Philosophy Of Simplified Models
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Presentation at Modeling and the LHC at Wuppertal on January 28, 2012.
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Philosophy Of Simplified Models
- 1. The Post-Model Building Era and Simplified Models Modeling and the LHC Wuppertal, Germany January 28, 2012 Jay Wacker SLAC
- 2. Question: How should we motivate LHC searches for signatures of physics beyond the Standard Model?
- 3. The Challenge Facing the LHC Last Year 300 Trillion Collisions 1 Billion Recorded Collisions
- 4. Very hard to make general predictions Space of experimental signatures is very high Njets < 12 x Nleptons < 5 x 3 ( pT, η, φ) ~600 dimensions x Nphotons < 4 Sparsely populated Can’t calculate predictions accurately in this full space of signatures
- 5. Must reduce dimensionality M2γγ= 2 pT1pT2( cosh(η1-η2) - cos(φ1-φ2) ) Combines 6 variables into 1 What theories/models are for
- 6. But theories have a high dimensional parameter space... MSSM has ~100 parameters Allowed parameter space has 19 parameters mSUGRA has 5, but introduces theory prejudice
- 7. “Theory” Set of rules based upon principles used for predicting outcomes Most Model Building is Theory Building use principles to create new theories (naturalness, supersymmetry, unification)
- 8. “Model” A representation of a system Not necessarily physical Nevents f(Mγγ) Background Mγγ
- 9. Theory vs. Model Complete vs. Incomplete? Complete Theory Answer any physical question Ultimate goal of theoretical physics
- 10. Complete Theories Is “Complete” a criteria to select out theories?
- 11. Complete Theories Non-renormalizable theories are incomplete Comes with energy scale Λ Λ ~ “Cutoff of Theory” Questions with E> Λ cannot be answered
- 12. However Questions with E< Λ go as (E/Λ)N << 1 Effects are invisible at low energies
- 13. Complete Theories Used to be a criteria to prefer theories
- 14. Complete Theories This was a great simplifying criteria Type of Theory Number of parameters Renormalizable Finite Non-renormalizable Infinite
- 15. Complete Theories, In Principle Discover the particles Only finite number of measurements to fully specify the theory
- 16. Complete Theories Devil is in the details “Discover the particles” How? a Α φ b Β c d If EΑΒ<Mφ, can’t discover
- 17. How does an undiscovered particle of a complete theory manifest itself? L (A, B, ... ; φ) L’(A, B, ... ) L is a non-renormalizable theory ’ Λ = Mφ
- 18. How do we know we’ve discovered all the particles?
- 19. How do we know we’ve discovered all the particles? We know we haven’t Dark Matter (80% of the mass of the Universe)
- 20. May be not so bad L (A, B, ... ; φ) L’(A, B, ... )
- 21. May be not so bad L (A, B, ... ; φ) L’(A, B, ... ) Can any non-renormalizable theory be realized as a renormalizable theory with more particles?
- 22. Basically
- 23. Any theory comes with Cutoff Above Λ, theory may be arbitrarily complicated Insensitive to Cutoff scale physics at low energies Is the backdrop for all theory building Cannot write down complete theory with a straight face Using hypothetical principles to create new theories
- 24. Given that we can’t discover the complete theory of nature, how do we propose models? Can parameterize all deviations from Standard Model LSM(A, B, ... ) + LNon-Renormalizable (A, B, ... )
- 25. Given that we can’t discover the complete theory of nature, how do we propose models? Can parameterize all deviations from Standard Model LSM(A, B, ... ) + LNon-Renormalizable (A, B, ... ) We usually want to explore EAB > Mφ Need to incorporate φ into model
- 26. Modern Vision of Theories Beyond the Standard Model Λ Scale theory is no longer valid Energy φ New particles to be discovered SM What we’ve already seen Λ can be low ~ 10 TeV Λ can be high ~ 1016 TeV
- 27. Theory Building In Practice Pick a problem Build a theory that solves it Make predictions for experiment
- 28. Theory Building In Practice Pick a problem Build a theory that solves it Make predictions for experiment Argue about which theory is better while waiting
- 29. The Hierarchy Problem >50% of motivation for past 35 years Technicolor 1978
- 30. The Hierarchy Problem >50% of motivation for past 35 years Technicolor Susy 1978 1981
- 31. The Hierarchy Problem >50% of motivation for past 35 years Technicolor Susy 1978 1981 1991
- 32. The Hierarchy Problem >50% of motivation for past 35 years Technicolor Susy Large ED RS Small ED 1978 1981 1991 1998
- 33. The Hierarchy Problem >50% of motivation for past 35 years Technicolor Susy Large ED RS Small ED LH 1978 1981 1991 1998 2002 2012
- 34. The Hierarchy Problem >50% of motivation for past 35 years Technicolor Susy Large ED RS Small ED LH 1978 1981 1991 1998 2002 2012
- 35. Implications for Experimental Searches Technicolor Susy Large ED RS Small ED LH 1978 1981 1991 Could enumerate theories 1998 600 500 2002 Hd 2 2 1/2 (µ +m0) Hu Mass [GeV] 400 Lots of effort on the specific theories 300 200 M2 M1 M3 m1/2 squarks 100 m0 sleptons 2012 0 2 4 6 8 10 12 Log10(Q/1 GeV) 14 16 18
- 36. Implications for Experimental Searches Technicolor Susy Large ED RS Small ED LH 1978 1981 1991 1998 2002 Drowning in Possibilities 2012
- 37. Belief in any single theory or paradigm is at all-time low Ntheories Belief time Just examples of possibilities Model Building Era successful, but over
- 38. Huge pain for experimentalists Enormous work to test each theory Models help motivate where how separate signal from background Want to go to the Post-Model Building Era
- 39. Huge pain for experimentalists Enormous work to test each theory Models help motivate where how separate signal from background Want to go to the Post-Model Building Era Is this theory-ladeness acceptable/necessary?
- 40. Need a way of simplifying theories Theories Models
- 41. Simplified Models Models that are based upon well-established principles (e.g. local quantum field theories that contain Standard Model) Not based upon principles i.e. there is not explicit physical motivation Purpose: Reduce Theory-Ladeness
- 42. Simplified Models designed to avoid two types of problems
- 43. Type 1: Narrowly Focused Searches Theory Space Signature Space Experimental Searches
- 44. Type 2: Redundant Theories Theory Space Signature Space Experimental Searches
- 45. Simplified Models Start with Standard Model Postulate relevant particles for a search Start with 1,2 or 3 new particles Write down most general theory Usually small number of parameters
- 46. Simplified Models Can capture essential features of existing models Notice unexplored corners of theory space from lack of imagination No burden of top-down motivation No Principles
- 47. Simplified Model Example MASS ˜ g color octet majorana fermion (“Gluino”) THREE-BODY DECAY ¯ qq ˜ g 0 ˜ q 1 ˜ neutral majorana fermion (“LSP”)
- 48. Gluino Pair Production q ¯ q g ˜ g ˜ g g ˜ g ¯ q q
- 49. Gluino Pair Production q ¯ q p g ˜ g ˜ g p g ˜ g ¯ q q
- 50. Gluino Pair Production j j q ¯ q p g ˜ g ˜ g p g ˜ g ¯ q q j j
- 51. Gluino Pair Production j j q ¯ q p g ˜ g ˜ g ET p g ˜ g ¯ q q j j
- 52. Gluino Pair Production j j q ¯ q p g ˜ g ˜ g ET p g ˜ g ¯ q q j j Multijets + Missing Energy
- 53. Common Susy Search Strategy Base searches on mSUGRA Supersymmetry mg = 7m ˜ 0 Not general Risk Type 1 Failure
- 54. Allowed us to place limits on new theories with little data ˜ g ¯ qq LHC 70 nb-1 !prod = 3!" NLO-QCD 100 pb !prod = !" NLO-QCD 200 pb !prod = 0.3 !" NLO-QCD 300 pb !prod = 0.1 !" NLO-QCD 500 pb Sample theory 1 nb Tevatron 2 nb mSUGRA
- 55. summary Experiments are in the game now
- 56. Has led to more searches Modified Triggering More kinematic regions searched Unfortunately, no discoveries (yet)
- 57. Summary of Simplified Models Too many theories to search for Simp. Mods.: axes for decomposing all theories Reduce theory prejudice Represent natural extension of Effective Field Theory to the LHC In the Discovery Era Construct incomplete models to fit data When incomplete model doesn’t work extend model Then construct Theory (understand Principles)
- 58. End