Map
Why look for SUSY?
What can we sayabout what we’vefound?
Anything unusual out there
Was it reallySUSY?
How
can
we
disc
over
SUSY
at LH
C?
Just find SM Higgs
Alan Barr
Dark Matter
• Atoms ~ 4%• Evidence for Dark Matter from
– Rotation curves of galaxies– Microwave background radiation– Galaxy cluster collision
Invisible mass
Visible mass
Particle physicists should hunt: Weakly Interacting, Stable, Massive Particles
Particle physicists should hunt: Weakly Interacting, Stable, Massive Particles
• If exotics can be produced singly they can decay– No good for
Dark Matter candidate
• If they can only be pair-produced they are stable– Only
disappear on collision (rare)
Producing exotics?
Time
standard
exotic
Time
standard
exotic
Time
standard
exotics
Time
standardexotics
Require an even number of exotic legs to/from blobs(Conserved multiplicative quantum number)
Require an even number of exotic legs to/from blobs(Conserved multiplicative quantum number)
How do they then behave?
• Events build from blobs with 2 “exotic legs”
• A pair of cascade decays results
• Complicated end result
• Events build from blobs with 2 “exotic legs”
• A pair of cascade decays results
• Complicated end result
Time
standard
2 exotics
Production part
Time
standard
heavyexotic lighter
exotic
Decay part Time
Complete event
= exotic= standard
Candidates?• New particles by a
symmetry:– Supersymmetry
• Relationship between particles with spins differing by ½h
– Spatial symmetry
• With extra dimensions
– Gauge symmetry
• Extra force interactions (and often matter particles)
electron
quarks
exoticpartners?
Force-carriers
Related bysymmetry
Related bysymmetry
neutrino
x3x2
…?
…?
…?
Alreadyobserved
_
What is supersymmetry?• Nature permits
various only types of symmetry:– Space & time
• Lorentz transforms• Rotations and
translations– Gauge symmetry
• SU(3)c x SU(2)L x U(1)– Supersymmetry
• Anti-commuting (Fermionic) generators
• Relationship with space-time
• Consequences:– Q(fermion)=boso
n– Q(boson)=fermio
n
• Equal fermionic and bosonic DF– Double particle
content of theory– Partners not yet
observed– Must be broken!
• Otherwise we’d have seen it
{Q,Q†} = -2γμPμ
Why SUSY?• Higgs mass2
– Quadratic loop corrections
– In SM natural scale• Λcutoff ~ Mplanck • v. high!
– Need m(h) near electroweak scale• Fine tuning• Many orders of
magnitude
top
Δm2(h) Λ2cutoff
higgs higgs
stop
higgs higgs
• Enter SUSY– 2 x Stop quarks– Factor of -1 from
Feynman rules– Same coupling, λ– Quadratic
corrections cancel
λλλ λ
What does SUSY do for us?• Coupling of stop to
Higgs– RGE corrections – Make mHH coupling
negative– Drives electro-weak
symmetry breaking
• Predicts gauge unification– Modifies RGE’s– Step towards
“higher things”
stop
higgs higgs
+SUSY
Log10 (μ / GeV)
Hit!
1/α
Extended higgs sector(2 doublets)
(S)particles
SM SUSY
quarks (L&R)leptons (L&R) neutrinos (L&?)
squarks (L&R)sleptons (L&R)sneutrinos (L&?)
Z0
W±
gluon
BW0
h0
H0
A0
H±
H0
H±
4 x neutralino
2 x chargino
AfterMixing
gluino
Spin-1/2
Spin-1
Spin-0
Spin-1/2
Spin-0
BinoWino0
Wino±
gluino
~
~
Proton on Proton at 14 TeV
40 million bunch crossings/minute
Something to see it with
General featuresMass/GeV
“typical” SUSY spectrum(mSUGRA)
• 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
SUSY event
Jets
Missing transverse momentum
LeptonsHeavy quarks
Cross-sections etc
Lower backgrounds
Higher backgrounds
“Rediscover”
“Discover”
ZZ
WW
Discovering SUSY with jets
• Select a small number of high PT jets– Large signal cross-section– Large control statistics– Relatively well known SM
backgrounds• Relatively “model independent”
– Does not rely on leptonic cascades– Does not rely on hadronic cascades
SIGNAL topology
BACKGROUND topology (QCD)
Importance of detailed detector understanding
Lesson from the Tevatron
Et(miss)
Geant simulation showingfake missing energy
Suppressing backgrounds
QCD SUSY
Jet
Jet
Remove events with missing energy back-to-back with leading jets
Measuring Backgrounds
• Example: SUSY BG– Missing energy + jets
from Z0 to neutrinos– Measure in Z -> μμ– Use for Z ->
• Good match– Useful technique
• Statistics limited– Go on to use W => μ
to improve
Measure in Z -> μμ
Use in Z -> νν R: Z
B: Estimated
R: Z
B: Estimated
Di-jets + MET measurement
)2(j(2)TT
)1(j(1)TT
T)2()1(T2 ,,,max
minpppp
ppp
mmM
• Keeping it simple– >=2 jets
– ET (J1,2) > 150 GeV; |η1,2| < 2.5 Cambridge “Stransverse mass”
Dijet inclusive: - No lepton veto- No b-jet veto- No multi-jet veto
Dijet inclusive: - No lepton veto- No b-jet veto- No multi-jet veto
Discovering SUSY with leptons
• Particularly important if strongly interacting particles are heavy
Small Standard Model Backgrounds
Golden channel @ Tevatron
Top pair backgrounds
Leptons from b-decayscontribute to background
Use track isolation to reduce these
e
Again: measure the background
Measure this backgroundin same-sign leptons in semi-leptonic b-decays
After 10 fb-1
• Great discovery potential here…• Lots of other channels:
– M jets + N leptons + missing transverse energy
“Standard” SUSY point Very light SUSY point
signal
signal
mSUGRA A0=0, tan(b) = 10, m>0
mSUGRA A0=0, tan(b) = 10, m>0
Slepton Co-annihilation region
Slepton Co-annihilation region
‘Bulk’ region: t-channel slepton exchange
‘Bulk’ region: t-channel slepton exchange
‘Focus point’ region: annihilation to gauge bosons
‘Focus point’ region: annihilation to gauge bosons
WMAP constraints
Rule out with 1fb-1
Reach in cMSSM?
Mass scale?
Spectrum SUSY kinematicvariable“MTGEN”
ET sum / 2
What might we then know?• “Discovered supersymmetry?”• Can say:
– Undetected particles produced• missing energy
– Some particles have mass ~ 600 GeV, with couplings similar to QCD
• MTGEN & cross-section– Some of the particles are coloured
• jets– Some of the particles are Majorana
• excess of like-sign lepton pairs– Lepton flavour ~ conserved in first two generations
• e vs mu numbers– Possibly Yukawa-like couplings
• excess of third generation– Some particles contain lepton quantum numbers
• opposite sign, same family dileptons
Perhaps notwhat we think!
Mapping out the new world
• Some measurements make high demands on:– Statistics (=> time)– Understanding of detector– Clever experimental technique
LHC Measuremen
tSUSY
Extra Dimensions
MassesBreaking
mechanismGeometry &
scale
SpinsDistinguish
from EDDistinguish from SUSY
Mixings,Lifetimes
Gauge unification?Dark matter candidate?
Constraining masses• Mass constraints• Invariant masses in
pairs– Missing energy– Kinematic edges
Observable: Depends on:
Limits depend on angles betweensparticle decays
Frequently-studieddecay chain
Mass determination
• Basic technique– Measure edges– Try with different SUSY
points– Find likelihood of fitting
data
• Event-by-event likelihood– In progress
Measureedges
Variety of edges/variables
Try variousmasses in equations
• Narrow bands in ΔM• Wider in mass scale• Improve using cross- section information
SUSY mass measurements• Extracting
parameters of interest– Difficult problem– Lots of competing
channels– Can be difficult to
disentangle– Ambiguities in
interpretation– Lots of effort has
been made to find good techniques
Tryvariousdecaychains
Tryvariousdecaychains
Look forsensitive variables
(many of them)
Look forsensitive variables
(many of them)
Extractmasses
Extractmasses
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 scale• [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?
SUSY spin measurements
• The defining property of supersymmetry– Distinguish from e.g.
similar-looking Universal Extra Dimensions
• Difficult to measure @ LHC– No polarised beams– Missing energy– Indeterminate initial
state from pp collision
• Nevertheless, we have some very good chances…
Universal Extra Dimensions• TeV-scale universal extra
dimension model• Kaluza-Klein states of SM
particles– same QN’s as SM– mn
2 ≈ 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
• First KK level looks a lot like SUSY
• BUT same spin as SM
hep-ph/0205314 Cheng, Matchev
Radius of extra dimension ~ TeV-1
KK tower of masses n=0,1,…
Dubbed “Bosonic Supersymmetry”
R
S1/Z2
Spin 2 particle: looks same after 180° rotation
SPIN 2
Spin 1 particle : looks same after 360° rotation
SPIN 1
Spin ½ particle : looks different after 360° rotation indistinguishable after 720° rotation
SPIN ½
Measuring spins of particles
• Basic recipe:– Produce polarised particle– Look at angular distributions in its decay
spinθ
Left Squarks-> strongly interacting-> large production-> chiral couplings
mass/G
eV
Revisit “Typical” sparticle spectrum
Some sparticles omitted
10
–> Stable-> weakly interacting
Right slepton(selectron or smuon)-> Production/decayproduce lepton-> chiral couplings
LHC point 5
20 = neutralino2
–> (mostly) partnerof SM W0
10 = neutralino1
–> Stable-> weakly interacting
Spin projection factors
Approximate SM particles as massless-> okay since m « p
Lq~Lq
02
~1
0Lq
P
S
Chiral coupling
Spin projection factors
Lq~Lq
02
~
1
0~ LqP
S
0
1~02 S
Σ=0
Spin-0
Produces polarised neutralino
Approximate SM particles as massless-> okay since m « p
Spin projection factors
Approximate SM particles as massless-> okay since m « p
(near) Rl
θ*p
SLq~
Lq
Rl
~02
~Rl
Scalar
Fermion
Polarisedfermion
Spin projection factors
Approximate SM particles as massless-> okay since m « p
(near) Rl
θ*p
S
Lq~Lq
Rl
~02
~Rl
mql – measureinvariant mass
1
0~ LqP
S
lnearq invariant mass (1)
m/mmax = sin ½θ*
Back to backin 2
0 frame
θ*
quark
lepton
Phase space -> factor of sin ½θ*Spin projection factor in |M|2: l+q -> sin2 ½θ* l-q -> cos2 ½θ*
l+
l-
Phase space
Pro
bab
ility
Lq~ Lq
Rl
~02
~Rl
Invariant mass
After detector simulation
l+
l- parton-level * 0.6
-> Charge asymmetry survives detector simulation-> Same shape as parton level (but with BG and smearing)
detector-levelInvariant mass
Ch
arg
e a
sym
metr
y,
spin-0
Even
ts
SUSY
Change in shapedue to charge-blind cuts
Distinguishing between models
Sin (θ*/2)
dP/d
Sin
(θ*/
2)
SU
SY
No spin
UniversalExtra Dim.
ql+ or ql-_
dP/d
Sin
(θ*/
2)
Sin (θ*/2)
No spin
UniversalExtra Dim.
SUSY
ql- or ql+
As expected, UED differsfrom all-scalar (no-spin)and from SUSY
As expected, UED differsfrom all-scalar (no-spin)and from SUSY
Smillie et al.
What else can we do?
Predict WIMP relic density
Measure the invisible particle mass(WIMP mass)
Measure couplings from rates and branching ratios
Summary
• Discovering something new is an important step– Need to understand backgrounds and detector
very well
• Finding out what we have discovered is even more interesting!– Masses Spins Branching Ratios
• These tell us about– SUSY vs Extra Dimensions– Dark Matter– Unification– SUSY breaking
Extras
How is SUSY broken?• Direct breaking in
visible sector not possible– Would require
squarks/sleptons with mass < mSM
– Not observed!• Must be strongly
broken “elsewhere” and then mediated– Soft breaking terms
enter in visible sector
– (>100 parameters)
Stronglybrokensector
Weakcoupling(mediation)
Soft SUSY-breaking termsenter lagrangianin visible sector
Various models offer different mediation
mSUGRA – “super gravity”• A.K.A. cMSSM• Gravity mediated SUSY
breaking– Flavour-blind (no FCNCs)
• Strong expt. limits– Unification at high scales
• Reduce SUSY parameter space– Common scalar mass M0
• squarks, sleptons– Common fermionic mass
M½• Gauginos
– Common trilinear couplings A0
• Susy equivalent of Yukawas
Programs includee.g. ISASUSY,SOFTSUSY
1016 GeV
EW scale
Iterate usingRenormalisationGroupEquations
Unification of couplings
Correct MZ, MW, …
Production AsymmetryTwice as much squark as anti-squark pp collider Good news!
Squark Anti-squark
Note opposite shapes in distributions
Other suggestions• Gauge mediation
– Gauge (SM) fields in extra dimensions mediate SUSY breaking
• Automatic diagonal couplings no EWSB
– No direct gravitino mass until Mpl
• Lightest SUSY particle is gravitino• Next-to-lightest can be long-lived (e.g. stau or neutralino)
• Anomaly mediation– Sequestered sector (via extra dimension)
• Loop diagram in scalar part of graviton mediates SUSY breaking
• Dominates in absence of direct couplings– Leads to SUSY breaking RGE β-functions
• Neutral Wino LSP• Charged Wino near-degenerate with LSP lifetime • Interesting track signatures Not
exhaustive!
R-Parity
• Unrestricted couplings lead to proton decay:
LHUDDLQDLLEWRPV )(21
L-violating B-violating L-violating
General softbreaking terms include:
Pro
ton
u
d
u u_
e-Λ”112 Λ’112
s~_ P
ion Unacceptably high rate compared
to experimental limits (proton lifetime > 1033 years)
Strong limits on products ofcouplings
• Impose RP = (-1)3B+L+2S (by hand)
– Distinguishes SM from SUSY partners– Leads to stable LSP
• Required for dark matter
– Sparticles produced in pairs
Gauge Mediated SUSY Breaking
• Signature depends on Next to Lightest SUSY Particle (NLSP) lifetime
• Interesting cases:– Non-pointing
photons– Long lived staus
• Extraction of masses possible from full event reconstruction
• More detailed studies in progress by both detectors
R-hadrons
• Motivated by e.g. “split SUSY”– Heavy scalars– Gluino decay through
heavy virtual squark very suppressed
– R-parity conserved– Gluinos long-lived
• Lots of interesting nuclear physics in interactions– Charge flipping, mass
degeneracy, …
• Importance here is that signal is very different from standard SUSY
R-hadrons in detectors• Signatures:
1. High energy tracks (charged hadrons)
2. High ionisation in tracker (slow, charged)
3. Characteristic energy deposition in calorimeters
4. Large time-of-flight (muon chambers)
5. Charge may flip• Trigger:
1. Calorimeter: etsum or etmiss
2. Time-of-flight in muon system
– Overall high selection efficiency– Reach up to mass of 1.8
TeV at 30 fb-1
GEANT simulation of pair of R-hadrons
(gluino pair production)
Method 2: Angular distributions in direct slepton pair production
SUSY : qq slepton pair
UED : qq KK lepton pair
Phase Space :
Normalised cross-sections
AJB hep-ph/0511115
Sensitive variables?• cos θlab
– Good for linear e+e- collider
– Not boost invariant• Missing energy means Z
boost not known @ LHC• Not sensitive @ LHC
• cos θll*– 1-D function of Δη:
– Boost invariant– Interpretation as angle
in boosted frame– Easier to compare with
theory
N.B. ignore azimuthal angleN.B. ignore azimuthal angle
boos
t)tanh()tan2cos(cos 211* 2
1
ell
AJB hep-ph/0511115
l1l2
θ2lab
θ1lab
cos θlab
l1l2η2
lab
η1lab
ΔηΔη
l1Δη
l2
θl*θl
*
cos θ*ll
Slepton spin – LHC pt 5
• Statistically measurable
• Relatively large luminosity required
• Study of systematics in progress– SM background
determination– SUSY BG
determination– Experimental
systematics
Slepton spin AJB hep-ph/0511115
“Data” = inclusive SUSY after cuts
Snowmass points
SPS4 – non-universal cMSSMLarger mass LSPSofter leptonsSignal lost in WW background
SPS4 – non-universal cMSSMLarger mass LSPSofter leptonsSignal lost in WW background
SPS1a, SPS1b, SPS5mSUGRA “Bulk” pointsGood sensitivity
SPS1a, SPS1b, SPS5mSUGRA “Bulk” pointsGood sensitivity
SPS3 sensitiveCo-annihilation point(stau-1 close to LSP)Signal from left-sleptons
SPS3 sensitiveCo-annihilation point(stau-1 close to LSP)Signal from left-sleptons
Analysis fails in “focus point”region (SPS2). No surprise:Sleptons > 1TeV no xsection
Analysis fails in “focus point”region (SPS2). No surprise:Sleptons > 1TeV no xsection
Slepton spin AJB hep-ph/0511115
Statistical significance of spin measurementLHC design luminosity ≈ 100 fb-1 / year
Statistical significance of spin measurementLHC design luminosity ≈ 100 fb-1 / year
Smillie, Webberhep-ph/0507170
See also:Battaglia, Datta,De Roeck,Kong, Matchevhep-ph/0507284
SUSY vs UED: Helicity structure
• Both prefer quark and lepton back-to-back– Both favour large
(ql-) invariant mass
• Shape of asymmetry plots similar
Neutralino spin
SUSY case
UED case
Neutralino spin Smillie, Webberhep-ph/0507170
• For UED masses not measureable– Near-degenerate masses little asymmetry
• For SUSY masses, measurable @ SPS1a– but shape is similar– need to measure size as well as shape of asymmetry
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
Neutralino spin Goto, Kawagoe, Nojirihep-ph/0406317
Range of Validity• Limits:
– Decay chain must exist
– Sparticles must be fairly light
• Relatively small area of validity– ~ red +
orange areas in plot after cuts
Allanach & MahmoudiTo appear in proceedingsLes Houches 05
Decay chain kinematically forbidden
Spin Significance at the parton level – no cuts etc
Neutralino spin
Precise measurement of SM backgrounds: the problem
• SM backgrounds are not small
• There are uncertainties in– Cross sections– Kinematical
distributions– Detector response
W contribution to no-lepton BG
• Use visible leptons from W’s to estimate background to no-lepton SUSY search
Oe, Okawa,Asai
Normalising not necessarily good enough
Distributions arebiased by lepton selection
Distributions arebiased by lepton selection
Need to isolate individual components…
Then possible to get it right…
Similar story for other backgrounds – control needs careful selectionSimilar story for other backgrounds – control needs careful selection
Dark matter relic density consistency?• Use LHC measurements to
predict relic density of observed LSPs
• Caveats:– Can’t tell about lifetimes beyond
detector• To remove mSUGRA assumption
need extra constraints:1. All neutralino masses
• Use as inputs to gaugino & higgsino content of LSP
2. Lightest stau mass• Is stau-coannihilation important?
3. Heavy Higgs boson mass• Is Higgs co-annihilation important?
• More work is in progress– Probably not all achievable at LHC– ILC would help lots (if in reach)
mSUGRA
assumed
mSUGRA
assumed
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