Energy Flow Within Jets

Z’ at Design L 1

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Energy Flow Within JetsEnergy Flow Within Jets

Dan GreenFermilab

July, 2002

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MLLA - TheoryMLLA - Theory/ 2

/ 2

/ 2

/ (4 / 3)[ ( ) / ] {[cosh (1 2 )sinh ]/[4 / 3 ( / )]}

( (16 / 3) / sinh [cosh (1 2 )sinh ])log(1/ ), 2 /log(2 sin / )1 /

tanh( ) (2 1)101/810.23

( )( / 2)

B B

B

c

o

o

dN dy B d e p Y sinh

I Y py x x k MY M Qp y Y

ip

BQ GeV

N B z

11( )

16 / 3( )

BBI z

z Y

QCD in LLA predicts the x distribution of partons. LPD then gives hadron distribution in x in terms of basically 1 parameter. The value of Q is taken from CDF fits to data. The theory appears in J. Mod Phys. A 1875 (1992) and Z Phys C, 55, 107 (1992). The CDF fits appear in Fermilab – Pub – 02/096-E (June 2002).

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MLLA - NumericalMLLA - Numerical

102

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40<n> vs M at Fixed Cone Angle = 0.6

M(GeV)

<n>

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9dN/dy for M = 50, 100, 200, 400, 800 GeV

y=log(1/x)dN

dy

Numerical results were calculated. <n> increases rapidly with cone angle up to ~ 0.8. We expect ~ 30 hadrons in the jet at M=700 GeV., ~ 12 at M = 120 GeV. We can use D(z,M) as a guide to pileup in extracting jets. Basically angular ordering means that soft jet fragments occur at wide angles w.r.t. the parton axis.

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Z’(120) Clustering at Low LZ’(120) Clustering at Low L

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20 seeds > 1 GeV. 8 cones, R = 0.9, 8 jets, Rsep = 0.9. 27, 19 clusters (Et > 0.5 GeV in 2 highest Et jets). Find all seeds, then attach all clusters to cones, Rc, centered on seeds. Finally merge cones within Rsep. Etj1 = 49 GeV, Etj2 = 37.9 GeV, Mjj = 85 GeV

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Z’(120) at Design LZ’(120) at Design L

Clearly, towers are still sparsely populated. Equally clearly, we need to work harder to preserve the dijet mass resolution.

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Seeds, Clusters, ConesSeeds, Clusters, Cones

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120Number of Cones, Rc = 0.9, mean = 9.6

Number of Cones 0 10 20 30 40 50 60 70 800

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60Number of Seed Cluster, Et > 1 GeV, mean = 30.8

Number of Seeds

<Ns> = 30.8/event<Nc> = 9.6/event<Nj> = 9.3/eventEts> 1.0 GeV, Etc > 0.25 GeV, Rc = 0.9, Rsep = 0.9.There are many jets if seed threshold is made low.

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Leading JetLeading Jet

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50Z'(120), Et of Leading Jet

Etj(GeV)

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45Z'(120), Et of Leading Seed Cluster

Ets(GeV)

<Ns>j1 = 21 = # clusters in lead jet<Et>sj1 = 25.0 GeV = Et of seed cluster in lead jet<Et>j1 = 55 GeV ( 45.0 GeV for j2)

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Pileup in Z’(120) at Low LPileup in Z’(120) at Low L

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0.8Jet, Cone Rc = 0.8

log(x)

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0.8Jet, Cone Rc = 0.8, Centroid Offset in by /2

log(x)

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Use log(x) as the appropriate variable (MLLA). The jet shows the small angle, high momentum component. A cone at 90 degrees to the jet shows soft and wide angle underlying event and pileup behavior. Cuts are picked for high L. The sigma/mean is 17.8% at low L.

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Contours in Z’(120)Contours in Z’(120)

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log(x0 from (-6,0)

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om (

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et C

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20Jet with "Underlying Event" Subtracted

log(x)

dR

Contour for 60, 50, 40, 30, 20, 10

Estimate the true contour in (logx,dR) for a jet by subtracting the cones contour at 90 degrees to the jet for Z’(120) at low L. The pileup and the jet populate different regions of the energy-angle flow phase space.

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Pileup SubtractionPileup Subtraction

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11Z'(120) at Design Luminosity

Cone Radius

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ithin

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103 Z'(120) at Design Luminosity

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s in

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e, D

ijet M

ass

clusters mass

Must go to cone radius ~ 0.6 to capture all the jet fragments on average. However, the number of clusters is ~ 29 then (10.3 real + 18.3 pileup) and the mean dijet mass is 258 GeV

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M(GeV)

Z'(120) at Design Luminosity - Cuts Within Cone of Radius 0.6

After cuts on dR and logx the fitted mean is 119 GeV with a fitted sigma = 20.26 GeV or sigma/mean = 17.0 %. Thus the dijet mass resolution is maintained at design L. There is some residual high mass tail, however.

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• Seed Et > 10 GeV, <Ns> = 10.4 , <ETs1> = 198 GeV (leading seed cluster).

• Cone Rc = 0.8, <Nc> = 3.33• Jet – Merge Cones, <Nj> = 2.72• Clusters in Jet - <Ncl> = 55.5• Clusters at 90 degrees to jet, <Nclo> =

36.4. Difference = 19.1 (expect more in LLA, but there may be cluster merging at high density within the jet).

• <Etj1> = 352.2 GeV

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ClusteringClustering

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Nc

Mean = 21.0

For Z’(120) there are 24 clusters, Rc = 0.9, within the jet and 10 at 90 degrees – leading to 14 after subtraction. This is close to MLLA estimates. For Z’(700) at design L, the number of clusters within a cone is much larger due to pileup, 55.8. For 1/5 luminosity it is 21 clusters. For design luminosity it is ~ 56 – 36 clusters or ~ 19.

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45Z'(700), Rc = 0.8, Mean = 55.8

N (clusters in Jet 1)

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dR and log(x) for Z’(700)dR and log(x) for Z’(700)

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dR of clusters within cone, Rc = 0.8

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1200Z'(700) Data, x of Clusters

log(x)

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900Z'(700) Data, x of Clusters within Cone at =/2 to Jet

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Clearly the pileup has dNdR~R (area), while the jet shows a peak at R ~ 0.2. The pileup is al low x, while there is a peak at high x.

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Pileup Subtracted (logx,dR) Jet Pileup Subtracted (logx,dR) Jet contourscontours

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Jet With "Underlying Event" Defined at = /2 to Jet Subtracted

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dR

Z'(700) Data, (dR,log(x)), =/2 "Jet" Subtracted

log(x)

For both Z’(120) at low L and for Z’(700) at design L there is a core of the jet at small dR and large x.

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Fake Jets at Design LFake Jets at Design L

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0.4Fake Jet, Z'(700) at Design L

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Look at fake jets by taking cone at 90 degrees to jet at design L and normalizing x now to total Et within that cone. There is no jet “core” of high momentum at small angles.

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Dijet Mass in Z’(700)Dijet Mass in Z’(700)

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Mjj(GeV)

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70Z'(700), Cone = 0.8, Excluse dR > 0.3 * log(x) >< - 4.5

Mjj(GeV)

Mean ~ 614 GeV, sigma ~ 74 GeV. No major improvements.Rc = 0.4 or log(x) > -4 or a combined cut all about the same.

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ConclusionsConclusions• The pileup at design luminosity is not

too severe for Z’(700).• The appearance of a low Pt inclusive

pileup ~ uniform in cone area is confirmed.

• Pileup for Z’(120) is severe but it can be alleviated with well designed cuts on energy – angle flow within the jet.More incisive cuts than just a small cone or a threshold work well.

• Direct subtraction event by event does not work well.

Energy Flow Within Jets

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