Dynamical Supersymmetry Breaking in String Models

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

2. 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

3. 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

4. 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 IBM Basic Idea

5. Standard Model example SU(2)L • 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(1)X U(3)qcd QL uR,dR LL eR,nR U(1)L SU(2)R

6. 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)

7. 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 Ldyn 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?

8. Yukawa coupling a c • in IBM setup, Yukawa coupling arises from worldsheet instantons (Aldazabal, Franco, Ibanez, Rabadan, Uranga; Kachru, Katz, Lawrence, McGreevy; Cremades, Ibanez, Marchesano; Cvetic, Papadimitriou) • l 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 l to be small f1 f2 f3 b

9. Use small l 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 ~ x • additional terms due to axions • Green-Schwarz mechanism • all superpotential terms are non-perturbative • dominated by some small l

10. Scaling of VF and VD • of course, if l=0 we can set VF=VD=0 by sitting on a D-flat direction • take xa,c> 0, xb < 0 • D-flat direction - r • naturally get l g • i.e., g small, l exponentially small • VD VFx2 • moving on r is not a runaway direction for VF

11. 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 • x 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

12. How to mediate to SM? 10 • 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 5 U(1)

13. assume xGUT = 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….

14. 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?

15. 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) Setup SUSY MSSM hidden

16. 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?

17. 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

18. 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

19. 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

20. 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 = lXYLQL + lXYRuR +mYLYR l is O(1) with this scenario, GLAST could probe for halo density J ~ 3 , l ~ 0.3 this is the lower end of what various theories predict most dark matter models do not allow one to probe this region Indirect Detection possibilities

21. 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 l and MX in our range, not ruled out by direct detection • note, could have coupled to t instead of up-quark • then indirect detection sensitivity is basically the same • but no direct detection possibility Dan Hooper SUSY ‘07

22. 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 ….