Lecture III jets Marco van Leeuwen Utrecht University

Lecture III: jets Marco van Leeuwen, Utrecht University Lectures for Helmholtz School Feb/March 2011

Generic expectations from energy loss Ejet k. T~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 k. T – in-cone broadening of jet-profile 2

Medium modification of fragmentation MLLA calculation: good approximation for soft fragmentation extended with ad-hoc implementation medium modifications Borghini and Wiedemann, hep-ph/0506218 p. Thadron ~2 Ge. V for Ejet=100 Ge. V =ln(EJet/phadron) z 0. 37 0. 14 0. 05 0. 02 0. 007 Note small large z Suppression at high z, enhancement at low z 3

Fragmentation functions Qualitatively: Fragmentation functions sensitive to P(DE) Distinguish GLV from BDMPS? 4

Modified fragmentation functions Small-z enhancement from gluon fragments (only included in HT, not important for RAA) A. Majumder, Mv. L, ar. Xiv: 1002. 2206 Differences between formalisms large, both magnitude of supresion and z-dependence Can we measure this directly? Jet reconstruction 5

Jet shapes q-Pythia, Eur Phys J C 63, 679 Energy distribution in sub-jets Energy loss changes radial distribution of energy Several ‘new’ observables considered Discussion: sensitivity viability … ongoing 6

Fixing the parton energy with -jet events Input energy loss distribution T. Renk, PRC 74, 034906 Away-side spectra in -jet E = 15 Ge. V Nuclear modification factor Away-side spectra for -jet are sensitive to P(DE) -jet: know jet energy sensitive to P(DE) RAA insensitive to P(DE) 7

-jet in Au+Au Use shower shape in EMCal to form p 0 sample and -rich sample Combinatorial subtraction to obtain direct- sample 8

Direct- recoil suppression STAR, ar. Xiv: 0912. 1871 8 < ET, g < 16 Ge. V IAA(z. T) = DAA (z. T) Dpp (z. T) Large suppression for away-side: factor 3 -5 Reasonable agreement with model predictions NB: gamma p. T = jet p. T still not very large 9

Jet reconstruction algorithms Two categories of jet algorithms: • Sequential recombination k. T, anti-k. T, Durham – Define distance measure, e. g. dij = min(p. Ti, p. Tj)*Rij – Cluster closest • Cone – Draw Cone radius R around starting point – Iterate until stable h, jjet = <h, j>particles 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 For a complete discussion, see: http: //www. lpthe. jussieu. fr/~salam/teaching/Ph. D-courses. html 10

Collinear and infrared safety Illustration by G. Salam Jets should not be sensitive to soft effects (hadronisation and E-loss) - Collinear safe - Infrared safe 11

Collinear safety Illustration by G. Salam Note also: detector effects, such as splitting clusters in calorimeter (p 0 decay) 12

Infrared safety Illustration by G. Salam Infrared safety also implies robustness against soft background in heavy ion collisions 13

Clustering algorithms – k. T algorithm 14

k. T algorithm Various distance measures have been used, e. g. Jade, Durham, Cambridge/Aachen Current standard choice: • Calculate – For every particle i: distance to beam – For every pair i, j : distance • Find minimal d – If di. B, i is a jet – If dij, combine i and j • Repeat until only jets 15

k. T algorithm demo 16

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 • Naïve implementation slow (N 3). Not necessary Fastjet Alternative: anti-k. T Cambridge-Aachen: 17

Cone algorithm • Jets defined as cone • Iterate until stable: (h, j)Cone = <h, j>particles in cone • Starting points for cones, seeds, e. g. highest p. T particles • Split-merge prescription for overlapping cones 18

Cone algorithm demo 19

Seedless cone 1 D: 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 2 D (h, j) Limiting cases occur when two particles are on the edge of the cone 20

IR safety is subtle, but important G. Salam, ar. Xiv: 0906. 1833 21

Split-merge procedure • Overlapping cones unavoidable • Solution: split-merge procedure Evaluate Pt 1, Pt, shared – If Pt, shared/Pt 1> f f = 0. 5 … 0. 75 merge jets – Else split jets (e. g. assign Pt, shared to closest jet or split Pt, shared according to Pt 1/Pt 2) Jet 1 Jet 2 Merge: Pt, shared large fraction of Pt 1 Jet 2 Split: Pt, shared small fraction of Pt 1 22

Note on recombination schemes Simple Not boost-invariant for massive particles ET-weighted averaging: Most unambiguous scheme: E-scheme, add 4 -vectors Boost-invariant Needs particle masses (e. g. assign pion mass) Generates massive jets 23

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 Fast. Jet package: http: //www. lpthe. jussieu. fr/~salam/fastjet/ Really no excuse to use anything else (and potentially run into trouble) 24

Speed matters G. Salam, ar. Xiv: 0906. 1833 At LHC, multiplicities are large A lot has been gained from improving implementations 25

Jet algorithm examples simulated p+p event Cacciari, Salam, Soyez, ar. Xiv: 0802. 1189 26

Di-jet kinematics Pout PTh 2 PL, h PT, jet 2 PTh 1 k. T, xy PT, jet 1 JT k. T measures di-jet acoplanarity JT distribution measures transverse jet profile PL, h distribution measures longitudinal jet profile Use z=p. L, h/Ejet or = ln(Ejet/p. L, h) approx indep of Ejet Di-hadron correlations: naïvely assume PTh 1~PTjet 1: z. T = p. T, h 2/p. Th 1 Pout ~ JT Not a good approximation! 27

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) RAAjets < 1 - Modification of fragment distribution (in-cone radiation) softening of fragmentation function and/or broadening of jet structure 28

Jet reco p+p 200 Ge. V, p. Trec ~ 21 Ge. V STAR PHENIX p+p: no or little background Cu+Cu: some background 29

Jet finding in heavy ion events ~ 21 Ge. V Combinatorial background Needs to be subtracted pt per grid cell [Ge. V] Jets clearly visible in heavy ion events at RHIC STAR preliminary η j 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 http: //rhig. physics. yale. edu/~putschke/Ahijf/A_Heavy_Ion_Jet-Finder. html Fast. Jet: Cacciari, Salam and Soyez; ar. Xiv: 0802. 1188 30

Jet finding with background By definition: all particles end up in a jet With background: all h-j space filled with jets Many of these jets are ‘background jets’ 31

Background estimate from jets Single event: p. T vs area r = p. T/area Background level Jet p. T grows with area Jet energy density r ~ independent of h M. Cacciari, ar. Xiv: 0706. 2728 32

Background energy density (Ge. V) Background subtraction STAR Preliminary multiplicity Background density at RHIC: 60 -100 Ge. V Strong dependence on centrality Fluctuations remain after subtraction: RMS up to 10 Ge. V 33

Example of dp. T distribution SIngle particle ‘jet’ p. T=20 Ge. V embedded in 8 M real events Response over ~5 orders of magnitude Gaussian fit to LHS: • LHS: good representation • RHS: non-Gaussian tail Response over range of ~40 Ge. V (sharply falling jet spectrum) • Centroid non-zero(~ ± 1 Ge. V) contribution to jet energy scale uncertainty 34

Unfolding background fluctuations Pythia smeared Pythia unfolded d. PT distribution: ‘smearing’ of jet spectrum due to background fluctuations unfolding Large effect on yields Need to unfold Simulation Test unfolding with simulation – works 35

Jet spectra p+p Au+Au central STAR Preliminary Note kinematic reach out to 50 Ge. V • Jet energy depends on R, affects spectra • k. T, anti-k. T give similar results Take ratios to compare p+p, Au+Au 36

Jet RAA at RHIC M. Ploskon, STAR, QM 09 Jet RAA >> 0. 2 (hadron RAA) Jet finding recovers most of the energy loss measure of initial parton energy Some dependence on jet-algorithm? Under study… 37

Jet R dependence p+p G. Soyez, ar. Xiv: 1101. 2665 R=0. 2/R=0. 4 ratio agrees with Pythia, Herwig Hadronisation effects important NLO QCD not enough 38

Jet R dependence Au+Au STAR, M. Ploskon, QM 09 RAA depends on jet radius: Small R jet is single hadron Jet broadening due to E-loss? 39

Fragmentation functions Use recoil jet to avoid biases pt, rec(Au. Au)>25 Ge. V STAR Preliminary E. Bruna, STAR, QM 09 20<pt, rec(Au. Au)<25 Ge. V Suppression of fragmentation also small (>> 0. 2) 40

Di-jet spectra Jet IAA STAR Preliminary E. Bruna, STAR, QM 09 Away-side jet yield suppressed partons absorbed . . . due to large path length (trigger bias) 41 41

Emerging picture from jet results • Jet RAA ~ 1 for sufficiently large R – unbiased parton selection • Away side jet fragmentation unmodified – away-side jet emerges without E-loss • Jet IAA ~ 0. 2 – Many jets are absorded (large E-loss) Study vs R, E to quantify P(DE) and broadening 42

Jet broadening II Qualitatively, two different possible scenarios Diffuse broadening Radiated energy ‘uniformly’ distributed Hard radiation/splitting Radiated energy directional Different measurements: - R(0. 2/0. 4) - Transverse jet profile May have different sensitivities Interesting idea: sub-jet structure; so far no studies available 43

Jet-hadron correlations J. Putschke STAR, INT workshop 0. 1 < p. T < 1. 0 Ge. V 1. 0 < p. T < 2. 5 Ge. V Jet anti-k. T, R=0. 4, p. Tcut = 2 Ge. V p. Trec = 20 (10) Ge. V p. T > 2. 5 Ge. V ‘Trigger’ jet: reconstruction bias (e. g. large charged fraction) Look at recoil jet Broadening at low p. T Suppression-enhancement (high-low p. T) 44

Jet-hadron correlations Yield Redistribution of fragments in longitudinal momentum Width Soft radiation at larger angle NB: no correction for trigger bias (jet energy), jet energy resolution (background fluctuations) 45

Extra slides 46

Unfolding background fluctuations Formally: Definition of dp. T Measured distribution Jet Signal In practice: Corrected Spectrum Response due to background fluctuations AS: Signal jet area AB: Background jet area AC: some suitably large cutoff area Measured distribution Regularized inverse 47