1. Search for Supersymmetry

2. Outline Introduction to supersymmetry Phenomenology of the CMSSM
Non-universal scalar masses?
Non-universal Higgs masses (NUHM)
Options for the LSP
Gravitino dark matter
New possibilities for collider phenomenology

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

4. Other Reasons to like Susy
It enables the gauge couplings to unify
It predicts mH < 150 GeV
As suggested
by EW data
Approved by Fabiola Gianotti
JE, Nanopoulos, Olive + Santoso: hep-ph/

5. Astronomers say
that most of the
matter in the
Universe is
invisible
Dark Matter
Lightest Supersymmetric particles ?
We shall look for
them with the
LHC

6. Minimal Supersymmetric Extension of Standard Model (MSSM)
Particles + spartners
2 Higgs doublets, coupling μ, ratio of v.e.v.’s = tan β
Unknown supersymmetry-breaking parameters:
Scalar masses m0, gaugino masses m1/2,
trilinear soft couplings Aλ, bilinear soft coupling Bμ
Often assume universality:
Single m0, single m1/2, single Aλ, Bμ: not string?
Called constrained MSSM = CMSSM
Minimal supergravity (mSUGRA) predicts additional relations for gravitino mass, supersymmetry breaking:
m3/2 = m0, Bμ = Aλ – m0

7. Lightest Supersymmetric Particle
Stable in many models because of conservation of R parity:
R = (-1) 2S –L + 3B
where S = spin, L = lepton #, B = baryon #
Particles have R = +1, sparticles R = -1:
Sparticles produced in pairs
Heavier sparticles  lighter sparticles
Lightest supersymmetric particle (LSP) stable

8. Possible Nature of LSP No strong or electromagnetic interactions
Otherwise would bind to matter
Detectable as anomalous heavy nucleus
Possible weakly-interacting scandidates
Sneutrino
(Excluded by LEP, direct searches)
Lightest neutralino χ
Gravitino
(nightmare for astrophysical detection)

9. Constraints on Supersymmetry
Absence of sparticles at LEP, Tevatron
selectron, chargino > 100 GeV
squarks, gluino > 250 GeV
Indirect constraints
Higgs > 114 GeV, b -> s γ
Density of dark matter
lightest sparticle χ:
WMAP: < Ωχh2 < 0.124
gμ - 2

10. Current Constraints on CMSSM
Assuming the
lightest sparticle
is a neutralino
Excluded because stau LSP
Excluded by b  s gamma
WMAP constraint on relic density
Excluded (?) by latest g - 2
JE + Olive + Santoso + Spanos

11. Current Constraints on CMSSM
Different
tan β
sign of μ
Impact of
Higgs
constraint
reduced
if larger mt
Focus-point
region far up
JE + Olive + Santoso + Spanos

12. Sparticles may not be very light
Full
Model
samples
← Second lightest visible sparticle
Detectable
@ LHC
Provide
Dark Matter
Dark Matter
Detectable
Directly
Lightest visible sparticle →
JE + Olive + Santoso + Spanos

13. Missing Energy Detection @ LHC
Sensitive to missing transverse energy
carried away by neutral particles:
e.g., neutrinos, neutralinos

14. Supersymmetry Searches at LHC
LHC reach in
supersymmetric
parameter space
`Typical’ supersymmetric
Event at the LHC
Can cover most
possibilities for
astrophysical
dark matter

15. Supersymmetric Benchmark Studies
Lines in
susy space
allowed by
accelerators,
WMAP data
Specific
benchmark
Points along
WMAP lines
Sparticle
detectability
Along one
WMAP line
Calculation
of relic
density at a
benchmark
point
Battaglia, De Roeck, Gianotti, JE, Olive, Pape

16. Sparticle Signatures along WMAP lines
Relatively small
branching ratios in CMSSM Z h
Average numbers
of particles per
sparticle event τ 3l
Battaglia, De Roeck, Gianotti, JE, Olive, Pape

18. Summary of LHC Scapabilities … and Other Accelerators
LHC almost
`guaranteed’
to discover
supersymmetry
if it is relevant
to the mass problem
Battaglia, De Roeck, Gianotti, JE, Olive, Pape

19. Tests of Unification Ideas
For gauge couplings
For sparticle masses

20. Precision Observables in Susy
Can one estimate the scale of supersymmetry?
Precision Observables in Susy
Sensitivity to m1/2
in CMSSM
along WMAP lines
for different A mW
tan β = 10
tan β = 50
sin2θW
Present & possible
future errors
JE + Heinemeyer + Olive + Weiglein

21. More Observables b → sγ Bs → μμ gμ - 2 tan β = 10 tan β = 50
JE + Heinemeyer + Olive + Weiglein

22. Global Fits to Present Data
Including mW , sin2θW, b → sγ, gμ - 2
As functions of m1/2 in CMSSM for tan β = 10, 50
JE + Heinemeyer + Olive + Weiglein

23. Global Fits to Present Dataχ
χ2, χ ±
Global Fits to Present Data
χ3, χ2± τ1
Preferred
sparticle
masses for
tan β = 10 e1 e2
JE + Heinemeyer + Olive + Weiglein

24. Global Fits to Present Data
Preferred
sparticle
masses for
tan β = 10 g A
Within reach of LHC!
JE + Heinemeyer + Olive + Weiglein

25. Beyond the CMSSM

26. More General Supersymmetric Models
MSSM with more general pattern of supersymmetry breaking:
non-universal scalar masses m0
and/or gaugino masses m½
and/or trilinear couplings A0
Nature of the lightest supersymmetric particle (LSP)
Extended particle content:
non-minimal supersymmetric model (NMSSM)

27. Non-Universal Scalar Masses
Different sfermions with same quantum #s?
e.g., d, s squarks?
disfavoured by upper limits on flavour- changing neutral interactions
Squarks with different #s, squarks and sleptons?
disfavoured in various GUT models
e.g., dR = eL, dL = uL = uR = eR in SU(5), all in SO(10)
Non-universal susy-breaking masses for Higgses?
No reason why not!

28. Non-Universal Higgs Masses (NUHM)
Generalize CMSSM (+)
mHi2 = m02(1 + δi)
Free Higgs mixing μ,
pseudoscalar mass mA
Larger parameter space
Constrained by vacuum
stability

29. Sampling of (m1/2, m0) Planes in NUHM
New vertical
allowed strips
appear
JE + Olive + Santoso + Spanos

30. Low-Energy Effective Supersymmetric Theory
Assume universality for sfermions with same quantum numbers (but different generations)
Require electroweak vacuum to be stable (RGE not → negative mass2)
up to GUT scale (LEEST)
up to 10 TeV (LEEST10)
Qualitatively similar to NUHM
not much freedom to adjust squarks/sleptons

31. Sparticles may not be very light
Full
Model
samples
← Second lightest visible sparticle
Detectable
@ LHC
Provide
Dark Matter
Dark Matter
Detectable
Directly
Lightest visible sparticle →
JE + Olive + Santoso + Spanos

32. Gravitino Dark Matter?

33. Possible Nature of LSP No strong or electromagnetic interactions
Otherwise would bind to matter
Detectable as anomalous heavy nucleus
Possible weakly-interacting scandidates
Sneutrino
(Excluded by LEP, direct searches)
Lightest neutralino χ
Gravitino
(nightmare for astrophysical detection)

34. Possible Nature of NLSP
NLSP = next-to-lightest sparticle
Very long lifetime due to gravitational decay, e.g.:
Could be hours, days, weeks, months or years!
Generic possibilities:
lightest neutralino χ
lightest slepton, probably lighter stau
Constrained by astrophysics/cosmology

35. Different Regions of Sparticle Parameter Space if Gravitino LSP
masses
χ NLSP
stau NLSP
Density below
WMAP limit
Decays do not affect
BBN/CMB agreement
JE + Olive + Santoso + Spanos

36. Minimal Supergravity Model (mSUGRA)
More constrained than CMSSM: m3/2 = m0, Bλ = Aλ – 1
Excluded by b  s γ
Neutralino LSP
region
stau LSP
(excluded)
LEP constraints
On mh, chargino
Gravitino LSP
region
tan β fixed by vacuum conditions
JE + Olive + Santoso + Spanos

37. Light Nuclei: BBN vs CMB
Good agreement for D/H, 4He: discrepancy for 7Li?
Observations
Calculations
Cyburt + Fields + Olive + Skillman

38. Constraints on Unstable Relics
7Li < BBN?
Effect of relic decays?
Problems with D/H
3He/D too high!
Interpret as upper
limits on abundance
of metastable heavy
relics
JE + Olive + Vangioni

39. Different Regions of Sparticle Parameter Space if Gravitino LSP
χ NLSP
stau NLSP
Density below
WMAP limit
Decays do not affect
BBN/CMB agreement
JE + Olive + Santoso + Spanos

40. Regions Allowed in Different Scenarios for Supersymmetry Breaking
CMSSM
Benchmarks
NUHM
Benchmarks
GDM
Benchmarks
with neutralino NLSP
with stau NLSP
De Roeck, JE, Gianotti, Moortgat, Olive + Pape: hep-ph/

41. Spectra in NUHM and GDM Benchmark Scenarios
Typical example of
non-universal Higgs masses:
Models with gravitino LSP
Models with stau NLSP
De Roeck, JE, Gianotti, Moortgat, Olive + Pape: hep-ph/

42. Properties of NUHM and GDM Models
Relic density ~ WMAP in NUHM models
Generally < WMAP in GDM models
Need extra source of gravitinos at high temperatures, after inflation?
NLSP lifetime: 104s < τ < few X 106s
De Roeck, JE, Gianotti, Moortgat, Olive + Pape: hep-ph/

43. Neutralino Masses and Decay Modes
χh, χZ may be
large in NUHM
χh, χZ small
in CMSSM
De Roeck, JE, Gianotti, Moortgat, Olive + Pape: hep-ph/

44. Final States in GDM Models with Stau NLSP
All decay chains
end with lighter stau
Generally via χ
Often via heavier
sleptons
Final states contain
2 staus, 2 τ,
often other leptons
De Roeck, JE, Gianotti, Moortgat, Olive + Pape: hep-ph/

45. Kinematic Distributions: Point ε
Staus come with
many jets & leptons
with pT hundreds of GeV,
produced centrally
De Roeck, JE, Gianotti, Moortgat, Olive + Pape: hep-ph/

46. Kinematic Distributions: Point ζ
Staus come with
many jets & leptons
with pT hundreds of GeV,
produced centrally
De Roeck, JE, Gianotti, Moortgat, Olive + Pape: hep-ph/

47. Stau Mass Measurements by Time-of-Flight
Event-by-event
accuracy < 10%
< 1% with full sample
De Roeck, JE, Gianotti, Moortgat, Olive + Pape: hep-ph/

48. Numbers of Visible Sparticle Species
At different
colliders

49. Slepton Trapping at the LHC?
If stau next-to-lightest sparticle (NLSP)
may be metastable
may be stopped in detector/water tank?
Trapping
rate
Kinematics
Hamaguchi + Kuno + Nakaya + Nojiri
Feng + Smith

50. Stau Momentum Spectra βγ typically peaked ~ 2
Staus with βγ < 1 leave central tracker
after next beam crossing
Staus with βγ < ¼ trapped inside calorimeter
Staus with βγ < ½ stopped within 10m
Can they be dug out?
De Roeck, JE, Gianotti, Moortgat, Olive + Pape: hep-ph/

51. Extract Cores from Surrounding Rock?
Very little room for water tank in LHC caverns,
only in forward directions where few staus
Extract Cores from Surrounding Rock?
Use muon system to locate impact point on cavern wall with uncertainty < 1cm
Fix impact angle with accuracy 10-3
Bore into cavern wall and remove core of size 1cm × 1cm × 10m = 10-3m3 ~ 100 times/year
Can this be done before staus decay?
Caveat radioactivity induced by collisions!
2-day technical stop ~ 1/month
Not possible if lifetime ~104s, possible if ~106s?
De Roeck, JE, Gianotti, Moortgat, Olive + Pape: hep-ph/

52. Detect Staus in Mass Spectrometer?
Each core ~ 1cm × 1cm × 10m
‘Region of interest’ ~ 1m long
Contains ~ 2 × 1027 nucleons, i.e., 1027 protons
Present best limits from water ~ 10-29/proton
Sensitivity possible in principle
How quickly could the volume be searched?
Have at most a few weeks!
De Roeck, JE, Gianotti, Moortgat, Olive + Pape: hep-ph/

53. Detect Supersymmetric Decay Albedo?
Look for staus stopping ~ 10m from detector
Later decay → τ + gravitino
τ → μ with branching ratio ~ 16%
Characteristic energies ~ (1/6) mstau
~ 25 to 50 GeV
Geometric acceptance for upward-going μ ~ 1/12 → ~ 1.3% of stau decays detectable
→ ~ 100 events/year in benchmark scenario ε
De Roeck, JE, Gianotti, Moortgat, Olive + Pape: hep-ph/

54. Caveat Cosmic-Ray Background
Background of cosmic-ray μ
~ 100 events/year
Similar energy range
Signal might be visible in
benchmark scenario ε
Not in scenarios ζ and η
De Roeck, JE, Gianotti, Moortgat, Olive + Pape: hep-ph/

55. Potential Measurement Accuracies
Gravitino Dark Matter even more interesting
than Neutralino Dark Matter!
Measure stau mass to 1%
Measure m½ to 1%
via cross section, other masses?
Distinguish points ζ, η
De Roeck, JE, Gianotti, Moortgat, Olive + Pape: hep-ph/

56. Summary The ‘C’ in CMSSM signifies ‘conservative’
Many more exotic supersymmetric phenomenologies are possible
Gravitino dark matter is one example
Not to mention breaking of R parity …
… nor split supersymmetry
Supersymmetry is the most ‘expected’ surprise at the LHC
Expect it to appear in an unexpected way!

57. Elastic Scattering Cross Sections
From global fit to accelerator data
Latest experimental upper limit
JE + Olive + Santoso + Spanos: hep-ph/

58. Direct CDM detection in NUHM/LEEST
Cross section similar
in NUHM/LEEST
Cross section depends
on πN σ term
Cross section depends
on sign of μ
Some NUHM/LEEST
models already excluded
JE + Olive + Santoso + Spanos