Jet reconstruction with FastJet

Transcription

1 Jet reconstruction with FastJet Gavin P. Salam LPTHE, UPMC Paris 6 & CNRS Jets in Proton-Proton and Heavy-Ion Collisions Prague, 12 August 21 Based on work (some preliminary) with Matteo Cacciari, Juan Rojo, Sebastian Sapeta, Gregory Soyez

2 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 2 / 36 [Introduction] Jets in Heavy-Ion Collisions Radiation from high-momentum quarks & gluons traversing hot medium can tell us about the medium

3 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 2 / 36 [Introduction] Jets in Heavy-Ion Collisions ~ original JET quark? JET Radiation from high-momentum quarks & gluons traversing hot medium can tell us about the medium

4 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 3 / 36 [Introduction] Jets in LHC pp collisions JET µ + µ u Z σ _ b H _ u b JET Use jets to reconstruct quarks from decay of some new heavy object e.g. a Higgs boson proton anti proton At high luminosity, many simultaneous pp collisions not unlike AuAu/PbPb collision

5 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 3 / 36 [Introduction] Jets in LHC pp collisions JET µ + µ u Z σ _ b H _ u b JET Use jets to reconstruct quarks from decay of some new heavy object e.g. a Higgs boson proton anti proton x 2 At high luminosity, many simultaneous pp collisions not unlike AuAu/PbPb collision

6 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 4 / 36 [Introduction] Common challenge: large contamination A pp event (LHC 5.5 TeV, Pythia)

7 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 4 / 36 [Introduction] Common challenge: large contamination Contamination in jet RHIC AuAu: O(4 GeV) LHC PbPb: O(1 GeV) LHC pp (hi-lumi) O(5 4 GeV) A pp event (LHC 5.5 TeV, Pythia), embedded in a HI collision background (Hydjet 1.5)

8 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 4 / 36 [Introduction] Common challenge: large contamination Contamination in jet RHIC AuAu: O(4 GeV) LHC PbPb: O(1 GeV) LHC pp (hi-lumi) O(5 4 GeV) A pp event (LHC 5.5 TeV, Pythia), embedded in a HI collision background (Hydjet 1.5) and an actual STAR event

9 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 5 / 36 What are ingredients of jet finding in noisy environments? 1. Jets 2. Jet areas 3. Noise estimation 4. Noise subtraction [5. Noise suppression]

10 1. Jet algorithms Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 6 / 36

11 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 7 / 36 [Jet methods] [Jet algorithms] p t /GeV y Jets? A jet algorithms provides a mapping: particles jet.def. jets Simplest pp jet algorithm is Cambridge/Aachen Dokshitzer et al 97 Wengler & Wobisch 98 Repeatedly recombine closest pair of objects, until all separated by R 2 ij = y2 ij + φ2 ij > R2. R parameter sets angular resolution φ assumed for all towers

12 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 7 / 36 [Jet methods] [Jet algorithms] p t /GeV DeltaR_{ij} = y Jets? A jet algorithms provides a mapping: particles jet.def. jets Simplest pp jet algorithm is Cambridge/Aachen Dokshitzer et al 97 Wengler & Wobisch 98 Repeatedly recombine closest pair of objects, until all separated by R 2 ij = y2 ij + φ2 ij > R2. R parameter sets angular resolution φ assumed for all towers

13 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 7 / 36 [Jet methods] [Jet algorithms] p t /GeV y Jets? A jet algorithms provides a mapping: particles jet.def. jets Simplest pp jet algorithm is Cambridge/Aachen Dokshitzer et al 97 Wengler & Wobisch 98 Repeatedly recombine closest pair of objects, until all separated by R 2 ij = y2 ij + φ2 ij > R2. R parameter sets angular resolution φ assumed for all towers

14 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 7 / 36 [Jet methods] [Jet algorithms] p t /GeV DeltaR_{ij} = y Jets? A jet algorithms provides a mapping: particles jet.def. jets Simplest pp jet algorithm is Cambridge/Aachen Dokshitzer et al 97 Wengler & Wobisch 98 Repeatedly recombine closest pair of objects, until all separated by R 2 ij = y2 ij + φ2 ij > R2. R parameter sets angular resolution φ assumed for all towers

15 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 7 / 36 [Jet methods] [Jet algorithms] p t /GeV y Jets? A jet algorithms provides a mapping: particles jet.def. jets Simplest pp jet algorithm is Cambridge/Aachen Dokshitzer et al 97 Wengler & Wobisch 98 Repeatedly recombine closest pair of objects, until all separated by R 2 ij = y2 ij + φ2 ij > R2. R parameter sets angular resolution φ assumed for all towers

16 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 7 / 36 [Jet methods] [Jet algorithms] p t /GeV DeltaR_{ij} = y Jets? A jet algorithms provides a mapping: particles jet.def. jets Simplest pp jet algorithm is Cambridge/Aachen Dokshitzer et al 97 Wengler & Wobisch 98 Repeatedly recombine closest pair of objects, until all separated by R 2 ij = y2 ij + φ2 ij > R2. R parameter sets angular resolution φ assumed for all towers

17 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 7 / 36 [Jet methods] [Jet algorithms] p t /GeV y Jets? A jet algorithms provides a mapping: particles jet.def. jets Simplest pp jet algorithm is Cambridge/Aachen Dokshitzer et al 97 Wengler & Wobisch 98 Repeatedly recombine closest pair of objects, until all separated by R 2 ij = y2 ij + φ2 ij > R2. R parameter sets angular resolution φ assumed for all towers

18 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 7 / 36 [Jet methods] [Jet algorithms] p t /GeV DeltaR_{ij} = y Jets? A jet algorithms provides a mapping: particles jet.def. jets Simplest pp jet algorithm is Cambridge/Aachen Dokshitzer et al 97 Wengler & Wobisch 98 Repeatedly recombine closest pair of objects, until all separated by R 2 ij = y2 ij + φ2 ij > R2. R parameter sets angular resolution φ assumed for all towers

19 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 7 / 36 [Jet methods] [Jet algorithms] p t /GeV y Jets? A jet algorithms provides a mapping: particles jet.def. jets Simplest pp jet algorithm is Cambridge/Aachen Dokshitzer et al 97 Wengler & Wobisch 98 Repeatedly recombine closest pair of objects, until all separated by R 2 ij = y2 ij + φ2 ij > R2. R parameter sets angular resolution φ assumed for all towers

20 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 7 / 36 [Jet methods] [Jet algorithms] p t /GeV DeltaR_{ij} = y Jets? A jet algorithms provides a mapping: particles jet.def. jets Simplest pp jet algorithm is Cambridge/Aachen Dokshitzer et al 97 Wengler & Wobisch 98 Repeatedly recombine closest pair of objects, until all separated by R 2 ij = y2 ij + φ2 ij > R2. R parameter sets angular resolution φ assumed for all towers

21 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 7 / 36 [Jet methods] [Jet algorithms] p t /GeV y Jets? A jet algorithms provides a mapping: particles jet.def. jets Simplest pp jet algorithm is Cambridge/Aachen Dokshitzer et al 97 Wengler & Wobisch 98 Repeatedly recombine closest pair of objects, until all separated by R 2 ij = y2 ij + φ2 ij > R2. R parameter sets angular resolution φ assumed for all towers

22 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 7 / 36 [Jet methods] [Jet algorithms] p t /GeV DeltaR_{ij} = y Jets? A jet algorithms provides a mapping: particles jet.def. jets Simplest pp jet algorithm is Cambridge/Aachen Dokshitzer et al 97 Wengler & Wobisch 98 Repeatedly recombine closest pair of objects, until all separated by R 2 ij = y2 ij + φ2 ij > R2. R parameter sets angular resolution φ assumed for all towers

23 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 7 / 36 [Jet methods] [Jet algorithms] p t /GeV y Jets? A jet algorithms provides a mapping: particles jet.def. jets Simplest pp jet algorithm is Cambridge/Aachen Dokshitzer et al 97 Wengler & Wobisch 98 Repeatedly recombine closest pair of objects, until all separated by R 2 ij = y2 ij + φ2 ij > R2. R parameter sets angular resolution φ assumed for all towers

24 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 7 / 36 [Jet methods] [Jet algorithms] p t /GeV DeltaR_{ij} = y Jets? A jet algorithms provides a mapping: particles jet.def. jets Simplest pp jet algorithm is Cambridge/Aachen Dokshitzer et al 97 Wengler & Wobisch 98 Repeatedly recombine closest pair of objects, until all separated by R 2 ij = y2 ij + φ2 ij > R2. R parameter sets angular resolution φ assumed for all towers

25 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 7 / 36 [Jet methods] [Jet algorithms] p t /GeV y Jets? A jet algorithms provides a mapping: particles jet.def. jets Simplest pp jet algorithm is Cambridge/Aachen Dokshitzer et al 97 Wengler & Wobisch 98 Repeatedly recombine closest pair of objects, until all separated by R 2 ij = y2 ij + φ2 ij > R2. R parameter sets angular resolution φ assumed for all towers

26 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 7 / 36 [Jet methods] [Jet algorithms] p t /GeV DeltaR_{ij} = y Jets? A jet algorithms provides a mapping: particles jet.def. jets Simplest pp jet algorithm is Cambridge/Aachen Dokshitzer et al 97 Wengler & Wobisch 98 Repeatedly recombine closest pair of objects, until all separated by R 2 ij = y2 ij + φ2 ij > R2. R parameter sets angular resolution φ assumed for all towers

27 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 7 / 36 [Jet methods] [Jet algorithms] p t /GeV y Jets? A jet algorithms provides a mapping: particles jet.def. jets Simplest pp jet algorithm is Cambridge/Aachen Dokshitzer et al 97 Wengler & Wobisch 98 Repeatedly recombine closest pair of objects, until all separated by R 2 ij = y2 ij + φ2 ij > R2. R parameter sets angular resolution φ assumed for all towers

28 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 7 / 36 [Jet methods] [Jet algorithms] p t /GeV DeltaR_{ij} = y Jets? A jet algorithms provides a mapping: particles jet.def. jets Simplest pp jet algorithm is Cambridge/Aachen Dokshitzer et al 97 Wengler & Wobisch 98 Repeatedly recombine closest pair of objects, until all separated by R 2 ij = y2 ij + φ2 ij > R2. R parameter sets angular resolution φ assumed for all towers

29 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 7 / 36 [Jet methods] [Jet algorithms] p t /GeV y Jets? A jet algorithms provides a mapping: particles jet.def. jets Simplest pp jet algorithm is Cambridge/Aachen Dokshitzer et al 97 Wengler & Wobisch 98 Repeatedly recombine closest pair of objects, until all separated by R 2 ij = y2 ij + φ2 ij > R2. R parameter sets angular resolution φ assumed for all towers

30 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 7 / 36 [Jet methods] [Jet algorithms] p t /GeV DeltaR_{ij} > y Jets? A jet algorithms provides a mapping: particles jet.def. jets Simplest pp jet algorithm is Cambridge/Aachen Dokshitzer et al 97 Wengler & Wobisch 98 Repeatedly recombine closest pair of objects, until all separated by R 2 ij = y2 ij + φ2 ij > R2. R parameter sets angular resolution φ assumed for all towers

31 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 7 / 36 [Jet methods] [Jet algorithms] p t /GeV y Jets? A jet algorithms provides a mapping: particles jet.def. jets Simplest pp jet algorithm is Cambridge/Aachen Dokshitzer et al 97 Wengler & Wobisch 98 Repeatedly recombine closest pair of objects, until all separated by R 2 ij = y2 ij + φ2 ij > R2. R parameter sets angular resolution φ assumed for all towers

32 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 7 / 36 [Jet methods] [Jet algorithms] p t /GeV DeltaR_{ij} > y Jets? A jet algorithms provides a mapping: particles jet.def. jets Simplest pp jet algorithm is Cambridge/Aachen Dokshitzer et al 97 Wengler & Wobisch 98 Repeatedly recombine closest pair of objects, until all separated by R 2 ij = y2 ij + φ2 ij > R2. R parameter sets angular resolution φ assumed for all towers

33 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 7 / 36 [Jet methods] [Jet algorithms] p t /GeV y Jets? A jet algorithms provides a mapping: particles jet.def. jets Simplest pp jet algorithm is Cambridge/Aachen Dokshitzer et al 97 Wengler & Wobisch 98 Repeatedly recombine closest pair of objects, until all separated by R 2 ij = y2 ij + φ2 ij > R2. R parameter sets angular resolution φ assumed for all towers

34 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 7 / 36 [Jet methods] [Jet algorithms] p t /GeV DeltaR_{ij} > y Jets? A jet algorithms provides a mapping: particles jet.def. jets Simplest pp jet algorithm is Cambridge/Aachen Dokshitzer et al 97 Wengler & Wobisch 98 Repeatedly recombine closest pair of objects, until all separated by R 2 ij = y2 ij + φ2 ij > R2. R parameter sets angular resolution φ assumed for all towers

35 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 7 / 36 [Jet methods] [Jet algorithms] p t /GeV y Jets? A jet algorithms provides a mapping: particles jet.def. jets Simplest pp jet algorithm is Cambridge/Aachen Dokshitzer et al 97 Wengler & Wobisch 98 Repeatedly recombine closest pair of objects, until all separated by R 2 ij = y2 ij + φ2 ij > R2. R parameter sets angular resolution φ assumed for all towers

36 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 8 / 36 [Jet methods] [Jet algorithms] A full set of IRC-safe jet algorithms Generalise inclusive-type sequential recombination with d ij = min(k 2p ti,k 2p tj ) R 2 ij/r 2 d ib = k 2p ti Alg. name Comment time p = 1 k t Hierarchical in rel. k t CDOSTW 91-93; ES 93 NlnN exp. p = Cambridge/Aachen Hierarchical in angle Dok, Leder, Moretti, Webber 97 Scan multiple R at once NlnN Wengler, Wobisch 98 QCD angular ordering p = 1 anti-k t Cacciari, GPS, Soyez 8 Hierarchy meaningless, jets reverse-k t Delsart like CMS cone (IC-PR) N 3/2 SC-SM SISCone Replaces JetClu, ATLAS GPS Soyez 7 + Tevatron run II MidPoint (xc-sm) cones N 2 lnn exp. All these algorithms [& much more] coded in (efficient) C++ at (Cacciari, GPS & Soyez 5-1)

37 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 9 / 36 [Jet methods] [Jet algorithms] FastJet: time to cluster N particles t / s R=.7 KtJet k t CDF MidPoint (seeds > GeV) CDF MidPoint (seeds > 1 GeV) CDF JetClu (very unsafe) Seedless IR Safe Cone (SISCone) FastJet anti-k t Cam/Aachen k t 1-4 LHC lo-lumi LHC hi-lumi LHC Pb-Pb N

38 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 1 / Jet areas Measure jets susceptibility to contamination by noise

39 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [Jet methods] [Jet areas] Jet areas Jets are made of finite number of pointlike particles. Area not unambiguous concept Jet areas must be defined Add many soft particles to event 1 1 GeV each A # inside jet Cacciari, GPS & Soyez 8 measure of jet s susceptibility to contamination from soft radiation

40 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [Jet methods] [Jet areas] Jet areas Jets are made of finite number of pointlike particles. Area not unambiguous concept Jet areas must be defined Add many soft particles to event 1 1 GeV each A # inside jet Cacciari, GPS & Soyez 8 measure of jet s susceptibility to contamination from soft radiation

41 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [Jet methods] [Jet areas] Areas for 3 jet algorithms A family of algorithms, all cluster pair with smallest d ij : d ij = min(p 2p ti,p 2p tj ) R2 ij R 2 1 k t p = C/A 1 anti-k t

42 3. Noise estimation Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36

43 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [Jet methods] [Noise estimation] Estimating ρ background noise level 8 median (pt/area) Most jets in event are background 6 Theirp t iscorrelated withtheir area. P t,jet 4 2 dijet event + 1 minbias (Kt-alg, R=1) Estimate ρ: ρ median {jets} [ pt,jet A jet ] jet area Median limits bias from hard jets Cacciari & GPS 7

44 4. Noise subtration Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36

45 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [Jet methods] [Noise subtraction] Subtracting noise from jets p subtracted t,jet = p t,jet ρ A jet A jet = jet area ρ = p t per unit area from underlying event (or background ) This procedure is intended to be common to pp, pp with pileup (multiple simultaneous minbias) and HIC NB in AuAu at RHIC: p subtracted t,jet = 2 5 GeV, ρ 8 GeV and A jet.5

46 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 Use at RHIC? Let s examine some of the issues

47 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [An MC study for RHIC] [Context] Area/median method STAR jet results Method designed to minimise biases, but some still persist. Question: can we calculate size of biases? Can we further reduce them?

48 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [An MC study for RHIC] [Context] Area/median method STAR jet results Method designed to minimise biases, but some still persist. Question: can we calculate size of biases? Can we further reduce them?

49 JET JET JET quark? JET quark? Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [An MC study for RHIC] [Context] Framework for a theorists study ~ original ~ original Define: p t = p full(subtracted) t p hard t Study: average of p t, p t dispersion of p t, σ pt

50 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 2 / 36 [An MC study for RHIC] [Context] This study We don t have real background (or hard!) events, so use Hard event: Pythia 6.4, and optionally PyQyen 1.5 / QPythia Background: Hydjet 1.6 (Hydjet for cross-checks) Analysis: FastJet 2.4 (& 2.5-devel), R =.4 for all main jet finders (k t with R =.5 for bkgd estimation). Cacciari, Rojo, GPS & Soyez, to appear soon...

51 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 Example #1: non-zero p t (background does not just linearly add noise to jet)

52 Slide from M. Cacciari BACK REACTION

53 Slide from M. Cacciari BACK REACTION

54 Slide from M. Cacciari BACK REACTION

55 Slide from M. Cacciari BACK REACTION

56 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [An MC study for RHIC] [Biases] Soft & collinear approximation: Backreaction can be calculated (sort of...) δp BR t = B alg ρr 22C i π α sln p t ρr 2 Cacciari, GPS & Soyez 8 + large corrections jet alg B alg k t -.3 C/A -.3 anti-k t

57 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [An MC study for RHIC] [Biases] Soft & collinear approximation: δp BR t = B alg ρr 22C i π α sln p t ρr 2 Cacciari, GPS & Soyez 8 + large corrections jet alg B alg k t -.3 C/A -.3 anti-k t Backreaction can be calculated (sort of...) Back-reaction [GeV] Pythia + Hydjet + FastJet RHIC, -1% central y <1, R=.4, unquenched k t C/A anti-k t p t,hard [GeV] Cacciari, Rojo, GPS & Soyez, prelim. anti-k t bias =, as expected

58 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [An MC study for RHIC] [Biases] Soft & collinear approximation: δp BR t = B alg ρr 22C i π α sln p t ρr 2 Cacciari, GPS & Soyez 8 + large corrections jet alg B alg k t -.3 C/A -.3 anti-k t Backreaction can be calculated (sort of...) Back-reaction [GeV] Pythia + Hydjet + FastJet RHIC, -1% central y <1, R=.4, unquenched k t C/A anti-k t p t,hard [GeV] Cacciari, Rojo, GPS & Soyez, prelim. anti-k t bias =, as expected Different jet algorithms have different systematics Use of more than one provides important cross-checks

59 Example #2: fluctuations Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36

60 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [An MC study for RHIC] [Fluctuations] Fluctuations Fluctuations of amount of background / underlying-event in a square of unit area can be characterised in terms of σ UE, which is O(1 GeV) at RHIC. Dispersion in jet subtraction, σ jet is given by σ pt = σ UE A jet jet alg A jet k t.81πr 2 C/A.81πR 2 anti-k t πr 2 Put in numbers: σ UE 8 1 GeV σ pt 6 7 GeV What impact does this have? + p t -dependent scaling violations for k t and C/A

61 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [An MC study for RHIC] [Fluctuations] dσ/dp t [nb/gev] Context: a steeply falling X-section RHIC Inclusive jet spectrum pp, s = 2 GeV, no UE, Pythia 6.421, FastJet 2.4 C/A R=.6, y < Pythia p t [GeV]

62 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [An MC study for RHIC] [Fluctuations] dσ/dp t [nb/gev] Context: a steeply falling X-section RHIC Inclusive jet spectrum pp, s = 2 GeV, no UE, Pythia 6.421, FastJet 2.4 C/A R=.6, y < Pythia e -.3 p t /GeV [nb/gev] p t [GeV] To help think about impact of falling cross section at RHIC, approximate it as: dσ dp t exp(.3p t / GeV) Interplay of PDFs & 1/p 4 t matrix element

63 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [An MC study for RHIC] [Fluctuations] Exponential spectrum Gaussian fluctuations exp( ap t ) 1 ( ) exp p2 t 2πσ 2σ 2 Real fluctuations not quite Gaussian Real spectrum not quite exponential (especially at low & high p t!) But simple approximations give instructive analytical answers Convolution rescales spectrum by factor: ( ) 1 exp 2 a2 σ 2 1 for σ 7 GeV Convolution migrates p t s by aσ 2 15 GeV for σ 7 GeV

64 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 Reducing fluctuations, while limiting bias: filtering

65 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [Filtering] Filtering Idea to improve resolution for an LHC Higgs search in H b b decay mode! Keep hardest O(α s ) gluon emission in jet, while throwing out soft junk Butterworth, Davison, Rubin & GPS 8 1. Consider a jet 2. View it on smaller angular resolution scale R filt 3. Take (e.g.) 2 hardest subjets leading quark + 1 gluon 4. The result is a filtered jet Related ideas by Ellis, Vermillion & Walsh 9 and Krohn, Thaler & Wang 9

66 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [Filtering] Filtering Idea to improve resolution for an LHC Higgs search in H b b decay mode! Keep hardest O(α s ) gluon emission in jet, while throwing out soft junk Butterworth, Davison, Rubin & GPS 8 1. Consider a jet 2. View it on smaller angular resolution scale R filt 3. Take (e.g.) 2 hardest subjets leading quark + 1 gluon 4. The result is a filtered jet Related ideas by Ellis, Vermillion & Walsh 9 and Krohn, Thaler & Wang 9

67 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [Filtering] Filtering Idea to improve resolution for an LHC Higgs search in H b b decay mode! Keep hardest O(α s ) gluon emission in jet, while throwing out soft junk Butterworth, Davison, Rubin & GPS 8 1. Consider a jet 2. View it on smaller angular resolution scale R filt 3. Take (e.g.) 2 hardest subjets leading quark + 1 gluon 4. The result is a filtered jet Related ideas by Ellis, Vermillion & Walsh 9 and Krohn, Thaler & Wang 9

68 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [Filtering] Filtering Idea to improve resolution for an LHC Higgs search in H b b decay mode! Keep hardest O(α s ) gluon emission in jet, while throwing out soft junk Butterworth, Davison, Rubin & GPS 8 1. Consider a jet 2. View it on smaller angular resolution scale R filt 3. Take (e.g.) 2 hardest subjets leading quark + 1 gluon 4. The result is a filtered jet Related ideas by Ellis, Vermillion & Walsh 9 and Krohn, Thaler & Wang 9

69 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [Filtering] Filtering Idea to improve resolution for an LHC Higgs search in H b b decay mode! Keep hardest O(α s ) gluon emission in jet, while throwing out soft junk Butterworth, Davison, Rubin & GPS 8 1. Consider a jet 2. View it on smaller angular resolution scale R filt 3. Take (e.g.) 2 hardest subjets leading quark + 1 gluon 4. The result is a filtered jet Related ideas by Ellis, Vermillion & Walsh 9 and Krohn, Thaler & Wang 9

70 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 3 / 36 [Filtering] LHC Higgs-boson search & filtering Reconstructed mass for jets from decay of high-p t Higgs-boson [without pileup] Without Filtering With Filtering number of events / 2GeV no anal. number of events / 2GeV no anal. after MD after Filt m bb (GeV) m bb (GeV) Figure from Rubin Among the techniques adopted in search for H b b at LHC

71 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [Filtering] Impact of filtering on dispersion in HIC 8 σ pt [GeV] k t C/A anti-k t C/A(filt) RHIC, -1% central Doughnut(R,3R) range unquenched, y <1, R= p t,hard [GeV] Filtering reduces jet area by 1 2 Fluctuations A 1 2 should go down by And they do

72 [Filtering] Impact of filtering on dispersion in HIC 8 σ pt [GeV] k t C/A anti-k t C/A(filt) RHIC, -1% central Doughnut(R,3R) range unquenched, y <1, R= p t,hard [GeV] Filtering reduces jet area by 1 2 Fluctuations A 1 2 should go down by And they do Filtering s reduction of dispersion from 7 GeV to 5 GeV means experimental unfolding might be factor 3 instead of factor 1 Numbers are rough intended to give an idea of impact NB: Gaussian filtering (Cole & Lai 8) not the same thing Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36

73 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [Filtering] Full p t distributions 1/N dn/d p t [GeV -1 ] 1/N dn/d p t [GeV -1 ] RHIC, -1% central y <1, 3<p t,hard <35 GeV Doughnut(R,3R) R=.4 p t = -3.4 GeV σ pt = 7. GeV p t [GeV] p t [GeV] k t p t =.5 GeV σ pt = 7.5 GeV 1/N dn/d p t [GeV -1 ] PRELIMINARY anti-k t 1/N dn/d p t [GeV -1 ] C/A p t = -1.4 GeV σ pt = 6.8 GeV p t [GeV].1 PRELIMINARY C/A(filt) p t =.5 GeV σ pt = 4.7 GeV p t [GeV]

74 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [Filtering] Full p t distributions dp/d p dp/d p t [GeV -1 t [GeV -1 ] ] RHIC, y <1 k t Gaussian p t =-3.42 GeV σ pt =6.95 GeV p t [GeV] 3<p t,hard <35 GeV anti-k t Gaussian p t =.47 GeV σ pt =7.54 GeV p t [GeV] dp/d p t [GeV -1 ] R=.4 PRELIMINARY dp/d p t [GeV -1 ] C/A Gaussian p t =-1.36 GeV σ pt =6.79 GeV p t [GeV] Doughnut(R,3R) PRELIMINARY C/A(filt) Gaussian p t =.53 GeV σ pt =4.66 GeV p t [GeV]

75 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 Does filtering introduce new biases in jets in quenched case? Vacuum QCD: we know how much gluon radiation we lose QCD in medium: extra medium-induced radiation lost?

76 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [Filtering] PT SHIFT p t [GeV] UNQUENCHED RHIC, -1% central y <1, R=.4, unquenched Doughnut(R,3R) range k t C/A anti-k t C/A(filt) p t,hard [GeV] Summary RHIC (Pythia/Hydjet) 8 DISPERSION σ pt [GeV] k t C/A anti-k t C/A(filt) RHIC, -1% central Doughnut(R,3R) range unquenched, y <1, R= p t,hard [GeV]

77 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [Filtering] PT SHIFT p t [GeV] UNQUENCHED RHIC, -1% central y <1, R=.4, unquenched Doughnut(R,3R) range k t C/A anti-k t C/A(filt) p t,hard [GeV] Summary RHIC (Pythia/Hydjet) p t [GeV] RHIC, -1% central QUENCHED y <1, R=.4, quenched Doughnut(R,3R) range k t C/A anti-k t C/A(filt) preliminary p t,hard [GeV] 8 DISPERSION σ pt [GeV] k t C/A anti-k t C/A(filt) RHIC, -1% central Doughnut(R,3R) range unquenched, y <1, R= p t,hard [GeV] σ pt [GeV] k t C/A anti-k t C/A(filt) RHIC, -1% central Doughnut(R,3R) range preliminary quenched, y <1, R= p t,hard [GeV]

78 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [Filtering] PT SHIFT p t [GeV] UNQUENCHED LHC, -1% central y <2.4, R=.4, unquenched k t C/A anti-k t C/A(filt) -9 Doughnut(R,3R) range p t,hard [GeV] Summary LHC (Pythia/Hydjet) DISPERSION σ pt [GeV] k t C/A anti-k t C/A(filt) LHC, -1% central Doughnut(R,3R) range unquenched, y <2.4, R= p t,hard [GeV]

79 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [Filtering] PT SHIFT p t [GeV] UNQUENCHED LHC, -1% central y <2.4, R=.4, unquenched k t C/A anti-k t C/A(filt) -9 Doughnut(R,3R) range p t,hard [GeV] Summary LHC (Pythia/Hydjet) p t [GeV] LHC, quenched y <2.4, R=.4 QUENCHED Doughnut(R,3R) range k t C/A anti-k t C/A(filt) preliminary p t,hard [GeV] DISPERSION σ pt [GeV] k t C/A anti-k t C/A(filt) LHC, -1% central Doughnut(R,3R) range unquenched, y <2.4, R= p t,hard [GeV] σ pt [GeV] k t C/A anti-k t C/A(filt) preliminary y <2.4, R=.4 LHC, quenched Doughnut(R,3R) range p t,hard [GeV]

80 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [Conclusions] Conclusions It s still early days for jet-finding in HIC (& high-luminosity LHC) It s a tough job to accurately remove 4 GeV of noise from a 4 GeV hard jet in the context of a steeply falling cross-section. Theory calculations can guide the choices one makes Give us an idea of size of corrections semi-independently of Monte Carlo Some of them are rather large Tell us which approaches are complementary in their systematics Adding to robustness of experimental measurements, e.g. k t v. anti-k t NB: it s still hard to estimate how quenching affects systematics Guide design of new tools that have smaller systematics Like filtering, yet to be tried out at RHIC Important potential for cross-fertilization between ideas in HIC and LHC pp programs.

81 EXTRAS Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36

82 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [Extras] [Centrality dependence] Disperson for non central AuAu p t dispersion [GeV] solid: anti-k t dashed: C/A(filt) RHIC, unquenched, y <1, R=.4, Donut(R,3R) p t,hard [GeV]

83 [Extras] [Centrality dependence] P t shift for non central AuAu p t shift [GeV] p t shift [GeV] p t shift [GeV] RHIC, unquenched y <1, R=.4 anti-k t, Donut(R,3R) -1% 1-2% 2-4% 4-75% anti-k t, Strip(3R) C/A(filt), Donut(R,3R) Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36

84 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August 21 4 / 36 Example #2: another bias is ρ measured correctly?

85 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [Extras] [ρ estimation] Bias in median estimate for ρ? What could go wrong? Rapidity and azimuth dependence of ρ distribution means ρ near jet ρ measured over large region. So try various regions: Global StripRange( ) CircularRange( ) DonutRange(δ, ) jet δ -y max y max y jet y jet + Median estimate mean contamination. Can be studied in toy models: ( ρ median ρ true 1 1 ) 3νR 2 ν = number of particles / unit area With ν = 1, R =.4, O(2%) O(1 GeV) on jet p t Cacciari, GPS & Sapeta 9, for measuring ρ 2 GeV in pp collisions!

86 Gavin Salam (LPTHE, Paris) Jet reco with FastJet Prague, August / 36 [Extras] [ρ estimation] Bias in median estimate for ρ? What could go wrong? Rapidity and azimuth dependence of ρ distribution means ρ near jet ρ measured over large region. So try various regions: Global StripRange( ) CircularRange( ) DonutRange(δ, ) jet δ -y max y max y jet y jet + Median estimate mean contamination. Can be studied in toy models: ( ρ median ρ true 1 1 ) 3νR 2 ν = number of particles / unit area With ν = 1, R =.4, O(2%) O(1 GeV) on jet p t Cacciari, GPS & Sapeta 9, for measuring ρ 2 GeV in pp collisions!