Sequestered SUSY breaking Sven Krippendorf Rudolf Peierls Centre - - PowerPoint PPT Presentation

Sequestered SUSY breaking

Sven Krippendorf

Rudolf Peierls Centre for Theoretical Physics String Group Seminar, Liverpool, 28/10/2014

based on:

• L. Aparicio, M. Cicoli, SK, A. Maharana, F. Muia, F. Quevedo:

Sequestered dS string scenarios: soft terms 1409.1931

• R. Blumenhagen, J. Conlon, SK, S. Moster, F. Quevedo:

Sequestered soft-masses in LVS 0906.3297

• M. Cicoli, SK, C. Mayrhofer, F. Quevedo, R. Valandro: Global

realisations 1206.5237

Motivation

Status of SUSY

• 126 GeV Higgs, no sign of SUSY yet but not excluded.
• How is the hierarchy problem addressed?


`Best fit’ SUSY (compared to: compositeness, just SM, X-dim):
 a) particular corner of MSSM (e.g. natural SUSY, NRMSSM)
 b) split SUSY
 c) large (intermediate) SUSY breaking scale

• Problems: a) Why this special corner? b) Fine-tuning for

hierarchy problem. c) Even more fine-tuning

Problems should be addressed in UV completion of SM (guidance, explicit realisations, alternatives)

String Models of SUSY: crucial ingredients

soft-term spectrum

Classical question: do classes of string models addressing these issues lead to distinct SUSY models?

String Models of SUSY: crucial ingredients

visible sector moduli stabilisation de Sitter (uplifting) soft-term spectrum

Classical question: do classes of string models addressing these issues lead to distinct SUSY models?

String Models of SUSY: crucial ingredients

visible sector moduli stabilisation de Sitter (uplifting)

Construct dS vacua
 with stabilised moduli Realise moduli stabilisation with chirality

soft-term spectrum

Classical question: do classes of string models addressing these issues lead to distinct SUSY models?

String Models of SUSY: crucial ingredients

visible sector moduli stabilisation de Sitter (uplifting)

Construct dS vacua
 with stabilised moduli Realise moduli stabilisation with chirality

soft-term spectrum

Classical question: do classes of string models addressing these issues lead to distinct SUSY models? how realistic? realised explicitly in a global compactification? stable? all moduli? explicit?

Why now?

• Progress in string constructions (chiral, global, de

Sitter models with branes at singularities)


Cicoli, (Klevers), SK, Mayrhofer, Quevedo, Valandro (2012, 2013)

• Spectrum of soft-masses relevant for cosmology

(dark matter, CMP, dark radiation, CAB)


work by Cicoli, Conlon, Marsh, Quevedo, et al.

• LHC14, future SUSY searches. Can string theory

be relevant in SUSY phenomenology discussion?


➥ golden opportunity: interpolating between
 scenarios in UV setups

cartoon of moduli space

split large SUSY natural SUSY CMSSM

?

What’s new?

• towards complete models 


global realisation with visible sector and dS moduli stabilisation

• uplifting dependence of soft-masses determined
• D-terms in LVS soft-masses
• pheno-ready soft-masses/parametrisation
• UV realisations of interesting SUSY

phenomenology scenarios (split susy, non- universal soft-masses)

Content

• Explicit type IIB models with moduli stabilisation,

dS, chirality and broken SUSY

• Soft-terms for sequestered models

Strategy: general

• Find classes of consistent compactification +

ingredients (branes + fluxes)

• Determine EFT, stabilise moduli
• Determine phenomenological UV soft-terms
• Analyse soft-terms @ low-energies

A roadmap towards realistic string vacua in IIB

global realisation: MC, SK, CM, FQ, RV 1206.3297

A roadmap towards realistic string vacua in IIB

TB(ig) TS(mall)

global realisation: MC, SK, CM, FQ, RV 1206.3297

A roadmap towards realistic string vacua in IIB

RR, NSNS fluxes

TB(ig) TS(mall)

global realisation: MC, SK, CM, FQ, RV 1206.3297

A roadmap towards realistic string vacua in IIB

RR, NSNS fluxes

TB(ig) TS(mall) ED3, g.c.

global realisation: MC, SK, CM, FQ, RV 1206.3297

A roadmap towards realistic string vacua in IIB

RR, NSNS fluxes

TB(ig) TS(mall) ED3, g.c.

• ther hidden sectors

(e.g. uplifting) global realisation: MC, SK, CM, FQ, RV 1206.3297

A roadmap towards realistic string vacua in IIB

RR, NSNS fluxes

TB(ig) TS(mall) ED3, g.c.

O-Involution

• ther hidden sectors

(e.g. uplifting) global realisation: MC, SK, CM, FQ, RV 1206.3297

A roadmap towards realistic string vacua in IIB

RR, NSNS fluxes

TB(ig) TS(mall) ED3, g.c. TSM

O-Involution

• ther hidden sectors

(e.g. uplifting) global realisation: MC, SK, CM, FQ, RV 1206.3297

A roadmap towards realistic string vacua in IIB

RR, NSNS fluxes

TB(ig) TS(mall) ED3, g.c. TSM BSM D-brane setup

O-Involution

• ther hidden sectors

(e.g. uplifting) global realisation: MC, SK, CM, FQ, RV 1206.3297

here: BSM D-brane setup from D-branes at singularities

Realisation of Roadmap

• CY in Kreuzer-Skarke database with desired properties: LVS

(blow-up), O-involution exchanging 2 dPn singularities for BSM D-brane models, no intersection non-perturbative and blow-up SM divisor

• add D-branes, world-volume fluxes, check consistency

conditions

• stabilise Kähler moduli (and complex structure moduli)

explicitly

• analyse low-energy theory…

global realisation: MC, (DK), SK, CM, FQ, RV 1206.3297, (1404.7127)

A benchmark model

…taken from a whole class

1206.5237

A benchmark model

• From search in Kreuzer-Skarke database, h1,1=4,

h1,2=112: visible sector 2xdP0, hidden sector 1xdP0

• O-involution exchanging visible sector, can realise

g.c. on hidden sector and simple visible sector with trinification model

• All consistency conditions satisfied (tadpoles, K-

theory charges)

3C 3R 3L

Moduli Stabilisation

• complex structure assumed to be stabilised with 3-form fluxes (D3 tadpole allows to

turn on fluxes.)

• EFT:


• singularity stabilisation: D-term minimum at ξi=0 and Ci=0 (soft-masses), F-terms sub-leading

K = −2 ln V + ζ g3/2

s

! + (T+ + ¯ T+ + q1V1)2 V + (G + ¯ G + q2V2)2 V + Ci ¯ Ci V2/3 ,

V = 1 9 r 2 3 ⇣ τ 3/2

b

− √ 3τ 3/2

s

⌘

W = Wlocal + Wbulk = W0 + yijk CiCjCk + As e− π

3 Ts + Ab e− π 2 Tb

VD = 1 Re(f1) X

i

q1iKiCi − ξ1 !2 + 1 Re(f2) X

i

q2iKiCi − ξ2 !2 ,

ξ1 = −4q1 τ+ V

ξ2 = −4q2 b V

Moduli Stabilisation

• F-term potential


• FW flux on large four-cycle (matter fields), D-term potential


• can account for dS/Minkowski minima...

4106 6106 8106 1107 Vol 2.1023 4.1023 6.1023 8.1023 1.1022 V

VF ' 8 3(asAs)2pτs e−2 asτs V 4 asAsW0τs e−asτs V2 + 3 4 ζW 2 g3/2

s

V3

hVi ' 3W0 pτs 4asAs eashτsi

hτsi ' ✓3ζ 2 ◆2/3 1 gs

Vtot = VD + VF ' p1 V2/3 @X

j

qbj|φc,j|2 p2 V2/3 1 A

2

+ X

j

W 2 2V2 |φc,j|2 + VF (T)

W0 ' 0.2 gs ' 0.03 As ' 1 ζ ' 0.522

V ' p W 2 V8/3 + VF (T)

hV i = W 2 hVi3 (

• 3

4 a3/2

s

s ln ✓hVi W0 ◆ + p 9 hVi1/3 )

Two ways of getting dS

• dS1: Hidden matter fields (1206.5237):


balancing 10 vs. 100 (log(V) vs V1/3), get on with what’s there


• dS2: Dilaton dependent non-perturbative effects

(MC, AM, FQ, CB 1203.1750)

WdS = AdS(U, S) e−adS(S+κdSTdS)

KdS = λdS τ 2

dS

V

Vtot = VO(V−3) + (κdSadSAdS)2 λdSs e−2adSs V

✓dSadSAdS W0 ◆2 e−2adSs = 9dS 32 ✏s ˆ ⇠ V2

hV i = W 2 hVi3 (

• 3

4 a3/2

s

s ln ✓hVi W0 ◆ + p 9 hVi1/3 )

SUSY-breaking

SUSY breaking in LVS

TB(ig) TS(mall) ED3, g.c. TSM BSM D-brane setup

• ther hidden sectors

(e.g. uplifting)

SUSY LVS minimum breaks SUSY

Conlon, Quevedo, Suruliz, …

m3/2 = ✓ g2

s

2 √ 2π ◆ W0MP V + . . .

What are msoft?

3 SUSY scenarios

• Unsequestered GUT scale scenarios (FTSM≠0):


Ms~MGUT, V~103-107, MSOFT~m3/2
 (intermediate-scale SUSY, no CMP, W0 tuning)

• Unsequestered intermediate scale strings (FTSM≠0)


Ms~1010 GeV, V~1010-1015, MSOFT~m3/2~1 TeV
 (mild hierarchies, low-scale SUSY, CMP)

• Sequestered high scale string models (FTSM=0)


Ms~1015 GeV, V~106-107, MSOFT << m3/2


(compatible with GUT, split and low-scale SUSY scenarios, no CMP)

Focus: sequestered scenarios

• rientifold involution

visible sector

visible sector

singularity singularity

D3/E(-1)

NP effects

small

cycle E3/D7 effects NP big cycle

singularity

• SM

b

• s

b

dS ,

SM

• ,

b

• r

i e n t i f

• l

d i n v

• l

u t i

• n

v i s i b l e s e c t

• r

v i s i b l e s e c t

• r

s i n g u l a r i t y s i n g u l a r i t y

E3/D7 NP effects small cycle big cycle

• S

M

b ,

s b

dS

• S

M

b ,

dS1: hidden matter dS2: dilaton dep. no-effects

EFT

• Kähler matter potential


• Gauge kinetic function

• Superpotential

˜ Kα = fα(U, S) V2/3 1 − cs ˆ ξ V + ˜ KdS + cSMτ p

SM + cbbp

!

fa = δaS + κakTk fa = S + κaTSM

Kmatter = ˜ Kα(M, M)C

αCα + [Z(M, M)HuHd + h.c.]

W = Wflux(U, S) + As(U, S) e−asTs + WdS + Wmatter Wmatter = µ(M)HuHd + 1 6Yαβγ(M)CαCβCγ + · · ·

K = −2 ln V + ˆ ξ 2 ! − ln(2s) + λSM τ 2

SM

V + λb b2 V + KdS + Kcs(U) + Kmatter

dS dep. on minimum and F-terms

• Sub-leading shift in LVS minimum:


• F-terms

⌧ 3/2

s

= ˆ ⇠ 2 [1 + fdS(✏s)]

✏s ⌘ 1 4as⌧s ⇠ O ✓ 1 ln V ◆ ⌧ 1

fdS2 = 3✏s + 12✏2

s

fdS1 = 18✏s + 297✏2

s

V = 3√⌧sW0easτs 4asAs (1 − 4✏s) (1 − ✏s)

F Tb ⌧b ' 2m3/2 1 + xdS a3/2

s

Vp✏s !

F Ts ⌧s ' 6m3/2✏s

F S s ' 3!0

S(U, S)

8a3/2

s

m3/2 V✏3/2

s

F Ui ' KUiU j 2s2 ωU j(U, S) ω0

S(U, S) F S ⌘ βUi(U, S)F S

F φdS φdS ' m3/2 F TdS ' 3 4 p 2a3/4

s

m3/2 ✏1/4

s

xdS1 = −45/16

xdS2 = 0

Soft-terms in detail

soft-term formulae: Brignole, Ibanez, Munoz; Dudas Vempati; …

Gaugino Masses

Ma = 1 2Re (fa)F I∂Ifa F G = F TSM = 0 fa = S + κaTSM

M1/2 = F S 2s ' 3!0

S(U, S)

16a3/2

s

m3/2 V✏3/2

s

⇠ O m3/2 (ln V)3/2 V ! ⌧ m3/2

(Ultra)-Local

• Additional no-scale cancellations:


• Local: Holds at V-1, Ultra-Local: Holds exactly

= ˜ Kα  m2

3/2 − ¯

F ¯

m

✓ ∂ ¯

m∂n

K 3 ◆ F n

• = − ˜

Kα V0 3 = 0

m2

α =

h m2

3/2 + V0 − ¯

F ¯

m ⇣

∂ ¯

m∂n log( ˜

Kα) ⌘ F ni

˜ Kα = hα(S, U) eK/3 ' hα(U, S) eKcs/3 (2s)1/3V2/3 1 ˆ ξ 3V + 1 3KdS !

ˆ Yαβγ = eK/2 Yαβγ(U, S) q ˜ Kα ˜ Kβ ˜ Kγ

Scalar masses

Scalar masses

mij = ∂i∂jV = rirjV

Scalar masses

−g2

ADA

⇣ Gj∂iDA + Gi∂jDA − ∂i∂jDA ⌘ + g2

A∂iDA∂jDA

◆ ⇣ ˜ Ki ˜ Kj ⌘−1/2

m2

ij =

✓ eG h Gij + riGkrjGk RijklGkGli + 1 2g2

AD2 A

⇣ GiGj Gij ⌘

Scalar masses

m2

ij =

✓ eG h Gij − RijklGkGli − 1 2g2

AD2 AGij + g2 ADA∂i∂jDA

◆ ⇣ ˜ Ki ˜ Kj ⌘−1/2

Scalar masses

m2

ij =

✓ eG h Gij − RijklGkGli − 1 2g2

AD2 AGij + g2 ADA∂i∂jDA

◆ ⇣ ˜ Ki ˜ Kj ⌘−1/2

dS1: dS2: local: ultra-local: m2

α = cαM 2 a 6= 0

m2

• F ' m2

3/2

✓F Tb 2 ◆2 ∂2

τb ln ˜

K ' 5

• cs 1

3

• ω0

S

m3/2M1/2 ⇠ O m2

3/2

(ln V)3/2 V !

m2

• D = 6✏s

!0

S

m3/2M1/2 ∼ O m2

3/2

√ ln V V !

ultra-local:

mu-term

• Kähler potential contributions

Bˆ µ|F = ⇢ 2m2

3/2Z − m3/2F I∂IZ + m3/2F I h

∂IZ − Z∂I ln ⇣ ˜ KHu ˜ KHd ⌘i −F IF

J h

∂I∂JZ − ∂IZ∂J ln ⇣ ˜ KHu ˜ KHd ⌘i ⇣ ˜ KHu ˜ KHd ⌘−1/2 , Bˆ µ|D = ⇣ ˜ KHu ˜ KHd ⌘−1/2 X

i

g2

i Di∂Hu∂HdDi − VD,0Z

!

Z = γ(U, S) ˜ K

ˆ µ = cµM1/2 Bˆ µ = cBm2

ˆ µ = ✓ m3/2Z − F

I∂IZ

◆ ⇣ ˜ KHu ˜ KHd ⌘−1/2 and Bˆ µ = Bˆ µ|F + Bˆ µ|D

mu-term

• superpotential contributions


• via matter fields (model dependent)

T = Ts and a = nas

ˆ µ ' cµ(U, S) Vn+ 1

3

and Bˆ µ ' cB(U, S) Vn+ 4

3

W ⊃ e−b(S+κT )HuHd ⇒ µeff = e−b(S+κT )

W ⊃ e−aT HuHd ⇒ µeff = e−aT

Bˆ µ = µ eK/2 h F I ⇣ KI + ∂I ln µ − ∂I ln ⇣ ˜ KHu ˜ KHd ⌘⌘ − m3/2 i ⇣ ˜ KHu ˜ KHd ⌘−1/2

ˆ µ = µ eK/2 ⇣ ˜ KHu ˜ KHd ⌘−1/2

Soft term Local Models Ultra Local dS1 Ultra Local dS2 M1/2 c1/2 m3/2

m3/2 MP

h ln ⇣

MP m3/2

⌘i3/2 m2

α

c0 m3/2M1/2 c0

m3/2M1/2 ln(MP /m3/2)

(c0)α M 2

1/2

Aαβγ (cA)αβγ M1/2 ˆ µ cµ M1/2 (contribution from K) cµMP h m3/2

MP

in+1/3 (contribution from W) Bˆ µ cB m2 (contribution from K) cBm3/2 h m3/2

MP

in+1/3 (contribution from W)

Summary of soft-terms

W ⊃ AHe−nasTsHuHd

Z = γ(U, S) ˜ K

Future goals

• Reduce assumptions by increasing string theory input:

• MSSM vs. real D-brane configurations

• Improved understanding of EFT: Kähler matter metric (non-

universalities)


• Realising more uplifting scenarios explicitly
• Phenomenology analysis
• Making string SUSY landscape more precise:


cartoon of moduli space

split large SUSY natural SUSY CMSSM

?

Conclusions

• Global models with dS moduli stabilisation and chiral

matter, allow more refined view on SUSY breaking in LVS

• New benchmark scenarios for sequestered SUSY
• breaking. Stay tuned for phenomenological analysis
• D-terms are important and interesting for soft-masses
• Low-energy SUSY can address hierarchy problem, fluxes

used for mild hierarchies

• Way of flux landscape interpolating between local and

ultra-local scenarios

Thank you!