Lecture III: jets Marco van Leeuwen, Utrecht University Lectures for Helmholtz School Feb/March 2011 2 Generic expectations from 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 k T in-cone broadening of jet-profile kT~kT~ E jet fragmentation after energy loss? 3 = ln( E Jet / p hadron ) p T hadron ~2 GeV for E jet =100 GeV Borghini and Wiedemann, hep-ph/ Medium modification of fragmentation MLLA calculation: good approximation for soft fragmentation extended with ad-hoc implementation medium modifications Note small large z Suppression at high z, enhancement at low z z 4 Fragmentation functions Qualitatively: Fragmentation functions sensitive to P( E) Distinguish GLV from BDMPS? 5 Modified fragmentation functions Small-z enhancement from gluon fragments (only included in HT, not important for R AA ) Differences between formalisms large, both magnitude of supresion and z-dependence Can we measure this directly? Jet reconstruction A. Majumder, MvL, arXiv: 6 Jet shapes Energy distribution in sub-jets Energy loss changes radial distribution of energy Several new observables considered Discussion: sensitivity viability ongoing q-Pythia, Eur Phys J C 63, 679 7 Fixing the parton energy with -jet events T. Renk, PRC74, -jet: know jet energy sensitive to P( E) R AA insensitive to P( E) Nuclear modification factor Away-side spectra in -jet E = 15 GeV Away-side spectra for -jet are sensitive to P( E) Input energy loss distribution 8 -jet in Au+Au Use shower shape in EMCal to form 0 sample and -rich sample Combinatorial subtraction to obtain direct- sample 9 I AA (z T ) = D AA (z T ) D pp (z T ) Direct- recoil suppression Large suppression for away-side: factor 3-5 Reasonable agreement with model predictions 8 < E T, < 16 GeVSTAR, arXiv: NB: gamma p T = jet p T still not very large 10 Jet reconstruction algorithms Two categories of jet algorithms: Sequential recombination k T, anti-k T, Durham Define distance measure, e.g. d ij = min(p Ti,p Tj )*R ij Cluster closest Cone Draw Cone radius R around starting point Iterate until stable , jet = particles For a complete discussion, see:Sum particles inside jet Different prescriptions exist, most natural: E-scheme, sum 4-vectors Jet is an object defined by jet algorithm If parameters are right, may approximate parton 11 Collinear and infrared safety Illustration by G. Salam Jets should not be sensitive to soft effects (hadronisation and E-loss) -Collinear safe -Infrared safe 12 Collinear safety Note also: detector effects, such as splitting clusters in calorimeter ( 0 decay) Illustration by G. Salam 13 Infrared safety Infrared safety also implies robustness against soft background in heavy ion collisions Illustration by G. Salam 14 Clustering algorithms k T algorithm 15 k T algorithm Calculate For every particle i: distance to beam For every pair i,j : distance Find minimal d If d iB, i is a jet If d ij, combine i and j Repeat until only jets Various distance measures have been used, e.g. Jade, Durham, Cambridge/Aachen Current standard choice: 16 k T algorithm demo 17 k T algorithm properties Everything ends up in jets k T -jets irregular shape Measure area with ghost particles k T -algo starts with soft stuff background clusters first, affects jet Infrared and collinear safe Nave implementation slow (N 3 ). Not necessary Fastjet Alternative: anti-k T Cambridge-Aachen: 18 Cone algorithm Jets defined as cone Iterate until stable: ( , ) Cone = particles in cone Starting points for cones, seeds, e.g. highest p T particles Split-merge prescription for overlapping cones 19 Cone algorithm demo 20 Seedless cone Limiting cases occur when two particles are on the edge of the cone 1D: slide cone over particles and search for stable cone Key observation: content of cone only changes when the cone boundary touches a particle Extension to 2D ( , ) 21 IR safety is subtle, but important G. Salam, arXiv: 22 Split-merge procedure Overlapping cones unavoidable Solution: split-merge procedure Evaluate P t1, P t,shared If P t,shared /P t1 > f merge jets Else split jets (e.g. assign P t,shared to closest jet or split P t,shared according to P t1 /P t2 ) Jet1 Jet2 Merge: P t,shared large fraction of P t1 Jet1 Jet2 Split: P t,shared small fraction of P t1 f = 0.5 0.75 23 Note on recombination schemes E T -weighted averaging: Simple Not boost-invariant for massive particles Most unambiguous scheme: E-scheme, add 4-vectors Boost-invariant Needs particle masses (e.g. assign pion mass) Generates massive jets 24 Current best jet algorithms Only three good choices: k T algorithm (sequential recombination, non-circular jets) Anti-k T algoritm (sequential recombination, circular jets) SISCone algorithm (Infrared Safe Cone) + some minor variations: Durham algo, different combination schemes These are all available in the FastJet package:Really no excuse to use anything else (and potentially run into trouble) 25 Speed matters At LHC, multiplicities are large A lot has been gained from improving implementations G. Salam, arXiv: 26 Jet algorithm examples Cacciari, Salam, Soyez, arXiv: simulated p+p event 27 Di-jet kinematics k T measures di-jet acoplanarity J T distribution measures transverse jet profile P L,h distribution measures longitudinal jet profile Use z=p L,h /E jet or = ln(E jet /p L,h ) approx indep of E jet P T,jet1 P T,jet2 k T,xy P Th1 JTJT P Th2 P out P L,h Di-hadron correlations: navely assume P Th1 ~P Tjet1 : z T = pT,h2 /p Th1 P out ~ J T Not a good approximation! 28 Relating jets and single hadrons High-p T hadrons from jet fragmentation Qualitatively: Inclusive hadrons are suppressed: -Suppression of jet yield (out-of-cone radiation) R AA jets < 1 -Modification of fragment distribution (in-cone radiation) softening of fragmentation function and/or broadening of jet structure 29 Jet reco p+p 200 GeV, p T rec ~ 21 GeV p+p: no or little background Cu+Cu: some background STAR PHENIX 30 Jet finding in heavy ion events p t per grid cell [GeV] STAR preliminary ~ 21 GeV FastJet:Cacciari, Salam and Soyez; arXiv: Jets clearly visible in heavy ion events at RHIC Use different algorithms to estimate systematic uncertainties: Cone-type algorithms simple cone, iterative cone, infrared safe SISCone Sequential recombination algorithms k T, Cambridge, inverse k T Combinatorial background Needs to be subtracted 31 Jet finding with background By definition: all particles end up in a jet With background: all - space filled with jets Many of these jets are background jets 32 Background estimate from jets M. Cacciari, arXiv: Single event: p T vs area = p T /area Jet p T grows with area Jet energy density ~ independent of Background level 33 Background subtraction STAR Preliminary multiplicity Background energy density (GeV) Background density at RHIC: GeV Strong dependence on centrality Fluctuations remain after subtraction: RMS up to 10 GeV 34 Example of p T distribution Response over ~5 orders of magnitude Response over range of ~40 GeV (sharply falling jet spectrum) SIngle particle jet p T =20 GeV embedded in 8M real events Gaussian fit to LHS: LHS: good representation RHS: non-Gaussian tail Centroid non-zero(~ 1 GeV) contribution to jet energy scale uncertainty 35 Unfolding background fluctuations unfolding Pythia Pythia smeared Pythia unfolded Simulation P T distribution: smearing of jet spectrum due to background fluctuations Large effect on yields Need to unfold Test unfolding with simulation works 36 p+pAu+Au central STAR Preliminary Jet spectra STAR Preliminary Note kinematic reach out to 50 GeV Jet energy depends on R, affects spectra k T, anti-k T give similar results Take ratios to compare p+p, Au+Au 37 Jet R AA at RHIC Jet R AA >> 0.2 (hadron R AA ) Jet finding recovers most of the energy loss measure of initial parton energy M. Ploskon, STAR, QM09 Some dependence on jet-algorithm? Under study 38 Jet R dependence p+p G. Soyez, arXiv: R=0.2/R=0.4 ratio agrees with Pythia, Herwig Hadronisation effects important NLO QCD not enough 39 Jet R dependence Au+Au STAR, M. Ploskon, QM09 R AA depends on jet radius: Small R jet is single hadron Jet broadening due to E-loss? 40 Fragmentation functions STAR Preliminary p t,rec (AuAu)>25 GeV 20

0.2) E. Bruna, STAR, QM09 41 Di-jet spectra 41 STAR Preliminary E. Bruna, STAR, QM09 Jet I AA Away-side jet yield suppressed partons absorbed... due to large path length (trigger bias) 42 Emerging picture from jet results Jet R AA ~ 1 for sufficiently large R unbiased parton selection Away side jet fragmentation unmodified away-side jet emerges without E-loss Jet I AA ~ 0.2 Many jets are absorded (large E-loss) Study vs R, E to quantify P( E) and broadening 43 Jet broadening II Diffuse broadening Hard radiation/splitting Qualitatively, two different possible scenarios Different measurements: -R(0.2/0.4) -Transverse jet profile May have different sensitivities Interesting idea: sub-jet structure; so far no studies available Radiated energy uniformly distributed Radiated energy directional 44 Jet-hadron correlations J. Putschke STAR, INT workshop 0.1 < p T < 1.0 GeV 1.0 < p T < 2.5 GeV p T > 2.5 GeV Jet anti-k T, R=0.4, p T cut = 2 GeV p T rec = 20 (10) GeV Trigger jet: reconstruction bias (e.g. large charged fraction) Look at recoil jet Broadening at low p T Suppression-enhancement (high-low p T ) 45 Jet-hadron correlations Yield Width Redistribution of fragments in longitudinal momentum Soft radiation at larger angle NB: no correction for trigger bias (jet energy), jet energy resolution (background fluctuations) 46 Extra slides 47 Unfolding background fluctuations In practice: A S : Signal jet area A B : Background jet area A C : some suitably large cutoff area Formally: Measured distribution Corrected Spectrum Jet Signal Response due to background fluctuations Measured distribution Regularized inverse Definition of p T