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
Slide2: 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
Slide3: 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 !
Slide4: The full non-perturbative superpotential is
where the gauge kinetic function
Introduce an effective meson field
For and hidden sector gauge groups:
, , , where Overview of the model dual Coxeter number SU(N): ck=N
SO(2N): ck=2N-2
E8: ck=30
Slide5: 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
Slide6: The N=1 supergravity scalar potential is given by
Slide7: When there exists a dS minimum if the following condition is satisfied, i.e.
with moduli vevs
with meson vev Moduli Stabilization (dS)
Slide8: Moduli vevs and the SUGRA regime Since ai~1/N we need to have large enough
in order to remain in the SUGRA regime from threshold corrections Friedmann-Witten: hep-th/0211269 For SU(5): ,where integers can be made large
O(10-100) dual Coxeter numbers
Slide9: When there exists a dS minimum with a tiny CC if the following condition is satisfied, i.e.
moduli vevs
meson vev
Slide10: Recall that the gravitino mass is given by
where
Take the minimal possible value and tune . .Then
Scale of gaugino condensation is completely fixed!
Slide11: 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
Slide12: 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
Slide13: Anomaly mediated gaugino masses
Lift the Type IIA result to M-theory. Yields flavor universal scalar masses
Bertolini et. al.: hep-th/0512067 - constants
- rational where Gaillard et. al.: hep-th/09905122, Bagger et. al.: hep-th/9911029
Slide14: 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!
Slide15: Gaugino masses at the unification scale
Slide16: 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
Slide17: Trilinear couplings. If we require zero CC at tree-level and :
Hence, typically
Slide18: 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
Slide19: - 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 in superpotential from Kahler potential. (Guidice-Masiero)
Slide20: 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 Electroweak Symmetry Breaking
Slide21: 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
Slide22: 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. PRECISION GAUGE UNIFICATION
Slide23:
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:
Slide24: t = log10 (Q/1GeV) Two loop precision gauge unification for the SU(5) model α2-1 α1-1 α3-1
Slide25: After RG evolution, can plot M1, M2, M3 at low scale as a function of for ( here ) M3
M2
M1
Slide26: Can also plot M1, M2, M3 at low scale as a function of In both plots as M3
M2
M1
Slide27: 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
Slide28: 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
Slide29: For , get
Compute physical masses:
Dominant production modes:
(s-channel gluon exchange)
(s-channel exchange)
(s-channel exchange)
almost degenerate! Example
Slide30: Decay modes: very soft! ~37% ; ~20.7% ; ~19% ; ~8.3% ; ~12% ; ~3% ; ~ 50% ; ~ 50% ; is quasi-stable!
Slide31: 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
Slide32: L2 cut Before L2 cuts After L2 cuts Before L2 cuts After L2 cuts
Slide33: 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
Slide34: 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 Phases
Slide35: 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
Slide36: 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