3. Supersymmetry

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3. Supersymmetry
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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

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• 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 GeV
• accidental? or suggests unification of forces!?

MSSM
SM
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• 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 .

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3.2 D4, N1 SUSY

supersymmetry
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quick view of SUSY
Wess-Baggers text book

• 4D N1 supersymmetry (SUSY)
• Superfields on superspace
• quark/lepton/Higgs ? chiral superfield
  (multiplet)
• gauge bosons ? vector superfield
  (multiplet)

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Superfields

• Minkowski space
• Superfields on superspace
• supersymmetry tr. translation along ? coordinate

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

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

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• example 1
• ? scalar mass spinor massm

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• example 2

SUSY relation of couplings
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• Vector Superfield

Generalized gauge transformation U(1)
Gauge invariant Lagrangian
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Wess-Zumino gauge
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• gauge kinetic term

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Minimal Supersymmetric Standard Model(MSSM)

• Chiral Multiplets

We need two Higgs multiplets for anomaly
cancellation.
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• Vector Multiplets

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Superpotential
-- After EW symmetry breaking
? quark/lepton masses
-- m weak scale is imposed. Why? and How?
? m problem
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Absence of Quadratic Divergence

• Radiative corrections to Higgs boson mass
• schematic view at one loop
• more sophisticated and rigorous way
• non-renormalization theorem
• Superpotential does not receive
  radiative corrections

Cancellation between boson and fermion loop
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• another way to understand

SUSY
fermion
boson
chiral sym.
mf0
mb0
SUSY chiral symmetry ? small (vanishing)
boson mass
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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!

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• 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

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Spontaneous SUSY breaking

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

Lorentz inv. is assumed.
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Origin of soft SUSY breaking masses

• scalar masses
• gaugino masses
• These come from Kaehler potential and gauge
  kinetic function

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

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3.4 Mediation Mechanisms of SUSY Breaking

• Soft SUSY breaking masses should
• be light enough to solve the naturalness problem
  associated with EW scale
  --- may not be easy to quantify
  the statement
• be heavy enough to escape detection at collider
  experiments
  
• not induce too large FCNC or CP
  
• have neutral LSP (cosmology)

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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

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

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Solutions to SUSY Flavor Problem

• degeneracy
• 2) alignment
• squarks quarks simultaneous
  diagonalization
• ? family symmetry?
• decoupling
• masses of 1st and 2nd generations 10-100
  TeV

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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)
• .

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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 non-trivial dependence on hidden
  sector.

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

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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 (Cij0).
  maybe realized as brane separation

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minimal supergravity (mSUGRA)

• Assume the special Kaehler potential
• mSUGRA
• universality ? no dangerous FCNC
• simple, good bench mark for phenomenology
• justification of universality??

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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
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Very different phenomenolgy cosmology
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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

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• Scalar mass
• sleptons SU(2), U(1) asymptotic non-free
• ? negative slepton mass2
• attempts to solve the tachyonic slepton masses

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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)

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• Set-up (in Planck unit)
• superpotential
• Kaeher potential
• supersymmetric AdS vacuum
• Needs up-lifting potential to get Minkowski
  space
• Moduli has suppressed SUSY breaking

Moduli-mediation is comparable to
anomaly-mediation.
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mass scales little hierarchy

• soft masses
• gravitino mass
• moduli mass

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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
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General Features of Mixed- Modulus-Anomaly
Mediation (or Mirage Mediation)
Endo-MY-Yoshioka 05 Choi-Jeong-Okumura 05

• Compact Sparticle Mass Spectrum
• small m parameter (M1)
• ? small gluino mass/ RGE
• LSP neutralino
• admixture of gauginos and higginos
• stau tends to be light
• Mass Spectrum is very different from mSUGRA
  (CMSSM).
• gauge mediation anomaly mediation
• Testable at future collider experiments (LHC/ILC)

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Mass Spectrum Case Study
Endo,MY,Yoshioka 05
n1,l1/3
n3,l0 (KKLT)