Gauge mediation with a local flavour Felix Brümmer partly based on 1312.0935 (with M. McGarrie, A. Weiler) Felix Brümmer Gauge mediation with a local flavour 1 / 33
Outline Review: Messenger gauge mediation 1 Gauge-mediated models with light 3rd generation squarks 2 Flavour gauge messengers: Model building 3 Flavour gauge messengers: Consequences 4 Conclusions 5 Felix Brümmer Gauge mediation with a local flavour 2 / 33
Review: Messenger gauge mediation Felix Brümmer Gauge mediation with a local flavour 3 / 33
The Standard Model of Elementary Particle Physics Felix Brümmer Gauge mediation with a local flavour 4 / 33
The Minimal Supersymmetric Standard Model Felix Brümmer Gauge mediation with a local flavour 5 / 33
Gauge-mediated supersymmetry breaking TeV-scale SUSY has many nice features: hierarchy, unification, DM. . . But most general parameterization of SUSY breaking introduces O ( 100 ) new free parameters even in minimal SUSY Standard Model � � L = − 1 g + M 2 � W � W + M 1 � B � M 3 ˜ g ˜ B + h.c. 2 � � d ˜ a IJ u c q J H 2 − a IJ d c q J H 1 − a IJ e c I ˜ u ˜ I ˜ I ˜ e ˜ − ℓ J H 1 + h.c. ℓ IJ ˜ I ˜ d IJ ˜ ˜ − m 2 q ∗ q J − m 2 ℓ ∗ ℓ J − m 2 u c ∗ u c J − m 2 d c ∗ d c J − m 2 e c ∗ e c q IJ � I � u IJ ˜ I ˜ e IJ ˜ I ˜ I J � � H 1 | H 1 | 2 − m 2 H 2 | H 2 | 2 − − m 2 m 2 3 H 2 H 1 + h.c. How are SUSY breaking terms generated? Supertrace theorem: not by tree-level renormalizable couplings to ✘✘✘ SUSY “Gravity mediation”: use non-renormalizable interactions / HD operators “Gauge mediation”: use loops Felix Brümmer Gauge mediation with a local flavour 6 / 33
Messenger gauge mediation massive dynamical (M)SSM messengers SUSY Yukawa SM gauge interactions interactions Simplest construction: → Dine/Nelson/Nir/Shirman early ’90s W = X Φ � (Φ , � Φ) ∼ 5 ⊕ ¯ � X � = M + F θ 2 Φ 5 of SU ( 5 ) ⊃ G SM X = background field: “goldstino superfield” M = SUSY mass for scalars and fermions contained in Φ and � Φ F = ✘✘✘ SUSY mass splitting Felix Brümmer Gauge mediation with a local flavour 7 / 33
Minimal messenger gauge mediation √ √ � 2 θ � Messengers Φ = ϕ + 2 θ ψ + . . . , Φ = � ϕ + ψ + . . . L tree = − M ψ ) − M 2 ( | ϕ | 2 + | � ϕ + ϕ ∗ � 2 ( ψ � ψ + ψ � ϕ | 2 ) − F ( ϕ � ϕ ∗ ) + . . . Gaugino mass induced @ 1 loop: ∼ ψ ψ g 2 F ⇒ M 1 / 2 = 16 π 2 M ∼ ϕ, ϕ Scalar soft masses induced @ 2 loops: � � 2 � � g 2 � 2 � F m 2 ⇒ 0 ∼ 16 π 2 M Figure stolen from → Martin ’97 Felix Brümmer Gauge mediation with a local flavour 8 / 33
Messenger gauge mediation features SUSY messengers: visible sector hidden sector massive chiral SSM superfields superpotential couplings SM gauge interactions very few parameters: M , F , (# of Φ ⊕ � Φ pairs) completely renormalizable, well controlled model (no reliance on Planck-scale physics) predictions independent on dynamical ✘✘✘ SUSY details (what generates F and M ?) flavour-blind ✘✘✘ SUSY soft terms: no FCNC problems Felix Brümmer Gauge mediation with a local flavour 9 / 33
Messenger gauge mediation bugs SUSY messengers: visible sector massive chiral hidden sector SSM superfields superpotential couplings SM gauge interactions µ/ B µ problem: no higgsino mass µ induced simplest extensions generating µ have too large Higgs mass mixing B µ embedding in dynamical model nontrivial ( R -symmetry / M 1 / 2 issues) trilinear A -terms small ⇒ hard to get m h = 125 GeV in MSSM no soft mass for singlets: must be extended to work with NMSSM flavour-blind ✘✘✘ SUSY soft terms: generation-independent squark masses Cannot have 3rd generation squarks � 1 TeV and 1st two generation squarks above LHC bounds at the same time (“natural SUSY” / “effective SUSY” / “inverted hierarchy”) Felix Brümmer Gauge mediation with a local flavour 10 / 33
Messenger gauge mediation: Bugs & features How to fix the bugs ( µ/ B µ , A -terms, singlet masses, generation universality) without ruining the features (predictivity, calculability, no flavour problem) ? To address Higgs sector problems, need extra couplings to Higgs sector → next slide To address flavour issue, need extra couplings to matter → rest of this talk Felix Brümmer Gauge mediation with a local flavour 11 / 33
A nonminimal extension: Gauge-Higgs mediation Allow for superpotential couplings between messengers and Higgs sector see e.g. model of → Craig/Knapen/Shih ’13 SM gauge interactions visible sector matter SUSY messengers: massive chiral hidden sector superfields Higgs fields superpotential couplings µ, B µ � trilinears � soft terms for singlets � flavour � × Felix Brümmer Gauge mediation with a local flavour 12 / 33
Aim of this talk Construct a gauge-mediated model with light 3rd generation squarks, heavy and degenerate 1st and 2nd 1 FCNCs under control 2 Crucial ingredients: SU ( 3 ) C × SU ( 2 ) L × U ( 1 ) Y × SU ( 3 ) F gauge group Both chiral + gauge messengers Felix Brümmer Gauge mediation with a local flavour 13 / 33
Gauge-mediated models with light 3rd generation squarks Felix Brümmer Gauge mediation with a local flavour 14 / 33
1. Yukawa-deflected GM / Flavoured GM → Chacko/Ponton’02, . . . Shadmi/Szabo ’11, Kang et al. ’12, Albaid/Babu ’12, Abdullah et al. ’12, Calibbi/Paradisi/Ziegler ’13, Galon/Perez/Shadmi ’13. . . Introduce also matter-messenger couplings in W : generically large flavour violation (can be averted with extra flavour symmetries) Example: → Abdullah/Galon/Shadmi/Shirman ’12 � � W = Y u QUH u + Y d QDH d + Y ′ u QU � Φ + Y ′ ΦΦ + � � d QD Ψ + X ΨΨ + . . . flavour problems ameliorated if Y u aligned with Y ′ u and Y d with Y ′ d u , d | 2 | F X | 4 tachyonic one-loop contribution to soft masses at order | Y ′ | X | 6 → Evans/Ibe/Yanagida ’12 for low messenger scales ( F X ≈ X 2 ): light 3rd generation squarks Felix Brümmer Gauge mediation with a local flavour 15 / 33
2. Higgsed gauge mediation Introduce chiral messengers charged under gauged horizontal symmetry → Craig/McCullough/Thaler ’12 Example: Gauge SU ( 3 ) F with Q , U , D ∼ 3 Yukawa couplings from supersymmetric SU ( 3 ) F breaking: Σ , Σ ′ ∼ ¯ 6 , Λ QUH u + Σ ′ � Σ � ′ W = Σ � Σ � Λ QDH d , = Y u , = Y d Λ Λ SU ( 3 ) F contributes to gauge-mediated soft masses. Largest contribution to first two generations Light 3rd generation squarks Felix Brümmer Gauge mediation with a local flavour 16 / 33
3. This talk: Flavour gauge messengers Gauge SU ( 3 ) F and break non-supersymmetrically → FB/McGarrie/Weiler ’13 Some fields charged under SU ( 3 ) F pick up nonzero F -term VEVs Gauge messengers: SUSY breaking mass splittings within massive vector multiplet vector Messengers = massive chiral superfields ✘ ✘✘ SUSY visible sector hidden sector SSM massive vector multiplets of gauged horizontal symmetry Negative contributions to squark soft masses. Largest for 3rd generation if F -terms aligned with 3rd gen. Yukawas Light 3rd generation squarks Felix Brümmer Gauge mediation with a local flavour 17 / 33
Flavour gauge messengers: Model building Felix Brümmer Gauge mediation with a local flavour 18 / 33
Brief history of gauge messengers Invented in 1980s GUT model building → Witten’s inverted hierarchy ’81, Dimopoulos/Raby ’83, Kaplunovsky ’83,. . . More detailed studies in late ’90s (product gauge groups broken to SM) → Dimopoulos et al. ’97, Murayama ’97, Giudice/Rattazzi ’97,. . . Briefly resurrected in 2000s → Dermisek/Kim/Kim ’06 Again of interest in GGM context → Buican/Komargodski ’09,Intriligator/Sudano ’10 Also related: Tree-level GM → Nardecchia/Romanino/Ziegler ’09 Never very popular for (GUT-)model building (we’ll see why) Now use idea for gauged flavour symmetry Felix Brümmer Gauge mediation with a local flavour 19 / 33
A simplistic model SSM Quark superfields Q , U , D ∼ 3 under SU ( 3 ) F Yukawa couplings from Σ , Σ ′ ∼ ¯ 6 , hidden sector: X ∼ 3 Break SU ( 3 ) F → SU ( 2 ) F by 0 � X � = 0 F X θ 2 Simultaneously break SU ( 3 ) F → 0 by y u 0 0 � Σ ′ � � Σ � , = 0 y c 0 = Y d Λ Λ 0 0 y t Felix Brümmer Gauge mediation with a local flavour 20 / 33
A simplistic model SUSY-breaking X VEV: SUSY-breaking mass splittings between gauge fields and gauginos Dominant effect: Tachyonic one-loop squark mass 2 → Intriligator/Sudano ’10 broken gauge fields and gauginos ~ ~ ~ ~ q q q q Alignment of X with 3rd generation: largest effect for 3rd generation squarks 13 0 0 D = − g 2 | F X | 2 24 δ m 2 Q = δ m 2 U = δ m 2 F 13 0 0 16 π 2 Σ 2 24 7 33 0 0 6 One-loop SU ( 3 ) F tachyon comparable with usual 2-loop GM masses if g F small Felix Brümmer Gauge mediation with a local flavour 21 / 33
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