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 Vamanhep-th/0606262, Phys. Rev. Lett. 2006

andB. 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 TeVOm )100(23

PlanckMTeVOm )101.0(~23

!

• The full non-perturbative superpotential is

where the gauge kinetic function

• Introduce an effective meson field

• For and hidden sector gauge groups:

, , , where

fibfiba eAeAW 2121

1 cNPP

b2

1 Q

b2

2

)( cNSU )(QSU

Pa

2

ie02

1

Q~

2Q

N

iii zNf

1

Overview of the model

kk cb

2 dual Coxeter number

SU(N): ck=NSO(2N): ck=2N-2E8: ck=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/0203061, Acharya, Denef, Valandro. hep-th/0502060

)4ln(3 73/1 VK

2G

N

i

aiisV

17

2G

3

7

1

N

iiaia

after we add charged matter

• The N=1 supergravity scalar potential is given by

)[( 210212122

222

220

21

213

7

cos248

1121

20

atNbbeAAbbeAbeAbV

eV abbaababa

abbaababai

N

ii eAAbbeAbeAbaa

212102121

2222

220

211

2

1

(3

abbaababa eAAeAeAatNbb

1121021

222

220

2121 23cos ()

ababa eAea

AatNbb

21 22

22

2

20

20

21

2021 1

4

3cos ()

)]2120

021 cos12 11

atNbbea

AA abba

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

with moduli vevs

with meson vev

Moduli Stabilization (dS)

PA

QA

PQ

PQ

N

as

i

ii

2

1ln14

3

PQ

PQ

PAQA

PPQPQ

21

2

3

ln

721

21

2

1

20

0

ln

2883

1

2

QAPA

PPQ

00 V

2 PQ

Moduli vevs and the SUGRA regime

PA

QA

PQ

PQ

N

as

i

ii

2

1ln14

3

PQ

Since ai~1/N we need to have large enough in order to remain in the SUGRA regime

10

16162

2

2

2

MGUT gg

kk CPA from threshold corrections

•Friedmann-Witten: hep-th/0211269

2

1lnC

CPQ

q

5

sin4ln 2For SU(5): ,where

q

eCSU

5sin4

1

2)5(

integers

2

1lnC

CPQ can be made large

O(10-100)

1is

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

PQ

0

ln

2883

1

2

QAPA

PPQ

00 V

83

6

PQ

Q

N

as

i

ii

PQPQPQPQ

21

221

4

11

8

120

• Recall that the gravitino mass is given by

where

Take the minimal possible value and tune . .Then

• Scale of gaugino condensation is completely fixed!

3 PQ

fQ

plQg

plg ememIm

3

2

3

82

2

Q

sNfN

iii

14Im

1

GeVemplg14328 1015.2

TeVOm )100(23

237

3

238

1~

Vmmm

pl

gpl

00 V

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

sm

smnmmnK

p fi

fFKemM

Im2

2ˆ

21

N

ii

smism zNf

1

• 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!

23

2

120

20

2

1

21

ln

721

ln

m

PAQA

PPQ

PAQA

P

eM

Wi

2321 024.0 meM Wi

00 V 3 PQ& 84ln2

1

PA

QAP - very robust

• Anomaly mediated gaugino masses

• Lift the Type IIA result to M-theory. Yields flavor universal scalar masses

Bertolini et. al.: hep-th/0512067

KFeCKFeCCWeCC

gM m

mKam

mKaa

Kaa

aama

~ln23

162ˆ2ˆ*2ˆ

2

2

2

1

1 )(

)1(~

n

i i

iK

liii sc tan

- constants - rational

icl )1(O

where

Gaillard et. al.: hep-th/09905122, Bagger et. al.: hep-th/9911029

• 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!

232sin2

1048.06556.13

4mlCCCCCeM

iiiaaaaa

GUTiama

W

3 PQ

251GUT

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

23m

2G

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

• Hence, typically

N

P

Y

CemA Wi )3(14

ln7ln245.10024.04876.1 [(23

3 PQ

])2sin2

1

)(

)1(ln

2

1

iii

i

i l

23mA

• Scalar masses. Universal because the lifted Type IIA matter Kahler metric we used is diagonal. If we require zero CC at tree-level and :3 PQ

iiiiiiii lllmm

2sin24sin2sin4

0013.01 2222

232

23mm • 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

212ˆ

232ˆ

* ~~

du HHmmKK KKZFeZme

W

W

ZVmmKFee

W

WKKB mm

mKKHH du 0

22323

2ˆ2ˆ*

212lnˆ~~

)1(~ OZ)(~ 23mO

physical

in superpotential from Kahler potential. (Guidice-Masiero)

2G

• 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

tan

Electroweak Symmetry Breaking

BZM

)1(~tan O

)(~ 23mOB

)(~ 23mOB

• Prediction of alone depends on precise values of

and

• Generic value

• Fine tuning – Little Hierarchy Problem

• Since , the Higgs cannot be too heavy

ZM B

)(~ 23mOM Z

M3/2=35TeV

1 < Zeff < 1.65

23mZeff

)1(~tan O

● 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 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

3111

2 Qcompact V

MM

217

11 V

MM Pl

31

5

2

qeMM compactunif

– 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:

GUT GUTGUT

GUT5.261~GUT

t = log10 (Q/1GeV)

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

α2

-1

α1

-1

α3

-1

After RG evolution, can plot M1, M

2, M

3 at low scale as a

function of for ( here )01GUT TeVmTeV 5027 23

M3

M2

M1

Can also plot M1, M

2, M

3 at low scale as a function of

In both plots as 23m

GeVmGeV h 123119

M3

M2

M1

67.158.1 effZ

• 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

23600 mM

2396.1 mm

TeVOm )100(~23

2382.2 mm

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

2

For , getCompute physical masses:

Dominant production modes:

(s-channel gluon exchange)

(s-channel exchange) (s-channel exchange)

pbgggg 33.1)~~(

pbCCqq 2.6)~~

( 11 pbNCqq 1.12)

~~( 11

TeVm 3523 TeV7.45

GeVmg 733GeVm

N6.111

1~ GeVm

C76.111

1~

GeVmN

7.2282

~

W

0Z

almost degenerate!

45.1tan Example

4.261 GUT

GeVmh 121

pbggqq 46.0)~~(

Decay modes:

g~ 2

~Ntt

11

~~CbtCbt

1

~Cjets

1

~Nbb

2

~N WC1

~

11

~~NC

very soft!

~37% ;

~20.7% ;

~19% ;

~8.3% ;

1

~Nqq

2

~Nqq

~12% ;

~3% ;

~ 50% ;

~ 50% ; WC1

~

110

C~ C

~sec10~τ

1 is quasi-stable!

MeV160mm11 N

~C~

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

GeVmg 14662 ~

11

~~NC

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 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

NsbaNtbbiNsbaNtbi

NsbNtibiNsbNtibiaai

eAeeAe

eeAeeeAW

22121122

222111

2])[(

01)(

201

Phases

1])cos[( 2121 aNtbb

)( 22 NtbW

tl

2

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

TeVOm )100(23

)1(~tan O

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