Top Physics at the LHC

1. Top Physics at the LHC Manchester Christmas Meeting 2006 Chris Tevlin

2. 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

3. Experimental Work

4. 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

5. 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

6. 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!

7. 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?)

8. 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]

9. 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]

10. 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 (R=0.4) KtJet

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

12. 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] PxCone (R=0.4) KtJet

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

14. 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? 

15. 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

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

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

18. Theoretical ‘Work’

19. 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, m+1 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

20. 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)

21. 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 ‘3 jet’ ‘2 jet’