Building Better Jets A Work in Progress

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Building Better JetsA Work in Progress

• (Largely with Joey Huston, Matthias Tönnesmann,
  Dave Soper and Walter Giele)

S. D. Ellis
CDF/D0/Theory Jet Workshop 12/16/02
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The Goal is 1 strong Interaction Physics (where
Run I was 10)

• Want to precisely connect
• What we can measure, e.g., E(y,?) in the detector
• To
• What we can calculate, e.g., arising from small
  numbers of partons as functions of E, y,?
• Issues Uncertainties in pdfs
• Higher orders in perturbation theory
• Non-perturbative hadronization ( showering)
• Details (especially differences between
  groups) of algorithms kinematics

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• Warning
• We must all use the same algorithm!!

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Why Jet Algorithms?

• We understand what happens at the level of
  partons and leptons, i.e., LO theory is simple.
• We want to map the observed (hadronic) final
  states onto a representation that mimics the
  kinematics of the energetic partons ideally on a
  event-by-event basis.
• But we know that the partons shower
  (perturbatively) and hadronize (nonperturbatively)
  , i.e., spread out.

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Thus we want to associate nearby hadrons or
partons into JETS

• Nearby in angle Cone Algorithms - issue is
  splashout
• Nearby in momentum space kT Algorithm - issue
  is splashin
• But mapping of hadrons to partons can never be 1
  to 1, event-by-event!

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Think of the algorithm as a microscope for
seeing the (colorful) underlying structure -
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Note 2 logically distinct phases

• Identify contents of jet particles, calorimeter
  towers or partons jet IDscheme
• Combine kinematic properties of jet contents
  (e.g., 4-vectors) to find jet kinematic
  properties recombination scheme
• May not want to do both steps with the same
  parameters!?

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History Starting in Snowmass

• Start over 10 years ago with the Snowmass
  Accord (or the Snowmass Cone Algorithm).
• Idea was to have an agreed upon algorithm (hence
  accord) that everyone would use. But, in
  practice, it was flawed
• Was not efficient experimenters used seeds to
  limit where one looked for jets this introduces
  IR sensitivity at NNLO
• Did not treat issue of overlapping cones
  split/merge question

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Snowmass Cone Algorithm

• Cone Algorithm particles, calorimeter towers,
  partons in cone of size R, defined in angular
  space, e.g., Snowmass (?,?)
• CONE center - (?C,?C)
• CONE i ? C iff
• Energy
• Centroid

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• Flow vector
• Jet is defined by stable cone
• Stable cones found by iteration start with cone
  anywhere (and, in principle, everywhere),
  calculate the centroid of this cone, put new cone
  at centroid, iterate until cone stops flowing,
  i.e., stable ? Proto-jets (prior to split/merge)
  ? unique, discrete jets event-by-event (at
  least in principle)

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Consider the Snowmass Potential

• In terms of 2-D vector ordefine
  a potential
• Extrema are the positions of the stable cones
  gradient is force that pushes trial cone to the
  stable cone, i.e., the flow vector

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But note

• Theoretically can look everywhere and find all
  stable cones
• Experimentally reduce size of analysis by putting
  initial cones only at seeds energetic towers or
  clusters of towers thus introducing undesirable
  IR sensitivity and missing certain possible
  2-jets-in-1 configurations
• May NOT find 3rd (middle) cone

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For example, consider 2 partons yields potential
with 3 minima trial cones will migrate to
minimum
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One of a list of HIDDEN issues, all of which
influence the result

• Energy Cut on towers kept in analysis (e.g., to
  avoid noise)
• (Pre)Clustering to find seeds (and distribute
  negative energy
• Energy Cut on precluster towers
• Energy cut on clusters
• Energy cut on seeds kept
• Starting with seeds find stable cones by
  iteration
• In JETCLU, once in a seed cone, always in a
  cone, the ratchet effect

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• Overlapping stable cones must be split/merged
• Depends on overlap parameter fmerge
• Order of operations matters
• All of these issues impact the content of the
  found jets
• Shape may not be a cone
• Number of towers can differ, i.e., different
  energy
• Corrections for underlying event must be tower
  by tower

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To address these issues, the Run II Study group
Recommended

• Both experiments use
• (legacy) Midpoint Algorithm always look for
  stable cone at midpoint between found cones
• Seedless Algorithm
• kT Algorithms
• Use identical versions except for issues required
  by physical differences all of this in
  preclustering??
• Use (4-vector) E-scheme variables for jet ID and
  recombination

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E-scheme (4-vector)

• CONE i ? C iff
• 4-vector
• Centroid
• Stable (Arithmetically more complex than
  Snowmass)

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Actually used by CDF and D? in run I for cone
finding, and approximately equivalent to
Snowmass. For jet ET used -

• Snowmass (D?)
• CDF -
• E-Scheme (Run II study proposal)
• The differences matter! (in a 1 game)

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For example, consider 2 partons p1zp2
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Thus ET,4D, CDF may be larger or smaller than
ET,scalar, depending on the kinematics
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5 Differences (at NLO) !!
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A different (and not completely consistent) view
comes from Matthias EKS style NLO calculation
with CTEQ4m pdfs
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Note that the PDFs are also still different on
this scale
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Streamlined Seedless Algorithm

• Data in form of 4 vectors in (?,?)
• Lay down grid of cells ( calorimeter cells) and
  put trial cone at center of each cell
• Calculate the centroid of each trial cone
• If centroid is outside cell, remove that trial
  cone from analysis, otherwise iterate as before
• Approximates looking everywhere converges
  rapidly
• Split/Merge as before

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Split/Merge

• Stable cones yield proto-jets
• Process in decreasing energy order
• Merge if shared energy gt fmerge of lower energy
  proto-jet
• Split if shared energy lt fmerge of lower energy
  proto-jet, award to closer proto-jet

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kT Algorithm

• Combine partons, particles or towers pair-wise
  based on closeness in momentum space, beginning
  with low energy first.
• Jet identification is unique no merge/split
  stage
• Resulting jets are more amorphous, energy
  calibration seemed difficult (subtraction for
  UE?), and analysis can be very computer intensive
  (time grows like N3)

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Recent issues

• kT vacuum cleaner effect DØ - over estimate
  ET? Come back to this.
• Engineering issue with streamlined seedless
  must allow some overlap or lose stable cones near
  the boundaries (M. Tönnesmann)

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A NEW issue for Midpoint Seedless Cone
Algorithms

• Compare jets found by JETCLU (with ratcheting) to
  those found by MidPoint and Seedless Algorithms
• Missed Energy when energy is smeared by
  showering/hadronization do not always find 2
  partons in 1 cone solutions that are found in
  perturbation theory, underestimate ET new kind
  of Splashout
• See Ellis, Huston Tönnesmann, hep-ph/0111434

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Lost Energy!? (?ET/ET1, ??/?5)
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Missed Towers How can that happen?
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Consider a simple model with 2 partons, ET in
ratio z and separated in angle by r
Look at energy in cone of radius R ? Energy
Distribution
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NLO Perturbation Theory r parton separation,
z E2/E1Rsep simulates the cones missed due to
no middle seed
Naïve Snowmass
With Rsep
r
r
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Consider the corresponding potential with 3
minima, expect via MidPoint or Seedless to find
middle stable cone
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But in real life the partons energy is smeared
by hadronization, etc. Simulate with gaussian
smearing in angle of width s. Smooths the energy
in the cone distribution, larger s, larger
effect. Still the desired cones are obvious!?
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But in real life the partons energy is smeared
by hadronization, etc. Simulate with gaussian
smearing in angle of width s. Smooths the energy
in the cone distribution, larger s, larger
effect. First s 0.1 -
Smeared parton energy
Energy in cone
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Next s 0.25 - larger effect, but the desired
cones are still obvious!?
Smeared parton energy
Energy in cone
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But it matters for the potential as we increase
?we wash out middle minimum and lose middle cone
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Then washout out second minima, find only 1
stable cone
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Fix

• Use R?ltR, e.g.,R/?2, during stable cone
  discovery, less sensitivity to energy at
  periphery
• Use R during jet construction
• ? restores right cone, but not middle cone
• Helps some with Midpoint algorithm
• Does not help with Seedless (need even smaller R?
  ?)
• ? still no stable middle cone

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The Fixed potential (in red)
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With Fix
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Consider the number of events versus the jet ET
difference for various R' values, distribution
symmetric for 1/?2 reduction
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Make a second pass to find jets in the
leftovers, R2nd R/?2, most have previously
found jet neighbors
Irreducible (JetClu) level at about R R/2 R
?0.25
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The ? -z plane, from Matthiasblack 1 jet,
green 2 jets, red 3 jets (merged to 1)
? 0
? 0.1
? 0.25
? 0.25, fix50
? 0.25, fix25
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But Note we are fixing to match JETCLU which
is NOT the same as perturbation theory
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Racheting Why did it work?Must consider seeds
and subsequent migration history of trial cones
yields separate potential for each seed
INDEPENDENT of smearing, first potential finds
stable cone near 0, while second finds stable
cone in middle (even when right cone is washed
out)! NLO Perturbation Theory!!
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The ratcheted potential function looks
likeNote the missing ? functions,
those terms can be positive far from the seed,
hence the cutoffs
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With the kT algorithm we can avoid seeds, Rsep,
merging etc., but splash-in can be an issue

• In this algorithm we deal with a list of
  4-vectors (preclusters and/or protojets) in
  terms of a size parameter D define
• If the smallest object is dii, remove i from the
  list and define it to be a jet, if the smallest
  object is dij, remove i and j from the list and
  replace them with the merged object. For the new
  list (with one fewer item), repeat the
  calculation as above, until the list is empty.

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? -z plane from Matthias
? 0
? 0.1
? 0.25
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Apply to a the simple 2 parton configuration we
used earlier, find 2 jets for ? gt D even for ?
0.25 unless z is small
D 0.7, ? 0.71, z 1.0
D 0.7, ? 0.8, z 0.1
2 jets
1 jet
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So little splash-out problem but splash-in is
real vacuums up extra energy that happens to be
around
A more realistic (Pythia) DØ event with D 1.0,
and preclustering last view shows R 1
circles around jets
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To test the robustness of the kT jets found
consider the results of various analyses applied
to the event we just looked at ETs of leading
2 jets only the leading jet is nearly invariant
(but ET still varies)
2x2 preclusters, ET gt 0 41.1 GeV 33.29 GeV
All towers, ET gt 0 GeV 42.1 GeV 26.2 GeV
All towers ET gt 100 MeV 36.3 GeV 30.9 GeV
All towers ET gt 200 MeV 30.6 GeV 18.4 GeV
All towers 26.1 GeV 22.1 GeV
Seedless Cone 25.6 GeV 21.9 GeV
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At NLO the kT algorithm is just the cone
algorithm with Rsep 1 and D R. The original
study suggested that R 0.7 (Rsep 2) was
comparable to D 1. For the better
(phenomenological) value Rsep 1.3, D 0.83 is
a better match to R 0.7.
Snowmass Kinematics
4-D kinematics
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Better yet, DØ has data for D 1.0 (4-D)
Assume 2 Gev Splash-in
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With more Modern pdfs
Assume 1 GeV Splash-in
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To Test for splash-in try measuring the D
dependence of the cross section assume splash-in
? D2 (area)At ET 100 GeV
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BUT .. Want to get rid of seeds, ratcheting and
all that!Time for a new idea!! (?)Forget jets
event-by-eventUse JEF Jet Energy Flow

• See Tkachov, et al. (circa 1995) Giele Glover
  (1997) Sterman, et al. (2001), Berger, et al.
  hep-ph/0202207 (Snowmass 2001)

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Each event produces a JEF distribution,not
discrete jets

• Each event list of 4-vectors
• Define 4-vector distribution where the unit
  vector is a function of a
  2-dimensional angular variable
• With a smearing function e.g.,

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We can define JEFs

• or
• Corresponding to
• The Cone jets are the same function evaluated at
  the discrete solutions of (stable cones)

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Simulated calorimeter data JEF
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Typical CDF event in y,??
Found cone jets
JEF distribution
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Here is the JEF version of the event we saw
earlier
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Since JEF yields a smooth distribution for each
event (compared to non-analytic algorithms), we
expect that

• The JEF analysis is more amenable to resummation
  techniques and power corrections analysis in
  perturbative calculations.
• The required multi-particle phase space
  integrations are largely unconstrained, i.e.,more
  analytic, and easier (and faster) to implement.
• The analysis of the experimental data from an
  individual event should proceed more quickly (no
  need to identify jets event-by-event).
• Signal to background optimization can now include
  the JEF parameters (and distributions).

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The trick with JEF is defining observables, e.g.

• The probability distribution (for a CDF type
  rapidity acceptance and CDF ET E sin?
  definition) is i.e., probabilities ?
  area/?R2
• The corresponding number of jets (JEFs) above
  ET,min, per event, is

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Apply to the CDF event and find, where
the data points are the CDF found jets

• Jet ET

Jet ET
Jet ET
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Apply to Pythia event, see cone (R 0.7)
analysis jets as bumps in the distribution
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The JEF definition in NLO yields a cross section
much like the usual cone algorithm
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• The mass of a single JEF (jet) is
• With probability density
• And event occupancy probability

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Applied to a W?1 jet in (simulated events)
From J.M. Butterworth
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Summary

• There are many challenges before we get to 1
  precision QCD! The details now matter!
• At the same time we have many possible avenues to
  study! Need to optimize Cone kT
  algorithms Study the JEF idea
• It is essential that we share the details during
  Run II! (which often did not happen in Run I)