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Dynamical Supersymmetry Breaking in String Models Jason Kumar University of California, Irvine

Dynamical Supersymmetry Breaking in String Models Jason Kumar University of California, Irvine

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Dynamical Supersymmetry Breaking in String Models

Jason Kumar

University of California, Irvine

String Theory, Cosmology and Phenomenology

• LHC is coming soon, WMAP is here, DM direct and indirect– good chance to probe EWSB, SUSY, dark matter, inflation, etc.

• goal for string theory– not necessarily to use LHC “prove or falsify string theory” – instead, use string theory to provide insight about lower-energy physics

which you can probe at experiments• string theory can access gravity, gauge, matter

– insights can connect to LHC, cosmology, phenomenology• many string models

– don’t want to take one specific model and beat it to death– instead, focus on lessons common to many models

• doesn’t give a “prediction of string theory”– gives a motivated idea for what new physics might look like at the EFT

level

String models

• recent focus Type IIA/B– non-perturbative physics gives many options

• gauge group, matter multiplicity and representations, etc.

– D-branes/open strings are the key

• need to get chiral matter – branes at singularities– intersecting brane models (IBMs)

• much work on both…

• we study IBMs

IBM Basic Idea

• compactify IIA/B on orientifolded CY 3-fold– 10D 4D ; N=8 N=1

• O-planes have spacetime-filling charge need to cancel (Gauss’ Law / RR-tadpoles)

• D-branes do the job (D6-brane in IIA)

• open strings give gauge theory, chiral matter

• Iab counts bifundamental chiral matter– sym., anti-sym from O-planes

• tower of string excitations also

• we want an SM-sector, plus other sectors

• extra sectors are generic, since we need to cancel charge

• bifundamental matter is generic, since 3-cycles on a 6-manifold generally intersect

Standard Model example

• general features we can use– extra sectors with U(1)’s– representations: bifundamental, symmetric, anti-symmetric– SM particles not charged under U(1)X at tree-level

• pseudo-hidden sector– generic chiral matter

• mixed anomalies canceled by Green-Schwarz mechanism• cubic anomalies automatically cancel due to Gauss’ Law

– many excited string modes

U(3)qcdU(1)X

SU(2)L

U(1)L

SU(2)R

QL

LL

uR,dR

eR,R

A few different directions….• general phenomenological issues….

– dynamical supersymmetry breaking• arXiv:0710.4116

– mediation to Standard Model (w/ S. Kachru, E. Silverstein)• LHC collider phenomenology

– coupling SM gauge bosons to extra U(1)• arXiv:0707.3488 (w/ A. Rajaraman, J. Wells)

– modified trilinear WWZ couplings • arxiv:0801.2891 (w/ AR, JW)

• cosmology– inflation

• hep-th/0703278 (w/ B. Dutta, L. Leblond)• non-gaussianity (w/ B. Dutta, L. Leblond)

– baryogenesis• hep-th/0608188 (w/ B. Dutta)

– dark matter (w/ J. Feng)

Dynamical Supersymmetry Breaking

• would like to generate an exponentially low susy scale by dynamics– not only explain why it’s stable, but why it’s low

• standard way to generate low scale in EFT– dimensional transmutation– dynamics of non-abelian gauge group generates scale

• ISS; Kawano, Kitano, Ooguri, Ookouchi, etc.

• difficulties in gauge mediation– gauge messengers could cause Landau poles [ SU(5) NC > 5 – 10 ]– more scales (hierarchy between dyn and mq)– harder to arrange in simple IBM’s (get NF NC)– nice to have other options anyway

• AKS used D-instanton to generate low scale– no non-Abelian dynamics– inherently “stringy”– fits in with branes at singularities

• is there something similar for intersecting brane models?

Yukawa coupling

• in IBM setup, Yukawa coupling arises from worldsheet instantons (Aldazabal, Franco, Ibanez, Rabadan, Uranga; Kachru, Katz, Lawrence, McGreevy; Cremades, Ibanez, Marchesano; Cvetic, Papadimitriou)

– is exponentially suppressed

– in large volume regime (where moduli stabilization is understood), we get small number for free

• this is a stringy effect– from EFT point of view, no

reason for to be small

321 W

2sl

A

e

1

2 3

a

b

c

Use small to get a small scale

• D-terms will play a vital role• start with a simple example

3 intersecting branes– gauge theories have non-

trivial Fayet-Iliopoulos terms– assume they are of some

“natural” scale (perhaps GUT) which need not be small ~

– additional terms due to axions• Green-Schwarz mechanism

• all superpotential terms are non-perturbative– dominated by some small

213

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~ W

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Scaling of VF and VD

• of course, if =0 we can set VF=VD=0 by sitting on a D-flat direction– take a,c > 0, b < 0

• D-flat direction - r• naturally get g

– i.e., g small, exponentially small

– VD VF 2

– moving on r is not a runaway direction for VF

2

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Basic points

• not dependent on specific form of potential or brane configuration

• W coefficients exponentially suppressed– end up on D-flat direction “corrected” by F-terms

• more F-term equations than D-flat directions• F-term runaway direction is generically not a D-flat

direction• VD VF , but VF exponentially suppressed• depends on “hypermultiplet” moduli

– need to stabilize to avoid runaway to supersymmetric vacuum– but we need to stabilize closed string moduli anyway for

phenomenological reasons• we will assume closed string moduli stabilized

How to mediate to SM?

• consider an SU(5) GUT setup– extra U(1) brane

• 5 from bifundamental• 10 from antisymmetric

• generic bifund. matter– gauge mediation natural

• want to include both the SU(5) sector and DSB sector– need to add a few extra

branes for anomaly cancellation

– also to make sure generic superpotential involves all fields

• M1,2 gauge messengers

U(5)GUT

U(1)

10

5

• assume GUT = 0 to avoid breaking GUT at higher scale– needed in any case,

independent of DSB mech.

• assume one limit for simplicity• factors which affect pheno.

– scale of F– scale of messenger masses– scale of R-symmetry breaking

• gaugino masses

• each controlled by a different Yukawa in this setup

• involves interplay between D-term and F-term– would be nice to find a version

with only F-term dynamics, ala AKS

– working on this now….

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Dark Matter

• couple of interesting features inherent to IBM scenario– many hidden gauge sectors– gauge mediation between open string sectors generic (via

bifundamental matter)• can have stable particles charged only under hidden

sector– left over discrete symmetries could stabilize

• possible dark matter candidates?– no SM charge– if stable, they contribute to dark matter

• could be either good, or bad

• what are the general dark matter implications for this type of scenario?

Setup• one sector breaks SUSY• gauge mediation to multiple sectors,

including SM sector• unbroken discrete symmetries• not a detailed IBM scenario

– not worrying about details of genericity, # of sectors, size of Yukawas, discrete symmetries, etc.

– looking at a motivated EFT scenario• in each sector, low-energy scale set by

contribution to fermion/scalar splitting due to gauge interactions

– vector-like matter can be expected to get mass at high (GUT) scale

– non-vectorlike matter has no mass scale, except that generated by gauge mediation

– much as susy-breaking scale in MSSM sets the EWSB scale and everything else (up to small Yukawas)

SUSY

hidden MSSM

Gauge mediation

• “WIMP miracle”– stable matter with weak group coupling and EWSB

scale mass would lead to approximately the right relic density for dark matter

– R-parity can stabilize the LSP• expect to be couple with SU(2) strength and with mass ~

EWSB scale in gravity mediation• in gauge mediation, gravitino is LSP (very light)

– no good DM candidate gravitino DM density too large

– WIMP miracle points to gravity mediation and conserved R-parity

• lots of work connecting dark matter and the EWSB scale– but is the miracle really so miraculous?

Scaling

• we assume that F and Mmess are set by the dynamics of susy-breaking sector– same for all gauge sectors

• in each sector, ratio of gauge coupling to scalar mass is approximately fixed

• same ratio determines annihilation cross-section via gauge interactions– determines relic density– if MSSM gets it right, so does

every other sector

.2

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mess

messscalar m

FNgm

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messh

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Upshot• we find in this scenario, a generic charged stable particle should

have the right density (order of magnitude) to be dark matter• maybe WIMP miracle isn’t that miraculous … any gauge sector with

any coupling would have worked• in fact, it should have worked for the MSSM in gauge-mediation

– two stable particles the LSP and the electron– first accident electron Yukawa coupling is extremely (perhaps

unnaturally) small• mass much lighter than normal scale• a “natural” mass would be mtop

• if electron mass were ~ mtop, would have the right relic density– second accident in gauge mediation, the LSP is not gauge charged

• but in any other sector, a discrete symmetry can stabilize a hidden sector gauge charged particle– in the right ball-park for dark matter– distinct from gravity mediated result, where it really is a miracle

But what about detection?• if hidden sector not coupled to

visible sector, all DM annihilations could be invisible– in this case, could not detect

DM by direct, indirect or collider

• only by astronomical observation

• but if hidden sector couples to SM sector, very interesting detection scenarios– could couple to SM particles

via Yukawa or gauge couplings

– Yukawa coupling especially interesting, as it could be O(1)

• assume fewer SM final states

X X

SM SM

X X

SMSM

Y

'

Indirect Detection possibilities• dark matter at galactic center

annihilates to SM particles, which emit photons detected at gamma ray telescopes

– photon flux scales as (# density)2

– larger signal at small MX

• take scenario with Yukawa coupling to SM

– X is the light hidden sector scalar• stabilized by discrete symmetry• mass ~ 5 GeV

– Y is a fermion with both hidden and SM charge

• gains mass from both hidden and SM gauge interactions

• mass ~ 1 TeV

• coupled to SM up-quarks– W = XYLQL + XYRuR +mYLYR

– is O(1)

JscmEthr4129107

• with this scenario, GLAST could probe for halo density J ~ 3 , ~ 0.3– this is the lower end of

what various theories predict

– most dark matter models do not allow one to probe this region

Direct Detection limits• need to see if this is ruled out by direct

detection bounds• DM passing through earthbound

detector transfers momentum to nucleus via elastic scattering

• expect not bounded – direct detection sensitivity scales with

number density– goes bad ~ 10 GeV

• can compute direct detection limits

– for and MX in our range, not ruled out by direct detection

• note, could have coupled to instead of up-quark

– then indirect detection sensitivity is basically the same

– but no direct detection possibility

pb6854

Dan HooperSUSY ‘07

Conclusion

• string theory can be a powerful generator of ideas for new physics– the tight constraints of consistent quantum gravity can

illustrate new scenarios and features which otherwise would be less noticed

• phenomenology, collider physics, cosmology

– ideas aren’t exclusive to string theory (and thus neither prove nor falsify), but the question is if they satisfy the “usefulness” test

• much more to learn ….