Top Physics at the LHCTop Physics at the LHCManchester Christmas Meeting 2006Manchester Christmas Meeting 2006

Chris TevlinChris Tevlin

OutlineOutline

Experimental Work:Experimental Work: Comparison of two jet algorithms for reconstructing the top massComparison of two jet algorithms for reconstructing the top mass

Theoretical Work (to do!):Theoretical Work (to do!): Understanding/extending the dipole subtraction methodUnderstanding/extending the dipole subtraction method ResummationResummation Application of these to ttbar cross sectionApplication of these to ttbar cross section

Experimental WorkExperimental Work

Introduction - Jet AlgorithmsIntroduction - Jet Algorithms QCD - confinement (only colour singlets propagate over macroscopic QCD - confinement (only colour singlets propagate over macroscopic

distances)distances) No unique method of assigning (colourless) hadrons to (coloured) partonsNo unique method of assigning (colourless) hadrons to (coloured) partons Require a ‘sensible’ definition of a Jet - two of the main types of algorithm Require a ‘sensible’ definition of a Jet - two of the main types of algorithm

are:are: Cone AlgorithmsCone Algorithms Cluster AlgorithmsCluster Algorithms

Cone AlgorithmsCone Algorithms Geometrically motivatedGeometrically motivated

Fixes the angular extent of a jet with Radius in Fixes the angular extent of a jet with Radius in -- space (R space (R invariant under boosts along the beam direction)invariant under boosts along the beam direction)

Requires some prescription for removing overlaps between jetsRequires some prescription for removing overlaps between jets Not manifestly Infrared and collinear safe [Atlfast!]Not manifestly Infrared and collinear safe [Atlfast!]

Some Cone Algorithms UnsafeSome Cone Algorithms Unsafe ‘‘Mid-point’ Cone Algorithms SafeMid-point’ Cone Algorithms Safe

Clustering Algorithms (KtJet)Clustering Algorithms (KtJet) Kinematically motivated Kinematically motivated

[‘undoing’ the parton shower][‘undoing’ the parton shower] Theoretically favouredTheoretically favoured

Manifestly Infrared and Collinear SafeManifestly Infrared and Collinear Safe All objects assigned exclusively to one jetAll objects assigned exclusively to one jet

Motivation (Theoretical Issues)Motivation (Theoretical Issues)

Infrared safety - the algorithm is insensitive to the addition arbitrarily soft Infrared safety - the algorithm is insensitive to the addition arbitrarily soft partonspartons

Collinear safety - the algorithm is insensitive to the replacement of any Collinear safety - the algorithm is insensitive to the replacement of any (massless) object by a pair of (massless) collinear objects(massless) object by a pair of (massless) collinear objects

Infrared safety - IR and Collinear safetyInfrared safety - IR and Collinear safety Some Algorithms are classified as ‘Infrared Almost Safe’. The algorithm is Some Algorithms are classified as ‘Infrared Almost Safe’. The algorithm is

rendered safe in the presence of a detector with finite energy resolution and rendered safe in the presence of a detector with finite energy resolution and angular granularity - this is dangerous for several reasons:angular granularity - this is dangerous for several reasons:

1.1. In order to perform a perturbative calculation one would need to know geometry of In order to perform a perturbative calculation one would need to know geometry of detector, cell thresholds etcdetector, cell thresholds etc

2.2. Since the angular extent of calorimeter cells, and cell energy thresholds are small, Since the angular extent of calorimeter cells, and cell energy thresholds are small, each term in such a calculation would be large - poor convergence!each term in such a calculation would be large - poor convergence!

Motivation (Experimental Issues)Motivation (Experimental Issues) In the ‘Golden Channel’ the top mass reconstructed from 3 jetsIn the ‘Golden Channel’ the top mass reconstructed from 3 jets By clustering to a specific jet multiplicity, one may hope toBy clustering to a specific jet multiplicity, one may hope to

Remove the soft underlying event (Exclusive Mode)Remove the soft underlying event (Exclusive Mode) Solve Combinatorial issuesSolve Combinatorial issues Increase the purity of the sample (pay in efficiency?)Increase the purity of the sample (pay in efficiency?)

The algorithm (Exclusive Mode)The algorithm (Exclusive Mode)

1.1. For each object, j, compute the closeness parameter dFor each object, j, compute the closeness parameter d jBjB, [(E, [(EjjjBjB))2 2 for for jBjB0] 0] and for each pair of objects compute the parameters dand for each pair of objects compute the parameters d jkjk [min(E [min(Ejj,E,Ekk))22jkjk

2 2 for for jkjk0]0]

2.2. Find the smallest object from {dFind the smallest object from {djBjB,d,djkjk}. If this is a d}. If this is a djBjB, remove it from the list of , remove it from the list of objects. Else, if it is a dobjects. Else, if it is a djkjk combine the two objects according to some combine the two objects according to some recombination scheme recombination scheme

[eg 4momentum addition][eg 4momentum addition]3.3. Repeat stages 1 - 2 until some stopping criteria is fulfilled Repeat stages 1 - 2 until some stopping criteria is fulfilled

[eg some Jet Multiplicity][eg some Jet Multiplicity]

Analysis - Cuts Analysis - Cuts

RequireRequire >20GeV missing pT>20GeV missing pT At least one isolated lepton with pT>20GeV, |At least one isolated lepton with pT>20GeV, ||<2.5|<2.5

Remove all isolated leptons from the list of objects, and run the jet finder:Remove all isolated leptons from the list of objects, and run the jet finder: Cone (Radii of 0.4 and 0.7)Cone (Radii of 0.4 and 0.7) KtJet (Exclusive Mode - Cluster to 4 jets)KtJet (Exclusive Mode - Cluster to 4 jets)

Require at least 4 jets with pT>ptcut and |Require at least 4 jets with pT>ptcut and ||<2.5 [Cone like]|<2.5 [Cone like] Require 2 b-tagged jets [Truth]Require 2 b-tagged jets [Truth]

W reconstructionW reconstruction Choice of two light jets as W candidate - for events with only two light jets, Choice of two light jets as W candidate - for events with only two light jets,

plot their invariant massplot their invariant mass

Keep W candidates that lie within ±5Keep W candidates that lie within ±5 of the peak value, mjj. of the peak value, mjj. From the remaining W candidates, the W which minimises From the remaining W candidates, the W which minimises 22 is chosen is chosen

If this W lies in a mass window of If this W lies in a mass window of 22WW then it is accepted [Cone like?] then it is accepted [Cone like?]

KtJet PxCone(R=0.4)

W purityW purity

[Before the 2W cut]Seems to reconstruct the W better than PxCone

Top ReconstructionTop Reconstruction To reconstruct the top, choose the b quark which results in the highest pT 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]top combined with the W candidate [later on use ‘leptonic top’ - missing pT]

KtJet PxCone(R=0.4)

Top purity/efficiencyTop purity/efficiency

(Slightly) higher purity for low ptcut

Lower efficiency

Sub-Event AnalysisSub-Event Analysis Merging scales - eg the scale at which the event changes from 5 jets to Merging scales - eg the scale at which the event changes from 5 jets to

4jets4jets One can cut on the different merging scales (peturbative observables) in the One can cut on the different merging scales (peturbative observables) in the

eventevent

Eg ptcut = 40GeV

Red - good top candidatesBlue - bad top candidates

Cut?

A fifth jet (Hard Gluon emission)A fifth jet (Hard Gluon emission) So far always ran KtJet in the Exclusive mode, clustering until there were 4 So far always ran KtJet in the Exclusive mode, clustering until there were 4

jetsjets The signal (ttbar - Golden Channel) could include an additional jet from:The signal (ttbar - Golden Channel) could include an additional jet from:

The emission of a hard gluon - O(The emission of a hard gluon - O(SS) effect) effect

Extra jets from soft underlying event (In a fraction of events the ‘hardest’ Extra jets from soft underlying event (In a fraction of events the ‘hardest’ 4 jets may not be from the signal)4 jets may not be from the signal)

Expect increase in efficiencyExpect increase in efficiency The emission of a hard gluon will alter the structure of the event - sub jet The emission of a hard gluon will alter the structure of the event - sub jet

analysisanalysis

Results - W purityResults - W purity

[Before the 2W cut]Drop in purity -expected!

Can we improve withSubjet analysis?

Results - Top purity/efficiencyResults - Top purity/efficiency

Significant increase in efficiency - factor of 2

Theoretical ‘Work’Theoretical ‘Work’

Dipole subtraction MethodDipole subtraction Method In general at NLO a jet observable will have two contributions:In general at NLO a jet observable will have two contributions:

Real emissionsReal emissions Virtual loopsVirtual loops

These ‘graphs’ are integrated over different phase spaces (m parton, m+1 These ‘graphs’ are integrated over different phase spaces (m parton, m+1 parton) parton)

A method for canceling all infrared and collinear divergences for a A method for canceling all infrared and collinear divergences for a generalgeneral jet observable, that could be implemented in a Monte Carlo jet observable, that could be implemented in a Monte Carlo

[Nuc. Phys. B 485 (1997) 291-419][Nuc. Phys. B 485 (1997) 291-419][Nuc. Phys. B 627 (2002) 189-265][Nuc. Phys. B 627 (2002) 189-265]

Possible extension is to a case with a massive parton in the initial state (eg Possible extension is to a case with a massive parton in the initial state (eg tops)tops)

Interesting phenomenology?Interesting phenomenology?

ResummationResummation First measurement of bb cross section at Tevatron disagreed with NLO First measurement of bb cross section at Tevatron disagreed with NLO

calculation by a factor of ~2calculation by a factor of ~2

Extras - (1) Mid-point Cone Extras - (1) Mid-point Cone The IR safety of an Iterating Cone Algorithm is ensured by considering the The IR safety of an Iterating Cone Algorithm is ensured by considering the

mid-point of any pair of proto-jets as a seed directionmid-point of any pair of proto-jets as a seed direction

(Figure courtesy of Mike Seymour)

Extras - (2) Infrared SafetyExtras - (2) Infrared Safety

At NLO individual Feynman diagrams contain IR divergences - in any At NLO individual Feynman diagrams contain IR divergences - in any observable, these should cancel (eg the eobservable, these should cancel (eg the e++ee--jets cross section)jets cross section)

When we define some observable, eg the 3 jet cross section, we must make 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) sure that if a diagram with a divergence contributes to this, the diagram(s) which cancel it also contributewhich cancel it also contribute

‘2 jet’ ‘3 jet’