metastable susy breakingscipp.ucsc.edu/~haber/planck08/abel.pdfoutline 1. inevitability of...

Metastable SUSY breakingSAA w/ C.Durnford, J.Jaeckel, V.V.Khoze

Metastable SUSY breaking – p.1

Outline

1. Inevitability of Metastability: the Nelson-Seiberg theorem

2. ISS metastable SUSY breaking

3. Explicit vs. spontaneous R-breaking

4. Strong coupling and cascades


Inevitability of metastability


Metastability and Nelson-Seiberg

Consider low-energy, calculable models of SUSY breaking

The potential is V = |Fi|2 = | ∂W

∂Φi|2

Q: When is SUSY broken? i.e. when does Fi = 0 not have solutionsfor all i?

A: (Nelson-Seiberg) In a generic theory, when there is anR-symmetry.

Φi → eiRiαΦi

θ → eiαθ

W → e−2iαW



But gaugino mass terms Mλλαλα have non-zero R-charge (sinceWα = λα + . . ., and Lgauge =

∫

d2θWαW α)

Non-zero gaugino masses require both R-symmetry and SUSYbreaking but these are mutually exclusive!



Option 1: explicit R breaking

W = WR−sym + εWR−breaking

A global SUSY minimum develops O(1/ε) away in field space, withMλ ∝ ε



Option 2: spontaneous R breaking

The massless R-axion?

To give the massless R-axion a mass need additional R-symmetrybreaking εWR−breaking, but now Maxion ∝ ε



For gauge mediation the Universe is (probably) metastable!

Analysis in SUGRA more complicated because the Kahler potentialenters and minimum can be at > MPl (see H.Abe, T.Kobayashi,Y.Omura).


ISS metastable models


ISS meta-stable models

Content of the microscopic “electric model” (Intriligator, Seiberg, Shihhep-th/0602239)

N = 1 gauge SU(Nc)

mesons QjQj ; i, j = 1 . . .Nf

fundamental electric quarks Qai ; a = 1 . . . Nc

antifundamentals (Dirac mass mQ) Qia

If the beta function is negative b0 = 3Nc − Nf > 0 then the Wilsoniangauge coupling

e−8π2/g2(E) =

(

E

Λ

)

−b0

is strongly coupled in the IR (Λ is the Landau pole).



For certain values of parameters a Seiberg dual exists in the IRContent of the macroscopic “magnetic model”

N = 1 gauge SU(N) N = Nf − Nc

mesons Φji ; i, j = 1 . . . Nf

fundamental magnetic quarks ϕai ; a = 1 . . .N

antifundamentals ϕia

Exists if b0 = 3N − Nf < 0 so the Wilsonian coupling is runs to weakcoupling in the IR.



Thus we require

Nc + 1 ≤ Nf <3

2Nc

Lowest values are Nc = 5, Nf = 7.Assume minimal Kahler potential K = ϕϕ + ϕ ¯ϕ + ΦΦ


Characteristics of the IR theory

Magnetic theory contains tree-level plus ADS like dynamically generatedterm W = Wcl + Wdyn:

Wcl = h TrNf(ϕΦϕ) − hµ2TrNf

Φ

Wdyn = N

(

hNf detNfΦ

ΛNf−3N

)1

N

where µ2 ≈ mQΛ.



Near origin ignoring Wdyn we have an R-symmetry =⇒ |vac〉+:

FΦij

= h (ϕi.ϕj − µ2δj

i ) 6= 0

cannot be satisfied since ϕi.ϕj has rank N = Nf − Nc < Nf .

But Wdyn break this R-symmetry (anomalous) =⇒ |vac〉0:

0 2 4 6 8 10

2

4

6

8

10



The form of the O’Raifeartaigh IR superpotential is explained

The metastable potential long lived (ISS)

S4 ∼ 2π2 Φ40

V+

= 2π2 Φ40

h2µ4

New model building (Franco Uranga; Amariti Forcella Girardello Mariotto; Forste;Dine Feng Silverstein; Dine Mason; Kitano Ooguri Ookouchi; Murayama Nomura;Csaki Shirman Terning; Aharony Seiberg; SAA Durnford Jaeckel Khoze; Brummer;Feretti; Haba Maru; Ellwanger, Jean-Louis, Teixeira; Bajc, Melfo)

The metastable vacuum is favoured thermally (SAA Chu Jaeckel Khoze;Craig Fox Wacker; Fischler Kaplunovsky Krishnan Mannelli Torres)

Inflation (Craig; Davis Postma; Linde Westphal; Savoy Sil)

F-term uplift (Dudas Papineau Pokorski; Kallosh Linde; Lebedev Lowen MambriniNilles Ratz; Abe Higaki Kobayashi Omura; Brax Davis2 Postma)



Aside: the cosmological constant can be adjusted in an entirely separatehidden sector without affecting the gauge mediated phenomenology

V ∼ exp(K)

(

|F |2 − 3|W |2

M2

P

)

Fi = Wi +Ki

M2

P

W.

Then W ∼ M2s MP (e.g. Polonyi-like W → W + c), but since

Ki ∼ µ ≪ MP we have Fi = Fi + O(µ3/MP ).


Explicit vs spontaneousR-breaking


Explicit (naturalized) R-breaking

e.g Murayama Nomura; Aharony Seiberg; Kitano, Ooguri Ookouchi; Csaki,

Shirman, Terning; ....

How to generate an R-breaking Mλ without destabilizing? (NoteMλ = 0 at origin). Consider adding explicit R-symmetry breakingmessengers called f .

W ⊃λ

MPLQQ f.f + Mf.f

−→λΛ

MPLTr(Φ)f.f + Mf.f + ϕΦϕ − µ2Tr(Φ)


Explicit (naturalized) R-breaking

These would generate gaugino masses

with global SUSY now restored at

λΛ

MPL〈f.f〉 = µ2 ;

λΛ

MPLTr(〈Φ〉) = −M

Duality explains the smallness of explicit R-symmetry breaking.


Spontaneous R-breaking

Consider a “baryon-deformed” ISS (SAA, C.Durnford, J.Jaeckel, V.V.Khoze,

arXiv.0707.295, arXiv:0712.1812):

W = Φijϕi.ϕj − Tr(µ2Φ) + mεabεrsϕarϕb

s

where r, s = 1, 2 are the 1st and second generation numbers only.

We will use ϕ and ϕ to mediate to gauginos so let Nf = 7 and gaugeSU(5)f ⊃ GSM factor

take µ2ij = diag{µ2

2I2, µ25I5}


Spontaneous R-symmetry breaking

As prescribed by Shih (hep-th/0703196) the model has an R-symmetrywith R 6= 0, 2...

SU(5) SU(2) U(1)R

Φij ≡

0

@

Y Z

Z X

1

A

0

@

4 × 1 �

� Adj + 1

1

A

0

@

1 1

1 1

1

A 2

ϕ ≡

0

@

φ

ρ

1

A

0

@

1

�

1

A � 1

ϕ ≡

0

@

φ

ρ

1

A

0

@

1

�

1

A � −1



Runaway to broken SUSY with φ → ∞ and φ.φ = µ22, stabilized by

Coleman-Weinberg potential:

20 30 40 50 60

5

5.1

5.2

5.3

5.4

5.5

5.6

5.7



Gaugino mass is naively

Mλ ≈g2

A

16π2〈X〉

µ25

µ22

Get additional suppression (F 3χ required) (c.f. Izawa, Nomura, Tobe,

Yanagida)



Scalar masses can be much larger (don’t depend on R-symmetrybreaking):

Mscalar ∼g2

A

16π2µ5

The deformation m takes phenomenology continuously fromalmost-gauge-mediation-like to “split-SUSY-like”



Compare spontaneous and explicit R-breaking (SUSYGen)

tan β µMSSM eL, µL t1 χ01

χ± h0 , H0, A g

Sp 58.7 2891 4165 10345 60.8 100.7 124.8 184.5 414.2

Exp 38.9 939 747.9 1593 270.3 526.5 137.6 975.1 1500


Strong coupling andcascades

(in preparation)


The Landau pole issue

Since the additional fields are in SU(5) multiplets, the beta functions of theMSSM gauge couplings are modified universally as

bA = b(MSSM)A − 9

The SM gauge couplings at a scale Q > µ in our model are thereforerelated to the traditional MSSM ones as

α−1A = (α−1

A )(MSSM) −9

2πlog(Q/µ)

Λ(MSSM)

µ∼ 105

Are both the MSSM and the ISS sector magnetic duals?


The MSSM at the bottom of a cascade

c.f. Klebanov-Strassler cascade SU((k − 1)M) × SU(kM) with 2 flavours:

SU((k − 1)M) × SU(kM) → SU((k − 1)M) × SU((k − 2)M)

Wash, rinse, repeat: supergravity dual→field theory



Verlinde et al’s suggested equivalent for the MSSM based onLR-symmetric quiver (Heckman Vafa Verlinde Wijnholt);



Perhaps at the bottom of the cascade it goes;



ΦRR

ΦLL

ΦLR

f, f

f, f

ϕ, ϕ

The superpotential is of the MN form

W = λTr(Φ)f.f + Mf.f + hϕΦϕ − hµ2Tr(Φ)

with suppressed λ (comes from a 3 meson-coupling of the electric theory)



The ISS parameter µ is the scale of SU(2)R breaking

The Higgs is the pseudo-Goldstone mode ΦLR, hence mH ∼ h2µ8π

Gaugino masses Mλ ∼ g2

16π2

µ2

M requires M ∼ g2µ/(2πh2)


Summary

Metastability inevitable for low energy SUSY breaking

Extremely simple model of direct mediation from baryon-deformedISS

Phenomenology between gauge-mediation and split-SUSY - prefersheavy scalars

Different patterns of SUSY spectrum for explicit vs spontaneousR-breaking

Landau pole in MSSM → MSSM cascade?

Interesting possibilities for embedding ISS in cascade models

Can be done for both explicit and spontaneous R-breaking


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