Lecture II: spectra and di-hadrons Marco van Leeuwen, Utrecht University Lectures for Helmholtz School Feb/March 2011

Hard probes of QCD matter Heavy-ion collisions produce ‘quasi-thermal’ QCD matter Dominated by soft partons p ~ T ~ 100-300 MeV Hard-scatterings produce ‘quasi-free’ partons  Initial-state production known from pQCD  Probe medium through energy loss Use the strength of pQCD to explore QCD matter Sensitive to medium density, transport properties

Centrality examples peripheral mid-central central ... and this is what you see in a presentation This is what you really measure

Nuclear geometry: Npart, Nbin, L, e Npart: nA + nB (ex: 4 + 5 = 9 + …) Nbin: nA x nB (ex: 4 x 5 = 20 + …) Two limits: - Complete shadowing, each nucleon only interacts once, s  Npart No shadowing, each nucleon interact with all nucleons it encounters, s  Nbin Soft processes: long timescale, large s, stot  Npart Hard processes: short timescale, small s, stot  Nbin Transverse view Density profile r: rpart or rcoll y L Eccentricity x Path length L, mean <L>

Centrality dependence of hard processes Total multiplicity: soft processes Binary collisions weight towards small impact parameter ds/dNch 200 GeV Au+Au Rule of thumb for A+A collisions (A>40) 40% of the hard cross section is contained in the 10% most central collisions

Testing volume (Ncoll) scaling in Au+Au Direct g spectra PHENIX, PRL 94, 232301 PHENIX Centrality Scaled by Ncoll Direct g in A+A scales with Ncoll A+A initial state is incoherent superposition of p+p for hard probes

Testing Ncoll scaling II: Charm PRL 94 (2005) NLO prediction: m ≈ 1.3 GeV, reasonably hard scale at pT=0 Total charm cross section scales with Nbin in A+A Sizable disagreement between STAR and PHENIX – scaling error in one experiment?

Generic expectations from energy loss Ejet kT~m l fragmentation after energy loss? Longitudinal modification: out-of-cone  energy lost, suppression of yield, di-jet energy imbalance in-cone  softening of fragmentation Transverse modification out-of-cone  increase acoplanarity kT in-cone  broadening of jet-profile

Energy loss in QCD matter radiated gluon QCD bremsstrahlung (+ LPM coherence effects) propagating parton Energy loss probes: Density of scattering centers: Nature of scattering centers, e.g. mass: radiative vs elastic loss Transport coefficient

Radiation senses region with extent tf LPM interference Landau-Pomeranchuk-Migdal effect Formation time important l Zapp, QM09 radiated gluon propagating parton Radiation senses region with extent tf Lc = tf,max If l < tf, multiple scatterings add coherently: Energy loss w = 3 GeV, kT = 0.2 GeV, tf =20 fm/c Typical length in nucleus 2-5 fm

Questions about energy loss What is the dominant mechanism: radiative or elastic? Heavy/light, quark/gluon difference, L2 vs L dependence How important is the LPM effect? L2 vs L dependence Can we use this to learn about the medium? Density of scattering centers? Temperature? Or ‘strongly coupled’, fields are dominant? Phenomenological questions: Large vs small angle radiation Mean DE? How many radiations? Virtuality evolution/interplay with fragmentation?

p0 RAA – high-pT suppression : no interactions Hadrons: energy loss RAA = 1 RAA < 1 Hard partons lose energy in the hot matter

Two extreme scenarios RAA not sensitive to details of mechanism (or how P(DE) says it all) Scenario I P(DE) = d(DE0) Scenario II P(DE) = a d(0) + b d(E) 1/Nbin d2N/d2pT ‘Energy loss’ ‘Absorption’ p+p Downward shift Au+Au Shifts spectrum to left pT RAA not sensitive to details of mechanism P(DE) encodes the full energy loss process

Parton energy loss and RAA modeling Qualitatively: Parton spectrum Energy loss distribution Fragmentation (function) known pQCDxPDF extract `known’ from e+e- medium effect Medium effect P(DE) is only part of the story Parton spectrum and fragmentation function are steep  non-trivial relation between RAA and P(DE)

Four theory approaches Multiple-soft scattering (ASW-BDMPS) Full interference (vacuum-medium + LPM) Approximate scattering potential Opacity expansion (GLV/WHDG) Interference terms order-by-order (first order default) Dipole scattering potential 1/q4 Higher Twist Like GLV, but with fragmentation function evolution Hard Thermal Loop (AMY) Most realistic medium LPM interference fully treated No interference between vacuum frag and medium

Determining the medium density PHENIX, arXiv:0801.1665, J. Nagle WWND08 PQM (Loizides, Dainese, Paic), Multiple soft-scattering approx (Armesto, Salgado, Wiedemann) Realistic geometry For each model: Vary parameter and predict RAA Minimize 2 wrt data Models have different but ~equivalent parameters: Transport coeff. Gluon density dNg/dy Typical energy loss per L: e0 Coupling constant aS GLV (Gyulassy, Levai, Vitev), Opacity expansion (L/l), Average path length WHDG (Wicks, Horowitz, Djordjevic, Gyulassy) GLV + realistic geometry ZOWW (Zhang, Owens, Wang, Wang) Medium-enhanced power corrections (higher twist) Hard sphere geometry AMY (Arnold, Moore, Yaffe) Finite temperature effective field theory (Hard Thermal Loops)

Medium density from RAA ^ +2.1 - 3.2 PQM <q> = 13.2 GeV2/fm +270 - 150 +0.2 - 0.5 GLV dNg/dy = 1400 ZOWW e0 = 1.9 GeV/fm +200 - 375 +0.016 - 0.012 WHDG dNg/dy = 1400 AMY as = 0.280 Data constrain model parameters to 10-20% Method extracts medium density given the model/calculation Theory uncertainties need to be further evaluated e.g. comparing different formalisms, varying geometry But models use different medium parameters – How to compare the results?

Some pocket formula results GLV/WHDG: dNg/dy = 1400 T(t0) = 366 MeV PQM: (parton average) T = 1016 MeV AMY: T fixed by hydro (~400 MeV), as = 0.297 Large differences between models

Geometry Density profile Density along parton path Profile at t ~ tform known Longitudinal expansion dilutes medium  Important effect Space-time evolution is taken into account in modeling

Determining ASW: HT: AMY: Bass et al, PRC79, 024901 Large density: AMY: T ~ 400 MeV Transverse kick: qL ~ 10-20 GeV All formalisms give RAA ~ constant, but large differences in medium density Need more differential measurements to test formalisms At RHIC: DE large compared to E, differential measurements difficult

Energy loss spectrum <DE/E> = 0.2 R8 ~ RAA = 0.2 Typical examples with fixed L <DE/E> = 0.2 R8 ~ RAA = 0.2 Brick L = 2 fm, DE/E = 0.2 E = 10 GeV Significant probability to lose no energy (P(0)) Broad distribution, large E-loss (several GeV, up to DE/E = 1) Theory expectation: mix of partial transmission+continuous energy loss -- Can we see this in experiment?

Need to ask critical questions! Brian Cole, QM08 summary: Scrutinise theory, experiment and interpretation What do we know? What do we not know? How can we improve? Good understanding needed to communicate our results with other scientists (e.g. particle physicists)

Path length dependence I Collision geometry Au+Au Centrality Cu+Cu Out of plane <L>, density increase with centrality Vary L and density independently by changing Au+Au  Cu+Cu In-plane Change L in single system in-plane vs out of plane

Path length I: centrality dependence Comparing Cu+Cu and Au+Au RAA: inclusive suppression Away-side suppression B. Sahlmüller, QM08 6 < pT trig < 10 GeV O. Catu, QM2008 Modified frag: nucl-th/0701045 - H.Zhang, J.F. Owens, E. Wang, X.N. Wang Inclusive and di-hadron suppression seem to scale with Npart Some models expect scaling, others (PQM) do not

Npart scaling? PQM: no scaling of with Npart PQM - Loizides – private communication Geometry (thickness, area) of central Cu+Cu similar to peripheral Au+Au PQM: no scaling of with Npart

Path length II: RAA vs L RAA as function of angle with reaction plane PHENIX, PRC 76, 034904 Out of Plane In Plane Le 3<pT<5 GeV/c Suppression depends on angle, path length

RAA Le Dependence Au+Au collisions at 200GeV 0-10% 50-60% PHENIX, PRC 76, 034904 The pathlength weighted integral over the density is done on a Glauber model by assuming that the density goes like the Ncoll density. The data seem to imply that we don’t reach a regime that matches the energy dependence of purely radiative energy loss until high pT. Is this a signal that at lower pT’s collisional losses are significant? This is all in pretty good agreement with Magdelena’s calculations (see backup slide). Phenomenology: RAA scales best with Le Little/no energy loss for Le < 2 fm ?

Modelling azimuthal dependence A. Majumder, PRC75, 021901 RAA RAA pT (GeV) pT (GeV) RAA vs reaction plane sensitive to geometry model

RAA vs reaction plane angle Majumder, van Leeuwen, arXiv:1002.2206 Azimuthal modulation, path length dependence largest in ASW-BDMPS But why? – No clear answer yet Data prefer ASW-BDMPS

Path length dependence and v2 PHENIX PRL105, 142301 v2 at high pt due to energy loss Most calculations give too small effect

Path length III: ‘surface bias’ Near side trigger, biases to small E-loss Away-side large L Away-side suppression IAA samples different path-length distribution than inclusives RAA

Di­hadron correlations 8 < pTtrig < 15 GeV Combinatorial background associated pTassoc > 3 GeV  trigger Near side Away side Use di-hadron correlations to probe the jet-structure in p+p, d+Au and Au+Au

Di-hadrons at high-pT: recoil suppression d+Au Au+Au 20-40% Au+Au 0-5% pTassoc > 3 GeV pTassoc > 6 GeV High-pT hadron production in Au+Au dominated by (di-)jet fragmentation Suppression of away-side yield in Au+Au collisions: energy loss

Di­hadron yield suppression Away side Near side 8 < pT,trig < 15 GeV Yield in balancing jet, after energy loss Yield of additional particles in the jet trigger Near side associated trigger STAR PRL 95, 152301 Away side associated Near side: No modification  Fragmentation outside medium? Away-side: Suppressed by factor 4-5  large energy loss

Interpreting di-hadron measurements Scenario I: Some lose all, Some lose nothing Scenario II: All lose something Di-hadron measurement: Away-side yield is (semi-)inclusive, so does not measure fluctuations of energy loss Multi-hadron measurements potentially more sensitive All is encoded in energy loss distribution P(DE)

A closer look at azimuthal peak shapes 8 < pT(trig) < 15 GeV/c pT(assoc)>6 GeV Vitev, hep-ph/0501225 p Df Broadening due to fragments of induced radiation Induced acoplanarity (BDMPS): No away-side broadening: No induced radiation No acoplanrity (‘multiple-scattering’)

Comparing single- and di-hadron results Armesto, Cacciari, Salgado et al. RAA and IAA fit with similar density Calculation uses LPM-effect, L2 dependence

Near side trigger, biases to small E-loss Surface bias Near side trigger, biases to small E-loss (No suppression seen) Away-side large L Away-side suppression IAA samples longer path lengths than inclusives RAA

L scaling: elastic vs radiative T. Renk, PRC76, 064905 RAA: input to fix density Radiative scenario fits data; elastic scenarios underestimate suppression Indirect measure of path-length dependence: single hadrons and di-hadrons probe different path length distributions Confirms L2 dependence  radiative loss dominates

RAA at LHC ALICE PHENIX RAA at LHC has much stronger pT-dependence ? ALICE, PLB 696, 30 RAA at LHC has much stronger pT-dependence ?

RAA RHIC and LHC II Overlaying the two results: PHENIX p0 and ALICE h± pT-dependence not too different… N.B.: Large uncertainties in RHIC result at high pT

LHC results vs models ASW N=1 opacity DGLV N=1 opacity ASW MS Calculations: M. Verweij Radiative energy loss calculations do not reproduce the rise with pT

Heavy quark suppression Using non-photonic electrons Expected energy loss light M.Djordjevic PRL 94 Wicks, Horowitz et al, NPA 784, 426 PHENIX nucl-ex/0611018, STAR nucl-ex/0607012 Expect: heavy quarks lose less energy due to dead-cone effect Most pronounced for bottom Measured suppression of non-photonic electrons larger than expected Djordjevic, Phys. Lett. B632, 81 Armesto, Phys. Lett. B637, 362 Radiative (+collisional) energy loss not dominant? E.g.: in-medium hadronisation/dissociation (van Hees, et al)

Light flavour reference Armesto, Cacciari, Salgado et al. Note again: RAA and IAA fit same density

Heavy Quark comparison No minimum – Heavy Quark suppression too large for ‘normal’ medium density

Charm/bottom separation X.Y. Lin, hep-ph/0602067 Idea: use e-h angular correlations to tag semi-leptonic D vs B decay B D → e + hadrons B peak broader due to larger mass D The two points at delta phi = 0 are due to photonic electrons sneaking through, Shingo has an updated plot where the points are with the fit. Shingo Sakai Reference QM06 paper Extract B contribution by fitting: 46

Charm/bottom separation STAR, PRL 105, 202301 Almost fifty-fifty B and D contributions to non-photonic e’s at 5.5 < pT < 9 GeV/c and FONLL prediction is consistent with our data within errors. Combine rB and RAA to determine RAA for charm and bottom 47 47

RAA for c  e and b  e Combined data show: electrons from both pT > 5 GeV/c Combined data show: electrons from both B and D suppressed STAR, PRL 105, 202301 Large suppression suggests additional energy loss mechanism (resonant scattering, dissociative E-loss) Red line is using the mean value for RAA_eb and RAA_ec I: Djordjevic, Gyulassy, Vogt and Wicks, Phys. Lett. B 632 (2006) 81; dNg/dy = 1000 II: Adil and Vitev, Phys. Lett. B 649 (2007) 139 III: Hees, Mannarelli, Greco and Rapp, Phys. Rev. Lett. 100 (2008) 192301 48 48

D/B from e-K correlations B → e + D D → e + K Use e-K invariant mass to separate charm and bottom Signal: unlike-sign near-side correlations Subtract like-sign pairs to remove background Use Pythia to extract D, B yields arXiv:0903.4851 hep-ex Ntag counted as all pairs within 0.4 < M < 1.9.

Charm-to-Bottom Ratio arXiv:0903.4851 hep-ex At pt greater than 5, fraction of bottom found to be > 33% to 90% confidence level. **explain axes How are systematic errors estimated? Pythia dependent? **arrows PHENIX p+p measuments agree with pQCD (FONLL) calculation

Heavy-to-Light ratios at LHC Colour-charge and mass dep. of E loss Heavy-to-light ratios: mass effect For pT > 10 GeV charm is ‘light’ RD/h : colour-charge dependence of E loss RB/h : mass dependence of E loss Armesto, Dainese, Salgado, Wiedemann, PRD71 (2005) 054027

Color factors QCD : For SU(3) : Nc = 3 CA = 3, CF = 4/3 CA/CF=9/4 Color factors measured at LEP QCD : For SU(3) : Nc = 3 CA = 3, CF = 4/3 CA/CF=9/4 CF ~ strength of a gluon coupling to a quark CA ~ strength of the gluon self coupling TF ~ strength of gluon splitting into a quark pair Expect gluons radiate ~ twice more energy than quarks

Subprocesses and quark vs gluon PYTHIA (by Adam Kocoloski) gg qq gq p+pbar dominantly from gluon fragmentation

Comparing quark and gluon suppression Baryon & meson NMF PRL 97, 152301 (2006) STAR Preliminary, QM08 STAR Preliminary Curves: X-N. Wang et al PRC70(2004) 031901 Protons less suppressed than pions, not more No sign of large gluon energy loss

Quark vs gluon suppression GLV formalism BDMPS formalism WHDG + renk plot Renk and Eskola, PRC76,027901 Quark/gluon difference larger in GLV than BDMPS (because of cut-off effects DE < Ejet?) ~10% baryons from quarks, so baryon/meson effect smaller than gluon/quark Are baryon fragmentation functions under control? Conclusion for now: some homework to do...

Equalibration of rare probes Rare probes: not chemically equilibrated in the jet spectrum. Example 1: flavor not contained in the medium, but can be produced off the medium (e.g. photons) Need enough yield to outshine other sources of Nrare. Example 2: flavor chemically equilibrated in the medium E.g. strangeness at RHIC Coupling of jets (flavor not equilibrated) to the equilibrated medium should drive jets towards chemical equilibrium. R. Fries, QM09

Equilibration process: jet conversion Flavour of leading parton changes through interactions with medium hard parton path length L Quark gluon W. Liu, R.J. Fries, Phys. Rev. C77 (2008) 054902