolution Rapid thermalization z Initial particle production from strong fields

RHIC Initial Conditions • Au+Au @ 200 Ge. V per nucleon, = E/m 100. – Au diameter, d 14 fm, contracted d/ 0. 2 fm Crossing time < 0. 2 fm/c. • Add quantum mechanics: E ħc / t – Fluctuations with E > 1 Ge. V are “on shell” These are primarily gluons (~ 200/collision) RHIC is a gluon collider! (10 Ge. V/fm 3)

“Saturation” @ low x • @ High energy nuclei are highly Lorentz contracted – Except for soft gluons – Which overlap longitudinally – And recombine producing broadened k. T distribution Generates a new scale: Qs Typical k. T of gluons • If Qs >> QCD, perturbative calculations possible. Large occupation #s for k. T<Qs classcial fields • Saturation is a result of unitarity in QCD

QCD: Evolution • Quarks radiate copiously Evolution of proton (e. g. ) parton distribution functions Growth of gluon distribution @ low x • @ high gluon density recombination starts to limit growth. • Qs - resolution scale where recombination starts to dominate • Limiting density Qs 2/ s – ~ Classical field

Saturation @ HERA? Golec-Biernat and Wusthoff (GBW) Saturation Model (empirical) • Measurements of DIS cross-section vs x, Q 2 for x < 0. 01. • Plotted vs • All x dependence in the saturation scale. – “Geometric scaling” • Precursor to saturation in PDF evolution

RHIC Particle Multiplicities Multiplicity per colliding nucleon pair • Multiplicity @ RHIC on low end of predicted range • Slow growth with impact parameter (Npart) – Inconsistent with factorized mini-jet production – Best described by saturation model

d. N/d But, Have We Created “Matter” ? • “Pressure” converts spatial anisotropy to momentum anisotropy. • Requires early thermalization. • Unique to heavy ion collisions • Answer: yes z y x

“Elliptic Flow” • Parameterize variation by “v 2” parameter – • Compare to “eccentricity”: • Data consistent w/ hydrodynamic calculations

(Ideal) Hydrodynamics in one slide

Estimating the (Shear) Viscosity • Relevant parameter for determining collective motion of quark-gluon plasma – viscosity to entropy ratio: /s. • Finite viscosity leads to dependence of flow strength on p. T. – Correction ( /s) p. T 2 • From data shown to right, obtain estimate: – /s ~ 0. 1 – Very small! s is “sound attenuation length” mean free path

Comparison to “Typical” Vicosities /s ~ 0. 1 • Thus the statement: – QGP is most perfect fluid every created

Lattice QCD Estimate of /s Shear viscosity in quenched QCD /s p. QCD Ad. S/CFT T/Tc Nakamura & Sakai, hep-lat/0510100

“Casual” Viscous Hydrodynamics P. Romatschke nucl-th/0701032 Comparison of viscous hydro results to meson spectra from PHENIX • Causal fix introduces a new scale, , relaxation time. Uncertainty in weakens /s constraint – Concludes /s < 0. 5, but elliptic flow?

Thermalization via Plasma Instabilities? Energy density • p. T vs pz anisotropy – Generates strong local chromo-magnetic fields – Lorentz forces produce rapid isotropization. • Pressure from macro-scopic color fields? !

Penetrating Probes of Created Matter t z Collisions between partons • Use self-generated quarks/gluons/photons as probes of the medium (classic physics technique!)

How to directly probe medium ? • Use quarks & gluons from high-Q 2 scattering – “Created” at very early times (~ 0. 1 fm). – Propagate through earliest, highest matter. • (QCD) Energy loss of (color) charged particle – ~ Entirely due to radiation – Virtual gluon(s) of quark multiply scatter. • e. g. GLV (Gyulassy, Levai, Vitev) formalism Experimentally measure using: Ø(Leading) high-p hadrons ØDi-jet correlations

Perturbative quantum chromo-dynamics From Collins, Soper, Sterman Phys. Lett. B 438: 184 -192, 1998 STAR p-p di-jet Event • Factorization: separation of into – Short-distance physics: – calculable using perturbation theory** – Long-distance physics: ’s – universal, measured separately. • Valid @ large momentum transfer – high p. T particles

p. QCD – Single Hadron Production Add fragmentation to hadrons Phys. Rev. Lett. 91, 241803 (2003) data vs p. QCD • D(z) – fractional momentum distribution of particles in “jet” KKP Kretzer

PHENIX Au-Au 0 Spectra p. T spectrum Expected • Observe 20% of expected yield @ high p. T Deduce energy density ~15 Gev/fm 3 Compare crit ~ 1 Ge. V/fm 3 100 x normal nucleus energy density! Calculations with no energy loss Calculations with energy loss RAA Observed/Expected Using p-p data as baseline

PHENIX: Au-Au High-p. T 0 Suppression

0 Suppression: d. E/dx Comparisons • Quark & gluon d. E/dx analysis: Turbide et al (Mc. Gill) – Essentially an ab initio calculation – Compared to precision (relatively) data

Prompt Photon Production • Prompt photons provide an independent control measurement for jet quenching. – Produced in hard scattering processes – But, no final-state effects (? ? ? )

Au-Au Prompt Photon Production • Photon control measurement shows no quenching • p. QCD calculations OK, quenching a final-state effect

High-p. T Single Particle Summary To explain data: Unscreened color charge dn/dy~1000 Energy density ~15 Ge. V/fm 3 > 10 “critical” energy density • 5 violation of factorization up to 20 Ge. V/c – In hadron production (jets), but not prompt Hard scatterings occur at expected rates Suppression from final-state energy loss

Analysis of Single Hadron Data: BDMS-Z-SW • “Thick medium” energy loss calculation Central 200 Ge. V Au+Au Transport coefficient: for radiated gluon • Baier [Nucl. Phys. A 715, 209 (2003)]: – C = 2 expected for ideal QGP – 14 Ge. V/fm 2 c = 8 -10!! Strong coupling [Eskola et al, Nucl. Phys. A 747, 511 (2005)]

STAR Experiment: “Jet” Observations proton-proton jet event Number of pairs Analyze by measuring (azimuthal) angle between pairs of particles 0º 180º Angle between high energy particles Ø In Au-Au collisions we see only one “jet” at a time ! Ø How can this happen ? Ø Jet quenching! q q

Di-jet Distortion vs “Impact Parameter”

(di)Jet Angular Correlations (PHENIX) • PHENIX (nucl-ex/0507004): moderate p. T

Origin of di-jet Distortion? Mach cone? • Jets may travel faster than the speed of sound in the medium. • While depositing energy via gluon radiation. • QCD “sonic boom”

Mach Cone (2) • Ideal QGP, cs 2 = 1/3 • Cos M = cs M = 55º • Detailed calculation taking into account evolving speed of (gluon) sound from hydrodynamics. – • But, other possible mechanisms proposed.

What I Didn’t Show You • Charm quarks also are quenched –And show rapid thermalization! • Large charm quark elliptic flow signal – Can only be established at the quark level. • Large baryon excess for 2 < p. T < 5 Ge. V/c – Hadron formation by quark recombination • We see final state particle flavor distributions consistent with “freeze-out” from chemically equilibrated system. – We are rapidly approaching stage where QGP is ONLY viable interpretation of data

RHIC Physics • Since start of RHIC, substantial progress on development of a rigorous foundation for understanding stages of a heavy ion collision: – Particle production from strong gluon fields – Thermalization (ideas but not yet understood) – Hydrodynamic evolution – Hadronization • With jets as calibrated probe – But jet quenching is still not completely understood • We are probing the properties of the QGP – with surprising results – Strong coupling – why? – Speed of sound?

Comparison to “Typical” Vicosities /s ~ 0. 1 • But what is this “viscosity bound”? – Calculation of viscosity using string theory – Huh? ?

Ad. S/CFT Correspondence Main idea • Duality between string theory in anti-De. Sitter space and conformal field theories. – Weakly coupled string theory strongly coupled CFT • Example conformal theory: – N=4 supersymmetric Yang-Mills – Which is not QCD (e. g. no running of s) – But similar enough? ? • Ad. S/CFT now being applied to many apsects of RHIC physics – Viscosity, /s. – Jet quenching – “Sound” waves

Why Heavy Ions @ LHC? • Low x – Gluon production from saturated initial state • Energy density – ~ 50 Ge. V/fm 3 (? ) • Rate – “copious” jet production above 100 Ge. V • Jets – Full jet reconstruction • Detector – necessary detector “for free”!

Heavy Ion Initial Conditions: Modern • At LHC we (think we) will be able to study “classical” gluon fields in nuclei – And their quantum evolution

A+A Multiplicity vs Energy RHIC 200 Ge. V Saturation? Something else? • LHC measurements will provide an essential test of whether we understand the mechanism responsible for bulk particle production. – e. g. does saturation correctly extrapolate?

Saturation: Geometric Scaling to A-A? Armesto, Salgado, Wiedemann Phys. Rev. Lett. 94 : 022002, 2005 • Extension of GBW analysis to NMC nuclear targets • Using k. T factorization calculate mult. (parton-hadron duality) • Compare to PHOBOS data Why should it work here?

Elliptic Flow @ LHC Can change horizontal scale by x 2 @ LHC ? ? • LHC data will provide an essential test of our understanding of elliptic flow data @ RHIC – And test whether QGP is still strongly coupled – Extremely high priority given the possible relevance of Ad. S/CFT. • Large ATLAS acceptance a big advantage

Why Jets @ LHC? Rate @ High p. T 80 Ge. V Jet in Pb+Pb • Can access jet energies in excess of 100 Ge. V • Complete jet measurements greater precision in use of jet tomography as a probe

Jets as Color Antennas • A high-energy quark/gluon acts like a “color antenna” • In vacuum, radiation strongly affected by quantum interference. • But, in medium thermal gluons “regulate” radiation. • Studies of modified jets in heavy ion collisions may shed light on a “fundamental” problem in (particle) physcs

LHC Physics Opportunity • Create & study quark-gluon plasma at T = 0. 8~Ge. V • Study particle production from strong gluon fields. • New program with w/ new discoveries ~ guaranteed – If RHIC is any guide … • p. T reach, rates, detector capabilities at LHC allow for qualitatively different (better!) measurements. • Overlap w/ many other sub-fields of physics ØParticle physics ØPlasma physics ØFluid/hydro dynamics ØThermal field theory, lattice & non-lattice ØString theory (!? ) – Ad. S-CFT correspondence ØGeneral relativity (gluon production as Unruh radiation? )

RAA PHENIX: Cu-Cu 0 RAA

PHENIX p-p Prompt Production Points: PHENIX Curve: PQCD • Absolute comparison, no fudge factors. • p. QCD very well reproduces prompt cross-section.

“Centrality” Dependence of Suppression • Measure yield above 4. 5 Ge. V/c. • Find suppression relative to p-p. • Plot vs nuclear overlap. – Npart = number of “participating” nucleons • Test against “best” energy loss model – GLV = Gyulassy, Levai, Vitev • Good agreement

PHENIX: High-p. T 0 v 2 (Reaction Plane) From parallel session talk by D. Winter • Clear observation of decreasing v 2 @ high p. T

V 2(p. T): Energy Loss Calculations v 2 PQM: Dainese, Loizides, Paic, Eur. Phys. J. C 38: 461 2005

PHENIX: Reaction Plane Angle Dependence(2) Look in bin #4 PHENIX Preliminary • For PHENIX reaction plane resolution & chosen bin sizes, trig bin 4 has smallest flow effects. • Even without subtracting flow contribution, a dip is seen for central collisions.

PHENIX: Reaction Plane Angle Dependence • Study (di)jet correlations vs angle of trigger hadron relative to reaction plane – J. Bielcikova et al, trig Phys. Rev. C 69: 021901, 2004 – trig = trig - – 6 bins from 0 to /2. • Flow systematics change completely vs trig • Can study dependence of distortion on geometry. Shoulder and dip seen in all trig bins. From Poster by J. Jia ?

Jet Conversion Photons • There is a new source of “hard” photons in QGP – High p. T quarks/gluons convert into photons in medium • This extra contribution must be present – @ large enough t, incident jet sees unscreened partons • What about at low-t ? – In principle, pole in the t channel produces “large” • But medium screens @ low-t & regulates pole. – Jet-conversion rate sensitive to screening mass. – And potentially also to quark/gluon thermal masses.

Jet Quenching: Photon Bremstrahlung • For light quarks (and gluons? ? ), in-medium energy loss dominated by radiation. – Interference between vacuum & induced radiation. – For large parton p. T (> ~10 Ge. V/c) coherence crucial. • Unfortunately, we can’t measure the gluons. • But we could measure photon bremstrahlung! Direct measurement of medium properties.

Put it all together … Shamelessly stolen from Simon’s talk. • Extremely rich mixture of physics contributing to the photon spectrum in ~ 4 -10 Ge. V/c range. • How to unravel all of the different pieces?

Measuring the Initial ? ? Bjorken Hydrodynamics: ~ 150 fm 2 Formation time • For 0 = 0. 2 fm (kt ~ 1 Ge. V) – Bj = 20 Ge. V/fm 3 !!! – d. Ng/d. A ~ 6/fm 2 • But, estimate too model dependent. • Need experimental probe of initial state … PHENIX

Quark-Gluon Thermodynamics Lattice QCD • Sudden change in # DOF in strongly interacting matter Quark-Gluon Plasma • Critical temperature (Karsch et al) – Tc = 150 – 170 Me. V • Energy density: – Large uncertainty due to T 4 dependence. – But accessible in heavy ion collisions /T 4 – = 0. 3 – 1. 3 Ge. V / fm 3 Karsch, hep-lat/0106019 T/T

Hard high-Q 2 processes are abundant at collider energy • Production of hard partons is a standard candle, unaffected by medium • Hard partons interact with medium during propagation