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

Metastable SUSY breaking – p.2

Inevitability of metastability

Metastable SUSY breaking – p.3

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

Metastable SUSY breaking – p.4

Metastability and Nelson-Seiberg

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!

Metastable SUSY breaking – p.5

Metastability and Nelson-Seiberg

Option 1: explicit R breaking

W = WR−sym + εWR−breaking

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

Metastable SUSY breaking – p.6

Metastability and Nelson-Seiberg

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

Metastable SUSY breaking – p.7

Metastability and Nelson-Seiberg

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).

Metastable SUSY breaking – p.8

ISS metastable models

Metastable SUSY breaking – p.9

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).

Metastable SUSY breaking – p.10

ISS meta-stable models

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.

Metastable SUSY breaking – p.11

ISS meta-stable models

Thus we require

Nc + 1 ≤ Nf <3

2Nc

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

Metastable SUSY breaking – p.12

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.

Metastable SUSY breaking – p.13

Characteristics of the IR theory

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

Metastable SUSY breaking – p.14

Characteristics of the IR theory

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)

Metastable SUSY breaking – p.15

Characteristics of the IR theory

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 ).

Metastable SUSY breaking – p.16

Explicit vs spontaneousR-breaking

Metastable SUSY breaking – p.17

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)

Metastable SUSY breaking – p.18

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.

Metastable SUSY breaking – p.19

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}

Metastable SUSY breaking – p.20

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

Metastable SUSY breaking – p.21

Spontaneous R-symmetry breaking

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

Metastable SUSY breaking – p.22

Spontaneous R-symmetry breaking

Gaugino mass is naively

Mλ ≈g2

A

16π2〈X〉

µ25

µ22

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

Yanagida)

Metastable SUSY breaking – p.23

Spontaneous R-symmetry breaking

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”

Metastable SUSY breaking – p.24

Spontaneous R-symmetry breaking

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

Metastable SUSY breaking – p.25

Strong coupling andcascades

(in preparation)

Metastable SUSY breaking – p.26

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?

Metastable SUSY breaking – p.27

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

Metastable SUSY breaking – p.28

The MSSM at the bottom of a cascade

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

Metastable SUSY breaking – p.29

The MSSM at the bottom of a cascade

Perhaps at the bottom of the cascade it goes;

Metastable SUSY breaking – p.30

The MSSM at the bottom of a cascade

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)

Metastable SUSY breaking – p.31

The MSSM at the bottom of a cascade

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)

Metastable SUSY breaking – p.32

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

Metastable SUSY breaking – p.33