Jet reconstruction in heavy-ion collisions

Transcription

1 Jet reconstruction in heavy-ion collisions Grégory Soyez IPhT, Saclay CERN In collaboration with Gavin Salam, Matteo Cacciari and Juan Rojo BNL March p. 1

2 Plan Motivations Why jets in heavy-ion collisions Why jets in heavy-ion collisions is a non-trivial problem Howto recap on jets in general background subtraction as the main tool (already in use) refinements: filtering, local ranges Practical application: what kind of precision do we expect? p. 2

3 Motivations p. 3

4 Motivation: why jets in HI Jets bunch of collimated particles = hard partons Example: LEP (OPAL) events 2 jets 3 jets In other words a jet is a better pqcd object than, say, a pion. Access to a series of measurements like the jet broadening i.e. information on the HI medium p. 4

5 Motivation: why is it tough p t [GeV] pp antikt (R=.6) p t pp+pu [GeV] siscone (R=.7) φ y φ y 1 2 Huge underlying event background hard to see the jets p t [GeV] AA antikt (R=.6) φ y 1 2 p. 5

6 Motivation: why is it tough background per unit area Hydjet++ v2.1 y <.5, -1% central C/A, R=.5 RHIC LHC counts ρ [GeV] ρ 9 GeV ρ 25 GeV p. 6

7 Motivation: why is it tough background per unit area background fluctuations counts Hydjet++ v2.1 y <.5, -1% central C/A, R=.5 RHIC LHC counts RHIC LHC Hydjet++ v2.1 y <.5, -1% central C/A, R= ρ [GeV] σ [GeV] ρ 9 GeV ρ 25 GeV σ 1 GeV σ 19 GeV p. 6

8 Motivation: why is it tough background per unit area background fluctuations counts Hydjet++ v2.1 y <.5, -1% central C/A, R=.5 RHIC LHC counts RHIC LHC Hydjet++ v2.1 y <.5, -1% central C/A, R= ρ [GeV] σ [GeV] ρ 9 GeV ρ 25 GeV σ 1 GeV σ 19 GeV For a typical jet with R =.4 (and area = πr 2 ) (δp t ) RHIC 45±5 GeV (δp t ) LHC 125±1 GeV range 1 p t 5 GeV range 5 p t 5 GeV (δp t ) PU,LHC 2 GeV p. 6

9 Quick summary on jets in general p. 7

10 Jet definitions Jets bunch of collimated particles is not sufficient in practice collinear has some arbitraryness 2 jets 3 jets? jets p. 8

11 Jet definitions Jets bunch of collimated particles is not sufficient in practice collinear has some arbitraryness 2 jets 3 jets? jets In practice: use of a jet definition jet particles {p i } jets {j k } definition Jet algorithm: the recipe (insufficient!) Jet definition: algorithm + the parameters p. 8

12 Useful jet algorithms Only a handful of theoretically well-behaved/infrared-safe algorithm (For hadron collisions): k t algorithm [Catani,Dokshitzer,Seumour,Webber;Ellis,Soper, 93] Cambridge/Aachen algorithm [Dokshitzer,Leder,Moretti,Webber, 97;Wobish, 99] anti-k t algorithm SISCone algorithm [M.Cacciari,G.Salam,GS, 8] [G.Salam,GS, 7] Each have their pros and cons! p. 9

13 Useful jet algorithms Only a handful of theoretically well-behaved/infrared-safe algorithm (For hadron collisions): k t algorithm p = 1 recombine according to QCD soft and collinear divergences Cambridge/Aachen algorithm p = matches collinear div; simple geometric algorithm anti-k t algorithm p = 1 produces circular hard jets; default for CMS and ATLAS SISCone algorithm safe version of the Tevatron s algs ;low background sensitivity Succesive recombination of the closest pair with d ij = min(k 2p t,i,k2p t,j )( y2 ij + φ2 ij ) NB: all have a parameter R controlling the size p. 9

14 Useful jet algorithms Only a handful of theoretically well-behaved/infrared-safe algorithm (For hadron collisions): k t algorithm recombine according to QCD soft and collinear divergences Cambridge/Aachen algorithm matches collinear div; simple geometric algorithm anti-k t algorithm produces circular hard jets; default for CMS and ATLAS SISCone algorithm safe version of the Tevatron s algs ;low background sensitivity All (and others) implemented in FastJet [M.Cacciari,G.Salam,GS] p. 9

15 Algorithm timings 1 1 CDF midpoint (s= GeV) CDF midpoint (s=1 GeV) KtJet SISCone k t (FastJet) anti-k t (FastJet) run time (s) N Recombination algorithms very fast [M. Cacciari, G. Salam, 6] Heavy-ion collisions: 2-4 particles area computations (see later): +O(1) particles p. 1

16 Background effects: 1. pollution Background particles end up in the jets 1/N dn/dm (GeV -1 ) M Z =3 GeV k t (R=.6) SISCone (R=.6) no pileup with pileup Example: Z q q 2 jets M=3 GeV Reconstruct the dijet invariant mass reconstructed Z mass (GeV) width = 29.5 GeV width = 21. GeV position shifted, amount πr 2 ρ peak smeared because ρ fluctuates between the events p. 11

17 Background effects: 2. back-reaction Background particles affect the hard particles clustering gain: m 2 no medium: p t = p t1 medium: p t = p t1 +p t2 +p tm loss: m no medium: p t = p t1 +p t2 medium: p t = p t1 +p tm p. 12

18 Background effects: 2. back-reaction Background particles affect the hard particles clustering tractable analytically k t Cambridge > SISCone anti-k t 1/N dn/dp t (GeV -1 ) SISCone (f=75) Cam/Aachen k t anti-k t R=1 Pythia 6.4 LHC (high lumi) 2 hardest jets p t,jet > 1 TeV y < p t (B) (GeV) p. 12

19 Reconstruction recipe so far: background subtraction using jet areas p. 13

20 Jet areas [M.Cacciari, G.Salam, GS, 8] Area region where the jet catches soft particles Recipe: add infinitely soft particles (aka ghosts) Recipe: and see in which jet they are clustered 2 methods: Passive area: add one ghost at a time and repeat many times Active area: add a set of ghosts and cluster once Idea: ghost background particle active area uniform background passive area pointlike background Notes: passive = active for large multiplicities require an IR-safe algorithm! generic/universal definition (e.g. independent of a calorimeter) p. 14

21 Jet area: examples Example: active area for a simple event k t anti-k t p. 15

22 Note: analytic control Example: perturbative expansion of areas (at order α s ) A(p t,r) = A + C ( ) F,A αs (Q ) b π πr2 d log α s (Rp t ) area πr 2, area const. coefficients computable Q IR regulator background density A /(πr 2 ) passive active passive active k t Cam/Aachen anti-k t 1 1 SISCone 1 1/ d p. 16

23 Pileup subtraction (for uniform backgrounds) Basic idea: [M.Cacciari, G.Salam, 8] p t,subtracted = p t,jet ρ pileup Area jet Jet area: [M.Cacciari, G.Salam, G.S., 8] region where the jet catches infinitely soft particles (active/passive) analytic control and understanding in pqcd median Pileup density per unit area: ρ pileup e.g. estimated from the median e.g. of p t,jet /Area jet P t,jet / Area jet η p. 17

24 Pileup subtraction (for uniform backgrounds) Basic idea: [M.Cacciari, G.Salam, 8] p t,subtracted = p t,jet ρ pileup Area jet Jet area: [M.Cacciari, G.Salam, G.S., 8] region where the jet catches infinitely soft particles (active/passive) analytic control and understanding in pqcd Pileup density per unit area: ρ pileup e.g. estimated from the median e.g. of p t,jet /Area jet P t,jet / Area jet hard jets median background jets η p. 17

25 Pileup subtraction (for uniform backgrounds) Basic idea: [M.Cacciari, G.Salam, 8] p t,subtracted = p t,jet ρ pileup Area jet Jet area: [M.Cacciari, G.Salam, G.S., 8] region where the jet catches infinitely soft particles (active/passive) analytic control and understanding in pqcd Pileup density per unit area: ρ pileup e.g. estimated from the median e.g. of p t,jet /Area jet P t,jet / Area jet hard jets median background jets implemented in FastJet on an event-by-event basis η p. 17

26 Effect on dijet reconstruction Pileup unsubtracted pileup subtracted 1/N dn/dm (GeV -1 ) M Z =3 GeV k t (R=.6) SISCone (R=.6) no pileup with pileup 1/N dn/dm (GeV -1 ) M Z =3 GeV k t (R=.6) SISCone (R=.6) no pileup with pileup reconstructed Z mass (GeV) reconstructed Z mass (GeV) width = 29.5 GeV width = 21. GeV width = 21. GeV width = 17.7 GeV position reasonnable dispersion reduced (thanks to the event-by-event approach) used by STAR for the first jet analysis in heavy-ions p. 18

27 Improvements: #1 local ranges p. 19

28 Idea #1: use a local range to compute ρ bkg Fluctuating background determine the background density ρ bkg from jets in the vicinity of the jet we want to subtract Global StripRange( ) CircularRange( ) DonutRange(δ, ) jet δ -y max y max y jet y jet + p. 2

29 Idea #1: use a local range to compute ρ bkg Fluctuating background determine the background density ρ bkg from jets in the vicinity of the jet we want to subtract Global StripRange( ) CircularRange( ) DonutRange(δ, ) jet δ -y max y max y jet y jet + Exclude the hardest jets from the determination of ρ bkg reduce the bias in the computation median ρ ρ =.55πR2 A R σ ρ n hard RHIC: σ 1, y < 1, R =.4 ρ.22 GeV LHC: σ 2, y < 2.4, R =.4 ρ.18 GeV p. 2

30 Improvements: #2 filtering p. 21

31 Filtering p t [GeV] Cam/Aachen (R=1.) cluster with Cambridge/Aachen(R) φ y 1 2 p. 22

32 Filtering p t [GeV] Hardest jet cluster with Cambridge/Aachen(R) for each jet φ y 1 2 p. 22

33 Filtering p t [GeV] Cam/Aachen (R=.5) cluster with Cambridge/Aachen(R) for each jet recluster with Cambridge/Aachen(R/2) φ y 1 2 p. 22

34 Filtering p t [GeV] Filtered cluster with Cambridge/Aachen(R) for each jet recluster with Cambridge/Aachen(R/2) 5 keep the 2 hardest subjets φ y 1 2 p. 22

35 Filtering p t [GeV] Filtered cluster with Cambridge/Aachen(R) for each jet recluster with Cambridge/Aachen(R/2) 5 keep the 2 hardest subjets φ y 1 2 Idea: keep perturb. radiation remove UE Proven useful for boosted jet H b b tagging [J.Butterworth, A.Davison, M.Rubin, G.Salam, 8] Proven useful for kinematic reconstructions [M.Cacciari, J.Rojo, G.Salam, GS, 8] p. 22

36 Expected practical effects p. 23

37 Framework for study Hard event (quenched or unquenched) cluster subtract Hard jets p t embed Hard event + Background event cluster subtract Full jets average dispersion Hard event: Pythia(v6.4) or Pythia(v6.4)+PyQuen(v1.5) Background: Hydjet++(v2.1) (cross-checked with others) Analysis: FastJet(v2.4) Ideally: smallest p t shift, smallest p t dispersion Note: in what follows, R fixed to.4 p. 24

38 Effect of choosing a local range p t shift [GeV] RHIC, -1% central unquenched y <1, R=.4 anti-k t algorithm Global Global, 2 excl Circ(3R), 2 excl Donut(R,3R) Strip(2R), 2 excl Strip(3R), 2 excl p t shift [GeV] LHC, unquenched y <2.4, R=.4 anti-k t algorithm Global Global, 2 excl Circ(3R), 2 excl Donut(R,3R) Strip(2R), 2 excl Strip(3R), 2 excl p t,hard [GeV] p t,hard [GeV] effect.5-1 GeV differences between local ranges subtraction uncertainty for limited acceptance, global range local range hard rejection agrees with analytic estimates p. 25

39 Effect of choosing a local range Number of jets in a range range area n jets Circ(2R) 4πR Circ(3R) 9πR 2 1 Donut(R,2R) 3πR Donut(R,3R) 8πR 2 9 Strip(2R) 4πR 11 (R =.4,R ρ =.5) p t shift [GeV] RHIC, -1% central, unquenched anti-k t, y <1, R=.4 Circ(2R) Circ(2R), 2 excl Circ(3R), 2 excl Donut(R,2R) Donut(R,3R) p t,hard [GeV] rule of thumb: at least 7-8 jets needed to estimate ρ p. 26

40 Results: RHIC kinematics p t shift [GeV] RHIC, -1% central y <1, R=.4, unquenched k t C/A anti-k t C/A(filt) average p t shift: anti-k t and C/A+filt. Ok -3-4 Donut(R,3R) range p t,hard [GeV] p. 27

41 Results: RHIC kinematics p t shift [GeV] RHIC, -1% central y <1, R=.4, unquenched Donut(R,3R) range k t C/A anti-k t C/A(filt) p t,hard [GeV] 8 average p t shift: anti-k t and C/A+filt. Ok p t shift dispersion: C/A+filt. better p t dispersion [GeV] k t C/A anti-k t C/A(filt) RHIC, -1% central Donut(R,3R) range unquenched, y <1, R= p t,hard [GeV] p. 27

42 Results: RHIC kinematics p t shift [GeV] p t dispersion [GeV] RHIC, -1% central y <1, R=.4, unquenched Donut(R,3R) range k t C/A anti-k t C/A(filt) p t,hard [GeV] k t C/A anti-k t C/A(filt) RHIC, -1% central Donut(R,3R) range Back-reaction [GeV] average p t shift: anti-k t and C/A+filt. Ok p t shift dispersion: C/A+filt. better watch out C/A+filt. average: back-reaction compensated RHIC, -1% central y <1, R=.4, unquenched k t C/A anti-k t C/A(filt) unquenched, y <1, R= p t,hard [GeV] p t,hard [GeV] p. 27

43 Results: LHC kinematics 9 p t shift [GeV] LHC, unquenched y <2.4, R=.4 k t C/A anti-k t C/A(filt) average p t shift: anti-k t and C/A+filt. Ok Donut(R,3R) range p t,hard [GeV] p. 28

44 Results: LHC kinematics p t shift [GeV] LHC, unquenched y <2.4, R=.4 k t C/A anti-k t C/A(filt) average p t shift: anti-k t and C/A+filt. Ok Donut(R,3R) range p t dispersion [GeV] p t,hard [GeV] 35 k t C/A 3 anti-k t C/A(filt) y <2.4, R=.4 LHC, unquenched Donut(R,3R) range p t,hard [GeV] p t shift dispersion: C/A+filt. better anti-k t Ok p. 28

45 Results: quenching RHIC, Donut(R,3R) y <1, R=.4 Pythia PyQuen LHC, Donut(R,3R) y <2.4, R=.4 Pythia PyQuen p t shift [GeV] p t shift [GeV] : anti-k t x: C/A(filt) p t,hard [GeV] : anti-k t x: C/A(filt) p t,hard [GeV] Performances not much affected by quenching 1 GeV for p t = 5 GeV at the LHC is only a 2% effect anti-k t s rigidity in action just illustrative: more quenching models needed p. 29

46 Results: centrality dependence 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) 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] p t shift [GeV] C/A(filt), Donut(R,3R) good subtraction for every centrality bin p t shift [GeV] C/A(filt), Strip(3R) p t,hard [GeV] dispersion decreases with centrality p. 3

47 Results: comments anti-k t s soft-resilience is the reason for p t p. 31

48 Results: comments anti-k t s soft-resilience is the reason for p t C/A+filt s smaller area is the reason for smaller dispersion in agreement with the estimate: dispersion A jet σ bkg p. 31

49 Results: comments anti-k t s soft-resilience is the reason for p t C/A+filt s smaller area is the reason for smaller dispersion in agreement with the estimate: dispersion A jet σ bkg C/A+filt s small p t result from BR and subtraction bias Most of QCD radiation in the hardest subjet Bias: filtering picking the 2 nd hardest jet as the hardest background fluctuation Estimate for Gaussian fluctuations: ( p t ) filt. 3.55π(R filt R) 2 2 π σ.56rσ 2 GeV at RHIC, 5.8 GeV at the LHC i.e. nice agreement p. 31

50 Effects of shift and dispersion RHIC pp jet cross-section is well approximated by dσ dp t = µσ e µp t bare Shift p t and dispersion σ (with Gaussian approx.) gives dσ dp t = dσ obs. dp t e µ pt e µ2 σ 2 /2. bare µ =.3, p t =, σ = 7 gives factor 9 µ =.3, p t =, σ = 4.5 gives factor 2.5 p. 32

51 Effects of shift and dispersion RHIC pp jet cross-section is well approximated by dσ dp t = µσ e µp t bare Shift p t and dispersion σ (with Gaussian approx.) gives dσ dp t = dσ obs. dp t e µ pt e µ2 σ 2 /2. bare µ =.3, p t =, σ = 7 gives factor 9 µ =.3, p t =, σ = 4.5 gives factor 2.5 Unfolding the dispersion is an important source of uncertainty C/A+filt would help p. 32

52 Fake jets Fake jet = hard fluctuation of the soft background Estimate: Fakes: Gaussian spectrum with σ from studies above scaled by the number of binary collisions scaled by the number of jets in the acceptance Hard cross-section: Pythia simulation (approximately) convoluted with Gaussian fluctuations p. 33

53 Fake jets Fake jet = hard fluctuation of the soft background dσ/dp t [mb/gev] RHIC anti-k t alg(r=.4) Fake jets Hard jets σ = 7 GeV p t [GeV] Need for a good fake-jet rejection mechanism p. 33

54 Fake jets Fake jet = hard fluctuation of the soft background dσ/dp t [mb/gev] RHIC anti-k t alg(r=.4) Fake jets Hard jets σ = 7 GeV dσ/dp t [mb/gev] RHIC C/A(filt), R=.4 Fake jets Hard jets σ = 4 GeV p t [GeV] p t [GeV] Need for a good fake-jet rejection mechanism Significant improvement Not much of a problem at the LHC p. 33

55 A word on the RHIC results p. 34

56 Generic method First jet measurements in heavy-ion collisions STAR k t and anti-k t algorithms FastJet s background subtraction method statistical fake jets rejections dispersion unfolding from MC in AuAu PHENIX Gaussian filter ([Y.S.Lai,B.A.Cole,8]) Gaussian filter for fake jets rejections dispersion unfolding from pp in CuCu p. 35

57 results p. 36

58 results (cont d) Compute x-section ratio: σ(r =.2) σ(r =.4) pp: less than 1 out of jet radiation AA: less than pp broadening p. 37

59 A word of caution Take a closer look at the ratio in pp 1..9 anti-k t.8 (dσ R=.2 /dp t )/(dσ R=.4 /dp t ) STAR p t [GeV] p. 38

60 A word of caution Take a closer look at the ratio in pp 1..9 anti-k t.8 (dσ R=.2 /dp t )/(dσ R=.4 /dp t ) STAR QCD O(α s ) p t [GeV] p. 38

61 A word of caution Take a closer look at the ratio in pp 1..9 anti-k t.8 (dσ R=.2 /dp t )/(dσ R=.4 /dp t ) STAR QCD O(α s ) 2 QCD O(α s ) p t [GeV] p. 38

62 A word of caution Take a closer look at the ratio in pp 1..9 anti-k t.8 (dσ R=.2 /dp t )/(dσ R=.4 /dp t ) STAR.1 QCD O(α s ) 2 QCD O(α s ) Pythia - parton p t [GeV] p. 38

63 A word of caution Take a closer look at the ratio in pp 1..9 anti-k t.8 (dσ R=.2 /dp t )/(dσ R=.4 /dp t ) STAR QCD O(α s ).1 2 QCD O(α s ) Pythia - parton Pythia - hadron p t [GeV] p. 38

64 A word of caution Take a closer look at the ratio in pp 1..9 anti-k t.8 (dσ R=.2 /dp t )/(dσ R=.4 /dp t ) STAR QCD O(α s ) 2 QCD O(α s ).1 Pythia - parton Pythia - hadron Pythia - full p t [GeV] p. 38

65 A word of caution Take a closer look at the ratio in pp 1. anti-k.9 t a single gluon in the medium likely not sufficient pp analytic calc on its way.8 (dσ R=.2 /dp t )/(dσ R=.4 /dp t ) STAR QCD O(α s ) 2 QCD O(α s ).1 Pythia - parton Pythia - hadron Pythia - full p t [GeV] p. 38

66 Conclusions p. 39

67 Conclusions Already tested: Jets hard to see in large HI background first measurements recently at RHIC Background subtraction using jet areas plays an important role p. 4

68 Conclusions Already tested: Jets hard to see in large HI background first measurements recently at RHIC Background subtraction using jet areas plays an important role To be tested: Use of local ranges/hard jet removal subtraction uncertainty algorithm: anti-k t does a good job, C/A+filt reduces dispersion probably want to try both Watch out for back-reaction and filter bias Centrality and quekching OK Most of the effects behave as expected analytically p. 4

69 Conclusions Already tested: Jets hard to see in large HI background first measurements recently at RHIC Background subtraction using jet areas plays an important role To be tested: Use of local ranges/hard jet removal subtraction uncertainty algorithm: anti-k t does a good job, C/A+filt reduces dispersion probably want to try both Watch out for back-reaction and filter bias Centrality and quekching OK Most of the effects behave as expected analytically measurements A one-gluon-emission approach not sufficient p. 4