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

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Phenomenology of M-theory compactifications on G2 manifolds

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Phenomenology of m theory compactifications on g2 manifolds

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


Phenomenology of m theory compactifications on g2 manifolds

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


Phenomenology of m theory compactifications on g2 manifolds

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

!


Phenomenology of m theory compactifications on g2 manifolds

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


Phenomenology of m theory compactifications on g2 manifolds

  • 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


Phenomenology of m theory compactifications on g2 manifolds

  • The N=1 supergravity scalar potential is given by


Phenomenology of m theory compactifications on g2 manifolds

Moduli Stabilization (dS)

  • When there exists a dS minimum if the following condition is satisfied, i.e.

  • with moduli vevs

  • with meson vev


Phenomenology of m theory compactifications on g2 manifolds

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


Phenomenology of m theory compactifications on g2 manifolds

  • When there exists a dS minimum with a tiny CC if the following condition is satisfied, i.e.

  • moduli vevs

  • meson vev


Phenomenology of m theory compactifications on g2 manifolds

  • Recall that the gravitino mass is given by

  • where

  • Take the minimal possible value and tune . .Then

  • Scale of gaugino condensation is completely fixed!


Phenomenology of m theory compactifications on g2 manifolds

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


Phenomenology of m theory compactifications on g2 manifolds

  • 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


Phenomenology of m theory compactifications on g2 manifolds

  • 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


Phenomenology of m theory compactifications on g2 manifolds

  • 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!


Phenomenology of m theory compactifications on g2 manifolds

Gaugino masses at the unification scale


Phenomenology of m theory compactifications on g2 manifolds

  • 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


Phenomenology of m theory compactifications on g2 manifolds

  • Trilinear couplings. If we require zero CC at tree-level and :

  • Hence, typically


Phenomenology of m theory compactifications on g2 manifolds

  • 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


Phenomenology of m theory compactifications on g2 manifolds

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


Phenomenology of m theory compactifications on g2 manifolds

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


Phenomenology of m theory compactifications on g2 manifolds

  • 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


Phenomenology of m theory compactifications on g2 manifolds

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.


Phenomenology of m theory compactifications on g2 manifolds

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.


Phenomenology of m theory compactifications on g2 manifolds

α1-1

α2-1

α3-1

t = log10 (Q/1GeV)

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


Phenomenology of m theory compactifications on g2 manifolds

M3

M2

M1

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


Phenomenology of m theory compactifications on g2 manifolds

M3

M2

M1

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


Phenomenology of m theory compactifications on g2 manifolds

  • 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


Phenomenology of m theory compactifications on g2 manifolds

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


Phenomenology of m theory compactifications on g2 manifolds

Example

For , get

Compute physical masses:

Dominant production modes:

(s-channel gluon exchange)

(s-channel exchange)

(s-channel exchange)

almost degenerate!


Phenomenology of m theory compactifications on g2 manifolds

Decay modes:

~37% ;

~ 50% ;

~20.7% ;

~ 50% ;

~19% ;

~8.3% ;

~12% ;

very soft!

~3% ;

is quasi-stable!


Phenomenology of m theory compactifications on g2 manifolds

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


Phenomenology of m theory compactifications on g2 manifolds

After L2 cuts

Before L2 cuts

L2 cut

Before L2 cuts

After L2 cuts


Phenomenology of m theory compactifications on g2 manifolds

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


Phenomenology of m theory compactifications on g2 manifolds

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


Phenomenology of m theory compactifications on g2 manifolds

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


Phenomenology of m theory compactifications on g2 manifolds

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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