Phenomenology of M-theory compactifications on G2 manifolds Bobby Acharya, KB, Gordon Kane, Piyush Kumar and Jing Shao, hep-th/ , B. Acharya, KB, G. Kane, P. Kumar and Diana Vaman hep-th/ , Phys. Rev. Lett and B. Acharya, KB, P. Grajek, G. Kane, P. Kumar, and Jing Shao - in progress Konstantin Bobkov MCTP, May 3, 2007

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

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 !

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): c k =N SO(2N): c k =2N-2 E 8 : c k =30

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/ , Acharya, Denef, Valandro. hep-th/ after we add charged matter

The N=1 supergravity scalar potential is given by

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

Moduli vevs and the SUGRA regime Since a i ~1/N we need to have large enough in order to remain in the SUGRA regime from threshold corrections Friedmann-Witten: hep-th/ For SU(5):,where integers 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/ 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/ constants - rational where Gaillard et. al.: hep-th/ , Bagger et. al.: hep-th/

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

- 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)

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

Prediction of alone depends on precise values of and Generic value Fine tuning – Little Hierarchy Problem Since, the Higgs cannot be too heavy M 3/2 =35TeV 1 < Z eff < 1.65

● Threshold corrections to gauge couplings from KK modes (these are constants) and heavy Higgs triplets are computable. ● Can compute M unif at which couplings unify, in terms of M compact 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

– 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 M 3 /M 2 (not like split susy) – For SU(5) if higgs triplets lighter than M unif 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:

t = log 10 (Q/1GeV) Two loop precision gauge unification for the SU(5) model α 2 -1 α 1 -1 α 3 -1

After RG evolution, can plot M 1, M 2, M 3 at low scale as a function of for ( here ) M3M2M1M3M2M1

Can also plot M 1, M 2, M 3 at low scale as a function of In both plots as M3M2M1M3M2M1

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

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

Decay modes: very soft! ~37% ; ~20.7% ; ~19% ; ~8.3% ; ~12% ; ~3% ; ~ 50% ; 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

L2 cut Before L2 cuts After L2 cuts 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

In the superpotential: Minimizing with respect to the axions t i 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

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