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Jet Physics: Past, Present and Future

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Jet Physics: Past, Present and Future. Or. What Have We Learned Recently? (Largely with Joey Huston and Matthias T nnesmann) S. D. Ellis TeV-Scale Physics 7/18/02 ... – PowerPoint PPT presentation

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Title: Jet Physics: Past, Present and Future


1
Jet Physics Past, Present and Future
  • Or What Have We Learned Recently?
  • (Largely with Joey Huston and Matthias Tönnesmann)

S. D. Ellis
TeV-Scale Physics
7/18/02
2
The Goal is 1 strong Interaction Physics (if 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,?
  • Warning
  • We must all use the same algorithm!!

3
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.

4
Thus we want to associate nearby hadrons or
partons into JETS
  • Nearby in angle Cone Algorithms
  • Nearby in momentum space kT Algorithm
  • But mapping of hadrons to partons can never be 1
    to 1, event-by-event!

5
Think of the algorithm as a microscope for
seeing the (colorful) underlying structure -
6
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!?

7
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

8
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

9
  • 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)

10
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

11
For example, consider 2 partons yields potential
with 3 minima trial cones will migrate to
minimum
12
But
  • 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

13
History 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
  • 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

14
  • 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

15
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

16
E-scheme (4-vector)
  • CONE i ? C iff
  • 4-vector
  • Centroid
  • Stable (Arithmetically more complex than
    Snowmass)

17
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 matters! (in a 1 game)

18
5 Differences!!
19
Note that the PDFs are also still different on
this scale
20
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

21
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

22
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)

23
Recent issues
  • kT vacuum cleaner effect DØ - over estimate
    ET?
  • Engineering issue with streamlined seedless
    must allow some overlap or lose stable cones near
    the boundaries (M. Tönnesmann)

24
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

25
Lost Energy!? (?ET/ET1, ??/?5)
26
Missed Towers How can that happen?
27
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
28
NLO Perturbation Theory r parton separation,
z E2/E1Rsep simulates the cones missed due to
no middle seed
Naïve Snowmass
With Rsep
r
r
29
Consider the corresponding potential with 3
minima, expect via MidPoint or Seedless to find
middle stable cone
30
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!?
31
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
32
Next s 0.25 - larger effect, but the desired
cones are still obvious!?
Smeared parton energy
Energy in cone
33
But it matters for the potential as we increase
?we wash out middle minimum and lose middle cone
34
Then washout out second minima, find only 1
stable cone
35
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

36
The Fixed potential (in red)
37
With Fix
38
Consider the number of events versus the jet ET
difference for various R' values, distribution
symmetric for 1/?2 reduction
39
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
40
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!!
41
The ratcheted potential function looks
likeNote the missing ? functions,
those terms can be positive far from the seed,
hence the cutoffs
42
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)

43
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.,

44
We can define JEFs
  • or
  • Corresponding to
  • The Cone jets are the same function evaluated at
    the discrete solutions of (stable cones)

45
Simulated calorimeter data JEF
46
Typical CDF event in y,??
Found cone jets
JEF distribution
47
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).

48
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

49
Apply to the previous event and find,
where the data points are the CDF found
jets
  • Jet ET

Jet ET
Jet ET
50
The JEF definition in NLO yields a cross section
much like the usual cone algorithm
51
  • The mass of a single JEF (jet) is
  • With probability density
  • And event occupancy probability

52
Applied to a W?1 jet in (simulated events)
From J.M. Butterworth
53
Summary
  • There are many challenges before we get to 1
    precision QCD! The details now matter!
  • At the same time we have many possible solutions
    to study! Need to optimize Cone kT
    algorithms Consider the ETMAX cone? Study the
    JEF idea
  • It is essential that we share the details during
    Run II! (which often did not happen in Run I)

54
ETMAX Cone Algorithm
  • Define a potential without
    factori.e., just find the maxima of the
    energy in a cone function (they didnt get washed
    out by the smearing)
  • Make an ET,Jet ordered list of cones start with
    largest ET and delete all overlapping cones
    continue down the list in same way

55
Very similar cross section to usual cone NLO
result ( 30 larger)
56
Finally consider the 1997 di-jet analysis of
Giele and Glover
  • Constraints
  • Probability distribution

57
Yields the following results, indicating reduced
sensitivity to both higher orders and to the
phase space cuts compared to standard cone jets.
58
Perturbation Theory (Narrow), d shower
spacing, z E2/E1
A Both in 1 stable cone B 2 stable cones, 2
in 1 plus 1 in 1 C 3 stable cones,
including 2 in 1 D 1 stable cone with
just 1 inside E 2 stable cones,
merged F 2 stable cones, split D is BAD -
Splashout!
59
Consider simple 1-D distribution of 2 partonsz
E2/E1, ?,r angular separation, ? smearing
  • 3 stable cones, merge to 1

60
Add (gaussian) smearing (showering/hadronization)
Lose middle cone
  • Lose right cone

Restore right cone
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