Determination of SUSY
Parameters at LHC/ILC
Hans-Ulrich Martyn
RWTH Aachen & DESY
Outline
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H-U Martyn
Why and how to explore supersymmetry
Discovery and measurements at LHC
Precision measurements at ILC
Reconstructing supersymmetry
Dark matter and colliders
Scenarios off mainstream
Summary and outlook
SUSY parameter determination at LHC/ILC
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Why supersymmetry
Most attractive extension of Standard Model
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ensures naturalness of hierarchy scales
unification of fundamental gauge forces
provides cold dark matter candidate
stabilisation of light Higgs mass corrections
local SUSY incorporates gravity
additional sources of CP violation
maximal symmetry of fermions & bosons
Ellis et al 06
EW data consistent with weak-scale SUSY
LHC experiments
outcome extremely important, huge impact on future
projects - ILC, VLHC, superB, super…
discovery - revolution in particle physics
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SUSY parameter determination at LHC/ILC
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MSSM
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Building blocks SM  MSSM
– duplication of particles  sparticles
– 105 new parameters in MSSM R-parity conserving
Biggest mystery - symmetry breaking
invoke hidden sector
Hidden sector
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Flavour blind
mediators
MSSM sector
Plethora of mediation mechanisms:
gravity, gauge, gaugino, anomaly, string inspired, …
 reduced set of parameters
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what are dominant effects producing couplings of hidden sector
and MSSM fields: tree-level, loop-induced, ..., ?
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Soft parameters
GUT scale
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low scale MSSM
mSUGRA:
m0, m1/2, A,
tanβ, sign 
string inspired
models
Observables
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masses, decay widths,
spin, couplings, mixings,
quantum numbers,
cross-sections
, tanβ, Af
RPV, CPV, LFV …
GMSB
neutralinos/charginos
sleptons
squarks
Higgs (h,H,A)
AMSB
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at present
RGE
MGUT, MX, MS, HO corrections, renormalisation scheme..., ?
H-U Martyn
SUSY parameter determination at LHC/ILC
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Soft parameters
GUT scale
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low scale MSSM
mSUGRA:
m0, m1/2, A,
tanβ, sign 
string inspired
models
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Observables
masses, decay widths,
spin, couplings, mixings,
quantum numbers,
cross-sections
, tanβ, Af
RPV, CPV, LFV …
GMSB
neutralinos/charginos
sleptons
squarks
Higgs (h,H,A)
AMSB
…..
in future
all obstacles solvable with sufficient precision data -H-U Martyn
need new techniques at hadron colliders
SUSY parameter determination at LHC/ILC
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Experimental facilities
ILC
LHC
pp
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14 TeV
2007 commissioning @ 0.9 TeV
2008 start operation @ 14 TeV
goal: few fb-1 per experiment
2010 reliable results on new
physics, discoveries?
huge discovery potential up to
scales of m ~ 2.5 TeV
H-U Martyn
e+e-
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1 TeV
2006 reference design
2009 technical design
2010 + … ready for decision
7 - 8 years construction
polarised e+e-, e-e-, γγ
high-precision measurements up
to kinematic limit 0.5 - 1 TeV
SUSY parameter determination at LHC/ILC
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Exploring supersymmetry
LHC
Dominant production of strongly
interacting squarks, gluinos
Many states produced at once,
long decay chains  complicated
final states
ILC
Production of non-colored sleptons,
neutralinos, charginos
Select exclusive reactions, bottom-up
approach, model independent analysis
Considerable synergy between LHC and ILC
combined analyses, concurrent running
SPS 1a’ mSUGRA benchmark
favourable for LHC & ILC
H-U Martyn
SUSY parameter determination at LHC/ILC
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Discovering SUSY at LHC
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Signatures from gluino/squark decay chain:
high pT multi-jets, isolated leptons,
large missing energy
Inclusive search Meff=∑1,4ETi + ETmiss
QCD background reliably calculable?
W, Z, tt production
 Anastasiou
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Early discovery of SUSY at LHC?
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Is there New Physics?
What is the scale?
Science community expects fast and reliable
answers, e.g. planning for future facilities
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Understanding detector and ETmisss
spectrum crucial!
Discovery potential vs luminosity
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SUSY parameter determination at LHC/ILC
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Reconstructing masses at LHC
Exploit variety of invariant mass distributions, low & high end points
Construct kinematic constraints on sparticle masses
 precise mass differences
 seriously limited by poor neutralino mass
strong slR - χ1 correlation
Nojiri, SUSY06
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Reconstructing masses at LHC
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End point method: waste of statistics and information
Mass relation method: exact kinematics using complete events
bbll channel
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5 masses: each event define 4-dim hypersurface in 5-dim mass space
5 events sufficient to solve mass equations
many events: overconstraint fit, solve for masses, improved resolution
All sparticle masses known:  reconstruction LSP momentum
Kawagoe, Nojiri, Polesello 2004
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Spin, L/R sfermion?
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Shape of decay distribution carry spin information
Problems: pick up correct combination
quark + near lepton, tell ql+ from anti-ql+
Solution: lepton charge asymmetry
Assumptions: more squarks than antisquarks
squarks/sleptons dominantly left or right
neutralino spin ½
Distinct from other models, e.g. UED
spinless
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Finding sparticles with help of ILC
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Light neutralinos and chargino found at ILC
 Prediction of masses of heavy neutralinos
and chargino
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may not be accessible at ILC
New particle can be identified at LHC via
‘edge’ in the di-lepton mass spectrum
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LHC/ILC interplay:
Phys.Rept.426 (2006) 47
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SPS 1a’ spectrum from LHC
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LHC analysis
access to high mass
states, sleptons and
gauginos via cascades
resolution limited by
strong correlations with
neutralino LSP
mass differences much
more accurate
Correct interpretation?
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neutralino
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sneutrino
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Aguilar-Saavedra et al 2006
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KK photon
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Masses at ILC
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Energy spectrum, end points
flat energy spectrum
δm ~ 0.1 GeV
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Threshold excitation curve
characteristic β dependence, steep rise
δm ~ 0.05 - 0.2 GeV
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Masses -stau
Stau production
flat energy spectrum distorted to
triangular shape
fit upper end point  mstau
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E+
E-
mstau = 173 GeV
δm ~ 0.3 GeV
Coannihilation region
small Δm = mstau-mχ  3 GeV accessible
difficult measurement due to huge γγ bkg
important to get DM constraint
very problematic for LHC
Point D’
mstau = 218 GeV
Δm = 5 GeV
δm ~ 0.15 GeV
h-um 04
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Masses - gauginos
Neutralino production
Chargino production
Many reactions to get the mass of the lightest
neutralino very accurately!
δm ~ 0.05 GeV
H-U Martyn
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Masses - cascade decays
Decay chains à la LHC
kinematics of cascade decay provides access
to intermediate slepton
2-fold ambiguity for mass solutions
 extremely narrow mass peak
δm/m ~ 5∙10-5
Similarly: selectron reconstruction
H-U Martyn
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Berggren 05
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Masses & mixings
Chargino sector
Mass matrix
masses from threshold excitation
Mixings
polarised cross sections σL,R[11] and σL,R[12]
disentangle ambiguities and determine
mixing angles cos 2ΦLR
Choi et al 2000
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Masses & mixings
Stop production
lightest squark in many scenarios, difficult to
detect at LHC
Mixing
polarised cross sections
SPS 5
Bartl et al 97
Minimal mass
reconstructed from kinematics, momentum
correlations, using mχ
peak at mstop
Finch et al 04
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Spin
Threshold production
and
Angular distribution
all masses known: reconstruction
polar angle Θ (2-fold ambiguity)
Unambiguous spin assignment
model inependent, distinct from e.g. UED
L/R quantum numbers via polarisation
R sfermions prefer right-handed electrons e-R
L sfermions prefer left-handed electrons e-L
H-U Martyn
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Choi et al 2006
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Couplings
Basic element of SUSY
identical gauge and Yukawa couplings
SU(2) gauge g = Yukawa ĝ
U(1) gauge g’ = Yukawa ĝ’
Slepton production
H-U Martyn
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Freitas et al, 04
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SPS 1a’ spectrum from LHC+ILC
Coherent LHC+ILC analysis
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complementary
spectrum completed
superior to sum of
individual analyses
accuracy increased by 1-2
orders of magnitude
Challenge:
experimental accuracy
matched by theory?
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Aguilar-Saavedra et al 2006
H-U Martyn
SUSY parameter determination at LHC/ILC
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How to proceed?
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We want to understand the relation between the visible sector,
observables, and the fundamental theory
 SUSY provides a predictive framework
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How precise can we predict masses, x-sections, branching ratios, couplings, … ?
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Which precision can be achieved on parameters of the MSSM Lagrangian?
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many relations between sparticle masses at tree-level, much worse at loop-level
choice of renormalisation scheme?
Lagrangian parameters not directly measurable
parameters not always directly related to a particular observable, e.g. µ,tan ß
fitting procedure, …
Can we reconsruct the fundamental theory at high scale?
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unification of couplings, soft masses, … ?
which SUSY breaking mechanism, origin of SUSY breaking?
Goals of the SPA Project
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SPA convention and project
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Supersymmetry Parameter Analysis
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SPA Convention
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Supported by ~100 theorists & experimentalists
renormalisation schemes / LE parameters / observables
Program repository
theor. & expt. analyses / LHC+ILC tools / Susy Les Houches Accord
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scheme translation, RGE & spectrum calculators, event generators, fitting, …
Theoretical and experimental tasks
short- and long-term sub-projects, SUSY calc. vs expt., LO  NLO  NNLO, …,
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new channels & observables, combine LHC+ILC data
Reference point SPS 1a’
 Hollik, Robens
derivative of SPS 1a, consistent with all LE and cosmological data
Future developments
CP-MSSM, NMSSM, RpV, effective string theory, etc.
You are invited to join!  http://spa.desy.de/spa/
H-U Martyn
SUSY parameter determination at LHC/ILC
EPJC 46 (2006) 43
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Extracting Lagrange parameters
Global fit of all available ‘data’ to most up-to-date HO calculations
input: masses, edges, x-sects, BRs from LHC & ILC
~120 values incl. realistic error correlations
theory: no errors (no reliable estimate available)
output: ~20 parameters
tools Fittino
(Bechtle, Desch, Wienemann), SFitter (Lafaye, Plehn, D. Zerwas)
Results SPS 1a’
high precision
LHC alone not able to constrain
most parameters
H-U Martyn
 Arkani-Hamed
SUSY parameter determination at LHC/ILC
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High-scale extrapolation
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Gauge couplings α-1
grand unification ~2σ / giU~2%
H-U Martyn
SUSY parameter determination at LHC/ILC
ε3 at ~8σ level
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High-scale extrapolation
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Universality of gaugino & scalar mass parameters in mSUGRA
1/Mi[GeV-1]
Mj2 [103 GeV2]
Mj2 [103 GeV2]
mSUGRA
GMSB
MM
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Q [GeV]
Q [GeV]
Q [GeV]
Evolution in GMSB distinctly different from mSUGRA
Bottom-up evolution of Lagrange parameters provides
high sensitivity to SUSY breaking schemes
 Porod
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Testing mSUGRA
mSUGRA fit excellent
Universality can be tested in bottom-up approach
non-coloured sector at permil to percent level
colored sector needs improvement
LHC+ILC: Telescope to Planck scale physics
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Dark matter & colliders
Cold dark matter in Universe ΩDM≈ 22%
ΩDMh2 = 0.105 ± 0.008
WMAP
Understanding nature of cold dark matter requires
• direct detection DM particle in astrophysical expt
• precise measurement of DM particle mass & spin at
colliders
• compare relic density calculation with observation
Ωχ h2~ 3 ∙10-27cm3s-1/<σv>
requires typical weak interaction annihilation cross
section
Candidates: neutralino, gravitino, sneutrino, axino, …
Formation:
freeze out of thermal equilibrium
in general Ωχ » 0.2, annihilation mechanism needed
thermal production
late decays
 Kraml, Allanach
H-U Martyn
SUSY parameter determination at LHC/ILC
metastable stau
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Neutralino dark matter
SPS 1a’
‘bulk region’
annihilation through slepton exchange
χχ  тт, bb
σχχ depends on light slepton masses & couplings
LHC: precision ~20% (very high lumi)
assuming mSUGRA, ‘a posteriori’ estimate/fix of
unconstrained parameters, e.g. mixings
LHC + ILC: precision ~1-2%
matches WMAP/Planck expts
 Reliable prediction for direct neutralino - proton
detection cross section
Baltz 06
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Neutralino dark matter
LCC2
‘focus point region’
heavy sfermions, light gauginos
annihilation ΧΧ  WW, ZZ
σχχ depends on M1, M2, μ, tanβ
LHC: study gluino decays, not enough constraints
to solve neutralino matrix
LHC + ILC: ~10% precision on relic abundance
μ
LHC multiple solutions
wino
bino
Higgsino
M1
parasitic LHC peak
at Ωχ ~ 0
ILC
resolves
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Gravitino dark matter
Gravitino mass set by SUSY breaking scale F of mediating interaction
m3/2 =F/√3∙MP
Planck scale MP =2.4∙1018 GeV
In general free parameter depending on scenario
supergravity, gaugino, gauge mediation
m3/2 = TeV … eV
Most interesting: gravitino LSP, stau NLSP
m3/2 = few GeV - few 100 GeV
Dominant decay
gravitational coupling, lifetime sec - years
Gravitino not detectable in astrophysical expts
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Gravitino dark matter
Detecting metastable staus & gravitinos
identify & record stopping stau  stau mass
wait until decay  stau lifetime
measure τ recoil spectra  gravitino mass
rare radiative decays  gravitino spin
γ- τ correlations in
LHC detectors not appropriate
stau mass ok, no lifetime or decay spectra
moderate rate, high background, busy timing
external absorber/calorimeter needed
ILC ideal environment
high rate, adjustable via cms energy
low duty cycle ~0.5%, excellent calorimetry
Hamaguchi et al 04, Feng, Smith 04, DeRoeck et al 05, H-UM 06
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Gravitino dark matter
GDM ε scenario
mo=m3/2=20 GeV, M1/2=440 GeV
ILC case study L=100 fb-1 @ 500 GeV (<1 year data taking)
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Prolific stau production
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Lifetime measurement
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Decay spectrum
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 Access to Planck scale / Newton’s constant
SUSY breaking scale
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Unique test of supergravity:
gravitino = superpartner of graviton
H-U Martyn
SUSY parameter determination at LHC/ILC
trap
H-U M, EPJC 48 (2006) 15
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Off mainstream scenarios
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Scenario SPS 1a’ is just a benchmark, a test bed
Nature may be very different from SPS 1a’, mSUGRA, or …
Other possibilities
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complex parameters, CP phases baryogenesis
lepton flavour violation neutrino masses
R-parity violation unstable LSP, neutrino masses
alternative SUSY breaking mediation anomaly, gauge, gaugino, …
mixed scenarios of SUSY breaking
additional matter/gauge fields
additional dimensions
split SUSY
and many more …
NMSSM, UMSSM, ESSM, …
Different signatures at LHC / ILC
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CP phases
SPS 1a
CPV in SUSY may explain baryon asymmetry
CP phases
Bartl et al
m=380 GeV
affect CP-even quantities
generate CP-odd observables (triple products)
EDM constraints for 1st, 2nd generation sfermions
and charginos/neutralinos
mSUGRA Φμ < 0.1-0.2
Stop decay widths
μ, At
strong phase dependence Φ(At) of stop  chargino + b
Neutralino sector in selectron production
μ, M1
pure Χi0 exchange in t and u channel
S/√L
transversely polarised e-e- beams
cross section
CP even
azimuthal asymmetry CP odd
complementary to
H-U Martyn
2 σ @ L=100 fb-1
pse_L∙(se1x se2)
 Kernreiter, Rolbiecki
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Lepton Flavour Violation
LFV in slepton pair production
Seesaw mechanism to generate neutrino masses mν
LR extension: νR singlet fields and superpartners
added to MSSM
sensitivity
σLFV ~ 0.1-1 fb
 Majorana mass scale MR~1013-1014 GeV
 radiative decay
Br(μeγ)~10-13
 Deppisch
Deppisch et al 04
μe
SPS 1a
τμ
Massive neutrinos affect RGEs of sleptons
flavour off-diagonal terms with large Yukawa
couplings for 3rd generation
kink in evolution of L3, H2
M(νR3) = (5.9±1.6) 1014 GeV
SPS 1a’
Blair et al 05
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Split SUSY
SUSY breaking scale split between scalar & gaugino sectors
Arkani-Hamed, Dimopoulos
Spectrum
light Higgs, neutralinos, charginos, gluino
squarks, sleptons, H, A extremely heavy
Signatures strongly dependent on gluino lifetime
long-lived gluino, R-hadrons
LHC
displaced vertices
stable R0  missing ET
Kilian et al 04
stable R+  balanced pT
Chargino/neutralino sector
LHC & ILC
conventional phenomenology for searches/masses
anomalous Yukawa couplings from gaugino-Higgsino mixing
Both LHC & ILC needed to establish SUSY Lagrangian
at common scalar mass scale m˜
 Provenza
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Summary & outlook
Experiments at LHC will tell if weak-scale supersymmetry is
realised in nature
Methods and techniques have been developed to discover and
explore supersymmetry. Close contacts between experiment and
theory are needed to go beyond basic discovery
 SPA project provides a platform for discussions
Both accelerators, the LHC and a future ILC, are necessary to
understand the sparticle spectrum in detail and to unravel in a
model-independent way the fundamental supersymmetry theory
High-precision measurements of low-energy Lagrange parameters
offer the unique possibility to perform reliable extrapolations
towards the GUT / Planck scale and to test the concepts of
unification of the laws of physics
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