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Phenomenology of M-theory compactifications on G2 manifolds

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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 Vaman

hep-th/0606262, Phys. Rev. Lett. 2006

and

B. Acharya, KB, P. Grajek, G. Kane, P. Kumar, and

Jing Shao - in progress

Konstantin Bobkov

MCTP, May 3, 2007

Outline

- 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

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

!

Overview of the model

- The full non-perturbative superpotential is
- where the gauge kinetic function
- Introduce an effective meson field
- For and hidden sector gauge groups:
- , , , where

SU(N): ck=N

SO(2N): ck=2N-2

E8: ck=30

dual Coxeter number

- 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

after we add

charged matter

- The N=1 supergravity scalar potential is given by

Moduli Stabilization (dS)

- When there exists a dS minimum if the following condition is satisfied, i.e.
- with moduli vevs
- with meson vev

Moduli vevs and the SUGRA regime

from threshold corrections

Since ai~1/N we need to have large enough

in order to remain in the SUGRA regime

- Friedmann-Witten: hep-th/0211269

integers

For SU(5): ,where

can be made large

O(10-100)

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

- Recall that the gravitino mass is given by
- where
- Take the minimal possible value and tune . .Then
- Scale of gaugino condensation is completely fixed!

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

- 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!

- 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

Gaillard et. al.: hep-th/09905122, Bagger et. al.: hep-th/9911029

where

- constants

- rational

- 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!

Gaugino masses at the unification scale

- 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

- Trilinear couplings. If we require zero CC at tree-level and :
- Hence, typically

- Scalar masses. Universal because the lifted Type IIA matter Kahler metric we used is diagonal. If we require zero CC at tree-level and :

- Universal heavy scalars

in superpotential

from Kahler potential. (Guidice-Masiero)

- - 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

physical

Electroweak Symmetry Breaking

- 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

- Prediction of alone depends on precise values of
- and
- Generic value
- Fine tuning – Little Hierarchy Problem
- Since , the Higgs cannot be too heavy

M3/2=35TeV

1 < Zeff < 1.65

PRECISION GAUGE UNIFICATION

- 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 Mcompact 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.

Details:

- 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.

α1-1

α2-1

α3-1

t = log10 (Q/1GeV)

Two loop precision gauge unification for the SU(5) model

M3

M2

M1

After RG evolution, can plot M1, M2, M3 at low scale as a function of for ( here )

M3

M2

M1

Can also plot M1, M2, M3 at low scale as a function of In both plots as

- 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

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

Example

For , get

Compute physical masses:

Dominant production modes:

(s-channel gluon exchange)

(s-channel exchange)

(s-channel exchange)

almost degenerate!

Decay modes:

~37% ;

~ 50% ;

~20.7% ;

~ 50% ;

~19% ;

~8.3% ;

~12% ;

very soft!

~3% ;

is quasi-stable!

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

After L2 cuts

Before L2 cuts

L2 cut

Before L2 cuts

After L2 cuts

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

Phases

- 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

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

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