Top Physics at the LHC

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Top Physics at the LHC

• Manchester Christmas Meeting 2006
• Chris Tevlin

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Outline

• Experimental Work
• Comparison of two jet algorithms for
  reconstructing the top mass
• Theoretical Work (to do!)
• Understanding/extending the dipole subtraction
  method
• Resummation
• Application of these to ttbar cross section

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Experimental Work
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Introduction - Jet Algorithms

• QCD - confinement (only colour singlets propagate
  over macroscopic distances)
• No unique method of assigning (colourless)
  hadrons to (coloured) partons
• Require a sensible definition of a Jet - two of
  the main types of algorithm are
• Cone Algorithms
• Cluster Algorithms

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• Cone Algorithms
• Geometrically motivated
• Fixes the angular extent of a jet with Radius in
  ?-? space (R invariant under boosts along the
  beam direction)
• Requires some prescription for removing overlaps
  between jets
• Not manifestly Infrared and collinear safe
  Atlfast!
• Some Cone Algorithms Unsafe
• Mid-point Cone Algorithms Safe
• Clustering Algorithms (KtJet)
• Kinematically motivated
• undoing the parton shower
• Theoretically favoured
• Manifestly Infrared and Collinear Safe
• All objects assigned exclusively to one jet

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Motivation (Theoretical Issues)

• Infrared safety - the algorithm is insensitive to
  the addition arbitrarily soft partons
• Collinear safety - the algorithm is insensitive
  to the replacement of any (massless) object by a
  pair of (massless) collinear objects
• Infrared safety - IR and Collinear safety
• Some Algorithms are classified as Infrared
  Almost Safe. The algorithm is rendered safe in
  the presence of a detector with finite energy
  resolution and angular granularity - this is
  dangerous for several reasons
• In order to perform a perturbative calculation
  one would need to know geometry of detector, cell
  thresholds etc
• Since the angular extent of calorimeter cells,
  and cell energy thresholds are small, each term
  in such a calculation would be large - poor
  convergence!

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Motivation (Experimental Issues)

• In the Golden Channel the top mass
  reconstructed from 3 jets
• By clustering to a specific jet multiplicity, one
  may hope to
• Remove the soft underlying event (Exclusive Mode)
• Solve Combinatorial issues
• Increase the purity of the sample (pay in
  efficiency?)

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The algorithm (Exclusive Mode)

• For each object, j, compute the closeness
  parameter djB, (Ej?jB)2 for ?jB?0 and for each
  pair of objects compute the parameters djk
  min(Ej,Ek)2?jk2 for ?jk?0
• Find the smallest object from djB,djk. If this
  is a djB, remove it from the list of objects.
  Else, if it is a djk combine the two objects
  according to some recombination scheme
• eg 4momentum addition
• Repeat stages 1 - 2 until some stopping criteria
  is fulfilled
• eg some Jet Multiplicity

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Analysis - Cuts

• Require
• gt20GeV missing pT
• At least one isolated lepton with pTgt20GeV,
  ?lt2.5
• Remove all isolated leptons from the list of
  objects, and run the jet finder
• Cone (Radii of 0.4 and 0.7)
• KtJet (Exclusive Mode - Cluster to 4 jets)
• Require at least 4 jets with pTgtptcut and ?lt2.5
  Cone like
• Require 2 b-tagged jets Truth

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W reconstruction

• Choice of two light jets as W candidate - for
  events with only two light jets, plot their
  invariant mass
• Keep W candidates that lie within 5? of the peak
  value, mjj.
• From the remaining W candidates, the W which
  minimises ?2 is chosen
• If this W lies in a mass window of ?2?W then it
  is accepted Cone like?

PxCone (R0.4)
KtJet
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W purity
Before the ?2?W cut
Seems to reconstruct the W better than PxCone
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Top Reconstruction

• To reconstruct the top, choose the b quark which
  results in the highest pT top combined with the W
  candidate later on use leptonic top - missing
  pT

KtJet
PxCone (R0.4)
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Top purity/efficiency
(Slightly) higher purity for low ptcut
Lower efficiency
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Sub-Event Analysis

• Merging scales - eg the scale at which the event
  changes from 5 jets to 4jets
• One can cut on the different merging scales
  (peturbative observables) in the event

Eg ptcut 40GeV Red - good top candidates Blue
- bad top candidates
Cut? ?
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A fifth jet (Hard Gluon emission)

• So far always ran KtJet in the Exclusive mode,
  clustering until there were 4 jets
• The signal (ttbar - Golden Channel) could include
  an additional jet from
• The emission of a hard gluon - O(?S) effect
• Extra jets from soft underlying event (In a
  fraction of events the hardest 4 jets may not
  be from the signal)
• Expect increase in efficiency
• The emission of a hard gluon will alter the
  structure of the event - sub jet analysis

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Results - W purity
Before the ?2?W cut

• Drop in purity
• expected!
• Can we improve with
• Subjet analysis?

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Results - Top purity/efficiency
Significant increase in efficiency - factor of 2
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Theoretical Work
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• Dipole subtraction Method
• In general at NLO a jet observable will have two
  contributions
• Real emissions
• Virtual loops
• These graphs are integrated over different
  phase spaces (m parton, m1 parton)
• A method for canceling all infrared and collinear
  divergences for a general jet observable, that
  could be implemented in a Monte Carlo
• Nuc. Phys. B 485 (1997) 291-419
• Nuc. Phys. B 627 (2002) 189-265
• Possible extension is to a case with a massive
  parton in the initial state (eg tops)
• Interesting phenomenology?
• Resummation
• First measurement of bb cross section at
  Tevatron disagreed with NLO calculation by a
  factor of 2

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Extras - (1) Mid-point Cone

• The IR safety of an Iterating Cone Algorithm is
  ensured by considering the mid-point of any pair
  of proto-jets as a seed direction

(Figure courtesy of Mike Seymour)
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Extras - (2) Infrared Safety

• At NLO individual Feynman diagrams contain IR
  divergences - in any observable, these should
  cancel (eg the ee-?jets cross section)
• When we define some observable, eg the 3 jet
  cross section, we must make sure that if a
  diagram with a divergence contributes to this,
  the diagram(s) which cancel it also contribute

3 jet
2 jet