Moduli Stabilization in M-theory and the Associated Phenomenology

1. Moduli Stabilization in M-theory and the Associated Phenomenology Jing Shao University of Michigan Based on Bobby Acharya, Konstantin Bobkov, Gordon Kane, Piyush Kumar & JS, hep-th/0701034 and work in Progress Pheno07, Madison May 7, 2007

2. Outline • Introduction and motivation • M theory on manifolds • Moduli stabilization and dS vacua • Phenomenology and LHC signatures • Conclusions

3. Introduction and Motivation Why do we study 4-dim M theory vacua? • Non-Abelian gauge symmetry • Chiral fermions • Hierarchical Yukawa couplings • Dynamical supersymmetry breaking • Gauge coupling unification However, we still need to explain why as opposed to - hence, the Hierarchy problem

4. Bottom-up: low scale SUSY is well motivated – have many good features and can stabilize the hierarchy (but can not explain it). • Top-down: N=1 SUSY can naturally arise from String/M theory compactifications to 4-d. The masses and couplings 4-d effective theory are functions of the moduli vevs. • In order to say something about low scale physics: have to -- Stabilize all the moduli -- Generate a stable hierarchy -- Find a set of dS vacua with spontaneously broken SUSY -- make predictions for low energy observables

5. M theory on G2 manifolds • Consider an M theory compactification on a singular 7-dmanifold with holonomy 4d N=1 SUSY • Non-Abelian gauge fields are localized on three-dimensional submanifolds along which there is an orbifold singularity. (Acharya: hep-th/9812205, hep-th/0011089, Acharya-Gukov: hep-th/0409191) • Example:locally, M theory on , where . , is 11-dim SUGRA coupled to a 7-dim SU(N) gauge theory.

6. Chiral fermions are localized at point-like conical singularities. (Atiyah-Witten, hep-th/0107177,Acharya-Witten, hep-th/0109152) • Can embed GUT like spectra locally. • Visible and hidden sector are on different 3d surfaces of the G2 manifold. SUSY breaking is gravity mediated. • In M theory on manifolds there is only one class geometric moduli are , where are the zero modes of the metric and are the zero modes of the three-form, i.e. the axions.

7. Where and for SU(N) gauge group. For simplicity, we consider the case with two hidden sectors. To be generic, include one “quark” charged under one of the hidden sector gauge group. Moduli Stabilization The non-perturbative superpotential is assumed to be generated by the strong gauge dynamics in the hidden sectors (very generic):

8. The Kahler potential: • where the 7-dim volume • and the positive rational parameters satisfy • (Beasley-Witten: hep-th/0203061, Acharya, Denef, Valandro. hep-th/0502060) • The full non-perturbative superpotential is then • where . For and hidden sector gauge groups: • , , where

9. Moduli are stabilized at • SUGRA approx: • When , there exists a dS minimum if the following condition is satisfied, i.e. • The dS vacuum is unique! (for a given set of microscopic parameters)

10. GravitinoMass for dS Vacua The scale of gravitino mass is determined by , which is roughly . In the following, focus on the casein which V0is tuned to be zero.

11. O(1016) GeV O(10) TeV O(10) TeV O(1014) GeV Distribution of log10(m3/2) with V0≈ 0 by scanning P, Q-P & N. (generically ) O(10) TeV

12. Result • For generic manifolds with a large # of moduli and “reasonable” hidden sector gauge group, we obtain : • It was crucial no extra anti-brane and flux is needed to obtain de Sitter vacua • SUSY is broken spontaneously and not explicitly!

13. Gaugino masses for dS vacua (at the unification scale) • Generically the gauge kinetic function includes threshold corrections, so define , where is the tree-level one. • Both contributions are suppressed and of the same order

14. Trilinear couplings • Scalar mass • μ term in the original superpotential is forbiden by a • discrete symmetry, but can be generated if there is a • Higgs bilinear term in the Kahler potential. (Guidice-Masiero) • If the Higgs bilinear coefficient Z~O(1) then typically • expect μ~m3/2

15. Low Scale Physics • Light gaugino and heavy scalar, which has to be decoupled at the scale m3/2 in the RGE running. • EWSB can happen, but Z boson mass generically of order m3/2, need fine-tuning- Little Hierarchy Problem • Predict small tanβ around 1.4 ~ 1.5 • Gauge coupling unification can be achieved at two-loop level, if the gluino mass is heavier enough than wino. • Higgs mass is generated from squark loop correction. So need large enough m3/2and top Yukawa coupling to get around the higgs mass limit.

17. A Benchmark Spectrum • Tune • Only is allowed • LSP is wino LSP

18. LHC Prospects • Gluino pair production- CS~2pb (104 events / 10 fb-1), peak at 1460GeV in the invariant mass distribution can be easily seen. • Gluino decay: 2 t N2: 40%; t b C1: 20%; bb N1:10% • N2 decay always to C1 and W boson • Same sign tops: 2400 events/ 10 fb-1 • Same sign dileptons: 200 events/ 10 fb-1 • Trileptons: 350 events/ 10 fb-1 • SSDL+4 b jets: 150 events/ 10 fb-1 • “Invisible” channel: Chargino pair production 7pb, Chargino-LSP production 13pb • LSP mass can be implied from the peak of the missing ET distribution

20. Conclusion • Strong gauge dynamics stabilizes all the moduli as well as generates a stable Hierarchy : Mplanck MEW • Supersymmetry is broken spontaneously in an essentially unique dS vacuum • When the tree-level CC is set to zero, almost always get gravitino ~ O(100) TeV!, for compactifications with large number of moduli. • Unique low scale spectrum: light gauginos and heavy scalars; wino LSP • Can be easily seen in LHC after a few year’s running, with very distinct signatures.