Accidental SUSY at the LHC Tony Gherghetta (University of Melbourne) PACIFIC 2011, Moorea, French Polynesia, September 12, 2011 with Benedict von Harling and Nick Setzer [arxiv:1104.3171] 1
What is the Higgs boson mass? LHC Exclusion August 2011 LHC Exclusion August 2011 2
Hierarchy Problem HIGGS MASS 114 GeV m H 145 GeV Direct experimental limits Standard Model prediction: e.g. top quark t H H t m 2 H = m2 0 + 3h2 t 16π 2 Λ2 Quadratic dependence on cutoff scale, Λ What is the value of the cutoff scale Λ? Inverse strength of fundamental forces hypercharge weak Λ 10 16 GeV m 2 H (100 GeV) 2!! strong 10 2 GeV 10 16 GeV Why is m H Λ 10 16 GeV? HIERARCHY PROBLEM 3
Natural Solutions of Hierarchy Problem Idea #1: Supersymmetry H t t H + H t H scalar top BUT m 2 H = m2 0 + 3h2 t 16π 2 Λ2 3h2 t 16π 2 Λ2 + 6h2 t 16π 2 (m2 t m2 t ) log Λ m t Thus, m H Λ provided m t Supersymmetric flavor problem e.g. K Kmixing: Higgs mass O(TeV) δ m 2 ds (10 TeV) < 2 (F/M)3 2 10 m (10 TeV) 3 or 1,2 1000 TeV m H 130 GeV with m t 1TeV LITTLE HIERARCHY PROBLEM 4
Idea #2: Strong dynamics t H t H m 2 H = m2 0 + 3h2 t 16π 2 Λ2 If Λ TeV mass correction 100 GeV O.K. BUT Flavor and CP problem 1 Λ 2 F Ψ i Ψ j Ψ k Ψ l Λ F 2 30 TeV Higgs mass Why is m H Λ? LITTLE HIERARCHY PROBLEM 5
Either supersymmetry or strong dynamics have little hierarchy problems... Combine both ideas to solve big and little hierarchy problems! (Big) Hierarchy Problem: Strong dynamics m H Λ strong M P Little Hierarchy Problem: Supersymmetry m H Λ strong 6
Natural framework: Warped Extra Dimension UV Explain hierarchies IR Λ UV e ky Slice of AdS [Randall, Sundrum 99] 5 k=ads curvature scale 0 y 5D metric : ds 2 = e 2ky dx 2 + dy 2 7
AdS/CFT dictionary [Arkani-Hamed, Randall, Porrati 00; Rattazzi, Zaffaroni 00] y 5D AdS E 4D energy scale UV Large N, strongly coupled 4D CFT UV 5th coordinate IR IR Slice of AdS CFT + Dynamical elementary source 8
UV 0 y Λ UV e ky IR πr UV localized field elementary source state UV Λ UV e ky 0 y IR πr IR localized field CFT bound state Kaluza-Klein tower... (2) Tower of resonances [e.g. large N QCD: Witten 79] F 2 n (1) (0) n=0 p 2 + m 2 n 9
Plan Use AdS/CFT to build strongly-coupled 4D model using 5D warped model: SUSY broken at UV scale L(M) = 1 4 F 2 µν + i λd.σλ strongly-coupled { + Dφ 0 2 + M 2 φ 0 2 } weakly-coupled e.g. Split SUSY + Dφ 2 + M 2 φ 2 + O( 1 M k ) SUSY breaking by irrelevant ops. flow to IR SUSY emerges at IR scale L = 1 4 F 2 µν + i λd.σλ + Dφ 2 accidental SUSY 5D gravity dual SUSY broken on UV brane transmit SUSYbreaking via bulk SUSY IR brane 10
Partial SUSY [TG, Pomarol, hep-ph/0302001] SUSY broken at UV scale elementary SUSY X ( ẽ e ) A µ,λ ( t t ) composite X H,H ( ψ φ ) e ( 1 2 c)ky bulk mass parameter Fermion mass spectrum determines sparticle spectrum! UV IR Low-energy SUSY spectrum t, H ( f 1,2,λ decouple) KK spectrum m (n) f m (n) f n =1, 2,... 11
BUT: Potentially large D-term contributions to soft masses L m 2 0D No light gaugino m 2 H g2 16π 2 Λ2 IR Limit to increasing Λ IR Sundrum: arxiv:0909.5430 [hep-th] Embed SM gauge group in Pati-Salam to avoid linear D-term Keep gaugino light with R-symmetry m 2 H g2 16π 2 Λ2 IR Implement in 5D model 12
5D Model [TG, von Harling,Setzer arxiv:1104.3171] (Φ, Φ) Stabilizing hypermultiplet A µ,λ SUSY + R-symmetry X light fermions + superpartners top, stop X H,H, S,S UV IR FEATURES Stabilizing bulk hypermultiplet Approximate R-symmetry (Φ, Φ) Extended Higgs sector (S, S) 13
{ Stabilization mechanism [Goh,Luty, Ng: arxiv:hep-th/0309103] SUSY-breaking potential (V = θ 4 U) UV brane SUSY-breaking potential: = Dimension of operator dual to Φ ω = radion Add UV and IR constant superpotential: C UV (C IR )=constant UV(IR) superpotential 14
4D potential: V 4 3 C6 IR M 2 4 ω 4 ( 3)M 4 SUSY ω 2 6 +... V 4 ω Minimum at: e k = e.g. Determines IR scale (m IR ke k ) =4.1 M SUSY 10 11 GeV m IR 10 TeV 15
{ { Sparticle mass spectrum UV-localized matter: O(1000 TeV) (c > 1 2 ) IR-localized matter: Higgs singlet term O(TeV) 1/3 16
Gaugino mass: An accidental R-symmetry forbids ΦW α W α. Instead: m UV q Also radion mediation: F T =0 m UV q 17
Higgs sector: Also: Barbieri, Hall, Nomura, Rychkov: arxiv:0607332 Gripaois, Redi: arxiv:1004.5114; Franceschini,Gori: arxiv:1005.1070 L 5 Composite Higgs sector λ 2 4π m H 300 GeV Ameliorates SUSY little hierarchy problem µ term µ = λs For large λ and κ<λ obtain 1 2 m h1 µ 3 2 m h 1 µ Λ IR Solves mu-problem 18
Hard SUSY breaking effects Heavy first and second family sfermions generate hard breaking: [Sundrum arxiv:0909.5430] Total contribution: (g 2 =0.6,γ 2 =1/12; g 3 =1,γ 3 =1/4) m 2 t = m2 hard + m 2 soft (600 GeV) 2 Tuning of Higgs mass is of order 20% 19
AdS calculation Consider bulk fermion (φ i, φ i ) 2 bulk hypermultiplets with same c value Φ i e ( 1 2 c)ky SUSY X X H,H 5D propagator: UV IR where with 20
Bulk hypermultiplet correction to Higgs mass (m IR =10TeV,m UV soft =1000TeV) IR localized UV localized At most 20% tuning if exclude 0.3 c 0.53 (m h 250 GeV) 21
Gravitational sector: Cancel energy density to obtain zero 4d cosmological constant: Gravitino is LSP when < 4 Radion: 22
Accidental SUSY spectrum: (Λ IR =40TeV,m IR =10TeV) SUSY flavor problem RS flavor problem SUSY little hierarchy problem 23
LHC 3rd generation limits: ATLAS-CONF-2011-130 17 August 2011 m g 500 GeV m t? 24
Summary Supersymmetry may be accidental or emergent at IR scale Together with a composite Higgs sector can solve big and little hierarchy problems Distinctive signals at LHC: -- only stops, Higgsinos, gauginos -- deviations in gauge/gaugino couplings -- composite Higgs sector Current LHC bounds are mild 25