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The Post-Model Building Era            and     Simplified Models           Modeling and the LHC     Wuppertal, Germany   Ja...
Question:   How should we motivate LHC searches forsignatures of physics beyond the Standard Model?
The Challenge Facing the LHC           Last Year    300 Trillion Collisions1 Billion Recorded Collisions
Very hard to make general predictions    Space of experimental signatures is very high    Njets < 12         x    Nleptons...
Must reduce dimensionalityM2γγ= 2 pT1pT2( cosh(η1-η2) - cos(φ1-φ2) )         Combines 6 variables into 1   What theories/m...
But theories have a high dimensional              parameter space...          MSSM has ~100 parameters Allowed parameter s...
“Theory”  Set of rules based upon principles    used for predicting outcomesMost Model Building is Theory Building     use...
“Model”    A representation of a system      Not necessarily physicalNevents         f(Mγγ)                          Backg...
Theory vs. Model    Complete vs. Incomplete?      Complete Theory  Answer any physical questionUltimate goal of theoretica...
Complete TheoriesIs “Complete” a criteria to select out theories?
Complete TheoriesNon-renormalizable theories are incomplete        Comes with energy scale Λ         Λ ~ “Cutoff of Theory...
HoweverQuestions with E< Λ go as      (E/Λ)N << 1     Effects are invisible at low energies
Complete TheoriesUsed to be a criteria to prefer theories
Complete Theories       This was a great simplifying criteria  Type of Theory            Number of parameters  Renormaliza...
Complete Theories, In Principle      Discover the particlesOnly finite number of measurements     to fully specify the theory
Complete Theories      Devil is in the details    “Discover the particles”              How?                              ...
How does an undiscovered particle of a  complete theory manifest itself?L (A, B, ... ; φ)            L’(A, B, ... )  L is ...
How do we know we’ve discovered all the particles?
How do we know we’ve discovered all the particles?                We know we haven’t                     Dark Matter      ...
May be not so badL (A, B, ... ; φ)        L’(A, B, ... )
May be not so badL (A, B, ... ; φ)         L’(A, B, ... )   Can any non-renormalizable theory             be realized as a...
Basically
Any theory comes with Cutoff    Above Λ, theory may be arbitrarily complicated   Insensitive to Cutoff scale physics at lo...
Given that we can’t discover the   complete theory of nature,  how do we propose models?Can parameterize all deviations fr...
Given that we can’t discover the   complete theory of nature,  how do we propose models?Can parameterize all deviations fr...
Modern Vision of              Theories Beyond the Standard Model         Λ                    Scale theory is no longer va...
Theory Building In Practice        Pick a problem  Build a theory that solves itMake predictions for experiment
Theory Building In Practice            Pick a problem     Build a theory that solves it   Make predictions for experimentA...
The Hierarchy Problem            >50% of motivation for past 35 years       Technicolor1978
The Hierarchy Problem            >50% of motivation for past 35 years       Technicolor   Susy19781981
The Hierarchy Problem            >50% of motivation for past 35 years       Technicolor   Susy197819811991
The Hierarchy Problem            >50% of motivation for past 35 years       Technicolor   Susy     Large ED RS Small ED197...
The Hierarchy Problem            >50% of motivation for past 35 years       Technicolor   Susy     Large ED RS Small ED LH...
The Hierarchy Problem            >50% of motivation for past 35 years       Technicolor   Susy     Large ED RS Small ED LH...
Implications for Experimental Searches         Technicolor   Susy   Large ED   RS                 Small ED LH197819811991 ...
Implications for Experimental Searches        Technicolor   Susy   Large ED   RS   Small ED LH19781981199119982002       D...
Belief in any single theory or paradigm            is at all-time low Ntheories                             Belief        ...
Huge pain for experimentalists   Enormous work to test each theoryModels help motivate where howseparate signal from backg...
Huge pain for experimentalists         Enormous work to test each theory     Models help motivate where how     separate s...
Need a way of simplifying theories Theories              Models
Simplified Models             Models that are based upon             well-established principles(e.g. local quantum field th...
Simplified Models designedto avoid two types of problems
Type 1: Narrowly Focused SearchesTheory Space                                     Signature Space    Experimental      Sea...
Type 2: Redundant TheoriesTheory Space                                     Signature Space         Experimental           ...
Simplified Models      Start with Standard ModelPostulate relevant particles for a search       Start with 1,2 or 3 new par...
Simplified ModelsCan capture essential features of existing models  Notice unexplored corners of theory space           fro...
Simplified Model ExampleMASS       ˜       g   color octet majorana           fermion (“Gluino”)     THREE-BODY DECAY      ...
Gluino Pair Production                             q       ¯                                     q                 g      ...
Gluino Pair Production                                 q       ¯                                         qp               ...
Gluino Pair Production                                             j                                                     j...
Gluino Pair Production                                             j                                                     j...
Gluino Pair Production                                             j                                                     j...
Common Susy Search StrategyBase searches on mSUGRA Supersymmetry           mg = 7m            ˜              0            ...
Allowed us to place limits on new theories             with little data      ˜      g           ¯                 qq      ...
summary
Experiments are in the game now
Has led to more searches        Modified TriggeringMore kinematic regions searchedUnfortunately, no discoveries (yet)
Summary of Simplified Models           Too many theories to search for     Simp. Mods.: axes for decomposing all theories  ...
End
Philosophy Of Simplified Models
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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. 1. The Post-Model Building Era and Simplified Models Modeling and the LHC Wuppertal, Germany January 28, 2012 Jay Wacker SLAC
  2. 2. Question: How should we motivate LHC searches forsignatures of physics beyond the Standard Model?
  3. 3. The Challenge Facing the LHC Last Year 300 Trillion Collisions1 Billion Recorded Collisions
  4. 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 populatedCan’t calculate predictions accurately in this full space of signatures
  5. 5. Must reduce dimensionalityM2γγ= 2 pT1pT2( cosh(η1-η2) - cos(φ1-φ2) ) Combines 6 variables into 1 What theories/models are for
  6. 6. But theories have a high dimensional parameter space... MSSM has ~100 parameters Allowed parameter space has 19 parametersmSUGRA has 5, but introduces theory prejudice
  7. 7. “Theory” Set of rules based upon principles used for predicting outcomesMost Model Building is Theory Building use principles to create new theories (naturalness, supersymmetry, unification)
  8. 8. “Model” A representation of a system Not necessarily physicalNevents f(Mγγ) Background Mγγ
  9. 9. Theory vs. Model Complete vs. Incomplete? Complete Theory Answer any physical questionUltimate goal of theoretical physics
  10. 10. Complete TheoriesIs “Complete” a criteria to select out theories?
  11. 11. Complete TheoriesNon-renormalizable theories are incomplete Comes with energy scale Λ Λ ~ “Cutoff of Theory” Questions with E> Λ cannot be answered
  12. 12. HoweverQuestions with E< Λ go as (E/Λ)N << 1 Effects are invisible at low energies
  13. 13. Complete TheoriesUsed to be a criteria to prefer theories
  14. 14. Complete Theories This was a great simplifying criteria Type of Theory Number of parameters Renormalizable FiniteNon-renormalizable Infinite
  15. 15. Complete Theories, In Principle Discover the particlesOnly finite number of measurements to fully specify the theory
  16. 16. Complete Theories Devil is in the details “Discover the particles” How? aΑ φ bΒ c dIf EΑΒ<Mφ, can’t discover
  17. 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. 18. How do we know we’ve discovered all the particles?
  19. 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. 20. May be not so badL (A, B, ... ; φ) L’(A, B, ... )
  21. 21. May be not so badL (A, B, ... ; φ) L’(A, B, ... ) Can any non-renormalizable theory be realized as arenormalizable theory with more particles?
  22. 22. Basically
  23. 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 buildingCannot write down complete theory with a straight face Using hypothetical principles to create new theories
  24. 24. Given that we can’t discover the complete theory of nature, how do we propose models?Can parameterize all deviations from Standard ModelLSM(A, B, ... ) + LNon-Renormalizable (A, B, ... )
  25. 25. Given that we can’t discover the complete theory of nature, how do we propose models?Can parameterize all deviations from Standard ModelLSM(A, B, ... ) + LNon-Renormalizable (A, B, ... ) We usually want to explore EAB > MφNeed to incorporate φ into model
  26. 26. Modern Vision of Theories Beyond the Standard Model Λ Scale theory is no longer validEnergy 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. 27. Theory Building In Practice Pick a problem Build a theory that solves itMake predictions for experiment
  28. 28. Theory Building In Practice Pick a problem Build a theory that solves it Make predictions for experimentArgue about which theory is better while waiting
  29. 29. The Hierarchy Problem >50% of motivation for past 35 years Technicolor1978
  30. 30. The Hierarchy Problem >50% of motivation for past 35 years Technicolor Susy19781981
  31. 31. The Hierarchy Problem >50% of motivation for past 35 years Technicolor Susy197819811991
  32. 32. The Hierarchy Problem >50% of motivation for past 35 years Technicolor Susy Large ED RS Small ED1978198119911998
  33. 33. The Hierarchy Problem >50% of motivation for past 35 years Technicolor Susy Large ED RS Small ED LH197819811991199820022012
  34. 34. The Hierarchy Problem >50% of motivation for past 35 years Technicolor Susy Large ED RS Small ED LH197819811991199820022012
  35. 35. Implications for Experimental Searches Technicolor Susy Large ED RS Small ED LH197819811991 Could enumerate theories1998 600 5002002 Hd 2 2 1/2 (µ +m0) Hu Mass [GeV] 400Lots of effort on the specific theories 300 200 M2 M1 M3 m1/2 squarks 100 m0 sleptons2012 0 2 4 6 8 10 12 Log10(Q/1 GeV) 14 16 18
  36. 36. Implications for Experimental Searches Technicolor Susy Large ED RS Small ED LH19781981199119982002 Drowning in Possibilities2012
  37. 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. 38. Huge pain for experimentalists Enormous work to test each theoryModels help motivate where howseparate signal from backgroundWant to go to the Post-Model Building Era
  39. 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 EraIs this theory-ladeness acceptable/necessary?
  40. 40. Need a way of simplifying theories Theories Models
  41. 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. 42. Simplified Models designedto avoid two types of problems
  43. 43. Type 1: Narrowly Focused SearchesTheory Space Signature Space Experimental Searches
  44. 44. Type 2: Redundant TheoriesTheory Space Signature Space Experimental Searches
  45. 45. Simplified Models Start with Standard ModelPostulate relevant particles for a search Start with 1,2 or 3 new particles Write down most general theory Usually small number of parameters
  46. 46. Simplified ModelsCan 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. 47. Simplified Model ExampleMASS ˜ g color octet majorana fermion (“Gluino”) THREE-BODY DECAY ¯ qq ˜ g 0 ˜ q 1 ˜ neutral majorana fermion (“LSP”)
  48. 48. Gluino Pair Production q ¯ q g ˜ g ˜ g g ˜ g ¯ q q
  49. 49. Gluino Pair Production q ¯ qp g ˜ g ˜ gp g ˜ g ¯ q q
  50. 50. Gluino Pair Production j j q ¯ qp g ˜ g ˜ gp g ˜ g ¯ q q j j
  51. 51. Gluino Pair Production j j q ¯ qp g ˜ g ˜ g ETp g ˜ g ¯ q q j j
  52. 52. Gluino Pair Production j j q ¯ qp g ˜ g ˜ g ETp g ˜ g ¯ q q j jMultijets + Missing Energy
  53. 53. Common Susy Search StrategyBase searches on mSUGRA Supersymmetry mg = 7m ˜ 0 Not general Risk Type 1 Failure
  54. 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. 55. summary
Experiments are in the game now
  56. 56. Has led to more searches Modified TriggeringMore kinematic regions searchedUnfortunately, no discoveries (yet)
  57. 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 dataWhen incomplete model doesn’t work extend model Then construct Theory (understand Principles)
  58. 58. End

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