1. Can we tell SUSY (from a hole in the ground)?
Alan Barr UCL
YETI06 11 Jan 2006

2. Scenario: 2006: New year’s resolutions:
End of first year of data taking
After careful calibration …
ATLAS observes excess of events with:
Missing transverse energy
Leptons
Jets
Produces letter
Definitely new physics!
But what sort of new physics?!?
2006: New year’s resolutions:
Give up assumptions
Exercise more caution
11 Jan 2005
Alan Barr, UCL

3. What will we find at the LHC
We expect to find:
All the Standard Model particles
W, Z, top, …
Including a Higgs boson
We hope to also find:
Explanation for the scale of the Higgs mass
Supersymmetry?
Extra gauge groups?
Extra dimensions? ?
… but not a one-horse race.
Susy in the lead … ?
11 Jan 2005
Alan Barr, UCL

4. What is supersymmetry? Nature permits only various types of symmetry:
Space & time
Lorentz transforms
Rotations and translations
Gauge symmetry
e.g. SM: SU(3)c x SU(2)L x U(1)
Supersymmetry
Anti-commuting (Fermionic) generators
Relationship with space-time
{Q,Q†} = -2γμPμ
Consequences:
Q(fermion)=boson
Q(boson)=fermion
Equal fermionic and bosonic DF
Double particle content of theory!
Partners not yet observed
Must be broken!
Otherwise we’d have seen it!
11 Jan 2005
Alan Barr, UCL

5. (S)particles SM SUSY quarks (L&R) leptons (L&R) neutrinos (L&?)
squarks (L&R) sleptons (L&R) sneutrinos (L&?)
Spin-1/2
Spin-0
After Mixing
 Z0 W±
gluon
B W0
Bino Wino0 Wino±
gluino
Spin-1
4 x neutralino
Spin-1/2
gluino h0 H0 A0 H± ~
H0 H± ~
2 x chargino
Spin-0
Extended higgs sector
(2 doublets)
11 Jan 2005
Alan Barr, UCL

6. “typical” susy spectrum (mSUGRA)
General features
Mass/GeV
Complicated cascade decays
Many intermediates
Typical signal
Jets
Squarks and Gluinos
Leptons
Sleptons and weak gauginos
Missing energy
Undetected LSP
Model dependent
Various ways of transmitting SUSY breaking from a hidden sector
“typical” susy spectrum (mSUGRA)
11 Jan 2005
Alan Barr, UCL
LHC Pt5

7. Constraining masses Mass constraints Invariant masses in pairs
Missing energy
Kinematic edges
Frequently-
studied decay chain
Observable:
Depends on:
Di-lepton invariant mass
Extract information about masses from edges in kinematical distributions
Limits depend on angles between sparticle decays
11 Jan 2005
Alan Barr, UCL

8. What particles are we seeing?
End points tell us something about masses but not:
Are these supersymmetric particles?
If so, which particles are participating?
Which neutralino?
Left or right slepton?
What sort of decays were involved?
Two or three body?
A nice example on how to include ambiguity in one’s analysis
Use Markov Chain Monte Carlo to explore the parameter space
Calculate likelihood at each point, including ambiguities
Able to explore high-dimensional parameter space efficiently
Still requires lots of CPU
Used for mass-space, unification-space and adding non-universal terms
Ambiguities in SUSY parameters from (2) and (3)
Lester, Parker, White hep-ph/
11 Jan 2005
Alan Barr, UCL

9. What particles are we seeing?
End points tell us something about masses but not:
Are these supersymmetric particles?
If so, which particles are participating?
Which neutralino?
Left or right slepton?
What sort of decays were involved?
Two or three body?
SUSY predicts particles with particular properties:
Couplings are SAME as SM partners
Spins differ by ½
Unbroken SUSY masses equal to SM partners
SUSY breaking terms dominate masses
A nice example on how to include ambiguity in one’s analysis
Use Markov Chain Monte Carlo to explore the parameter space
Calculate likelihood at each point, including ambiguities
Able to explore high-dimensional parameter space efficiently
Still requires lots of CPU
Used for mass-space, unification-space and adding non-universal terms
Does anything else look like SUSY?
Lester, Parker, White hep-ph/
11 Jan 2005
Alan Barr, UCL

10. Universal Extra Dimensions
TeV-scale universal extra dimension model
Kaluza-Klein states of SM particles
same QN’s as SM
mn2 ≈ m02 + n2/R2 [+ boundary terms]
KK parity:
From P conservation in extra dimension
1st KK mode pair-produced
Lightest KK state stable, and weakly interacting R
KK tower of masses n=0,1,…
Radius of extra dimension ~ TeV-1
S1/Z2
First KK level looks a lot like SUSY
BUT same spin as SM
Cheng, Matchev
Dubbed “Bosonic Supersymmetry”
11 Jan 2005
Alan Barr, UCL
hep-ph/

11. UED level-1 spectrum Example decay spectrum Cheng, Matchev
hep-ph/
1st excited KK level
(example masses)
After adding boundary terms
-> SUSY-like spectrum
Example decay spectrum
Stable lightest KK particle (weakly interacting)
11 Jan 2005
Alan Barr, UCL

12. Similarities and differences
SUSY
UED
One extra particle for each SM particle
Tower of extra particles for each SM particle
Spins differ by half unit
Same spins
Same couplings
R-parity  particles produced in pairs
KK parity  n=1 level particles produced in pairs
Weakly interacting Lightest SUSY particle
Weakly interacting Lightest KK particle
Can have good WIMP relic density
Mass spectrum depends on
method of SUSY breaking
Typically rather degenerate mass spectrum
11 Jan 2005
Alan Barr, UCL

13. 2nd KK mode? If 2nd KK mode light enough we can see it at LHC
Datta, Kong, Matchev hep-ph/
If 2nd KK mode light enough we can see it at LHC
Can even separate 2 and Z2
Good evidence in favour of UED
Problems:
May not be seen
Could have other interpretations (new gauge bosons?)
11 Jan 2005
Alan Barr, UCL

14. Similarities and differences
SUSY
UED
One extra particle for each SM particle
Tower of extra particles for each SM particle
Spins differ by half unit
Same spins
Same couplings
R-parity  particles produced in pairs
KK parity  n=1 level particles produced in pairs
Weakly interacting Lightest SUSY particle
Weakly interacting Lightest KK particle
Can have good WIMP relic density
Mass spectrum depends on
method of SUSY breaking
Typically rather degenerate mass spectrum
11 Jan 2005
Alan Barr, UCL

15. SPIN 2 Spin 2 particle : looks same after 180° rotation 11 Jan 2005
Alan Barr, UCL

16. SPIN 1 Spin 1 particle : looks same after 360° rotation 11 Jan 2005
Alan Barr, UCL

17. SPIN ½
Spin ½ particle : looks different after 360° rotation indistinguishable after 720° rotation

18. Measuring spins of particles
Basic recipe:
Produce polarised particle
Look at angular distributions in its decay
spin θ
Two methods for measuring SUSY particle so far…
11 Jan 2005
Alan Barr, UCL

19. Method 1 : 20 spin Use particular decay chain (right)
AJB hep-ph/
Method 1 : 20 spin
Use particular decay chain (right)
Make use of chiral couplings of Wino
Consider invariant mass of quark with lepton
Measure Angle
Mostly Wino: Polarised
11 Jan 2005
Alan Barr, UCL

20. Spin projection factors
Chiral coupling
Approximate SM particles as massless
-> okay since m « p
11 Jan 2005
Alan Barr, UCL

21. Spin projection factors
Σ=0 S
Spin-0
Produces polarised
neutralino
Approximate SM particles as massless
-> okay since m « p
11 Jan 2005
Alan Barr, UCL

22. Spin projection factors
Fermion θ* p S
Scalar
Polarised fermion
Approximate SM particles as massless
-> okay since m « p
11 Jan 2005
Alan Barr, UCL

23. Spin projection factors
mql – measure
invariant mass θ* p S
Approximate SM particles as massless
-> okay since m « p
11 Jan 2005
Alan Barr, UCL

24. lnearq invariant mass (1)
Back to back in 20 frame
quark
Probability θ* l+
lepton
Phase space
Invariant mass l-
m/mmax = sin ½θ*
Phase space -> factor of sin ½θ*
Spin projection factor in |M|2:
l+q -> sin2 ½θ*
l-q -> cos2 ½θ*
11 Jan 2005
Alan Barr, UCL

25. Experimental issues? How to distinguish between leptons?
Measure Inv Mass
How to distinguish between leptons?
Cant – becomes a combinatorial background
What about anti-squarks?
Asymmetry is reversed
Effect would cancel
However at pp collider more squark than anti-squark produced!
11 Jan 2005
Alan Barr, UCL

26. AJB hep-ph/
Charge asymmetry
ATLFAST-level
Charge asymmetry,
spin-0
SUSY PS
SUSY “data”
Demonstration that spin determination is LHC
Encouraging… but
Relies on presence of particular chain
Not a general technique.
UED has similar shape for asymmetry…
After cuts, detector simulation etc…
11 Jan 2005
Alan Barr, UCL

27. SUSY vs UED: Helicity structure
Neutralino spin
Smillie, Webber hep-ph/
Battaglia, Datta,
De Roeck,
Kong, Matchev
hep-ph/
SUSY vs UED: Helicity structure
Both prefer quark and lepton back-to-back
Both favour large (ql-) invariant mass
Shape of asymmetry plots similar
SUSY case
UED case
11 Jan 2005
Alan Barr, UCL

28. For UED masses not measureable For SUSY masses, measurable @ SPS1a
Neutralino spin
Smillie, Webber hep-ph/
For UED masses not measureable
Near-degenerate masses  little asymmetry
For SUSY masses, SPS1a
but shape is similar
need to measure size as well as shape of asymmetry
11 Jan 2005
Alan Barr, UCL

29. Range of Validity Limits: Relatively small area of validity
Neutralino spin
Range of Validity
Allanach & Mahmoudi
To appear in proceedings Les Houches 05
Sleptons too heavy
Universal SUSY fermion mass, m½
Universal SUSY scalar mass, m0
Limits:
Decay chain must exist
Sparticles must be fairly light
Relatively small area of validity
~ red + orange areas in plot after cuts
LEP excluded
11 Jan 2005
Alan Barr, UCL

30. Summary of spin method 1 Sensitive to neutralino-2 spin
Workable in some regions of parameter space
But those regions are not very large
Can give slepton mixing information
Sensitive to more than just spin
Works best when sparticles non-degenerate (SUSY-like)
Not workable when masses are near-degenerate (UED-like)
Similar shape for UED and SUSY
Size of asymmetry must be experimentally measured, not simply shape
11 Jan 2005
Alan Barr, UCL

31. Method 2: Angular distributions in direct slepton pair production
Z/ is polarised along the ±z axis
For slepton production
Measure m=0 at angle θ from direction where l=1, m=±1
Average over initial states
Sum over final states
P ~ 1 – cos2 θ
Favours θ ~ 90°
Slepton
Beam θ
Beam
Slepton
Incoming (anti-)quark spins? + or +
Z/ spin? or
Final state spin?
No component along slepton axis (m=0)
11 Jan 2005
Alan Barr, UCL

32. KK lepton pair production+ or
Relativistic limit:
With KK-lepton masses:
m=±1
m=0
KK lepton
Beam θ
Beam
KK lepton
Incoming (anti-)quark spins? + or +
Z/ spin? or
Final state spin? …
11 Jan 2005
Alan Barr, UCL

33. Angular distributions in direct slepton pair production
Normalised angular distributions
SUSY : qq  slepton pair :
“Perpendicular”
UED : qq  KK lepton pair :
“Parallel”
Phase Space :
“Flat”
Beam θ
Slepton
11 Jan 2005
Alan Barr, UCL

34. What we see experimentally
Invisible particle LSP or LKP
+ve lepton
Slepton or KK lepton (very short-lived)
Beam θ
Beam
Observables:
Pair of opposite sign, same family leptons
Sum of PT of invisibles: PTMISS
Invisible particle LSP or LKP
-ve lepton
Leptons “inherit” some knowledge of θ from their slepton or KK lepton mother
11 Jan 2005
Alan Barr, UCL

35. How to measure it? cos θlab cos θll* Good for linear e+e- collider
Not boost invariant
Missing energy means Z boost not LHC
Not LHC
cos θll*
1-D function of Δη:
Boost invariant
Interpretation as angle in boosted frame
Easier to compare with theory l1 l2
θ2lab
θ1lab
cos θlab l1 l2
η2lab
η1lab Δη
boost l1 Δη l2
θl*
cos θ*ll
N.B. ignore azimuthal angle
11 Jan 2005
Alan Barr, UCL

36. slepton  lepton correlations
Production angle
Observable angle
Slepton/KK lepton production angle not measurable
Lepton inherits from boost of slepton parent
Good correlation in plots above
Observable cos θ*ll smaller for SUSY than UED
11 Jan 2005
Alan Barr, UCL

37. Cuts and acceptance Need to beat down SM backgrounds
l+l- + missing energy signature
Z0Z0 background
Cut on l+l- invariant mass (not near Z)
W+W- background
Use mT2 variable to reduce this
Pseudorapidity of leptons Detector acceptance: |η| < 2.5
11 Jan 2005
Alan Barr, UCL

38. Slepton spin – LHC pt 5 Statistically measurable
“Data” = inclusive SUSY after cuts
Statistically measurable
Relatively large luminosity required
Study of systematics in progress
SM background determination
SUSY BG determination
Experimental systematics
No show-stoppers so far
11 Jan 2005
Alan Barr, UCL

39. Similar results at various SPS benchmark points
AJB hep-ph/
SPS1a
SPS1b
Similar results at various SPS benchmark points
fb-1 (2-3 years at design lumi)
Includes stat error from SM and SUSY BG subtraction No systematic uncertainty in backgrounds
SPS3
SPS5
11 Jan 2005
Alan Barr, UCL

40. Required luminosity? SPS1a, SPS1b, SPS5 mSUGRA “Bulk” points
Good sensitivity
SPS3 sensitive Co-annihilation point
(stau-1 close to LSP)
Signal from left-sleptons
SPS4 – non-universal cMSSM
Larger mass LSP
Softer leptons
Signal lost in WW background
Analysis fails in “focus point” region (SPS2). No surprise:
Sleptons > 1TeV  no xsection
Statistical significance of spin measurement LHC design luminosity ≈ 100 fb-1 / year
11 Jan 2005
Alan Barr, UCL

41. Summary of spin method 2 Sensitive to slepton spin
A more general method than method 1
Works at various SPS points
Sensitive when both:
sleptons are light
 reasonable x-sec
slepton-LSP mass difference is > mW
(for either slepton)  separate from WW
Possible extensions
Clean environment for measuring slepton pair production cross-section
Very useful constraint esp. if mass scale can be independently measured
11 Jan 2005
Alan Barr, UCL

42. So what can we tell from a hole in the ground?
LHC Observation
Importance for (SUSY) Phenomenology
New particles
“Death” of the Standard Model
Spin
SUSY or not SUSY?
Kinematical end points
Masses  How is SUSY broken?
Missing energy
Possible dark matter candidate
Branching ratios Detailed mass studies
Is LSP the major contribution to dark matter? Etc…
Extra excavations can extract:
Direct dark matter searches
Cosmologically stable LSP?
ILC measurements (when available)
Detailed properties of SUSY breaking, masses etc
11 Jan 2005
Alan Barr, UCL

43. Questions?
11 Jan 2005
Alan Barr, UCL

44. Paper trail
Phys.Rev. D64 (2001) Bounds On Universal Extra Dimensions
hep-ph/ Spin Correlations In Monte Carlo Simulations
hep-ph/ Bosonic Supersymmetry? Getting Fooled At The LHC
Phys.Lett. B596 (2004) 205 Determining the Spin of Supersymmetric Particles at the LHC Using Lepton Charge Asymmetry
hep-ph/ Study of the slepton non-universality at the CERN Large Hadronic Collider
hep-ph/ Probing Universal Extra Dimension at the International Linear Collider
JHEP 0507 (2005) 033 Contrasting Supersymmetry and Universal Extra Dimensions at the CLIC Multi-TeV e+ e- Collider
hep-ph/ Distinguishing Spins In Supersymmetric and Universal Extra Dimension Models at the Large Hadron Collider
hep-ph/ Discrimination of Supersymmetry and Universal Extra Dimensions at Hadron Colliders
hep-ph/ Measuring Slepton Spin at the LHC
11 Jan 2005
Alan Barr, UCL

45. Lepton non-universality
Neutralino spin
Goto, Kawagoe, Nojiri hep-ph/
Lepton non-universality
Lepton Yukawa’s lead to differences in slepton mixing
Mixing measurable in this decay chain
Not easy, but there is sensitivity at e.g. SPS1a
Biggest effect for taus – but they are the most difficult experimentally
11 Jan 2005
Alan Barr, UCL

46. Result of LHC analyses could be a supersymmetric sudoku puzzle!
True masses
Trial Masses
Wino
Bino
Slepton
Squark
Higgsino
Constraints from cross-sections (observables)
Ambiguities in where to place gauginos, LR sleptons etc
After Arkani-Hamed, Kane, Thaler, Wang hep-ph/
11 Jan 2005
Alan Barr, UCL

47. SUSY mass measurements:
LHC clearly cannot fully constrain all parameters of mSUGRA
However it makes good constraints
Particularly good at mass differences [O(1%)]
Not so good at mass scales
[O(10%) from direct measurements]
Mass scale possibly best “measured” from cross-sections
Often have >1 interpretation
What solution to end-point formula is relevant?
Which neutralino was in this decay chain?
What was the “chirality” of the slepton “ “ “ ?
Was it a 2-body or 3-body decay?
Long history of calculating masses from kinematical edges at LHC (since TDR)
Often can be measured with high experimental precision  experimentally clean
In cascades through sleptons, SM Backgrounds can be accurately determined from lepton different-flavour subtraction
Analytical expressions contain differences of masses squared
Edge variables most sensitive to mass differences (order 1%) than masses (order 10%)
Various factors lead to difficulties in interpretation
Provide non-trivial constraints on masses and mass-differences of particles
The extent to which ambiguities can be solved in LHC-only and LHC-ILC analyses is an area of active investigation
11 Jan 2005
Alan Barr, UCL