1. Supersymmetric Dark Matter in View of 1/fb of LHC Data
… nevertheless
Supersymmetric Dark Matter in View of 1/fb of LHC Data
John ELLIS,
King’s College London
& Guest CERN

2. Progress in LHC Luminosity
Instantaneous luminosity
Integrated luminosity

3. Outline
Models
Data
Techniques
Examples
Perspectives
Benchmarks

4. Supersymmetry? Would unify matter particles and force particles
Related particles spinning at different rates
½ /
Higgs - Electron - Photon - Gravitino – Graviton
Many phenomenological motivations
Would help fix particle masses
Would help unify forces
Predicts light Higgs boson
Could fix discrepancy in gμ - 2
Could provide dark matter for the
astrophysicists and cosmologists

5. Loop Corrections to Higgs Mass2
Consider generic fermion and boson loops:
Each is quadratically divergent: ∫Λd4k/k2
Leading divergence cancelled if
Supersymmetry! 2
x 2 5

6. Other Reasons to like Susy
It enables the gauge couplings to unify
It predicts mH < 150 GeV
As suggested
by EW data

7. Combining the Information from Direct Searches and Indirect Data
mH = 125 ± 10 GeV
Gfitter collaboration

8. There must be New Physics beyond the Higgs Boson
potential
collapses
Higgs
coupling
blows up
Higgs coupling less
than in Standard Model

9. Theoretical Constraints on Higgs Mass
Large → large self-coupling → blow up at low energy scale Λ due to
renormalization
Small: renormalization
due to t quark drives
quartic coupling < 0
at some scale Λ
→ vacuum unstable
Bounds on Higgs mass depend on Λ
Espinosa, JE, Giudice, Hoecker, Riotto, arXiv

10. Minimal Supersymmetric Extension of Standard Model (MSSM)
Double up the known particles:
Two Higgs doublets
- 5 physical Higgs bosons:
- 3 neutral, 2 charged
Lightest neutral supersymmetric Higgs looks like the single Higgs in the Standard Model

11. Minimal Flavour Violation: 13 parameters (+ 6 violating CP)
MSSM: > 100 parameters
Minimal Flavour Violation: 13 parameters
(+ 6 violating CP)
SU(5) unification: 7 parameters
NUHM2: 6 parameters
NUHM1 = SO(10): 5 parameters
CMSSM: 4 parameters
String?
mSUGRA: 3 parameters

12. Supersymmetric Models to Study
Gravity-mediated:
NUHM2
as below, mhu ≠ mhd
NUHM1
as below, common mh ≠ m0
CMSSM
m0, m1/2, tan β (B0), A0
VCMSSM
as above, & A0 = B0 + m0
mSUGRA
as above, & m3/2 = m0
RPV CMSSM
Other SUSY ✕ models:
Gauge-mediated
Anomaly-mediated
Mixed modulus-anomaly-mediated
Phenomenological 19-parameter MSSM
NMSSM ….
Also studied
in global fits
Most studied
in global fits
Less studied in global fits
Some
Global
fits
If model has N parameters,
sample 100 values/parameter:
102N points, e.g., 108 in CMSSM

13. Data Electroweak precision observables Flavour physics observables
gμ - 2
Higgs mass
Dark matter
LHC
MasterCode: O.Buchmueller, JE et al.

14. Electroweak Precision Observables
Inclusion essential for fair comparison with Standard Model
Some observables may be
significantly different
E.g., mW, Afb(b)
Advantage for SUSY?
Some may not be changed
significantly
Should be counted against/for all models

15. Flavour Physics Observables
Inclusion requires additional
hypotheses
E.g., minimal flavour violation
Many anomalies reported
E.g., top production asymmetry,
dimuon asymmetry, Bs J/ψ φ
Difficult to interpret within SUSY
Significant progress with Bs μ+μ-
Valuable constraint on SUSY models

16. Quo Vadis g - 2?
Strong discrepancy between BNL experiment and e+e- data:
now ~ 3.6 
Better agreement between e+e- experiments
Increased discrepancy between BNL experiment and  decay data
now ~ 2.4 
Convergence between e+e- experiments and  decay data
More credibility? 16

17. Mild preference for small masses even without gμ – 2 ?
To gμ – 2 or not to gμ – 2 ?
CMSSM
NUHM1
Pre-LHC fits:
Mild preference for small masses even without gμ – 2 ?
MasterCode: O.Buchmueller, JE et al.

18. Dark Matter Observables
Cosmological cold dark matter density
ΩCDM h2 = ±
Reduces dimensionality of SUSY space by ~ 1
Could be other sources of DM: little effect
Upper limit on spin-independent scattering
Other astrophysical constraints?
Annihilations inside Sun/Earth neutrinos?
Anomalies in cosmic-ray γ/e+/e- spectra?
Not explicable in models discussed here

19. XENON100 Experiment
Aprile et al: arXiv: 19

20. Supersymmetry Searches in CMS
Jets + missing energy (+ lepton(s)) 20

21. Supersymmetry Searches in ATLAS
Jets + missing energy + 0 lepton 21

22. Impact of LHC on the CMSSM
Assuming the
lightest sparticle
is a neutralino
tan β = 10 ✕ gμ - 2
tan β = 55 ✓ gμ - 2
LHC
Excluded because stau LSP
Excluded by b  s gamma
WMAP constraint on CDM density
Preferred (?) by latest g - 2
JE, Olive & Spanos

23. Limits on Heavy MSSM Higgses

24. Meta-Analyses: Cuts vs Likelihood
Theorists seek to combine many constraints
Simply imposing 95% CL contours as cuts is inadequate
Seek to construct global likelihood function
Want more information from experiments: several likelihood contours
Can be used to check our simulations
Otherwise, we will resort to unreliable estimates/guesses 

25. Current LHC Searches have Reduced Sensitivity to Compressed Spectra
Acceptance of typical
ATLAS MET search
Exclusion by typical
ATLAS MET search
LeCompte & Martin

26. Bayesian vs Frequentist
Bayesian: “probability is a measure of the degree of belief about a proposition”
Frequentist: “probability is the number of times the event occurs over the total number of trials, in the limit of an infinite series of equiprobable repetitions”
Louis Lyons: “Bayesians address the question everyone is interested in by using assumptions no–one believes, while frequentists use impeccable logic to deal with an issue of no interest to anyone”
Roszkowski

27. Sensitivities to Bayesian Priors
Pre-LHC: Logarithmic vs flat priors in (m1/2, m0) plane
Trotta, Feroz, Hobson, Roszkowski & Ruiz de Austri: arXiv:

28. Pre-LHC vs Post-LHC Uses MasterCode package LHC will push out in the
(m1/2, m0) plane if no SUSY
Illustration of possible
pre/post-LHC tension m1/2
Fittino: Bechtle, Desch, Dreiner, Kramer, O’Leary, Robens, Sarrazin, Wienemann

29. Including XENON100 200,000 points
Farina, Kadastik, Pappadopulo, Pata, Raidal, Strumia: arXiv:

32. O.Buchmueller, JE et al: arXiv:1106.2529

33. 68% & 95%
CL contours
….. pre-LHC
___ LHC 1/fb

34. O.Buchmueller, JE et al: arXiv:1110.3568
p-values
of fits
LHC 1/fb
p-values
of fits
Pre LHC
29.3
14%
780
450
-1100 41
27.4
16%
730
150
-910 41
O.Buchmueller, JE et al: arXiv:

35. Preliminary NUHM2 p-values p-values of fits of fits LHC 1/fb Pre LHC
29.3
14%
780
450
-1100 41
27.4
16%
730
150
-910 41
χ2 ~ 3.5 < NUHM1

36. Dropping gμ - 2 allows masses up to dark matter limit
Regions favoured by
gμ-2 constraint
….. pre-LHC
___ LHC 1/fb
Dropping gμ - 2 allows masses up to dark matter limit

37. Region allowed by
Ωχh2 constraint
CMSSM

38. Dropping gμ - 2 allows masses up to dark matter limit
Impact of dropping
gμ-2 constraint
….. pre-LHC
___ LHC 1/fb
Dropping gμ - 2 allows masses up to dark matter limit

39. MasterCode Collaboration: O.Buchmueller, JE et al: arXiv:1110.3568

40. Favoured values of gluino mass significantly
….. pre-LHC
___ LHC 1/fb
Favoured values of gluino mass significantly
above pre-LHC, > 1 TeV

41. Favoured values of Mh ~ 119 GeV:
Higgs mass
Favoured values of Mh ~ 119 GeV:
Coincides with value consistent with LHC !

42. Likelihoods for sparticle thresholds in e+e-
CMSSM
O.Buchmueller, JE et al: arXiv:
NUHM1

43. Favoured values of BR(Bs μ+μ-) above SM value !
+ LHCb
Bs μ+μ-
….. pre-LHC
___ LHC 1/fb
--- with CDF
Favoured values of BR(Bs μ+μ-) above SM value !
(due to increase in tan β)

44. Significant impact of XENON100 experiment:
Spin-independent
dark matter scattering
….. pre-LHC
___ LHC 1/fb
Significant impact of XENON100 experiment:
Prospects for coming years !

45. Much further below prospective experimental sensitivity ?
2010
35pb-1
Spin-dependent
dark matter scattering
Much further below prospective
experimental sensitivity ?

46. Neutrino Fluxes from CMSSM Dark Matter Annihilation in Sun
Spin-dependent scattering not dominant
Spin-independent scattering: ΣπN !
JE, Olive & Savage: arXiv:

47. Neutrino Fluxes from CMSSM Dark Matter Annihilation in Sun
Annihilation rate < capture rate in general
Dark matter not in equilibrium
JE, Olive & Savage: arXiv:

48. Neutrinos from Annihilations inside the Sun
LHC
JE, Olive, Savage and Spanos: arXiv:

49. Gamma Fluxes from Dark Matter Annihilation in the Galactic Centre
Detectable?
Detectable?
LHC mass limit
LHC mass limit
JE, Olive and Spanos: arXiv:

50. Gammas from Annihilations in the Centre of the Galaxy
LHC
JE, Olive and Spanos: arXiv:

51. Anomalies in e+/e- Spectra?
Shoulder in e+ + e- spectrum?
Rising e+/e- ratio
Uncertainties in cosmic-ray production, propagation?
Nearby sources?
SUSY interpretation difficult, unnecessary?

52. Antiprotons and Antideuterons from Dark Matter Annihilation?
… standard cosmic rays
--- possible supersymmetric model
__ including production at source
Antideuterons could provide
another window of opportunity?

53. AMS-02 on the International Space Station (ISS)

54. AMS-02 and Dark Matter Measurement of e+ spectrum to higher E
Precision measurement of antiproton spectrum

55. Long-Lived Gravitino & BBN
Conventional Big-Bang Nucleosynthesis calculations agree well with D, 3He, 4He data
Constraints on abundance of long-lived relic
Apparent discrepancy for Lithium:
Globular clusters:
BBN calculation:
Can discrepancy be removed by decays of long-lived relic, e.g., gravitino?
Cyburt, JE, Fields, Luo, Olive & Spanos: arXiv:

56. Nuclear Reactions
Relevant interactions of non-thermal particles from relic decay showers
Incorporate errors in measurements
Make global likelihood analysis
Cyburt, JE, Fields, Luo, Olive & Spanos: arXiv:

57. Improvements in Fit to BBN Data
Standard BBN: χ2 = 31.7
Best fit to halo Li data: χ2 ~ 5.5
Best fit to globular cluster Li data: χ2 ~ 2.7
Allowing for higher D/H error: χ2 ~ 1.1
Cyburt, JE, Fields, Luo, Olive & Spanos: arXiv:

58. Effect of Annihilations during Big-Bang Nucleosynthesis on 6Li Abundance
LHC
Standard Big-Bang nucleosynthesis predicts
6Li/H ~ 10-14
Some observations suggest enhancement to
6Li/H ~ 10-11
Late dark matter annihilations may enhance to 6Li/H ~ 10-12
JE, Fields, Luo, Olive and Spanos: arXiv:

59. Summary & Perspectives
LHC data putting pressure on popular models
Theorists want to combine various constraints
Seek to construct global likelihood function
Tension between LHC and gμ – 2
Mitigated at larger tan β
Need more information than 95% CL
Desirable to improve TH-EXP dialogue
Non-accelerator dark matter searches start to bite