1. Jets in top quark mass measurement Tobias Göttfert IMPRS colloquium 13 th June 2008

2. Max-Planck Institut für Physik What is a jet? According to Wikipedia, „jet“ has more than 60 meanings:  a stream of material  an aircraft propelled by a reaction engine that discharges a fast moving jet of fluid to generate thrust  an experimental nuclear fusion reactor (Joint European Torus)  the name of various bands  the name of various sports teams  the name of various movie and comic characters  a town in Alfalfa County, Oklahoma, USA  a cone of hadrons 13.6.2008Jets for top mass measurement 2

3. Max-Planck Institut für Physik What is a jet?  Experimentalist: „A jet is a narrow aggregation of energy deposit in my calorimeter“  Theorist: „A jet is the colour-singlet final state of a parton after undergoing the non-perturbative QCD known as fragmentation and hadronisation“  Goal: reconstruct parton properties from observables of the jet 13.6.2008Jets for top mass measurement 3

4. Max-Planck Institut für Physik Jet algorithms  provide a prescription to make jets that is feasible in both theory and experiment  reconstruct the observables of parton that made the jet Two big classes of algorithms: 13.6.2008Jets for top mass measurement 4 Cone-type (successive) Clustering- type

5. Max-Planck Institut für Physik Cone-type jet algorithms  many variants around: „basic cone“, mid-point-iterating, SiSCone  well-established in hadron collider physics  basic principle: look at cones with fixed radius in η-φ-space: ΔR 2 = Δφ 2 +Δη 2 (φ : Azimuthal angle η : Pseudorapidity η = - ln tan (θ/2) ) 13.6.2008Jets for top mass measurement 5 basic cone algorithm: 1. choose seed directions 2. calculate jet axis for every cone of fixed radius (e.g. 0.4) around the seed directions 3. if jet axis and seed direction are not equal, let jet axis become the new seed direction and go back to 2. 4. take all individual stable jets remaining basic cone algorithm: 1. choose seed directions 2. calculate jet axis for every cone of fixed radius (e.g. 0.4) around the seed directions 3. if jet axis and seed direction are not equal, let jet axis become the new seed direction and go back to 2. 4. take all individual stable jets remaining

6. Max-Planck Institut für Physik Standard cone how-to 13.6.2008Jets for top mass measurement 6 all clusters of one event in the η-φ-plane

7. Max-Planck Institut für Physik Standard cone how-to 13.6.2008Jets for top mass measurement 7 cone jets with R=0.4 cone jets with R=0.4

8. Max-Planck Institut für Physik Standard cone how-to 13.6.2008Jets for top mass measurement 8 cone jets with R=0.4 + true partons from ttbar decay cone jets with R=0.4 + true partons from ttbar decay μ+ν b b b b light quarks

9. Max-Planck Institut für Physik Standard cone how-to 13.6.2008Jets for top mass measurement 9 cone jets with R=0.7 cone jets with R=0.7 unwanted merging of two jets unwanted merging of two jets

10. Max-Planck Institut für Physik Cone-type jet algorithms Pros:  fast and easy to apply in experiment  well-known and tuned over years Cons:  not a one-to-one mapping, need to treat overlaps  not infrared-safe, not collinear-safe (can be overcome by a more complicated algorithm) 13.6.2008Jets for top mass measurement 10

11. Max-Planck Institut für Physik Clustering-type jet algorithms  known as Durham or k T algorithm  originally developed for lepton collider experiments, extended to hadron physics  extremely flexible and steerable  basic principle: look at relative transverse momenta of objects as criterion to successively merge them (inspired by „reversing“ showering models)  results in „fuzzy“ jets (no cone shape) 13.6.2008Jets for top mass measurement 11

12. Max-Planck Institut für Physik Example k T algorithm The k T (exclusive mode): 1. take a list of protojets and define distances: d i = p Ti 2 d ij = min(p Ti 2, p Tj 2 ) ΔR 2 (ΔR 2 = Δφ 2 +Δη 2 ) 2. find d min, the smallest of all d i, d ij 3. if it’s a d i, declare protojet as “beam jet”, if it’s a d ij, merge the two jets i and j according to p μ ij = p μ i + p μ j (E recombination scheme) 4. iterate until d min >d cut The k T (exclusive mode): 1. take a list of protojets and define distances: d i = p Ti 2 d ij = min(p Ti 2, p Tj 2 ) ΔR 2 (ΔR 2 = Δφ 2 +Δη 2 ) 2. find d min, the smallest of all d i, d ij 3. if it’s a d i, declare protojet as “beam jet”, if it’s a d ij, merge the two jets i and j according to p μ ij = p μ i + p μ j (E recombination scheme) 4. iterate until d min >d cut 13.6.2008Jets for top mass measurement 12

13. Max-Planck Institut für Physik k T how-to 13.6.2008Jets for top mass measurement 13 all clusters of one event in the η-φ-plane

14. Max-Planck Institut für Physik k T how-to 13.6.2008Jets for top mass measurement 14 k T exclusive running k T exclusive running

15. Max-Planck Institut für Physik k T how-to 13.6.2008Jets for top mass measurement 15 jets for k T exclusive with d cut =(30GeV) 2 jets for k T exclusive with d cut =(30GeV) 2 μ+ν b b b b light quarks

16. Max-Planck Institut für Physik Clustering-type jet algorithms  Pros: well-defined in both theory and experiment, one-to-one mapping of input objects inherently infrared- and collinear-safe gives you more information about the event than just the four- momenta of resulting jets  extract information from the merging scales d min  Cons: how to treat hadron remnants in hadron collisions? computationally expensive for large multiplicities of calorimeter clusters (can be overcome by smart bookkeeping)  k T has different sources of systematic errors than cone algorithms 13.6.2008Jets for top mass measurement 16

17. Max-Planck Institut für Physik Top mass reconstruction signature in the ttbar lepton+jets channel: 13.6.2008Jets for top mass measurement 17 1 high energetic lepton missing transverse energy 2 light jets simple method of reconstructing the top mass on the hadronic side: combine those three jets whose p T sum is maximal b-jet

18. Max-Planck Institut für Physik Top mass reconstruction 13.6.2008Jets for top mass measurement 18 tri-jet mass of all selected top candidates for lepton+jets signal and various sources of background tri-jet mass of all selected top candidates for lepton+jets signal and various sources of background combinatoric background combinatoric background physics background physics background

19. Max-Planck Institut für Physik d Merge analysis  d min behaves like an event shape: the smallest relative p T when there are a certain number of jets left in the event  see whether signal and background behave differently  possibility to improve S/B with a cut 13.6.2008Jets for top mass measurement 19 cut at d min = (20GeV) 2 cut at d min = (20GeV) 2 d min for 4 jets left signal backg

20. Max-Planck Institut für Physik Conclusions  defining jets is complicated due to non-perturbative QCD effects (hadronisation, UE) and also experimental effects (pile-up)  Two major types of jet algorithms around: Cone-type and clustering-type (k T )  They suffer from different sources of systematics  combined analyses could improve on error  k T contains more information than just the four- momenta of jets  this could be used to separate signal from background or distinguish e.g. 4jet from 5jet events 13.6.2008Jets for top mass measurement 20

21. Max-Planck Institut für Physik Acknowledgments Thanks to:  Sven Menke  Stefan Kluth  arXiv:hep-ph/0609100v2  arXiv:hep-ph/9305266v1 13.6.2008Jets for top mass measurement 21