Understanding and Using Jet Substructure at the LHC

1. Understanding and UsingJet Substructureat the LHC • Jonathan Walsh • University of Washington • arXiv: 0903.5081, 0910.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? • Some recombination algorithms (kT, CA) 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. Approach to Jet Substructure Want to understand 3 aspects: 1. What are the kinematics and dynamics of a 1→2 decay, splitting in QCD?

9. 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?

10. Phase Space for Recombination Algorithms • Useful variables for a recombination ( ): • Recombination metrics: • Look at the phase space for single recombinations in terms of and

11. Phase Space for 1→2 m1 = 0, m2 = 0 m1 = 0.46, m2 = 0 • The allowed phase space in , for a fixed is nearly one-dimensional • QCD and decays will weight the phase space differently • Cutoffs on variables set by the kinematics, not the dynamics • Sample of phase space slices for different subjet masses, m1 = 0.9, m2 = 0 m1 = 0.3, m2 = 0.1

12. 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 (m1 = m2 = 0) • 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

13. 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

14. 1→2 Decay in a Jet a1 = 0, a2 = 0 Cutoffs are set by the kinematics - same between QCD and decay with fixed No enhancement at the lower limit in - unlike QCD Enhancement at the lower limit for - like QCD

15. 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 :

16. QCD Splittings: and a1 = 0, a2 = 0 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

17. 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?

18. 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

19. Reconstruction in a Jet • When can a decay be reconstructed in the final recombinations of a jet? • As the algorithm proceeds, more of the phase space is cut out by previous recombinations • Algorithm dependent effect • Certain decays will be reconstructed earlier in the algorithm, or not at all late intermediate late intermediate early early

20. 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

21. Comparing CA and kT: • Final recombinations for CA not QCD-like • No enhancement at small • Final recombinations for kT more QCD-like • Enhanced at small and • kT has poorer mass resolution • Soft objects recombined early in algorithm - more merged - tt sample from MadGraph/Pythia jet pT between 500-700 GeV

22. 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

23. 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

24. 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

25. 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.

26. Other jet substructure methods • Many other techniques use jet substructure to study jets and ID heavy particles: • y variable - Butterworth, Cox, Forshaw; Butterworth, Ellis, Raklev • ‘z’ variables - Thaler, Wang • shape variables - Almeida, Lee, Perez, Sterman, Sung, Virzi • new algorithms (variable R) - Krohn, Thaler, Wang • Groups have also pioneered new jet algorithms and techniques to analyze jets - from algorithm comparisons to the underlying event and pileup studies • Salam, Cacciari, Soyez, Rubin, Rojo • Reviews by Salam; Ellis, Huston, Hatakeyama, Loch, Tonnesmann

27. 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.

28. 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

29. 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

30. 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

31. 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

32. 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

33. 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

34. 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

35. 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

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

37. 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

38. 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

39. 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

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

41. 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

42. 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

43. 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

44. 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

45. 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!

46. 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

47. 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

48. 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

49. What’s next for jet substructure? • 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) • Verification of jet substructure tools at the LHC • Rediscovery of the Standard Model a good testing ground

50. Thank you