SPLIT SUPERSYMMETRY
G.F. Giudice CERN
IFAE Catania, 31 marzo 2005
• Motivazioni per Split Supersymmetry
• Conseguenze osservative di Split Supersymmetry
Arkani-Hamed Dimopoulos hep-th/0405159
Giudice Romanino hep-ph/0406088
Arkani-Hamed Dimopoulos Giudice Romanino hep-ph/0409232
1
MW << MPl  nuova fisica a L ~ TeV
Problema del sapore  L > 10 3-4 TeV
Piccola gerarchia
 L > 5-10 TeV
mK me g
eK bs g
EW precision data
Contact int. at LEP2
LCC << MPl  nuova fisica a L ~ 10-3 eV
Gravità modificata a questa scala oppure
fallimento del criterio di naturalezza
Riconsideriamo il problema della gerarchia:
la scala elettrodebole è determinata dalla
dinamica o dalla statistica ?
2
Idea del multiverso emerge
dalla teoria dell’inflazione
Landscape delle teorie di stringa:
10100 vuoti che corrispondono a
diverse costanti di accoppiamento
Come la vita si è sviluppata su un pianeta con acqua liquida, con
massa tale da trattenere l’atmosfera, con campo magnetico tale da
proteggere dal vento solare, in un’orbita galattica con limitato impatto
di comete, …così il nostro universo si è sviluppato in un vuoto con
3
LCC ~ 10-3 eV , v ~ 102 GeV
Abandon hierarchy problem (speculations on probability distributions
of theories) and use only observational hints
Gauge-coupling unification: motivated by theory that addresses
fundamental structure of SM and by measurements on ai
Dark matter: connection between weak scale and new particle masses
0.1 pb
 rel h 
v
2
Proposal of SPLIT SUPERSYMMETRY: retain at the weak scale
only gauginos, higgsinos and one Higgs boson (squarks, sleptons and
~
extra Higgs at the scale m)
4
Eliminate :
• Excessive flavour and CP violation
• Fast dim-5 proton decay
• Tight constraints on the Higgs mass
Retain :
• DM & gauge-coupling unification
Gauge-coupling
unification as
successful (or better)
than in ordinary SUSY
5
Not unique solution, however…
• Minimality: search for unification with single threshold, only
fermions in real reps, and 1015 GeV < MGUT < 1019 GeV 
SpS has the minimal field content consistent with gaugecoupling unification and DM
• Splitting of GUT irreps: in SpS no need for new split reps
either than SM gauge and Higgs
• Light particles: R-symmetry protects fermion masses
• Existence and stability of DM: R-parity makes c stable
• Instability of coloured particles: coloured particles are
necessary, but they decay either by mixing with quarks
(FCNC!) or by interactions with scale < 1013 GeV
SpS not unique, but it has all the necessary features built in
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Why Supersymmetry?
~
X  1   2m
4
*
*
2
~2  m
~2
~
d

X
X
Q
Q

m
d

X
W
W

M

m
~
Q
a a
g


4
*
~2
d

X
X
H
H

B

m
1
2
m

2
3
~
d

X
Q

A

m

4
*
~
d

X
H
H

m

m
1
2

R - invariant soft terms
(choose R[ H 1 H 2 ]  0 so that
2
d
  H 1 H 2 forbidden)
R - violating soft terms
(R[ X ]  0, R - symmetry
broken by FX )
• R-symmetry “splits” the spectrum (Mg~ and m mix through renorm.)
• R-invariant  dim = 2
R-violating  dim = 3
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Split Supersymmetry determined by susy-breaking pattern
~2
D - breaking Y  1   4 m
4
*
4
~2  m
~2
~2
d

YQ
Q

m
d

YH
H

B

m
Q
1 2
m


Non renorm. operators
~2
1
m
4
3
d

YQ
 A

M*
M*
~2
1
m
4
d
 YWaWa  M g~ 

M*
M*
~2
1
m
4
2
H 1 H 2   m 
d

YD

M*
M*
• Analogy: in SM, L not imposed but accidental. mn small,
although L-breaking is O(1) in underlying theory
• In supergravity, m not generated at O(MPl) but only O(MS2/MPl)
~ but only O(m
~2/M )
• Here, M ~ and m not generated at O(m)
g
*
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OBSERVATIONAL CONSEQUENCES
OF SPLIT SUPERSYMMETRY
• Only one Higgs boson with SM properties
• With respect to MSSM, larger log corrections to l=g2
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Heavy squarks and sleptons suppress flavour & CP violation,
dim-5 proton decay
New source of flavour-diagonal CP violation remains
g~u * ~ ~
g~d
M ~~
~~
L  WW  m H u H d 
H WH u 
HWH d  h.c.
2
2
2
CP violation in

Im g~u* g~d* Mm

Effects on SM matter at two loops: EDM
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Eliminate phases in chargino mass matrix 



M
e2
~ mn

arg det M c  Fmn F M c   
2
~ g
32
2
M
g
W
d

~ mn
O H  H H Fmn F
*
df
e
-
Qf mf a
16 3
2 M W g~u g 


m

mixes with EDM operator
 g~u g~d
Im
 Mm
Mm

 log 2
mH

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Present limit: de < 1.7 × 10-27 ecm at 95% CL (DeMille et al.)
Future: DeMille et al. (Yale) 10-29 ecm in 3 years and 10-31 ecm in 5
years.
Lamoreaux et al. (Los Alamos): 10-31 ecm and eventually 10-35 ecm.
Results from Hinds et al. (Sussex) and Semertzidis et al.
(Brookhaven) plans to improve by 105 sensitivity on m EDM
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GLUINO: decays through intermediate heavy scalars
_
q
5
4
~
 TeV  
m

q


~
τ

~
 13
 0.4 Gyr
g
g


~
q
 M ~g   10 GeV 
c
CHARGINOS AND
NEUTRALINOS:
• m not determined by EWSB
• at LHC produced in DY, not in cascades
• decay chains with Higgs bosons
• couplings violate susy relations
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DARK MATTER IN SPLIT SUPERSYMMETRY
With respect to ordinary susy
• m not determined by EWSB
~
• B only interacts with Higgs-Higgsino
• c mixed state  c h  0.1 m M  m
2
2
2
1
 m
2 2
TeV 
4
c
• c Higgsino  c h 2  0.09m / TeV 2 DM for
m  1.0 - 1.2 TeV
 c h 2  0.02M 2 / TeV 
M 2  2.0 - 2.5 TeV
• c Wino
2
DM for
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Upper bound on mc from thermal relic abundance retained also
when gravitino decay contributes to DM
Spin-independent c scattering cross section off protons is
mediated by Higgs exchange
Present: CDMS & EDELWEISS: 10-42-10-41 cm2
Future:CDMS II: 10-44-10-43 cm2;
ZEPLIN, XENON, GENIUS: 10-46-10-44 cm2
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CONCLUSIONS
• Failure of naturalness argument for CC casts doubts on the
existence of a physical threshold at the weak scale
• Split Supersymmetry abandons hierarchy problem, but retains
gauge-coupling unification and dark matter
• Not unique solution but, under certain assumption, it is the
simplest option
• Certain patterns of susy breaking automatically lead to the
spectrum of Split Supersymmetry
• Observational consequences for collider searches, EDM, dark
matter and gravitino cosmology
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