1. A Comparison Between Different Jet Algorithms for top mass Reconstruction Chris Tevlin University of Manchester (Supervisor - Mike Seymour) Atlas UK top Meeting - RAL Nov 2005

2. Overview Introduction - Jet Algorithms Motivation - Why use KtJet? Analysis - Pre-selection Cuts - W reconstruction - top reconstruction - Inclusion of extra (5th) jet Conclusion

3. 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

4. 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

5. The Algorithm (Atlfast) 1. Find the object with the highest pT 2. Draw a fixed cone of Radius R around this in  -  space. All objects inside this are combined to form a ‘pre-cluster’ [combination scheme almost pT weighted!] 3. If the pT of the pre-cluster is above a threshold (default 5GeV) it becomes a cluster, and all objects that ended up in this cluster are removed from the list of objects

6. The Algorithm (PxCone) 1. For each seed object: 2. Draw a cone of radius R around it in  -  space 3. Add the momenta of all objects inside this cone according to some recombination scheme 4. If the direction of this result is different from the original seed direction, define the result to be the new seed direction and repeat steps 2-3 5. If this has not already been found, add it to the list of proto-jets 6. Consider the mid-point between each pair of proto-jets to be a seed direction and repeat steps 2-5

7. 7. Delete all proto-jets with more than 75% of their transverse energy contained within higher transverse energy proto-jets 8. Assign all particles that are in more than one proto-jet to the one whose centre is nearest in  -  space. 9. Delete all proto-jets whose transverse energy is less than 5GeV. All remaining proto-jets are now called jets

8. Clustering Algorithms (KtJet) Kinematically motivated [‘undoing’ the parton shower] Theoretically favoured Manifestly Infrared and Collinear Safe All objects assigned exclusively to one jet

9. The algorithm (Exclusive Mode) 1. For each object, j, compute the closeness parameter d jB, [(E j  jB ) 2 for  jB  0] and for each pair of objects compute the parameters d jk [min(E j,E k ) 2  jk 2 for  jk  0] 2. Find the smallest object from {d jB,d jk }. If this is a d jB, remove it from the list of objects. Else, if it is a d jk combine the two objects according to some recombination scheme [eg 4momentum addition] 3. Repeat stages 1 - 2 until some stopping criteria is fulfilled [eg some Jet Multiplicity]

10. 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:

11. 1. In order to perform a perturbative calculation one would need to know geometry of detector, cell thresholds etc 2. Since the angular extent of calorimeter cells, and cell energy thresholds are small, each term in such a calculation would be large - poor convergence!

12. 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?)

13. Analysis - Cuts Require >20GeV missing pT At least one isolated lepton with pT>20GeV, |  |<2.5 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 pT>ptcut and |  |<2.5 [Cone like] Require 2 b-tagged jets [Truth]

14. 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. KtJet PxCone (R=0.4)

15. W reconstruction 2 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?]

16. W purity [Before the  2  W cut] Seems to reconstruct the W better than PxCone

17. 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 (R=0.4)

18. Top purity/efficiency (Slightly) higher purity for low ptcut Lower efficiency

19. Subjet 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? 

20. A fifth jet 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

21. Hard Gluon Emission The emission of a hard gluon will alter the structure of the event - sub jet analysis

22. Results - W purity [Before the  2  W cut] Drop in purity -expected! Can we improve with Subjet analysis?

23. Results - Top purity/efficiency Significant increase in efficiency - factor of 2

24. Conclusion Cone algorithm in ATHENA is unsafe - can we implement a safe version [or even run analyses with KtJet too!] Simple ‘Cone like’ analysis - KtJet/PxCone perform similarly Can we improve on this using: Subjet analysis (purity)? Higher Multiplicity (efficiency)? Still plenty of work to be done. In progress: Atlfast Studies - Very Important! Backgrounds - Wbb+jets (ALPGEN)

25. 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)

26. Extras - (2) Infrared Safety At NLO individual Feynman diagrams contain IR divergences - in any observable, these should cancel (eg the e + e -  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 ‘2 jet’‘3 jet’