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, N R MSSM) 
 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 soft-term spectrum Classical question: do classes of string models addressing these issues lead to distinct SUSY models? de Sitter (uplifting)

String Models of SUSY: crucial ingredients Realise moduli stabilisation with chirality visible sector moduli stabilisation soft-term spectrum Classical question: do classes of string models addressing these issues lead to distinct SUSY models? Construct dS vacua 
 with stabilised moduli de Sitter (uplifting)

String Models of SUSY: crucial ingredients Realise moduli stabilisation with chirality visible sector moduli stabilisation how realistic? all moduli? realised explicitly in a soft-term spectrum explicit? global compactification? Classical question: do classes of string models addressing these issues lead to distinct SUSY models? Construct dS vacua 
 with stabilised moduli de Sitter (uplifting) stable?

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 natural SUSY large SUSY split CMSSM cartoon of moduli space ?

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 T S(mall) T B(ig) global realisation: MC, SK, CM, FQ, RV 1206.3297

A roadmap towards realistic string vacua in IIB RR, NSNS fluxes T S(mall) T B(ig) global realisation: MC, SK, CM, FQ, RV 1206.3297

A roadmap towards realistic string vacua in IIB RR, NSNS fluxes T S(mall) T B(ig) ED3, g.c. global realisation: MC, SK, CM, FQ, RV 1206.3297

A roadmap towards realistic string vacua in IIB RR, NSNS fluxes T S(mall) T B(ig) ED3, g.c. other hidden sectors (e.g. uplifting) global realisation: MC, SK, CM, FQ, RV 1206.3297

A roadmap towards realistic string vacua in IIB O-Involution RR, NSNS fluxes T S(mall) T B(ig) ED3, g.c. other hidden sectors (e.g. uplifting) global realisation: MC, SK, CM, FQ, RV 1206.3297

A roadmap towards realistic string vacua in IIB O-Involution RR, NSNS fluxes T S(mall) T B(ig) ED3, g.c. other hidden sectors (e.g. uplifting) T SM global realisation: MC, SK, CM, FQ, RV 1206.3297

A roadmap towards realistic string vacua in IIB O-Involution RR, NSNS fluxes T S(mall) T B(ig) ED3, g.c. BSM D-brane setup other hidden sectors (e.g. uplifting) T SM here: BSM D-brane setup from D-branes at singularities global realisation: MC, SK, CM, FQ, RV 1206.3297

Realisation of Roadmap • CY in Kreuzer-Skarke database with desired properties: LVS (blow-up), O-involution exchanging 2 dP n 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 global realisation: MC, (DK), SK, CM, FQ, RV 1206.3297, (1404.7127) • analyse low-energy theory…

A benchmark model …taken from a whole class 1206.5237

3 L 3 R A benchmark model 3 C • From search in Kreuzer-Skarke database, h 1,1 =4, h 1,2 =112: visible sector 2xdP 0 , hidden sector 1xdP 0 • 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)


 
 
 
 
 
 Moduli Stabilisation • complex structure assumed to be stabilised with 3-form fluxes (D3 tadpole allows to turn on fluxes.) + C i ¯ ! + ( T + + ¯ + ( G + ¯ C i T + + q 1 V 1 ) 2 G + q 2 V 2 ) 2 • ζ EFT: 
 K = − 2 ln V + V 2 / 3 , g 3 / 2 V V s W = W local + W bulk = W 0 + y ijk C i C j C k + A s e − π 3 T s + A b e − π 2 T b r V = 1 2 ⇣ √ ⌘ τ 3 / 2 3 τ 3 / 2 − s b 9 3 • singularity stabilisation: D-term minimum at ξ i =0 and C i =0 (soft-masses), F-terms sub-leading ! 2 ! 2 X X 1 1 V D = + q 1 i K i C i − ξ 1 q 2 i K i C i − ξ 2 , Re( f 1 ) Re( f 2 ) i i b τ + ξ 2 = − 4 q 2 ξ 1 = − 4 q 1 V V

V 
 
 
 
 
 
 1. � 10 � 22 Moduli Stabilisation 8. � 10 � 23 6. � 10 � 23 4. � 10 � 23 2. � 10 � 23 Vol 4 � 10 6 6 � 10 6 8 � 10 6 1 � 10 7 • F-term potential 
 e − 2 a s τ s e − a s τ s ζ ' 0 . 522 ζ W 2 V F ' 8 + 3 3( a s A s ) 2 p τ s 0 � 4 a s A s W 0 τ s g 3 / 2 V 2 4 V V 3 W 0 ' 0 . 2 s p τ s ◆ 2 / 3 1 ✓ 3 ζ h V i ' 3 W 0 g s ' 0 . 03 e a s h τ s i h τ s i ' 2 4 a s A s A s ' 1 g s • FW flux on large four-cycle (matter fields), D-term potential 
 2 0 1 W 2 p 1 p 2 2 V 2 | φ c,j | 2 + V F ( T ) @X X 0 q bj | φ c,j | 2 � V tot = V D + V F ' + A V 2 / 3 V 2 / 3 j j • can account for dS/Minkowski minima... s ( ) V ' p W 2 h V i = W 2 ✓ h V i ◆ 3 + p 9 h V i 1 / 3 0 0 � ln V 8 / 3 + V F ( T ) 4 a 3 / 2 h V i 3 W 0 s


 Two ways of getting dS • dS1: Hidden matter fields (1206.5237): 
 balancing 10 vs. 100 (log(V) vs V 1/3 ), get on with what’s there 
 s ( ) h V i = W 2 ✓ h V i ◆ 3 + p 9 h V i 1 / 3 0 � ln 4 a 3 / 2 h V i 3 W 0 s • dS2: Dilaton dependent non-perturbative effects (MC, AM, FQ, CB 1203.1750) τ 2 dS W dS = A dS ( U, S ) e − a dS ( S + κ dS T dS ) K dS = λ dS V ◆ 2 ✏ s ˆ ✓  dS a dS A dS V tot = V O ( V − 3 ) + ( κ dS a dS A dS ) 2 e − 2 a dS s e − 2 a dS s = 9 � dS ⇠ V 2 W 0 32 λ dS s V

SUSY-breaking

SUSY breaking in LVS LVS minimum breaks SUSY Conlon, Quevedo, Suruliz, … T S(mall) other hidden sectors T B(ig) (e.g. uplifting) SUSY ED3, g.c. BSM D-brane setup T SM ◆ W 0 M P g 2 ✓ s What are m soft ? m 3 / 2 = + . . . √ V 2 2 π

3 SUSY scenarios • Unsequestered GUT scale scenarios (F TSM ≠ 0): 
 M s ~M GUT , V~10 3 -10 7 , M SOFT ~m 3/2 
 (intermediate-scale SUSY, no CMP, W0 tuning) • Unsequestered intermediate scale strings (F TSM ≠ 0) 
 M s ~10 10 GeV, V~10 10 -10 15 , M SOFT ~m 3/2 ~1 TeV 
 (mild hierarchies, low-scale SUSY, CMP) • Sequestered high scale string models (F TSM =0) 
 M s ~10 15 GeV, V~10 6 -10 7 , M SOFT << m 3/2 
 (compatible with GUT, split and low-scale SUSY scenarios, no CMP)

Focus: sequestered scenarios dS1: hidden matter dS2: dilaton dep. no-effects � dS E3/D7 � s � 0 D3/E(-1) NP dS effects small singularity NP effects cycle big cycle � b o r i e n t i f o l d i n v o l u t i o n � E3/D7 s NP small s i n g u l a r i t y s i n g u l a r i t y � b effects cycle b , � b , � big 0 0 S M S M cycle v i s i b l e v i s i b l e s e c t o r s e c t o r orientifold involution singularity singularity b b � � 0 0 , , SM SM visible visible sector sector