Jet Substructure Tools for the LHC

1. Jet Substructure Toolsfor the LHC • Jonathan Walsh • University of Washington • arXiv: 0903.5081, 0911.xxxx • Collaborators: • Steve Ellis, Chris Vermilion • tinyurl.com/jetpruning

2. Overview • Jets and jet substructure • Parts of jet substructure • 1→2 processes (QCD, decays) • The QCD shower and the role of the jet algorithm • Finding heavy particles with jet substructure • Example: reconstructing the top quark • Pruning to improve heavy particle identification

3. Jets • Hard interactions in QCD produce collimated sprays of hadrons: jets • A jet algorithm builds jets (single 4-vectors) from a set of protojets (final state particles or calorimeter cells) • Not a unique procedure - a jet algorithm deals with color singlets! • Two main classes of jet algorithms: cone algorithms and recombination algorithms • Cone: Fits jets to a geometric shape • Recombination: Iteratively builds jets from protojets

4. Jets at the LHC • The LHC steps into a new frontier with jets and QCD • Heavy jets (masses > mEW, mtop) • Jets as a background to many signals of new physics • Complex backgrounds must be well understood • Good development of jet algorithms and jet-based analyses • Jet substructure offers a tool in understanding the physics of jets beyond jet counting • Jets become more useful in discriminating between signals and backgrounds

5. Recombination Algorithms • Recombination algorithms build jets from protojets with repeated 2→1 mergings • Two metrics determine the order of recombinations and promotions to jets: • The recombination metric : pairwise distance between protojets • The beam metric : distance for single protojets • Find the smallest of all the • If it is a , merge the protojets by adding their four-momenta: • If it is a , promote that protojet to a jet • Repeat until all protojets are in jets

6. Recombination Algorithms QCD jet recombined with CA • Recombination metrics for kT, CA: • Beam metrics for kT, CA: pT: momentum transverse to the beam direction ΔR: an angular measure used at hadron colliders low pTtohigh pT

7. Jet Substructure • A jet algorithm condenses many degrees of freedom into a single 4-vector — is information not being utilized? • kT, CA recombination algorithms based on the dominant physics of QCD • Can we use the jet substructure to tell us something about the physics of the jet? • Does it come from the decay of a heavy particle? The algorithm metric affects the substructure - introduces bias interpret last recombinations as a heavy particle or QCD jet

8. Variables for Recombination Algorithms • Useful variables for a recombination ( ): • Recombination metrics: • QCD and decays have different dynamics • QCD gives smaller than a decay (flat in ) and

9. 1→2 Decay in a Jet • Goal is to identify jets reconstructing a heavy particle and separate them from QCD jets • Take a 1→2 decay reconstructed in a jet, massless daughters • Requirement to be in a jet: - algorithm independent • Look at the decay in terms of the algorithm variables Large D is needed to reconstruct jets with a lower boost - use D = 1.0

10. 1→2 Decay in a Jet No enhancement at the lower limit in - unlike QCD Enhancement at the lower limit for - like QCD Decays not reconstructed: small , large J rest frame lab frame J (boost to the lab) J 2 2 1 beam direction 1

11. QCD Splittings Take a leading-log approximation of QCD: For small angles - good approximation for a splitting in a jet: This lets us fix (or ). Distribution in :

12. QCD Splittings: and Fix ( ), find distributions in and Limits set by the kinematics QCD will have many more soft (small ) splittings than decays do - QCD splittings are small , small enhanced Enhancement at the lower limit in - like decays Enhancement at the lower limit in - unlike decays

13. Dynamics of QCD and Decays: • Distributions in nearly identical (for fixed boost) • QCD enhanced at small , • Will these be represented in the last recombinations of a jet?

14. Effects of the Jet Algorithm • Recombination metrics: • Recombinations are almost always monotonic in the metric • The algorithm cuts out phase space in as it proceeds CA kT pTp dependent boundaries late intermediate late intermediate early early

15. Recombination Algorithms QCD jet recombined with CA low pTtohigh pT

16. Typical Late Recombinations • Late recombinations are set by the available phase space • For CA, must be near D, and the phase space tends to create small recombinations • For kT, will be larger, with a pT dependent cut • The soft (small ) radiation is recombined earlier in kT, meaning it is harder to identify - leads to poor mass resolution

17. Typical Late Recombinations • Late recombinations are set by the available phase space • For CA, must be near D, and the phase space tends to create small recombinations • For kT, will be larger, with a pT dependent cut • The soft (small ) radiation is recombined earlier in kT, meaning it is harder to identify - leads to poor mass resolution Matched QCD sample (2, 3, 4 partons) from MadGraph/Pythia, jet pT between 500-700 GeV last recombination last recombination

18. Top Quark Decay: Reconstruction with CA • In reconstructed tops, the W can be “buried” in the substructure In reconstructed parton level top decays, the opening angle of the W can be much less than the top The W reconstruction can happen much earlier in the algorithm than the top reconstruction

19. Top Quark Decay: Reconstruction with CA • The reconstruction rate is worse at higher pT • In reconstructed tops, the W can be “buried” in the substructure - tt sample from MadGraph/Pythia In reconstructed parton level top decays, the opening angle of the W can be much less than the top jets with the top mass jet pT: 200-500 GeV jets with the top mass jet pT: 500-700 GeV The W reconstruction can happen much earlier in the algorithm than the top reconstruction

20. Summary: Identifying Reconstructed Decays in Jets • Reconstruction of a decay can be hidden in the substructure • The jet algorithm significantly shapes the jet substructure • CA strongly shaped • Poorer mass resolution for kT • A method to deal with these issues: modify the jet substructure to remove algorithm effects, improve mass resolution, background rejection, and heavy particle identification - pruning

21. Jet substructure modification techniques • Techniques were previously developed that modify the jet substructure to improve identification of certain particles and better reject their backgrounds. • Higgs (MD-F) - Butterworth, Davison, Rubin, Salam • Top (top-tagging) - Kaplan, Rehermann, Schwartz, Tweedie • B-violating neutralino decays (more recent) - Butterworth, Ellis, Raklev, Salam • Pruning is based on the same principles - the jet substructure contains recombinations that obscure the physics of the jet. Removing these helps determine the source of the jet. • Pruning takes a more general approach, based on understanding the jet substructure and the role of the jet algorithm. It is intended to be used on a wide range of signals.

24. Pruning • Pruning removes soft, large angle recombinations from the substructure • Definition: • Start with jets found by an algorithm (e.g., CA) • Run CA or kT on the initial protojets in each jet. At each recombination, test whether: • If this is true, prune the recombination by vetoing on the merging and discarding the softer protojet. • Resulting jets are pruned jets. • and are parameters of the pruning procedure, and we will motivate reasonable values for them.

25. Pruning in Action typical jet Pruning of a QCD jet near the top mass with the CA algorithm Red is higher pT Blue is lower pT Green X is a pruning Start with cells with energy > 1 GeV pT: 600 → 590 GeV mass: 170 → 160 GeV

26. Pruning in Action atypical jet Pruning of a QCD jet near the top mass with the CA algorithm Red is higher pT Blue is lower pT Green X is a pruning Start with cells with energy > 1 GeV pT: 600 → 550 GeV mass: 180 → 30 GeV

27. Pruning studies • Quantify the performance of pruning: • Top reconstruction • W reconstruction • Do a comparison study - compare pruned jets to unpruned jets • Define a set of cuts to select “top” jets and “W” jets in signal and background samples • Use statistical measures to quantify the improvement that pruning the jets gives to signal identification and background separation • Also look at underlying event rejection

28. Monte Carlo samples • Monte Carlo samples (MadGraph + Pythia, no detector simulation): • Top study: • Signal: top pair production, all hadronic decays • Background: matched QCD multijet background (2, 3, 4 partons) • W study: • Signal: W pair production, 1 hadronic and 1 leptonic decay • Background: matched W+jets background (1, 2 partons), W decays leptonically • Divide each sample into 4 pT bins - will be useful to study the D dependence of heavy particle finding and pruning • Bin particles in massless calorimeter cells

29. Top and W jets • Define top and W jets by jet mass and subjet mass cuts • For each mass cut, fit the signal mass distribution with a Breit-Wigner, mass range is • Top jet: jet in the top mass range, daughter subjet in the W mass range • W jet: jet in the W mass range Breit-Wigner with skew sample fit : peak width : peak mass

30. Statistical Measures • Select jets in each pT bin and define jet counters: : number of top/W jets in the signal with (pA) and without (A) pruning : number of top/W jets in the background with (pA) and without (A) pruning

31. Statistical Measures • Select jets in each pT bin and define jet counters: • Relative measures to quantify pruning: : number of top/W jets in the signal with (pA) and without (A) pruning : number of top/W jets in the background with (pA) and without (A) pruning : relative efficiency, signal-to-background, signal-to-noise

32. Statistical Measures • Select jets in each pT bin and define jet counters: • Relative measures to quantify pruning: • If a measure > 1, pruning has improved over not pruning • Also add the relative jet mass width, - it tends to drive : number of top/W jets in the signal with (pA) and without (A) pruning : number of top/W jets in the background with (pA) and without (A) pruning : relative efficiency, signal-to-background, signal-to-noise

33. Ranges for the pruning parameters • No pruning when is small or is large no pruning no pruning

34. Ranges for the pruning parameters • No pruning when is small or is large • For large, we get over-pruning • Decreased improvements, good mass resolution no pruning no pruning over-pruning

35. Ranges for the pruning parameters • No pruning when is small or is large • For large, we get over-pruning • Decreased improvements, good mass resolution • For small, we get over-pruning • Decreased improvements, poor mass resolution no pruning no pruning over-pruning over-pruning “shower” pruning

36. Ranges for the pruning parameters • No pruning when is small or is large • For large, we get over-pruning • Decreased improvements, good mass resolution • For small, we get over-pruning • Decreased improvements, poor mass resolution • Findand are good choices for both the top and W studies • is an IR-safe measure of the opening angle of the jet no pruning optimal pruning no pruning over-pruning over-pruning shower pruning

37. Top and W Mass Ranges top study W study Pruning (open symbols)reduces the mass range of the reconstructed particles significantly

38. top study Results for pruning: CA jets kT jets • Look at statistical measures over all 4 pT bins, using a constant D = 1.0 • Pruning shows consistent improvements, dramatically increasing at high pT • Most noticeable: large differences in between CA and kT jets • CA is poor at identifying the W subjet to the top at high pT with D = 1.0 • Statistical error bars shown

39. W study W finding results: CA jets kT jets • For the W study, pruning also shows improvements over not pruning • The performances of CA and kT are similar - no subjet cut to find W jets • The same pruning parameters were used for the W study • For a search, pruning has good performance for a variety of signals without tuning the procedure

40. Results of Pruning • Pruning shows increased significance over not pruning, better mass resolution • Both top and W studies • Why does pruning perform much better at high pT? • The decay is collimated in the jet - extra phase space for wide angle radiation

41. D dependence of pruning • Pruning showed increasing improvements at higher pT • Pruning is able to remove wide angle radiation contributing to poor mass resolution • Test whether pruning jets with a smaller D at higher pT is better than using a constant D = 1.0 • Choose D value fit to the boost of the heavy particle for each pT bin • A good approximation: D = 2m/pT • Compare pruning with ‘fitted’ D to fixed D = 1.0 using the same statistical measures - label them • A measure > 1 (e.g, ) means pruning with fitted D improves over pruning with D = 1.0 (in that measure) • Also compare pruning to not pruning with a ‘fitted’ D

42. D Dependence: Pruning with Fitted D Compared to Fixed D top study W study CA jets kT jets CA jets kT jets The improvements in using a fitted D are minimal!

43. Comparing Pruning and Not Pruning with Fitted D top study W study CA jets kT jets CA jets kT jets Consistent improvements using pruning over a range in D

44. Underlying Event Rejection with Pruning The mass resolution of pruned jets is unchanged with or without the underlying event top study no pruning pruning CA kT

45. Conclusions • Jet substructure is a complex beast: • Shaping effects mean we cannot directly interpret the last recombinations as meaningful to the physics of the jet • Reconstructed decays may be obscured in the substructure • Pruning reduces many of the systematic effects and improves the ability to identify reconstructed heavy particle decays • Studies on top and W reconstruction are promising • Pruning reduces the D dependence in a search

46. What’s next for jet substructure? • Verification of jet substructure tools at the LHC • Rediscovery of the Standard Model a good testing ground • Build on our understanding of the relationship between the jet algorithm and the dynamics of jets • Identify the best variables to discriminate between QCD and non-QCD jets - currently masses are the most studied • Attack jet substructure with a more powerful theoretical framework • SCET offers a nice approach • Jet substructure studies can help improve Monte Carlo tools (e.g., matching)

47. Thank you

48. Approach to Jet Substructure • Goal: identify jets reconstructing a heavy particle decay, separate them from QCD jets • Focus on mass variables for jet substructure • Jet and subjet masses (e.g., a top quark jet has the top mass and a subjet with the W mass) • Use wide angle jets - reconstruct a higher fraction of decays • Identify jet substructure techniques to improve heavy particle identification and background rejection

49. Approach to Jet Substructure Want to understand 3 aspects: 1. What are the kinematics and dynamics of a 1→2 decay, splitting in QCD?

50. Approach to Jet Substructure Want to understand 3 aspects: 1. What are the kinematics and dynamics of a 1→2 decay, splitting in QCD? 2. How does this manifest in the last recombinations of a jet? 3. How does the jet algorithm affect the substructure?