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Supersymmetry Hitoshi Murayama Taiwan Spring School March 29, 2002

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2 Electroweak Symmetry Breaking In the MSSM, electroweak symmetry does not get broken Only after supersymmetry is broken, Higgs can obtain a VEV v~m SUSY Regard EWSB as a consequence of supersymmetry breaking EW symmetry and hierarchy “protected” by supersymmetry

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3 Origin of Hierarchy v<

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4 Dynamical Supersymmetry Breaking Simplest example: SO(10) with one 16 No moduli space, can’t analyze with Seibergian techniques “non-calculable” (Affleck-Dine-Seiberg) Add one 10, make it massive and decouple When M 10 =0, moduli space spanned by 161610, 10 2, generically SO(10) SO(7) SO(7) gaugino condensation generates dynamical superpotential Add W=M 10 10 2, lifts moduli space, breaks SUSY Decouple 10 smoothly (HM)

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5 Izawa-Yanagida- Intriligator-Thomas model Sp(N c ) gauge theory with N f =N c +1 Quantum modified moduli space Pf M = 2Nf for mesons M ij =Q i Q j Add superpotential with singlets S ij W=S ij Q i Q j forces M ij =0 Contradiction no SUSY vacua

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6 Issue of mediation Many gauge theories that break SUSY dynamically known The main issue: how do we communicate the SUSY breaking effects to the MSSM? “mediation”

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7 Spurion Supersymmetry is broken either by an F- component of a chiral superfield i = 2 F i 0 or a D-component of a vector superfield V= 2 D 0 Once they are frozen at their expectation values, they can be viewed as spurions of supersymmetry breaking order parameters

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8 Soft supersymmetry breaking Purpose of supersymmetry is to protect hierarchy Arbitrary terms in Lagrangian that break supersymmetry reintroduce power divergences “Soft supersymmetry breaking” classified: m, m 2 ij i* j, A ijk j j k, B ij j j, C i j Dark horse terms (not always allowed): j* j k, j, i j

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9 Spurion operators Spurion z = i /M= 2 F i /M generates soft terms M is the “mediation scale” where the effects of SUSY breaking are communicated m d 2 z c W W m 2 ij i* j d 4 z * z c ij i* j A ijk j j k d 2 z c ijk j j k B ij j j d 2 z c ij j j C i j d 2 z c i j Coefficients c are random at this point

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10 Supersymmetric flavor problem Random SUSY breaking excluded by FCNC constraints Consider scalar down quarks Take the off-diagonal terms to be perturbation:

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11 Supersymmetric flavor problem Random SUSY breaking excluded by FCNC constraints Want a reason why off-diagonal terms are suppressed K0K0 K0K0 _

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12 Two possible directions 1.Develop a theory of flavor that predicts not only the pattern of Yukawa matrices (masses, mixings), but also soft masses 2.Develop a theory of mediation mechanism of supersymmetry breaking that predicts (approximately) flavor-blind soft masses

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13 Gravity Mediation

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14 Supergravity Specify Kähler potential K and superpotential W Minimal supergravity K=|z| 2 + i | i | 2 W=W h (z)+W o ( ) SUSY broken if F z =zW * +W z 0, W 0 Universal scalar mass, trilinear couplings etc

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15 Lore Got universal scalar mass! “Of course, because gravity doesn’t distinguish flavor” Wrong! “Minimal” is a choice to obtain canonical kinetic terms with no Planck-suppressed corrections But in general there are such corrections in non- renormalizable theory and SUGRA not minimal

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16 Problems with Minimal SUGRA There is no fundamental reason to believe that Kähler potential in effective theory of quantum gravity is strictly minimal In many string compactifications, it isn’t –Direct coupling of observable fields with moduli in Käler potential that depend on their modular weights Thought to be an ad hoc convenient choice, not a theory of mediation But phenomenologically excellent start point, explaning EWSB, dark matter, absence of FCNC

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17 Problems with general SUGRA There may be arbitrary coupling between hidden and observable fields in Kähler potential under no control Generically, soft masses expected to be arbitrary, with flavor violation m 2 ij i* j d 4 z * z c ij i* j Phenomenogically disaster

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18 Remedy by flavor symmetry We need theory of flavor anyway The issue of flavor-violating soft masses is intimately tied to the origin of flavor, Yukawa couplings Seek for a common theory that solves the problem

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Flavor-blind Mediation Mechanisms Gauge Mediation Gaugino Mediation Anomaly Mediation

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20 Gauge Mediation

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21 Dine-Nelson-Shirman model Dynamical supersymmetry breaking sector Take SU(5) with 10+5 * (“non-calculable DSB model” add massive 5+5 * and can show DSB; HM) break it to SU(4) U(1) with non-anomalous global U(1) m (6 +2 +4 -3 +1 -8 ) +1 +(4 * -1 +1 +4 ) -3 W= 4 * -1 4 -3 1 +4 + 1 +4 1 +4 1 -8 breaks supersymmetry dynamically gauge global U(1) m as “messenger U(1)” Problem with FY D-term for messenger U(1) solved by changing the DSB model to SU(6) U(1) (Dine, Nelson, Nir, Shirman)

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22 Dine-Nelson-Shirman model Messenger sector a pair charged under messenger U(1) N F pairs of F+F * (5+5 * ) under SU(5) SU(3) SU(2) U(1) W= S + SFF * + S 3 acquire negative mass- squred from two-loops in messenger U(1) interaction triggers S to acquire both A- and F-component VEVs gives both mass and B- term to F+F * M= S F S >

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23 Dine-Nelson-Shirman model Because F+F * are charged under the standard model gauge groups, their one-loop diagrams generate gaugino masses, and two-loop diagrams generate scalar masses Generated scalar masses flavor-blind, because gauge interactions do not distinguish flavor

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24 Dine-Nelson-Shirman model Lightest Supersymmetry Particle: gravitino In general, a cosmological problem (overclosure) (de Gouvêa, Moroi, HM) Collider signatures may be unique: –Bino gravitino + photon –Decay length may be microns to km Should not have any new flavor physics below the mediation scale to screw-up flavor-blindness of soft masses

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25 Direct Gauge Mediation Too many sectors to worry about! DSB sector: Sp(4) with 5 flavors charged under SU(5) (HM)

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26 Gaugino Mediation (Kaplan, Kribs, Schmaltz) (Chacko, Luty, Nelson, Ponton) DSB in another brane Gauge multiplet in the bulk Gauge multiplet learns SUSY breaking first, obtains gaugino mass MSSM at the compactification scale with gaugino mass only Scalar masses generated by RGE

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27 Gaugino Mediation Phenomenology similar to minimal supergravity with zero universal scalar mass Gravitino heavy: less harmful Needs high (~GUT scale) compactification to jack up slepton mass high enough Should not have any new flavor physics below the compactification scale to screw-up flavor- blindness of soft masses

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28 Anomaly Mediation (Randall, Sundrum) (Giudice, Luty, HM, Rattazzi) Try not to mediate Zen of SUSY breaking If no coupling between DSB and MSSM, there is no supersymmetry breaking at tree-level But divergence of supercurrent in the same multiplet as the trace of energy momentum tensor Conformal anomaly induces supersymmetry breaking

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29 Weyl compensator formalism Conformal Supergravity “fixed” by Weyl compensator The only communication of SUSY breaking is through the auxiliary component of F d 4 * * d 2 (M Scale d 4 * d 2 ( M Only dimensionful parameters acquire SUSY breaking Massless theory no SUSY breaking

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30 Conformal Anomaly Any (non-finite) theory needs a regulator with an explicit mass scale –Pauli-Villars with heavy regulator mass –DRED with renormalization scale (Boyda, HM, Pierce) Regulator receives SUSY breaking SUSY breaking induced by regulator effect: anomaly

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31 Anomaly Mediation Anomaly mediation predicts SUSY breaking with theory given at the scale of interest UV insensitivity Can be checked explicitly by integrating out heavy fields that their loops exactly cancel the differences in -functions & anomalous dimensions (Giudice, Luty, HM, Rattazzi) (Boyda, HM, Pierce) SUSY breakings always stay on the RGE trajectory

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32 Too predictive! Anomaly mediation highly predictive with only one parameter: overall scale Slepton mass-squareds come out negative Phenomenologically dead on start Remedies: –Add uinversal scalar mass –Cause symmetry breaking via SUSY breaking Destroys UV insensitivity

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33 Viable UV-insensitive Anomaly Mediation Add U(1) B-L and U(1) Y D-terms Three SUSY-breaking parameters now Can show that UV- insensitive (Arkani-Hamed, Kaplan, HM, Nomura)

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34 Conformal sequestering Inspiration from AdS/CFT correspondence Make hidden sector nearly superconformal Dangerous coupling between hidden and observable fields suppressed because Kähler potential of hidden fields flow to IR fixed point (Luty, Sundrum) Can be extended to include U(1) breaking sector to make the scenario phenomenologically viable (Harnik, HM, Pierce)

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35 U(1) breaking sector SO(5) theory with 6 spinors, no mass parameters Gauge SU(4) SU(2) U(1) subgroup of global SU(6) symmetry Quantum modified moduli space breaks U(1) (and also SU(4) Sp(2)) D-term “non-calculable” because compositeness scale ~v U(1)-breaking scale Can be made calculable within the same universality class by (1) additional flavor >>v or (2) additional color&flavor <

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36 SUSY spectra

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Models of Flavor

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38 Question of Flavor What distinguishes different generations? –Same gauge quantum numbers, yet different Hierarchy with small mixings: Need some ordered structure Probably a hidden flavor quantum number Need flavor symmetry –Flavor symmetry must allow top Yukawa –Other Yukawas forbidden –Small symmetry breaking generates small Yukawas

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39 Broken Flavor Symmetry Flavor symmetry broken by a VEV ~0.02 SU(5)-like: –10(Q, u R, e R ) (+2, +1, 0) –5*(L, d R ) (+1, +1, +1) –m u :m c :m t ~ m d 2 :m s 2 :m b 2 ~ m e 2 :m 2 :m 2 ~ 4 : 2 :1

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40 Not bad! m b ~ m , m s ~ m , m d ~ m e @M GUT m u :m c :m t ~ m d 2 :m s 2 :m b 2 ~ m e 2 :m 2 :m 2

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41 New Data from Neutrinos Neutrinos are already providing significant new information about flavor symmetries If LMA, all mixing except U e3 large –Two mass splittings not very different –Atmospheric mixing maximal –Any new symmetry or structure behind it?

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42 Is There A Structure In Neutrino Masses & Mixings? Monte Carlo random complex 3 3 matrices with seesaw mechanism (Hall, HM, Weiner; Haba, HM)

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43 Anarchy No particular structure in neutrino mass matrix –All three angles large –CP violation O(1) –Ratio of two mass splittings just right for LMA Three out of four distributions OK –Reasonable Underlying symmetries don’t distinguish 3 neutrinos.

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44 Anarchy is Peaceful Anarchy (Miriam-Webster): “ A utopian society of individuals who enjoy complete freedom without government” Peaceful ideology that neutrinos work together based on their good will Predicts large mixings, LMA, large CP violation sin 2 2 13 just below the bound Ideal for VLBL experiments Wants globalization!

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45 More flavor parameters Squarks, sleptons also come with mass matrices Off-diagonal elements violate flavor: suppressed by flavor symmetries Look for flavor violation due to SUSY loops Then look for patterns to identify symmetries Repeat Gell-Mann–Okubo! Need to know SUSY masses

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46 To Figure It Out… Models differ in flavor quantum number assignments Need data on sin 2 2 13, solar neutrinos, CP violation, B-physics, LFV, EWSB, proton decay Archaeology We will learn insight on origin of flavor by studying as many fossils as possible –cf. CMBR in cosmology

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47 More Fossils: Lepton Flavor Violation Neutrino oscillation lepton family number is not conserved! –Any tests using charged leptons? –Top quark unified with leptons –Slepton masses split in up- or neutrino-basis –Causes lepton-flavor violation (Barbieri, Hall) –predict B( ), B( e ), e at interesting (or too- large) levels

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48 Barbieri, Hall, Strumia

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49 More Fossils: Quark Flavor Violation Now also large mixing between and –( , b R ) and ( , s R ) unified in SU(5) –Doesn’t show up in CKM matrix –But can show up among squarks –CP violation in B s mixing (B s J ) –Addt’l CP violation in penguin b s (B d K s ) (Chang, Masiero, HM)

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50 Conclusions Dynamical supersymmetry breaking successfully produces hierarchy Various mediation mechanisms –Gravity mediation + flavor symmetry –Gauge mediation –Anomaly mediation –Gaugino mediation

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