SPLIT

G.F. Giudice CERN IFAE Catania, 31 marzo 2005

• Motivazioni per Split Supersymmetry • Conseguenze osservative di Split Supersymmetry

Arkani-Hamed Dimopoulos hep-th/0405159 Giudice Romanino hep-ph/0406088 Arkani-Hamed Dimopoulos Giudice Romanino hep-ph/0409232

1 Λ Δ μ γ MW << MPl B nuova fisica a ~ TeV mK Je ε bJs γ Problema del sapore B Λ > 10 3−4 TeV K Piccola gerarchia B Λ > 5−10 TeV EW precision data Contact int. at LEP2

Λ Λ ∼ -3 CC << MPl B nuova fisica a 10 eV Gravità modificata a questa scala oppure fallimento del criterio di naturalezza

Riconsideriamo il problema della gerarchia: la scala elettrodebole è determinata dalla dinamica o dalla statistica ?

2 Idea del multiverso emerge Landscape delle teorie di stringa: dalla teoria dell’inflazione 10100 vuoti che corrispondono a diverse costanti di accoppiamento

Come la vita si è sviluppata su un pianeta con acqua liquida, con massa tale da trattenere l’atmosfera, con campo magnetico tale da proteggere dal vento solare, in un’orbita galattica con limitato impatto di comete, …così il nostro universo si è sviluppato in un vuoto con Λ -3 2 3 CC ~ 10 eV , v ~ 10 GeV Abandon (speculations on probability distributions of theories) and use only observational hints Gauge-coupling unification: motivated by theory that addresses α fundamental structure of SM and by measurements on i

Dark matter: connection between weak scale and new particle masses 0.1 pb Ω h 2 ≈ rel σ v

Proposal of SPLIT SUPERSYMMETRY: retain at the weak scale only , and one (squarks, sleptons and ∼ extra Higgs at the scale m)

4 Eliminate : • Excessive flavour and CP violation • Fast dim-5 • Tight constraints on the Higgs mass Retain : • DM & gauge-coupling unification

Gauge-coupling unification as successful (or better) than in ordinary SUSY

5 Not unique solution, however…

• Minimality: search for unification with single threshold, only 15 19 in real reps, and 10 GeV < MGUT < 10 GeV B SpS has the minimal field content consistent with gauge- coupling unification and DM • Splitting of GUT irreps: in SpS no need for new split reps either than SM gauge and Higgs • Light particles: R-symmetry protects masses • Existence and stability of DM: R-parity makes χ stable • Instability of coloured particles: coloured particles are necessary, but they decay either by mixing with (FCNC!) or by interactions with scale < 1013 GeV

SpS not unique, but it has all the necessary features built in

6 Why Supersymmetry? 2 ~ θ X = 1+ m 4 * * ~ 2 ~ 2 2 ~ d X X Q Q → m = m d X W W → M ~ = m θ ∫ Qθ ∫ g 4 * → = ~ 2 2 3 → = ~ d X X H1H 2 Bμ m d X Q A m ∫ ∫ α θ α d 4 X * H H → = m~ ∫ 1 2 R - invariant soft terms θ R - violating soft terms = = (choose R[H1H 2 ] 0 so that θ (R[X ] 0, R - symmetry d 2θ H H forbidden) broken by F ) ∫ 1 2 μ X

~ μ • R-symmetry “splits” the spectrum (Mg and mix through renorm.) • R-invariant B dim = 2 R-violating B dim = 3

7 θ

θ

Split Supersymmetry determinedθ by susy-breaking pattern D - breaking Y =1+ 4m~ 2 θ θ d 4 YQ*Q → m~ 2 = m~ 2 d 4 YH H → B = m~ 2 ∫ Q ∫ 1 2 μ ~ 2 1 4 α m Non renorm. operators d YW W → M ~ = ∫ θ α g M * M * 1 m~ 2 1 m~ 2 d 4 YQ3 → A = d 4 YD2 ()H H → μ = ∫ ∫ 1 2 M * M * M * M *

• Analogy: in SM, L not imposed but accidental. mν small, although L-breaking is O(1) in underlying theory μ 2 • In , not generated at O(MPl) but only O(MS /MPl) μ ~~2 • Here, Mg~ and not generated at O(m) but only O(m /M*) 8 OBSERVATIONAL CONSEQUENCES OF SPLIT SUPERSYMMETRY

• Only one Higgs boson with SM properties • With respect to MSSM, larger log corrections to λ=g2

9 Heavy squarks and sleptons suppress flavour & CP violation, dim-5 proton decay New source of flavour-diagonal CP violation remains M ~ ~ g~ ~ ~ g~ ~ ~ L = WW + μ H H + u H *WH + d HWH + h.c. 2 u d 2 u 2 d ()~* ~* μ CP violation in Im gu gd M

Effects on SM matter at two loops: EDM

10 π

Eliminate phases in chargino mass matrix B

χ μν 2 μν ⎛ M 2M g~ g ⎞ e ()~ = W u arg det M + F F M + ⎜ ⎟ 32 2 χ ⎜ ~ μ ⎟ ⎝ 2MW gd g ⎠

~ μν = * μν mixes with EDM operator O H H H F F

π d Q m α ⎛ g~ g~μ⎞ Mμ f = − f f Im⎜ u d ⎟log 3 ⎜ ⎟ 2 e 16 ⎝ M ⎠ mH

11 -27 Present limit: de < 1.7 × 10 ecm at 95% CL (DeMille et al.) Future: DeMille et al. (Yale) 10-29 ecm in 3 years and 10-31 ecm in 5 years. Lamoreaux et al. (Los Alamos): 10-31 ecm and eventually 10-35 ecm. Results from Hinds et al. (Sussex) and Semertzidis et al. 5 μ (Brookhaven) plans to improve by 10 sensitivity on EDM 12 : decays_ through intermediate heavy scalars q 5 ~ 4 q ⎛ TeV ⎞ ⎛ m ⎞ ~ τ~ ≈ ⎜ ⎟ ⎜ ⎟ 0.4 Gyr g ~ g ⎜ ⎟ 13 q χ ⎝ M~g ⎠ ⎝10 GeV ⎠

CHARGINOS AND • μ not determined by EWSB NEUTRALINOS: • at LHC produced in DY, not in cascades • decay chains with Higgs bosons • couplings violate susy relations

13 IN SPLIT SUPERSYMMETRY μ χ • not determined by EWSB With respect to ordinary susy ~ μμ • B only interacts with Higgs- 4 χ Ω 2 ≈ 2 ()2 + μ 2 2 () • mixed state h 0.1 M1 mχ TeV 2 2 • χ Higgsino Ωχ h ≈ 0.09()/ TeV DM for μ =1.0 −1.2 TeV χ Ω 2 ≈ ()2 = − • Wino χ h 0.02 M 2 / TeV DM for M 2 2.0 2.5 TeV

14 Upper bound on mχ from thermal relic abundance retained also when decay contributes to DM Spin-independent χ scattering cross section off protons is mediated by Higgs exchange

Present: CDMS & EDELWEISS: 10−42−10−41 cm2 Future:CDMS II: 10−44−10−43 cm2; ZEPLIN, XENON, GENIUS: 10−46−10−44 cm2 15 CONCLUSIONS

• Failure of argument for CC casts doubts on the existence of a physical threshold at the weak scale • Split Supersymmetry abandons hierarchy problem, but retains gauge-coupling unification and dark matter • Not unique solution but, under certain assumption, it is the simplest option • Certain patterns of susy breaking automatically lead to the spectrum of Split Supersymmetry • Observational consequences for collider searches, EDM, dark matter and gravitino cosmology

16