1. What prospects for Supersymmetry at the Large Hadron Collider ?
Some of the techniques
with which ATLAS and CMS intend
to constrain Supersymmetry
cern.ch

2. What are we going to cover?
Not a results talk! (WMAP etc)
Briefly look at supersymmetry
Look at RPV / RPC distinction from point of view of experiment
In no partiular order: look at a few
inclusive/widely applicable experimental techniques, also
less general but perhaps more powerful experimental techniques
July 2005
HCP2005 : SUSY at the LHC :

3. Supersymmetry – Extra particles
To stabilise the higgs mass NEED:
A scalar partner for every fermion
squark, slepton, (stop, sbottom, selectron, smuon, sneutrino, etc)
A fermion partner for ever boson:
gluino,
photino, wino, zino, higgsino
(mix to form 4 neutralinos)
Inexact symmetry – broken somehow
July 2005
HCP2005 : SUSY at the LHC :

4. R-Parity: Conservation/Violation
R=+1 for Standard Model particles
R= -1 for SUSY particles
Two main SUSY scenarios: (RPV/RPC)
RP-Conserving
RP-Violating
(L.S.P. = “lightest SUSY particle”)
July 2005
HCP2005 : SUSY at the LHC :

5. What do events look like?
RPV
RPV
(Lepton number violating)
(Baryon number violating)
RPC
RPC

6. So main signatures are:
Lots of jets
Lots of leptons
Lots of missing energy (RPC)
More on these a little later
ATLAS Trigger: ETmiss > 70 GeV, 1 jet>80 GeV. (or 4 lower energy jets). Gives low luminosity.
July 2005
HCP2005 : SUSY at the LHC :

7. What do we want to know? M.S.S.M.
Squark masses (12)
The gluino mass (1)
Slepton masses (9)
Neutralino masses (4)
Chargino masses (2)
Spins (?)
Mixing matrices (?)
Phases (?)
….. (plenty)
Other models:
RP-Violating M.S.S.M.
RPV couplings (45)
mSUGRA model
m0, m1/2, A0, tan β, sgn μ (5)
A.M.S.B. model
m0, m3/2, tan β, sgn μ (4)
G.M.S.B. model
λ, Mmes, N5, tan β, sgn μ, Cgrav (6)
There is no shortage of parameters which need to be determined!
July 2005
HCP2005 : SUSY at the LHC :

8. HCP2005 : SUSY at the LHC : Christopher.Lester@cern.ch
What can we measure?
“Lots, but it depends…”
The kinds of measurements which can be made, very much depend on the SUSY model which nature has chosen!
Two very different approaches:
(1) General techniques
(2) Non general .. specific techniques
Look at some specific RPV scenarios first
July 2005
HCP2005 : SUSY at the LHC :

9. R-Parity Violation RPV
L.S.P. = lightest SUSY particle
Easier than RPC?
The L.S.P. decays!
No missing energy, so reconstruct full event!
Case 1: Decays into leptons:
Multi-lepton signature
Case 2: Decays into jets:
Multi-jet signature
Case 3: Long lifetime:
looks like RPC scenario
Sparticles may be produced singly!
July 2005
HCP2005 : SUSY at the LHC :

10. Case 1: Lepton number violating RPV
λ’ijk couples a slepton to two quarks
Can have resonant sneutrino production
Cross section can place lower bound on λ’ijk
Expect to observe (within 3 years) either
900 GeV sneutrino if λ’211>0.05
350 GeV sneutrino if λ’211>0.01
(present limit: )
Reconstructed neutralino mass peak in mjjμ invariant mass distribution
λ’ijk =0.09
July 2005
HCP2005 : SUSY at the LHC :

11. Case 2: Baryon number violating RPV
Each L.S.P. decays to three quarks (u,d,s) forming three jets (jjj)
Require 2 leptons and at least 8 jets: (j+jjj)+(j+ll+jjj)
Look for L.S.P. / chargino peak in mjjj / m jjjll plane
msquark L = ± 5 ±12 GeV
mneutralino 2 = ± 0.3 ± 4 GeV
mslepton R = ± 3 ± 3 GeV
mneutralino 1 = ± 3 ± 3 GeV
July 2005
HCP2005 : SUSY at the LHC :

12. R-Parity Conservation RPC
L.S.P. = lightest SUSY particle
L.S.P. stable and weakly interacting, and so “goes missing”
Missing energy signature
Usually incomplete event reconstruction
Need to rely on long decay chains and kinematic variables (endpoints and distributions)
Sparticles are only produced in pairs
Double the trouble 
Missing information in BOTH halves of event! 
More general techniques available!
Half an event
July 2005
HCP2005 : SUSY at the LHC :

13. Inclusive reach in mSUGRA RPC
CMS 100 fb-1 (~3 years)
(Slide stolen from G.Polesello – SUSY2004)
July 2005
HCP2005 : SUSY at the LHC :

14. Squark/gluon mass scale RPC
What you measure:
events
Signal
S.M. Background
Peak of Meff distribution correlates well with SUSY scale “as defined above” for mSUGRA and GMSB models. (Tovey)

15. HCP2005 : SUSY at the LHC : Christopher.Lester@cern.ch
Kinematic edges: l+l- edge RPC
EXAMPLE:
l+l- edge
The l+l- invariant mass from the decay chain (right) has a kinematic endpoint.
For 100 fb-1, edge measured at ±0.13(stat) GeV
Dominant systematic error on lepton energy scale also ~0.1%
Maximum dilepton invariant mass is related to sparticle masses
July 2005
HCP2005 : SUSY at the LHC :

16. Plenty of other kinematic endpoints! RPC
Sequential
Talk about main differences to earlier work ...
Branched
July 2005
HCP2005 : SUSY at the LHC :

17. Edge positions
Talk about main differences to earlier work.

18. Fitted distributions S5 O1 ll llq ll llq lq high lq low lq high lq lowXq
llq Xq

19. HCP2005 : SUSY at the LHC : Christopher.Lester@cern.ch
Endpoint structure …
What different invariant mass distributions look like for a selection of plausible supersymmetric models.
( hep-ph/ )
Note that some edges are not simple!
July 2005
HCP2005 : SUSY at the LHC :

20. Coverage of edges / Problems RPC
However ...
… different processes can produce the same final state.
Can the process be identified?
Detailed study of the shape of the distributions can provide clues
Likely coverage?
Lepton edge observable over significant region of m0, m1/2 parameter space (CMS plot left)
See also hep-ph/ and hep-ph/ for more detailed analysis
Likely outcome?
Precise sparticle mass differences – 1%
if lucky with which chains are open
When chains are long enough, resolution on absolute mass scale improves and can measure mass of L.S.P.
July 2005
HCP2005 : SUSY at the LHC :

21. The sort of measurement you get
July 2005
HCP2005 : SUSY at the LHC :

22. Measuring spins in SUSY
hep-ph/
pp-collider!
Protons have more quarks than antiquarks
So LHC will make more squarks than antisquarks!
Spin-1/2 neutralino can tell the difference between:
q+l or qbar+lbar, and
q+lbar or qbar+l
Look for asymmetry between 1. and 2.
Asymmetry not washed out (completely) by lepton ambiguity!
5 years’ data
500 fb-1
1.5 years data (HL)
150 fb-1
July 2005
HCP2005 : SUSY at the LHC :

23. Non-edge RPC methods For LONG decay chains. At least 4 decays.
For LONG enough decay chains (4 or more 2-body decays) kinematics of decaying system are over-constrained by observed momenta
So can determine masses from small sample of events
O(N) events needed to determine N unknown masses
“Mass Relation Method” -- proof of principle using 1000 events (hep-ph/ )
For LONG decay chains. At least 4 decays.
Mass relation method
July 2005
HCP2005 : SUSY at the LHC :

24. Mass Relation Method Results
mneutralino (0 to 600 GeV)
mother (0 to 1000 GeV)
Gluino
Squark
Neutralino2
Slepton
Very good measurements of mass differences < 1%
Correlations still make overall mass scale hard to determine, without input from LC or say some other independent LHC technique
Reconstructed sparticle masses as function of reconstructed LSP mass
July 2005
HCP2005 : SUSY at the LHC :

25. Putting it all together!
Want to make fewer model assumptions
Huge parameter spaces / model spaces need to be explored
Have large number of different measurements we can make
Need Markov Chain techniques to explore likelihood surfaces efficiently
July 2005
HCP2005 : SUSY at the LHC :

26. HCP2005 : SUSY at the LHC : Christopher.Lester@cern.ch
Exploring non-linear experimental constraints upon susy model spaces
July 2005
HCP2005 : SUSY at the LHC :

27. HCP2005 : SUSY at the LHC : Christopher.Lester@cern.ch
LHC & Supersymmetry
What can the LHC provide if SUSY exists?
DISCOVERY ? ………………………………. YES!
Excellent prospects
Might even be “easy” !
Largely model-independent
PRECISE MEASUREMENTS ? …….... Plenty!
but more likely to be model-dependent
July 2005
HCP2005 : SUSY at the LHC :

28. HCP2005 : SUSY at the LHC : Christopher.Lester@cern.ch
The End
We can expect ATLAS and CMS to
Observe squarks and gluons below 2.5 TeV and observe sleptons below 300 GeV in inclusive measurements.
Accurately measure squark, slepton and neutralino masses using cascade decays (provided chains are sufficiently long and rates are favourable)
Determine spin of neutralinos
Success is expected in both RPV and RPC scenarios
Precise measurements: many can be made in principle, but which of them can measured in practice will depend strongly on the model which nature has chosen
Other areas of completed and ongoing research
which there was not time to discuss:
N.L.S.P. lifetime in G.M.S.B. models
(Non-pointing photons / slow heavy leptons)
A.M.S.B. models
Lepton flavour violation (via slepton mixing)
Measuring the gaugino mixing matrix
Direct slepton production
Non-minimal models
SUSY Higgs sector
Everything else which I have forgotten to mention ...
CMS
July 2005
HCP2005 : SUSY at the LHC :

29. Missing energy – early reach RPC
ATLAS
(Slide stolen from G.Polesello – SUSY2004)

30. Cross sections and rates
July 2005
HCP2005 : SUSY at the LHC :