Phenomenology of M-theory compactifications on G2 manifolds
Bobby Acharya, KB, Gordon Kane, Piyush Kumar and Jing Shao, hep-th/0701034,
B. Acharya, KB, G. Kane, P. Kumar and Diana Vamanhep-th/0606262, Phys. Rev. Lett. 2006
andB. Acharya, KB, P. Grajek, G. Kane, P. Kumar, and
Jing Shao - in progress
Konstantin Bobkov
MCTP, May 3, 2007
• Overview and summary of previous results
• Computation of soft SUSY breaking terms
• Electroweak symmetry breaking
• Precision gauge coupling unification
• LHC phenomenology
• Conclusions and future work
Outline
M-theory compactifications without flux
• All moduli are stabilized by the potential generated by the strong gauge dynamics
• Supersymmetry is broken spontaneously in a unique dS vacuum
• is the only dimensionful input parameter. Generically ~30% of solutions give Hence – true solution to the hierarchy problem
• When the tree-level CC is set to zero for generic compactifications with >100 moduli TeVOm )100(23
PlanckMTeVOm )101.0(~23
!
• The full non-perturbative superpotential is
where the gauge kinetic function
• Introduce an effective meson field
• For and hidden sector gauge groups:
, , , where
fibfiba eAeAW 2121
1 cNPP
b2
1 Q
b2
2
)( cNSU )(QSU
Pa
2
ie02
1
Q~
2Q
N
iii zNf
1
Overview of the model
kk cb
2 dual Coxeter number
SU(N): ck=NSO(2N): ck=2N-2E8: ck=30
• An N-parameter family of Kahler potentials consistent with holonomy and known to describe accurately some explicit moduli dynamics is given by:
where the 7-dim volume
and the positive rational parameters satisfy
Beasley-Witten: hep-th/0203061, Acharya, Denef, Valandro. hep-th/0502060
)4ln(3 73/1 VK
2G
N
i
aiisV
17
2G
3
7
1
N
iiaia
after we add charged matter
• The N=1 supergravity scalar potential is given by
)[( 210212122
222
220
21
213
7
cos248
1121
20
atNbbeAAbbeAbeAbV
eV abbaababa
abbaababai
N
ii eAAbbeAbeAbaa
212102121
2222
220
211
2
1
(3
abbaababa eAAeAeAatNbb
1121021
222
220
2121 23cos ()
ababa eAea
AatNbb
21 22
22
2
20
20
21
2021 1
4
3cos ()
)]2120
021 cos12 11
atNbbea
AA abba
• When there exists a dS minimum if the following condition is satisfied, i.e.
with moduli vevs
with meson vev
Moduli Stabilization (dS)
PA
QA
PQ
PQ
N
as
i
ii
2
1ln14
3
PQ
PQ
PAQA
PPQPQ
21
2
3
ln
721
21
2
1
20
0
ln
2883
1
2
QAPA
PPQ
00 V
2 PQ
Moduli vevs and the SUGRA regime
PA
QA
PQ
PQ
N
as
i
ii
2
1ln14
3
PQ
Since ai~1/N we need to have large enough in order to remain in the SUGRA regime
10
16162
2
2
2
MGUT gg
kk CPA from threshold corrections
•Friedmann-Witten: hep-th/0211269
2
1lnC
CPQ
q
5
sin4ln 2For SU(5): ,where
q
eCSU
5sin4
1
2)5(
integers
2
1lnC
CPQ can be made large
O(10-100)
1is
dual Coxeter numbers
• When there exists a dS minimum with a tiny CC if the following condition is satisfied, i.e.
moduli vevs
meson vev
PQ
0
ln
2883
1
2
QAPA
PPQ
00 V
83
6
PQ
Q
N
as
i
ii
PQPQPQPQ
21
221
4
11
8
120
• Recall that the gravitino mass is given by
where
Take the minimal possible value and tune . .Then
• Scale of gaugino condensation is completely fixed!
3 PQ
fQ
plQg
plg ememIm
3
2
3
82
2
Q
sNfN
iii
14Im
1
GeVemplg14328 1015.2
TeVOm )100(23
237
3
238
1~
Vmmm
pl
gpl
00 V
Computation of soft SUSY breaking terms
• Since we stabilized all the moduli explicitly, we can compute all terms in the soft-breaking lagrangian Nilles: Phys. Rept. 110 (1984) 1, Brignole et.al.: hep-th/9707209
• Tree-level gaugino masses. Assume SU(5) SUSY GUT broken to MSSM.
where the SM gauge kinetic function
sm
smnmmnK
p fi
fFKemM
Im2
2ˆ
21
N
ii
smism zNf
1
• Tree-level gaugino masses for dS vacua
• The tree-level gaugino mass is always suppressed for the entire class of dS vacua obtained in our model
The suppression factor becomes completely fixed!
23
2
120
20
2
1
21
ln
721
ln
m
PAQA
PPQ
PAQA
P
eM
Wi
2321 024.0 meM Wi
00 V 3 PQ& 84ln2
1
PA
QAP - very robust
• Anomaly mediated gaugino masses
• Lift the Type IIA result to M-theory. Yields flavor universal scalar masses
Bertolini et. al.: hep-th/0512067
KFeCKFeCCWeCC
gM m
mKam
mKaa
Kaa
aama
~ln23
162ˆ2ˆ*2ˆ
2
2
2
1
1 )(
)1(~
n
i i
iK
liii sc tan
- constants - rational
icl )1(O
where
Gaillard et. al.: hep-th/09905122, Bagger et. al.: hep-th/9911029
• Anomaly mediated gaugino masses. If we require
zero CC at tree-level and :
• Assume SU(5) SUSY GUT broken to MSSM
• Tree-level and anomaly contributions are almost the
same size but opposite sign. Hence, we get large
cancellations, especially when - surprise!
232sin2
1048.06556.13
4mlCCCCCeM
iiiaaaaa
GUTiama
W
3 PQ
251GUT
• Recall that the distribution peaked at O(100) TeV
• Hence, the gauginos are in the range O(0.1-1) TeV
• Gluinos are always relatively light – general prediction
of these compactifications!
• Wino LSP
23m
2G
• Trilinear couplings. If we require zero CC at tree-level and :
• Hence, typically
N
P
Y
CemA Wi )3(14
ln7ln245.10024.04876.1 [(23
3 PQ
])2sin2
1
)(
)1(ln
2
1
iii
i
i l
23mA
• Scalar masses. Universal because the lifted Type IIA matter Kahler metric we used is diagonal. If we require zero CC at tree-level and :3 PQ
iiiiiiii lllmm
2sin24sin2sin4
0013.01 2222
232
23mm • Universal heavy scalars
• - problem
• Witten argued for his embeddings that -parameter can vanish if there is a discrete symmetry
• If the Higgs bilinear coefficient then typically expect
• Phase of - interesting, we can study it
212ˆ
232ˆ
* ~~
du HHmmKK KKZFeZme
W
W
ZVmmKFee
W
WKKB mm
mKKHH du 0
22323
2ˆ2ˆ*
212lnˆ~~
)1(~ OZ)(~ 23mO
physical
in superpotential from Kahler potential. (Guidice-Masiero)
2G
• In most models REWSB is accommodated but not predicted, i.e. one picks and then finds , which give the experimental value of
• We can do better with almost no experimental constraints:
• since ,
• Generate REWSB robustly for “natural” values of , from theory
tan
Electroweak Symmetry Breaking
BZM
)1(~tan O
)(~ 23mOB
)(~ 23mOB
• Prediction of alone depends on precise values of
and
• Generic value
• Fine tuning – Little Hierarchy Problem
• Since , the Higgs cannot be too heavy
ZM B
)(~ 23mOM Z
M3/2=35TeV
1 < Zeff < 1.65
23mZeff
)1(~tan O
● Threshold corrections to gauge couplings from KK modes (these are constants) and heavy Higgs triplets are computable.
● Can compute Munif
at which couplings unify, in terms of M
compact and thresholds, which in turn depend on
microscopic parameters.
● Phenomenologically allowed values – put constraints on microscopic parameters.
● The SU(5) Model – checked that it is consistent with precision gauge unification.
PRECISION GAUGE UNIFICATION
3111
2 Qcompact V
MM
217
11 V
MM Pl
31
5
2
qeMM compactunif
– Here, big cancellation between the tree-level and anomaly contributions to gaugino masses, so get large sensitivity on
– Gaugino masses depend on , BUT in turn depends on corrections to gauge couplings from low scale superpartner thresholds, so feedback.
– Squarks and sleptons in complete multiplets so do not affect unification, but higgs, higgsinos, and gauginos do – μ, large so unification depends mostly on M3/M2 (not like split susy)
– For SU(5) if higgs triplets lighter than Munif their threshold contributions make unification harder, so assume triplets as heavy as unification scale.
– Scan parameter space of and threshold corrections, find good region for in full two-loop analysis, for reasonable range of threshold corrections.
Details:
GUT GUTGUT
GUT5.261~GUT
After RG evolution, can plot M1, M
2, M
3 at low scale as a
function of for ( here )01GUT TeVmTeV 5027 23
M3
M2
M1
Can also plot M1, M
2, M
3 at low scale as a function of
In both plots as 23m
GeVmGeV h 123119
M3
M2
M1
67.158.1 effZ
• Moduli masses:
one is heavy
N-1 are light
• Meson is mixed with the heavy modulus
•Since , probably no moduli or gravitino problem
• Scalars are heavy, hence FCNC are suppressed
23600 mM
2396.1 mm
TeVOm )100(~23
2382.2 mm
LHC phenomenology• Relatively light gluino and very heavy squarks and sleptons• Significant gluino pair production– easily see them at LHC. • Gluino decays are charge symmetric, hence we predict a very small charge asymmetry in the number of events with one or two leptons and # of jets • In well understood mechanisms of moduli stabilization in Type IIB such as KKLT and “Large Volume” the squarks are lighter and the up-type squark pair production and the squark-gluino production are dominant. Hence the large charge asymmetry is preserved all the way down
2
For , getCompute physical masses:
Dominant production modes:
(s-channel gluon exchange)
(s-channel exchange) (s-channel exchange)
pbgggg 33.1)~~(
pbCCqq 2.6)~~
( 11 pbNCqq 1.12)
~~( 11
TeVm 3523 TeV7.45
GeVmg 733GeVm
N6.111
1~ GeVm
C76.111
1~
GeVmN
7.2282
~
W
0Z
almost degenerate!
45.1tan Example
4.261 GUT
GeVmh 121
pbggqq 46.0)~~(
Decay modes:
g~ 2
~Ntt
11
~~CbtCbt
1
~Cjets
1
~Nbb
2
~N WC1
~
11
~~NC
very soft!
~37% ;
~20.7% ;
~19% ;
~8.3% ;
1
~Nqq
2
~Nqq
~12% ;
~3% ;
~ 50% ;
~ 50% ; WC1
~
110
C~ C
~sec10~τ
1 is quasi-stable!
MeV160mm11 N
~C~
Signatures• Lots of tops and bottoms. Estimated fraction of events (inclusive): 4 tops 14% same sign tops 23% same sign bottoms 29%
• Observable # of events with the same sign dileptons and trileptons. Simulated with 5fb-1 using Pythia/PGS with L2 trigger (tried 100,198 events; 8,448 passed the trigger; L2 trigger is used to reduce the SM background) Same sign dileptons 172 Trileptons 112
Dark Matter
• LSP is Wino-like when the CC is tuned
• LSPs annihilate very efficiently so can’t generate enough thermal relic density
• Moduli and gravitino are heavy enough not to spoil the BBN. They can potentially be used to generate enough non-thermal relic density.
• Moduli and gravitinos primarily decay into gauginos and gauge bosons
• Have computed the couplings and decay widths
• For naïve estimates the relic density is too large
• In the superpotential:
• Minimizing with respect to the axions ti and
fixes • Gaugino masses as well as normalized trilinears have the same phase given by• Another possible phase comes from the Higgs bilinear, generating the - term • Each Yukawa has a phase
NsbaNtbbiNsbaNtbi
NsbNtibiNsbNtibiaai
eAeeAe
eeAeeeAW
22121122
222111
2])[(
01)(
201
Phases
1])cos[( 2121 aNtbb
)( 22 NtbW
tl
2
Conclusions• All moduli are stabilized by the potential generated by the strong gauge dynamics• Supersymmetry is broken spontaneously in a unique dS vacuum • Derive from CC=0
• Gauge coupling unification and REWSB are generic
• Obtain => the Higgs cannot be heavy
• Distinct spectrum: light gauginos and heavy scalars
• Wino LSP for CC=0, DM is non-thermal
• Relatively light gluino – easily seen at the LHC
• Quasi-stable lightest chargino – hard track, probably won’t reach the muon detector
TeVOm )100(23
)1(~tan O
Our Future Work• Understand better the Kahler potential and the assumptions we made about its form
• Compute the threshold corrections explicitly and demonstrate that the CC can be discretely tuned
• Our axions are massless, must be fixed by the instanton corrections. Axions in this class of vacua may be candidates for quintessence
• Weak and strong CP violation
• Dark matter, Baryogenesis, Inflation
• Flavor, Yukawa couplings and neutrino masses
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