3 Supersymmetry 1 3 1 Motivations for Supersymmetry

3. Supersymmetry 1

3. 1 Motivations for Supersymmetry Solution to the naturalness problem Supersymmetry (SUSY) – symmetry between bosons and fermions No Quadratic Divergence in Higgs mass: – cancellation between bosons and fermions 2

Gauge Coupling Unification Gauge coupling constants change as energy scale changes Minimal Supersymmetric Standard Model Three couplings (SU(3), SU(2), U(1)) meet at one point ~1016 Ge. V strength 0. 12 MSSM 0. 1 SM 0. 08 0. 06 0. 04 0. 02 2. 5 5 7. 5 10 12. 5 15 energyscale accidental? or suggests unification of forces!? 3

Quantum Gravity SUSY softens UV divergence of quantum gravity superstring theory? Dark Matter Lightest superparticle (LSP) is a candidate for dark matter of the universe. LSP: neutralino, gravitino …. 4

3. 2 D=4, N=1 SUSY supersymmetry 5

quick view of SUSY • 4 D N=1 supersymmetry (SUSY) Wess-Bagger’s text book • Superfields on superspace quark/lepton/Higgs chiral superfield (multiplet) gauge bosons vector superfield (multiplet) 6

Superfields • Minkowski space • Superfields on superspace – supersymmetry tr. = translation along coordinate 7

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Chiral Superfield • SUSY transformation SUSY tr. of highest component total derivative • Counting of degrees of freedom 10

Lagrangian for chiral superfield • D-term (kinetic term) • F-term (Yukawa int. , mass etc) – superpotential: 11

• example　1 scalar mass = spinor mass=m 12

• example 2 SUSY relation of couplings 13

• Vector Superfield: Generalized gauge transformation: U(1) Gauge invariant Lagrangian 14

Wess-Zumino gauge 15

• gauge kinetic term 16

Minimal Supersymmetric Standard Model (MSSM) Chiral Multiplets We need two Higgs multiplets for anomaly cancellation. 17

Vector Multiplets 18

Superpotential -- After EW symmetry breaking quark/lepton masses -- ~ weak scale is imposed. Why? and How? problem 19

Absence of Quadratic Divergence Radiative corrections to Higgs boson mass • schematic view at one loop Cancellation between boson and fermion loop • more sophisticated and rigorous way: non-renormalization theorem Superpotential does not receive radiative corrections 20

• another way to understand: SUSY fermion boson mf=0 mb=0 chiral sym. SUSY+ chiral symmetry small (vanishing) boson mass 21

3. 3. Supersymmetry Breaking • Exact SUSY would predict “a scalar electron which has the same mass and charge as electron” – Such a scalar electron is immediately ruled out. • SUSY must be broken in some way. – shift of coupling: quadratic div. – shift of mass: No effect to UV. No quadratic div. Take this choice! 22

• Soft SUSY breaking terms: – mass terms which do not generate quadratic divergence • Classification: use of spurious fields • Superparticles (squark/slepton, gaugino) can become heavy to escape detection. • Origin of the spurious fields: spontaneous SUSY breaking 23

Spontaneous SUSY breaking • SUSY must be broken some way • Probably SUSY is a fundamental symmetry of the nature, if any. Spontaneous SUSY breaking Lorentz inv. is assumed. • origin of spurious fields 24

Origin of soft SUSY breaking masses • scalar masses • gaugino masses These come from Kaehler potential and gauge kinetic function 25

Three ingredients in general SUSY theory All interaction needed to give soft masses can be seen in the above Lagrangian. 26

Super. Higgs mechanism • supergravity • gravitino (spin 3/2) – superpartner of graviton – gauge field associated with local supersymmetry – gravitino is massless • Spontaneous SUSY breaking – Goldstino is absorbed into the longitudinal mode of gravitino massive gravitino 27

３. 4　Mediation Mechanisms of SUSY Breaking Soft SUSY breaking masses should 1) be light enough to solve the naturalness problem associated with EW scale --- may not be easy to quantify the statement 2) be heavy enough to escape detection at collider experiments 3) not induce too large FCNC or CP 4) have neutral LSP (cosmology) 28

SUSY flavor problem Remember the statement: Flavor Problem in Beyond SM – Standard Model is too good to hide all flavor mixing phenomena (GIM mechanism) – Introduction of new particles/interaction may give too large FCNCs. This is particularly the case for SUSY: “ SUSY flavor problem” 29

New source of flavor mixing: squark (slepton) masses – gauge inv. mass terms – Off-diagonal terms flavor mixing • Experimental constraints 30

Solutions to SUSY Flavor Problem 1) degeneracy 2) alignment squarks & quarks: simultaneous diagonalization family symmetry? 3) decoupling masses of 1 st and 2 nd generations~ 10 -100 Te. V 31

Mechanisms of Mediation The SUSY flavor problem has inspired various mechanisms of SUSY breaking & its mediation • gravity Mediation – minimal supergravity – Dilaton/moduli mediation – gaugino mediation • gauge mediation • anomaly mediation • mirage mediation (mixed moduli-anomaly medition) • ………. 32

Gravity Mediation … a bit misleading name • Use of non-renormalizable interaction in Kaehler potential/gauge kinetic function • Such interaction should always exist in supergravity • Hidden sector (SUSY breaking sector) interacts with visible sector (MSSM sector) via the non-renormalizable interaction • Scalar mass: Kaehler potential – ~gravitino mass – afraid of too large FCNC • gaugino mass: Gauge kinetic function – can be ~gravitino mass if the gauge kinetic function has nontrivial dependence on hidden sector. 33

• scalar mass • Cij should be controlled appropriately. Otherwise scalar masses are flavor dependent. • How to control non-renormalizable interaction? 34

Various approaches • minimal supergravity – Assume justification? – Probably we need more fundamental theory dilaton/moduli mediation • Gauge mediation: – small gravitino mass. Gravity mediation is suppressed. – Dominant contribution from gauge interaction • Anomaly mediation – with sequestered sector SUSY breaking (Cij=0). maybe realized as brane separation 35

minimal supergravity (m. SUGRA) • Assume the special Kaehler potential • m. SUGRA – universality no dangerous FCNC – simple, good bench mark for phenomenology – justification of universality? ? 36

Gauge Mediation Messenger of SUSY breaking =SM gauge interactions generation universality of scalar masses Scenario: – messenger sector: messenger quarks/leptons – messenger sector feels SUSY breaking – SUSY breaking is mediated to MSSM sector through gauge interaction e. g. gaugino mass 37

Very different phenomenolgy & cosmology 38

Anomaly Meditation Randall-Sundrum Giudice-Luty-Murayama-Rattazzi Mediation by superconformal anomaly • conformal compensator: • gauge kinetic function • gaugino mass one loop suppression • Wino is lightest among gauginos 39

• Scalar mass: • sleptons: SU(2), U(1) asymptotic non-free negative slepton mass^2 • attempts to solve the tachyonic slepton masses 40

Mirage Mediation (mixed anomaly-moduli mediation) Choi-Falkowski-Nilles-Olechowski ’ 05 Endo-MY-Yoshioka Choi-Jeong-Okumura, …. . • Moduli mediation contribution solves the tachyonic slepton mass problem. • Based on KKLT-type set up (moduli stabilization with flux and gaugino condensate) 41

Set-up (in Planck unit) superpotential: Kaeher potential: supersymmetric Ad. S vacuum Needs up-lifting potential to get Minkowski space Moduli has suppressed SUSY breaking Moduli-mediation is comparable to anomaly-mediation. 42

mass scales: little hierarchy • soft masses • gravitino mass • moduli mass 43

mirage mediation Choi, Jeong, Okumura 05 RG properties: Gaugino masses (as well as scalar masses) are unified at a mirage scale. from Lebedev, Nilles, Ratz 05 44

General Features of Mixed- Modulus-Anomaly Mediation (or Mirage Mediation) • Compact Sparticle Mass Spectrum • small parameter (~M 1) Endo-MY-Yoshioka 05 Choi-Jeong-Okumura 05 small gluino mass/ RGE • LSP: neutralino – admixture of gauginos and higginos • stau: tends to be light • Mass Spectrum is very different from m. SUGRA (CMSSM). gauge mediation & anomaly mediation • Testable at future collider experiments (LHC/ILC) 45

Mass Spectrum: Case Study Endo, MY, Yoshioka 05 n=1, l=1/3 n=3, l=0 (KKLT) 46