Phenomenology of M-Theory Compactifications on G2 Manifolds: Implications for SUSY and Gauge Unification

1. 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

2. 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

3. 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 !

4. 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

5. 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

6. The N=1 supergravity scalar potential is given by

7. Moduli Stabilization (dS) • When there exists a dS minimum if the following condition is satisfied, i.e. • with moduli vevs • with meson vev

8. 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

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

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

11. 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

12. 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

13. 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

14. 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!

15. Gaugino masses at the unification scale

16. 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

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

18. 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

19. 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

20. 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

21. 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

22. 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.

23. 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.

24. α1-1 α2-1 α3-1 t = log10 (Q/1GeV) Two loop precision gauge unification for the SU(5) model

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

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

27. 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

28. 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

29. Example For , get Compute physical masses: Dominant production modes: (s-channel gluon exchange) (s-channel exchange) (s-channel exchange) almost degenerate!

30. Decay modes: ~37% ; ~ 50% ; ~20.7% ; ~ 50% ; ~19% ; ~8.3% ; ~12% ; very soft! ~3% ; is quasi-stable!

31. 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

32. After L2 cuts Before L2 cuts L2 cut Before L2 cuts After L2 cuts

33. 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

34. 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

35. 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

36. 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