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1 Supersimmetria, naturalezza e selezione ambientale G.F. Giudice N. Arkani-Hamed, G.F.G., R. Rattazzi, in preparation N. Arkani-Hamed, A. Delgado, G.F.G., NPB 741, 108 (2006) A.Delgado, G.F.G., PLB 627, 155 (2005) N. Arkani-Hamed, S. Dimopoulos, G.F.G., A. Romanino, NPB 709, 3 (2005) N. Arkani-Hamed, S. Dimopoulos, JHEP 0506, 073 (2005) G.F.G., A. Romanino, NPB 699, 65 (2004)

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2 Central problem of particle physics: H 2 very sensitive to high-energy corrections No large tuning < TeV Can m H ~ 180 220 GeV reduce the tuning? NO! Abuse of effective theories: finite (or log-div) corrections at remain Ex.: in SUSY quadratic divergences cancel, but

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3 Cancellation of Existence of positron charm top eV?? CAVEAT EMPTOR electron self-energy + - 0 mass difference K L -K S mass difference gauge anomaly cosmological constant Naturalness < 1 TeV search for new physics n

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4 Supersymmetry: triumph of symmetry concept! Gauge-coupling unification Dark Matter Radiative EW breaking

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5 Hierarchy: a problem of criticality H2H2 broken phaseunbroken phase SM Exact supersymmetry on critical point Small breaking of supersymmetry

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6 In supersymmetry: less than 10% tuning Higgs mass The theory is tuned at few % or worse (not much wrt (M W /M GUT ) 2 ~10 -28, but it bites into LHC territory) ~ ~

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7 EW breaking computable as a function of soft terms In natural supersymmetry: M S <

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8 A measure of the fine tuning A characterization of the tuning

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10 DARK MATTER Natural thermal relic with DM h 2 =0.127 Quantitative difference after LEP & WMAP For M S >M Z : neutralino is almost pure state B-ino: annihilation through sleptons (too slow): m e 100 GeV) H-ino, W-ino: annihilation through gauge bosons (too fast) ~ ~

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11 DM is possible in “special” regions: coannihilation Higgs resonance “Well-tempered” or non-thermal Both M Z and DM can be reproduced by low-energy supersymmetry, but at the price of some tuning. Unlucky circumstances or wrong track?

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12 What determines the physical laws? The reductionist’s dream: Unique consistent theory defined by symmetry properties (no deformation allowed, no free parameters) Could God have made the Universe in a different way? Does the necessity of logical simplicity leave any freedom at all? Monotheistic view God M-theoristic view 2 nd string revolution String theory low-energy susy SM

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13 A different point of view Vacuum structure of string theory ~ vacua (N d.o.f in M config. make M N ) Expansion faster than bubble propagation Big bang universe expanding like an inflating balloon Unfolding picture of a fractal universe multiverse

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14 In which vacuum do we live? Large and positive blows structures apart Large and negative crunches the Universe too soon Weinberg Is the weak scale determined by “selection”? Are fermion masses determined by “selection”? Will these ideas impact our approach to the final theory? Not a unique “final” theory with parameters = O(1) allowed by symmetry but a statistical distribution Determined by “environmental selection” I will show two examples relevant to supersymmetry and LHC

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15 “A physicist talking about the anthropic principle runs the same risk as a cleric talking about pornography: no matter how much you say you are against it, some people will think you are a little too interested” S. Weinberg In 1595 Kepler asked the question “Why are there 6 planets?” It seems a proper scientific question ( “Why are there 3 quark families?” )

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16 Sphere Cube Tetrahedron Dodecahedron Icosahedron Octahedron Sphere Saturn Jupiter Mars Earth Venus Mercury “Mysterium Cosmographicum” gives a geometrical explanation Planetary orbits lie within the only 5 Platonic solids that can be both circumscribed and inscribed within a sphere. It well matched planetary distances known at that time. We are confident about the anthropic explanation because we observe a vast universe with a multitude of stars The ultimate Copernican revolution?

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17 Assume m i =c i M S, and M S scans Q c = M Pl f(c i, a ) does not depend on M S M S >Q c = 0, M S 0 Impose prior that EW is broken (analogy with Weinberg) Little hierarchy: Supersymmetry visible at LHC, but not at LEP (post-diction) Susy prefers to be broken at high scale Prior sets an upper bound on M S Susy near-critical Loop factor

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19 If and M S scan independently: solution to problem prediction for and tan

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20 A more radical approach: Split Supersymmetry SM + gauginos + higgsinos at TeV Squarks + sleptons at m ~ ABANDON NATURALNESS BUT REQUIRE: Gauge-coupling unification Dark matter no FCNC, no excessive CP dim-5 proton decay suppressed heavier Higgs boson With respect to ordinary susy:

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

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22 Not unique solution, however… Minimality: search for unification with single threshold, only fermions in real reps, and GeV < M GUT < GeV 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 fermion masses Existence and stability of DM: R-parity makes stable Instability of coloured particles: coloured particles are necessary, but they decay either by mixing with quarks (FCNC!) or by interactions with scale < GeV SpS not unique, but it has all the necessary features built in

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23 Why Supersymmetry? R-symmetry “splits” the spectrum (M g and mix through renorm.) R-invariant dim = 2 R-violating dim = 3 ~

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24 Split Supersymmetry determined by susy-breaking pattern Analogy: in SM, L not imposed but accidental. m small, although L-breaking is O(1) in underlying theory In supergravity, not generated at O(M Pl ) but only O(M S 2 /M Pl ) Here, M g and not generated at O(m) but only O(m 2 /M * ) ~~ ~

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25 Unavoidable R-breaking from CC cancellation Potentially larger effect from anomaly med. Eq. motion for conformal compensator In theories where susy breaking is tied to gravity and supersymmetry is restored in the flat limit, F 0 m 3/2 and m are in general independent parameters of SpS ~

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26 Higgs mass Gluino lifetime Gaugino couplings Electric dipole moments Dark Matter How to test Split Supersymmetry: HIGGS MASS

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27 ELECTRIC DIPOLE MOMENTS g ~ arg ( u d M ) g ~ ** Exp: d e < ecm d n < ecm Yale: d e ~ Sussex: d e ~ Los Alamos: d e d n ~ BNL: d ~

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28 GAUGINO COUPLINGS g ~ In SUSY, gauge (g) and gaugino ( ) couplings are equal Fit of M, , u, d from cross section and distributions H final states BR( H) g ~ g ~ At LHC ( / g -1) = At ILC ( / g -1) = g ~ g ~

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29 Charged R-hadrons. Time delay & anomalous ionization energy loss. At LHC, M<2.5 TeV. Mass resolution better than 1% Neutral R-hadrons. Tagged jet M<1.1 TeV. Once tagged, identify gluino small energy deposition Flippers. Difficulty in tagging Gluinonium. M<1 TeV, direct mass reconstruction Stopped gluinos. Possibility of measuring long lifetimes GLUINO LIFETIME Gluino hadronizes Age of the universe Decays outside detector Nucleosynthesis Gamma rays

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30 DARK MATTER Higgsino = TeV W-ino M 2 = TeV B-ino/Higgsino M 1 ~ B-ino/W-ino M 1 ~M 2 Higgs resonance M =m H Gravitino induced Present limit: cm 2 Future sensib.: cm 2

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31 CONCLUSIONS Supersymmetry is still the best candidate to overthrow the SM, but it suffers from tunings at the level of % Absence of new discoveries at LEP, failure to explain the cosmological constant, and developments in string landscape suggest a possible change of approach to the final theory Can we test “anthropic” solutions?

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