The latest and greatest tricks in studying missing energy events

1. The latest and greatest tricks in studying missing energy events Konstantin Matchev With: M. Burns, P. Konar, K. Kong, F. Moortgat, L. Pape, M. Park arXiv:0808.2472 [hep-ph], arXiv:0810.5576 [hep-ph], arXiv:0812.1042 [hep-ph], arXiv:0903.4371 [hep-ph], arXiv:0906.2417 [hep-ph], arXiv:090?.???? [hep-ph] Fermilab, LPC August 10-14, 2009

2. 67 pp 46 pp 32 pp 47 pp 37 pp Total No of pages : 229 pp These slides cover: • “A general method formodel-independentmeasurements of particle spins, couplings and mixing angles in cascade decays with missing energy at hadron colliders”, JHEP (2008) • Burns, Kong, KM, Park • “Using subsystem MT2 for complete mass determinations in decay chains with missing energy at hadron colliders”, JHEP (2009) • Burns, Kong, KM, Park • “s1/2min – a global inclusive variable for determining the mass scale of new physics in events with missing energy at hadron colliders”, JHEP (2009). • Konar, Kong, KM • “Using kinematic boundary lines for particle mass measurements and disambiguation in SUSY-like events with missing energy”, JHEP (2009) • Burns, KM, Park • “Precise reconstruction of sparticle masses without ambiguities”, JHEP (200?) • KM, Moortgat, Pape, Park

3. MET events: experimentalist’s view • What is going on here? This is why I am interested in MET!

4. Q: What do we do for a living?A: Hunt for new particles. How? • First make it, then detect it. Suppose it is: • Unstable, decays visibly to SM particles • Resonant mass peak. Example: Z’. EASY • Unstable, decays semi-visibly to SM particles • Jacobian peak (endpoint). Example: W’. EASY • Stable, charged • CHAMPs. Examples in J. Feng’s talk. EASY • Stable, neutral • Missing energy. Examples: LSP in SUSY, LKP in UED, … DIFFICULT! • Theory: Typically 2 missing particles per event, unknown mass • Experiment: MET is a challenging signature • Sociology: Don’t even try masses/spins at LHC, go to ILC.

5. e e b n W t W n W n W n t e b e Why MET signatures are important to study • Dark matter? Perhaps, but see J. Feng’s talk for counterexamples. • Challenging – need to understand the detector very well. • Guaranteed physics in the early LHC data!

6. The experimentalist asks: The theorist answers: Is it possible to have a theory model which gives signature X? Yes. No. Are there any well motivated such models? You bet. Let me tell you about those. Actually I have a paper… No. But I’m the wrong person to ask anyway. Is there any Monte Carlo which can simulate those models? MC4BSM workshops: http://theory.fnal.gov/mc4bsm/ This talk is being given • by a “theorist”

7. Ask the theorist! • Feel free to ask me questions on any topic • Some questions that I anticipate: • Suppose we discover SUSY. How would we know it is SUSY and not something else? • Almost all of our SUSY studies are based on LMx study points in MSUGRA. How much model dependence is introduced by the MSUGRA assumptions? Is it possible to design a model-independent SUSY search? • I see you wrote a paper on MT2. I keep hearing about this MT2 and could never understand what it is god for. Can you explain? • What are some safe cuts to use in our skims? Is there any magic (model-independent) cut which would cut the SM background yet preserve all of the (SUSY) signal?

8. MET events: experimentalist’s view • What is going on here?

9. MET events: theorist’s view • Pair production of new particles (conserved R, KK, T parity) • Motivated by dark matter + SUSY, UED, LHT • How do you tell the difference? (Cheng, KM, Schmaltz 2002) • SM particles xi seen in the detector, originate from two chains • How well can I identify the two chains? Should I even try? • What about ISR jets versus jets from particle decays? • “WIMPs” X0 are invisible, momenta unknown, except pT sum • How well can I reconstruct the WIMP momenta? Should I even try? • What about SM neutrinos among the xi’s?

10. In place of an outline pessimism optimism pessimism optimism

11. MET Today: invariant mass studies Hinchliffe et al. 1997 • Study the invariant mass distributions of the visible particles on one side of the event • Does not rely on the MET measurement • Can be applied to asymmetric events, e.g. • No visible SM products on the other side • Small leptonic BR on the other side • Well tested, will be done anyway. ATLAS TDR 1999 Nojiri et al. 2000 Allanach et al. 2000 Gjelsten et al. 2004

12. The classic endpoint method • Identify a sub-chain as shown. Combinatorics problem? • Form all possible invariant mass distributions • Mll, Mjll, Mjl(lo), Mjl(hi) • Measure the endpoints and solve for the masses of A,B,C,D • 4 measurements, 4 unknowns. Should be sufficient. • Not so fast! • The measurements may not be independent • Piecewise defined functions -> multiple solutions? The “ATLAS” approach

13. Lepton combinatorics Solution: OF subtraction Jet combinatorics Solution: Mixed Event subtraction Combinatorics problems

14. Example: dilepton invariant mass B on-shell MLL B off-shell MC-MA MB MA MC

15. Jet-lepton-lepton invariant mass • There are 6 different cases to consider: (Njll,-) MJLL

16. Jet-lepton invariant mass • But which is near and which is far? • Define “low” and “high” pairs as: MJL Allanach et al. 2000

17. “Low” jet-lepton pair invariant mass • 4 additional cases: (-,Njl) MJL(lo)

18. “High” jet-lepton pair invariant mass MJL(hi) • The same 4 cases as “low” jet-lepton pair: (-,Njl)

19. Recap • So far we measured the upper kinematic endpoints of four invariant mass distributions • Mll, Mjll, Mjl(lo), Mjl(hi) • They depend on 4 input masses: MA, MB, MC, MD • 4 measurements, 4 unknowns. Should be sufficient. Invert and solve for the masses. • However, 2+1 generic problems: • Piecewise defined functions -> multiple solutions? (next) • These four measurements may not all be independent, sometimes • This requires a new measurement. How precise is it?

20. How many solutions? • It could have been even worse, but 3 cases are impossible • (2,1), (2,2), (3,3) • Bad news: in (3,1), (3,2) and (2,3) the measured endpoints are not independent: (Njll,Njl) regions • The endpoints are piecewise functions of the masses • 11 cases altogether: (Njll,Njl).

21. An alternative to MJLL Nojiri et al, 2000, Allanach et al. 2000 MJLL MJLL(Ѳ>π/2) L L in the rest frame of C The MJLL(Ѳ>π/2) invariant mass “threshold”

22. MJLL versus MLL scatter plot The MJLL(Ѳ>π/2) invariant mass “threshold” Bounded by a hyperbola OWS and a line UV Lester,Parker,White 06 Burns, KM, Park (2009) , ,

23. Posing the LHC inverse problem R3 R4 R2 R1 • Njll not used: we have reduced the number of cases to four: • Njl=1, Region R1 • Njl=2, Region R2 • Njl=3, Region R3 • Njl=4, Region R4 • May cross-check the solution with (Njll,Njl) regions Find the spectrum of A,B,C,D, given the 4 endpoints

24. Solving the LHC inverse problem • Find the four masses of A, B, C, D, given the 4 endpoints • Solution: Burns, KM, Park (2009)

25. Multiple solutions? • Previously multiple solutions arose due to insufficient experimental precision or using an incomplete data set Gjelsten, Miller, Osland (2005); Gjelsten, Miller, Osland, Raklev (2006)

26. Mass ambiguities • Exactspectrum duplication in (3,1), (3,2) and (2,3) Burns, KM, Park (2009)

27. What have we learned so far? old • How the classic (ATLAS) endpoint method works • The inverse problem can be solved analytically • 5 endpoint measurements may not be enough to uniquely determine 4 masses • Good news: in theory, at most 2-fold ambiguity • Bad news: will get even worse in the real world (with error bars) • What can we do? • Improve precision at the LHC? Does not help. • Extra measurements from ILC? Expensive. • Longer decay chain? Not up to us. • Fresh new ideas? Yes! new

28. One fresh new idea Burns, KM, Park (2009) Costanzo, Tovey (2009) • Pretty obvious: a two-dimensional (scatter) plot contains more information than the two individual one-dimensional histograms. Look at the scatter plot! • There is even more information in the 3D distribution • Instead of looking for endpoints in 1D histograms, look at boundary lines in 2D scatter plots • For convenience, plot versus mass2 instead of mass • The shape of the scatter plot reveals the region Ri • Some special points provide additional measurements R1 R2 R3

29. JL scatter plots resolve the ambiguity (2,3) (3,1) (3,2) (2,3) Burns, KM, Park (2009) “Drop” • R1versus R3 “Foot” • R2versus R3

30. Precision problem • In theory OK, but • scatter plots require more statistics • the MJLL(Ѳ>π/2) “threshold” is hard to read Gjelsten, Miller, Osland (2004) Lester (2006)

31. Back to the drawing board KM, Moortgat, Pape, Park (2009) • Redesign the classic endpoint method • do not use distributions whose endpoints are piecewise-defined functions: Mjll, Mjl(lo) or Mjl(hi) • do not use the poorly measured MJLL(Ѳ>π/2) “threshold” • do not use scatter plots • derive the shapes of all differential distributions • Sounds impossible? Must introduce new observable distributions.

32. New jet-lepton distributions KM, Moortgat, Pape, Park (2009) Don’t ask, don’t tell: always use the two jet-lepton entries in a symmetric fashion • But which is near and which is far? • ATLAS: define “low” and “high” as: Allanach et al. 2000

33. The combined jet-lepton distribution • Simply plot “near” and “far” together KM, Moortgat, Pape, Park (2009) • Read the two endpoints • These two are not piecewise defined

34. The generalized sums • Plot the combination KM, Moortgat, Pape, Park (2009) • Alpha is a continuous parameter: infinitely many possibilities! • Alpha=1 is not piecewise defined:

35. The product and the difference • Unfortunately, both endpoints piecewise defined

36. The bottom line • If we use only the 4 unambiguous endpoints • The masses are found from • Despite the 2-fold near-far confusion, the answers for A, C and D are unique! • Remember that there are (infinitely) many more endpoint measurements • Allow measurement of MB • Improve precision KM, Moortgat, Pape, Park (2009)

37. Summary • There now exists a “CMS” version of the invariant mass endpoint method. • It uses a different set of (in principle, infinitely many) invariant mass distributions • It avoids multiple solution ambiguities • (Allegedly) it leads to better precision • more measurements • better measured endpoints

38. BACKUPS

39. Mathematics of duplication • Compose the two maps • Apply to each pair of different regions • e.g. R2 and R1 • This pair is safe! • Only “boundary” effect due to the finite experimental precision

40. Bad news! • Examples of “real” duplication • Regions R1 and R3, namely (3,1) and (2,3) • Regions R2 and R3, namely (3,2) and (2,3) • The extra measurement of MJLL does not help • Part of region R3 is safe

41. R3 R4 R1 R2 Understanding shapes • Let’s start with “near” versus “far” JL pairs (unobservable) • The shape is a right-angle trapezoid ONPF • Notice the correspondence between regions and point P • Notice available measurements: n, f, p, perhaps also q

42. From “near-far” to “low-high” • This reordering is simply origami: a 45 degree fold

43. The four basic JL shapes

44. Animation: Region R1 • Green dot: Mjln endpoint • Blue dot: Mjlf endpoint • Red dot: point P • Endpoints given by (Low,High)=(Near,Far) Region R1 M2jlf M2jl(hi) M2jl(lo) M2jln

45. Animation: Region R2 Region R2 M2jlf M2jl(hi) M2jl(lo) M2jln • Green dot: Mjln endpoint • Blue dot: Mjlf endpoint • Red dot: point P • Black dot: “Equal” endpoint • Endpoints given by (Low,High)=(Equal,Far)

46. Animation: Region R3 Region R3 M2jlf M2jl(hi) M2jl(lo) M2jln • Green dot: Mjln endpoint • Blue dot: Mjlf endpoint • Red dot: point P • Black dot: “Equal” endpoint • Endpoints given by (Low,High)=(Equal,Near)

47. Animation: Region R4 (off-shell) Region R4 (off-shell) M2jlf M2jl(hi) M2jln M2jl(lo) • The shape is fixed: always a triangle • “Low” and “High” endpoints are related:

48. Scatter plots resolve the ambiguity (2,3) (3,1) (3,2) (2,3) “Drop” • R1versus R3 “Foot” • R2versus R3

49. MJLL versus MLL scatter plot Bounded by a hyperbola OWS and a line UV Lester,Parker,White 06 , , The MJLL(Ѳ>π/2) invariant mass “threshold”

50. Animation: MJLL versus MLL scatter plot Several additional measurements besides the 1D endpoints: M2JLL (1,3) (1,2) (2,3) (4,3) (5,4) (1,1) (4,1) (4,2) (3,1) (6,4) (3,2) M2LL (6, 4 ) (5, 4 ) Region (1, - ) Region (2, - ) , (3, - ) Region (4, - )