SUSY breaking and the nature of *.inos - Institute for Particle Physics ...

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasWhat is SUSY?SUSY is a space-time (ST) symmetry}Q|Fermion〉 = |Boson〉Qs generate a ST symmetryQ|Boson〉 = |Fermion〉{Q, Q † } = P ⇐⇒ [θQ, θ † Q † ] = θθ † P

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasMotivating SUSYSolving the Higgs Hierarchy ProblemQuick Higgs revisionStandard Model Higgs potentialV (H) ∼ µ 2 |H| 2 + λ|H| 4Higgs vacuum expectation value (VEV)√〈H〉 = −µ 2 /2λ ∼ 174 GeVImplies a Higgs massm 2 H = −µ2 ∼ 100 GeV

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasMotivating SUSYSolving the Higgs Hierarchy ProblemHiggs self-energy at one-loop−L ⊂ λ s |s| 2 |H| 2 + λ f H¯f fsH H ∼ −λ s m 2 S ln ( Λm S)sss = scalarsf = fermionsHH∼ λ s Λ 2fH H ∼ −λ 2 f Λ2f

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasMotivating SUSYSolving the Higgs Hierarchy ProblemUV cut-off at one-loopAt one-loopm 2 H −→ m2 H + Λ2 ( ∑Natural Higgs massscalarsλ s −∑fermionsλ 2 f)− ∑scalars( ) Λλ s ms 2 lnm sΛ ∼ m Pl=⇒ m nat ∼ m Pl

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasMotivating SUSYSolving the Higgs Hierarchy ProblemHiggs self-energy at one-loopf−L ⊃ λ f φf¯fφ φ = π f φφ (0)π f φφ (0) = −2N(f )λ2 f¯f∫[d 4 k 1(2π) 4 k 2 − mf2+]2mf2(k 2 − mf 2)2

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasMotivating SUSYSolving the Higgs Hierarchy ProblemHiggs self-energy at one-loop∗−L ⊃ A f λ f φ˜f L˜f R + ˜λ ( f φ 2 |˜f L | 2 + |˜f R | 2) + v ˜λ f φ(|˜f L | 2 + |˜f R | 2)˜f˜fφ φ += π˜fφφ (0)φφ˜f⎡⎤∫ dπ˜f 4 kφφ (0) = −˜λ f N(˜f ) ⎣1(2π) 4 + (L ↔ R) ⎦ + · · ·k 2 − m 2˜fL

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasMotivating SUSYSolving the Higgs Hierarchy ProblemHiggs self-energy at one-loop∫ []dπφφ f 4 (0) = −2N(f k 1 2m )λ2 f2f(2π) 4 k 2 − mf2 +(k 2 − mf 2 ⎡⎤)2∫ dπ˜f 4 kφφ (0) = −˜λ f N(˜f ) ⎣1(2π) 4 + (L ↔ R) ⎦k 2 − m 2˜fL⎡⎤) ∫ 2 d+(˜λ 4 k ⎢ 1⎥f v N(˜f )(2π) 4 ⎣ ) 2+ (L ↔ R) ⎦(k 2 − m 2˜fL∫+ |λ f A f | 2 N(˜f )d 4 k(2π) 4 1(k 2 − m 2˜fL ) (k 2 − m 2˜fR )

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasMotivating SUSYSolving the Higgs Hierarchy ProblemHiggs self-energy at one-loop˜λ f = −λ 2 f , N(˜f ) = N(f )π f +˜fφφ (0) = i λ2 f N(f )[16π 2 − 2mf2+ 2m 2˜f( )1 − log m2 fµ 2 + 4mf 2 log m2 fµ 2( )1 − log m2˜fµ 2 − 4mf 2 log m2˜fµ 2]− |A f | 2 log m2˜fµ 2

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasMotivating SUSYSolving the Higgs Hierarchy ProblemHiggs self-energy at one-loop˜λ f = −λ 2 f , N(˜f ) = N(f ), m˜f= m f , A f = 0π f +˜fφφ (0) = 0

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasMotivating SUSYSolving the Higgs Hierarchy ProblemYou saved us... thanks supersymmetry!ψ/φ pairings+ ˜λ f = −λ 2 f+ A f = 0Unavoidable withsupersymmetry

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasMotivating SUSYGauge Coupling Unification50Α 1 1403060 2 4 6 8 10 12 14 16 18 10605040Α 1Α 2 130202010Α 3 1Figure: RGE of α −1i2 4 6 8 10 12 14 16 18Log 10 Q1 GeVin SM (dashed) and MSSM (solid)

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasThe Sad TruthEvidenceDegeneracy in (s)particle mass spectrum not observed⎫Standard Particlesu c t⎧⎪ ⎨P 2 d s bν ν ν⎪ ⎩eeQuarksμμττLeptonsγgZWHHiggsForce Particles~ u c t⎪⎬⎧⎪ ⎨ ~ ~ ~≠ P 2 d s b~ ~ ~ν ν ν⎪ ⎩⎪⎭SUSY Particles~ ~ ~ ~γ~g~e μ τ Z~ ~ ~ ~eSquarksIf SUSY is realized, it is broken at low energiesμτSleptonsW~HHiggsinoSUSY ForceParticles⎫⎪⎬⎪⎭

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasGeneric FeaturesPropertiesTheory is SUSY but scalar potential V admits ✘✘ ✘ SUSY vacuaQ|vacuum〉 ≠ 0 ⇐⇒ V (vacuum) > 0VΦVΦGAUGEΦSUSY✭✭✭✭GAUGEΦSUSYVΦVΦGAUGEΦ✘SUSY✘ ✘✭✭✭✭GAUGEΦ✘SUSY✘ ✘

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasGeneric FeaturesRecipeU(1) VSF spurion 〈W α 〉 = θ α DGauge-singlet χSF spurion 〈X〉 = θ 2 FHow does this work?

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasGeneric FeaturesThe Standard Model Higgs MechanismΛ > Λ EWSBVΦ¯Q Ld RGAUGEΦ−L ⊃ y d ¯QL φd Ry dφ

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasGeneric FeaturesThe Standard Model Higgs MechanismΛ > Λ EWSBVΦ¯Q Ld RGAUGEΦ−L ⊃ y d ¯QL φd Ry dφΛ < Λ EWSBφ −→ (0, ν + H)VΦ✭✭✭✭GAUGEΦ−L ⊃ y d ν}{{}m d¯dL d R¯dL d Rm d

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasGeneric FeaturesSUSY Breaking in Wess-Zumino ModelΛ > Λ ✘ ✘ SUSY∫L =∫d 2 θ M ij Φ i Φ j + Y ijk Φ i Φ j Φ k + h.c. +} {{ }W (Φ i )d 2 θd 2 θ †Φ ∗i Φ i} {{ }K (Φ ∗i ,Φ i )⊃ −M ij ( φ i F j + ψ i ψ j)− Y ijk φ i φ j F k + h.c. + F ∗i F iVΦSUSYΦφ iF jψ iψ jM ij M ijφ iφ jY ijkF k

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasGeneric FeaturesSUSY Breaking in Wess-Zumino ModelΛ > Λ ✘ ✘ SUSY∫L =∫d 2 θ M ij Φ i Φ j + Y ijk Φ i Φ j Φ k + h.c. +} {{ }W (Φ i )d 2 θd 2 θ †Φ ∗i Φ i} {{ }K (Φ ∗i ,Φ i )⊃ −M ∗ ik Mkj φ ∗i φ j − M ij ψ i ψ jVΦSUSYΦφ ∗iφ jM ∗ ik Mkj ψ iψ jM ij

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasGeneric FeaturesSUSY Breaking in Wess-Zumino ModelΛ > Λ ✘ ✘ SUSY∫L =() ∫d 2 θ MΦ 2 + Y Φ 2 X + h.c. +d 2 θd 2 θ † Φ ∗ Φ⊃ −M (φF φ + ψψ) − Y φφF X + h.c. + |F φ | 2 + |F X | 2VΦSUSYΦφMF φψMψφφYF X

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasGeneric FeaturesSUSY Breaking in Wess-Zumino ModelΛ < Λ ✘ ✘ SUSY〈X〉 = θ 2 F∫L =() ∫d 2 θ MΦ 2 + Y Φ 2 X + h.c. +d 2 θd 2 θ † Φ ∗ Φ⊃ −Mψψ − (|M| 2 ± |YF X |)|φ ± | 2VΦφ ∗ ±φ ±ψψ✘✘✘SUSYΦ|M| 2 ± |YF X |M

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasDirac vs. Majorana FermionsDirac and Majorana particles=⎛ ⎞⎜⎝⎟⎠†

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasDirac vs. Majorana FermionsDirac and Majorana particles=⎛ ⎞⎜⎝†⎟⎠=⎛⎜⎝†⎞⎟⎠

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasDirac vs. Majorana FermionsMass termsMajorana mass( )−L Majorana ⊃ M M ¯Ψ M Ψ M = M M (ξξ + ξ † ξ † ξ) Ψ M =ξ †Dirac mass( )−L Dirac ⊃ M D ¯Ψ D Ψ D = M D (ξχ + ξ † χ † ξ) Ψ D =χ †−L MSSMsoft⊃ M 3 ˜g˜g + M 2 ˜W ˜W + M 1 ˜B˜B

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasParameter space limitationsApproximate SQCD β Functionsdm2˜q∼ m2˜q+ M2˜gdtddt M˜g ∼ M˜gQ M Λ SUSY Λm2˜q(Q) ∼ m2˜q(M) + a m2˜q(M) + b M2˜g(Q)

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasParameter space limitationsThe Forbidden Zone25002000msquark1500100050010 5 GeVMM GUTno high scale model00 500 1000 1500 2000 2500M gluino11 Jaeckel, J., Khoze, V. V., Plehn, T., & Richardson, P. (2011). Travels on the squark-gluino mass plane.http://arxiv.org/abs/1109.2072

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasR−symmetryWhat is R−symmetry?{Q, Q † } = PInvariant underQ → e iRQθ Q, Q † → Q † e −iRQθ , P → PChoose R Q = −1[Q, R] = Q[θ, R] = −θ[Q † , R] = −Q † [θ † , R] = θ †

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasR−symmetryR-charge of GauginosV = V † =⇒ R V = 0V ⊃ θ †2 θλR θ = −R θ † = 1 =⇒ R λ = 1

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasR−symmetryMajorana Gaugino Masses−L gauginoMajorana ⊃ M M(λλ + λ † λ † )λλ U(1) R−−−→ e 2iθ λλMajorana gaugino masses violate U(1) R symmetry

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasR−symmetryDirac Gaugino Masses−L Dirac ⊃ M D (λχ + λ † χ † )λχ U(1) R−−−→ e i(1+Rχ)θ λχDirac gaugino masses can preserve U(1) R symmetry

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasR−symmetryThe ideaU(1) R ←−−−−−−−−−−→ ✘✘ U(1) ✘ RM M → 0 M M ∼ M DM MM D≫ 1

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasR−symmetryThe Forbidden Zone25002000msquark1500100050010 5 GeVMM GUTno high scale model00 500 1000 1500 2000 2500M gluino22 Jaeckel, J., Khoze, V. V., Plehn, T., & Richardson, P. (2011). Travels on the squark-gluino mass plane.http://arxiv.org/abs/1109.2072

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasR−symmetryMinimal Dirac GauginosR χg = −1, O g ⊃ θχ g , 〈W ′ α〉 = θ α DNames Superfield SU(3) C U(1) RRHGs O g Ad 0GFs W 3α Ad 1∫L Diracgluino =d 2 θ W′ αΛ Tr [ W 3α O g]⊃ −mD λ 3 χ gm D = D Λ(1)N = 2 vector multiplet (O g , V 3 )

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasHiggs SectorMSSM HiggsW MSSM = y u ūQ · H u + y d ¯dQ · Hd + µH u · H d + · · ·Λ < Λ EWSBVΦH 0 u −→ ν u + · · ·✭✭✭✭GAUGEΦ Hd 0 −→ ν d + · · ·∫L ⊃ d 2 θW (Φ i ) ⊃ −µ˜H u · ˜H d

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasHiggs SectorDirac HiggsinosSuperfield SU(2) L U(1) Y U(1) R1H u □201R d □22H d □ − 1 20R u □ − 1 22W Higgs =( )µ u + λ S u S H u · R u + λ T u H u · TR u + (u ↔ d)N = 2 Hypermultiplet (H u , R d )

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasHiggs SectorIs R−symmetry useful?Dangerous ∆L = ∆B = 1 operators forbiddenProton decay through Q L Q L Q L L L , U R U R D R E R forbiddenMajorana Neutrino mass H u H u L L L L allowed 33 Kribs, G., Poppitz, E., & Weiner, N. (2008). Flavor in supersymmetry withan extended R symmetry. Physical Review D, 78(5) 055010

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasHiggs SectorSummary of MRSSMAll *.inos are DiracHiggs and Gauge sector form N = 2 representationsGauginos much heavier than squarks possible

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasHiggs SectorOutlookHigh-scale completion? Gauge mediation? 4Create a consistent effective theory at the high scaleIdentify important phenomenology using simplified models4 Benakli, K., & Goodsell, M. D. (2008). Dirac Gauginos in GGM.arXiv:0811.4409

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasWork in progressMessenger completionDirac gaugino D-termsλQ ∗ DQψχ∼ gλQY 1 [ ( )]DD216π 2 1 + OM Mess MMess4

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasWork in progressMessenger completionAdjoint scalar D-termsΣQDQ ∗Σ ∗D+ Q ∗ QΣ ψ Σ ∗∼ 116π 2 DQ|λ|2 + 1 D 216π 2 MMess2 Q 2 |λ| 2ΣQ ∗ DQψΣ∼ − 1 D 216π 2 MMess2 Q 2 |λ| 2

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasWork in progressMessenger completionDirac gaugino F-termsFQλψ˜QχQF∼ λ|κ| 2 116π 2 |F| 2M 3 Mess

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasWork in progressMessenger completionAdjoint scalar F-termsFQΣψ˜QΣ ∗Q+ (more diagrams) ∼ |λ| 2 |κ| 2 116π 2 |F| 2M 2 MessFFQΣψ˜QΣQ+ (more diagrams) ∼ −|λ| 2 |κ| 2 116π 2 |F| 2M 2 MessF

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasWork in progressMessenger completionAimIdentify minimal set of parameters to describe theory at highscale, e.g.m D (M), m 2 Σ (M), m2 q(M) = f ( Λ 〈D〉 , Λ 〈F 〉 , M )

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasWork in progressThanksThanks for listening!

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasWhere to Break SupersymmetryHidden sectorsSUSY breakingorigin(hidden sector)mediationmechanismMSSM(visible sector)

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasHow to Communicate ✘ ✘✘✘ SUSYTree-level?

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasHow to Communicate ✘SUSY✘✘✘Tree-level?Supertrace Theorem:tree level communication+renormalizable couplings⎫⎬⎭SUSY partner lighterthan SM counterpart

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasHow to Communicate ✘SUSY✘✘✘Tree-level?Supertrace Theorem:tree level communication+renormalizable couplings⎫⎬⎭SUSY partner lighterthan SM counterpartNon-renormalizable =⇒ Planck-Scale Mediated ✘✘ ✘ SUSYNon-tree-level =⇒ Gauge Mediated ✘ ✘ ✘ SUSY (GMSB)

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasParticle Content and Superpotentialblank

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasMessenger mass spectrumMessenger mass spectrumm 2φ, ¯φ M 2 ± F 2ψ, ¯ψ M 2

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasMessenger mass spectrumMessenger mass spectrumm 2φ, ¯φ M 2 ± F 2ψ, ¯ψ M 2SUSY is broken!

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasSoft Mass GenerationMajorana Gaugino masses at one-loopφF ¯φ˜W, ˜B, ˜g ˜W, ˜B, ˜g¯ψMψM a ∝ α a ΛΛ = F M

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasSoft Mass GenerationSquark/Sleptonφmasses F at two-loop ¯φ˜W, ˜B, ˜g ˜W, ˜B, ˜g¯ψMψFFFHH HH HHm 2 sq, sl ∝ Λ 2 ∑ aα 2 aΛ = F M

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasSolving the Higgs Hierarchy ProblemUV cut-off at one-loopAt one-loopm 2 H −→ m2 H + Λ2 ( ∑Natural Higgs massscalarsλ s −∑fermionsλ 2 f)− ∑scalars( ) Λλ s ms 2 lnm sΛ ∼ m Pl=⇒ m nat ∼ m Pl

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasSolving the Higgs Hierarchy ProblemDim-reg at one-loopAt one-loopm 2 H −→ m2 H − ∑scalarsλ s m 2 s ln( )msµm H sensitive to heaviest particles Higgs couples to!Why is m H so small?

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasSolving the Higgs Hierarchy ProblemSome two loop Higgs self-energy processes−L ⊂ m F ¯FFFF = fermionsHH∼ g 4 (Λ 2 + m 2 F ln ( Λm F))FHH

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasSolving the Higgs Hierarchy ProblemSome two loop Higgs self-energy processes−L ⊂ m F ¯FFFF = fermionsHFH∼ g 4 m 2 F ln (mFµ)HH

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasGauge Coupling Unification50Α 1 1403060 2 4 6 8 10 12 14 16 18 10605040Α 1Α 2 130202010Α 3 1Figure: RGE of α −1i2 4 6 8 10 12 14 16 18Log 10 Q1 GeVin SM (dashed) and MSSM (solid)

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasDark Matter, Triggering EWSBIn R-parity conserving SUSY, LSP is DM candidateGauge Mediated ✘SUSY ✘ ✘→ ˜GGravity Mediated ✘✘✘SUSY → ˜χ 0 1

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasDark Matter, Triggering EWSBIn R-parity conserving SUSY, LSP is DM candidateGauge Mediated ✘SUSY ✘ ✘→ ˜GGravity Mediated ✘✘✘SUSY → ˜χ 0 1Renormalization Group Evolution (RGE) triggers EWSBVΦVΦGAUGEΦ−→RGE✭✭✭✭GAUGEΦ

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasDark Matter CandidateProton decayGeneral MSSM =⇒ rapid proton decay⎧d⎪⎨p u⎪⎩ u˜sL (e + , µ + ), (ν e , ν µ )}Q(π 0 , K 0 ), (π + , K + )uForbid these interactions by imposing symmetries

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasDark Matter CandidateR−parityDefine a multiplicatively conserved quantum number P RLet all (supersymmetric) particles have P R =(−)1⇑⇓Interaction vertices contain even numbers of superpartnersForbids process mediating rapid proton decayThe lightest supersymmetric particle (LSP) is stableDark matter candidate!

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasFlavour Changing Neutral Currentsµ − → e − γ is highly constrained experimentallyγ˜µ ẽµ − ˜Be −˜W −γµ − ˜ν µ˜ν ee −Forbid/suppress the additional loop processes from SUSY

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasPros and ConsAdvantagesFlavour-blind communication automaticTheory is renormalizable

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasPros and ConsAdvantagesFlavour-blind communication automaticTheory is renormalizableProblemsHiggs ‘b’ term difficult to generateLSP is always gravitino

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasFlavour Universality−L MSSMsoftEasiest way:⊂∑φ=Q,L,u,d,e˜φ † mφ 2 ˜φ(+ ũa u ˜QHu −˜da d ˜QHd −Assume supersymmetry breaking is ‘universal’(m i ) jk= m i δ jk , i = (Q, L, u, d, e)Assume that the (scalar) 3 couplings are ∝ thecorresponding Yukawa couplingsa i ∝ y i , i = (u, d, e))ẽa e˜LHd + h.c.

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasConsequencesWe find...At any RG scale, the squark and slepton mass matrices appear⎛⎞( ) mmφ2 φ 2 ⎜ 10 0≈ ⎝ 0 mφ 2 ⎟ij10 ⎠ φ = (Q, L, u, d, e)0 0 mφ 2 3ij

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasHow to Communicate ✘SUSY✘✘✘Tree-level?For tree-level renormalizable couplingsSTrM 2 = ∑ J(−1) 2J (2J + 1)M 2 J = 0,⇑⇓superpartner lighter than SM counterpart

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasHow to Communicate ✘SUSY✘✘✘Tree-level?For tree-level renormalizable couplingsSTrM 2 = ∑ J(−1) 2J (2J + 1)M 2 J = 0,⇑⇓superpartner lighter than SM counterpartNon-renormalizable =⇒ Planck-Scale Mediated ✘✘ ✘ SUSYNon-tree-level =⇒ Gauge Mediated ✘ ✘ ✘ SUSY (GMSB)

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasMinimal ModelContentExtra field contentSU(3) C SU(2) L U(1) YΦ − 1 3¯Φ ¯ ¯ + 1 3S 1 1 0

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasMinimal ModelContentExtra field contentSU(3) C SU(2) L U(1) YΦ − 1 3¯Φ ¯ ¯ + 1 3S 1 1 0SuperpotentialW = λ¯ΦXΦX is goldstino superfield〈X〉 = M + θ 2 F

ConceptsSpontaneous✘✘ SUSY Dirac *.inos MRSSM Optional extrasMSSM Soft LagrangianThe most general set of positive mass dimension terms whoobey SM symmetries but break SUSY aresoft = − 1 ()M 3 ˜g˜g + M 2 ˜W ˜W + M 1 ˜B˜B + c.c.(2)− ũa u ˜QHu − ˜da d ˜QHd − ẽa e˜LHd + c.c.L MSSM− ˜Q † m 2 Q ˜Q − ˜L † m 2 L˜L − ũm 2 uũ† − ˜dm 2 d˜d † − ẽm 2 e ẽ†− m 2 H uH ∗ u H u − m2 H dH ∗ d H d − (b H u H d + c.c),and form the soft supersymmetry breaking Lagrangian density