Supersymmetry

1
Supersymmetry

• Hitoshi Murayama
• Taiwan Spring School
• March 29, 2002

2
Electroweak Symmetry Breaking

• In the MSSM, electroweak symmetry does not get
  broken
• Only after supersymmetry is broken, Higgs can
  obtain a VEV vmSUSY
• Regard EWSB as a consequence of supersymmetry
  breaking
• EW symmetry and hierarchy protected by
  supersymmetry

3
Origin of Hierarchy

• vltltMPl because vmSUSYltltMPl
• Why mSUSYltltMPl?
• Idea dimensional transmutation
• SUSY broken by strong gauge dynamics with
• Dynamical supersymmetry breaking

4
Dynamical Supersymmetry Breaking

• Simplest example SO(10) with one 16
• No moduli space, cant analyze with Seibergian
  techniques
• non-calculable (Affleck-Dine-Seiberg)
• Add one 10, make it massive and decouple
• When M100, moduli space spanned by 161610, 102,
  generically SO(10)?SO(7)

• SO(7) gaugino condensation generates dynamical
  superpotential
• Add WM10102, lifts moduli space, breaks SUSY
• Decouple 10 smoothly(HM)

5
Izawa-Yanagida-Intriligator-Thomas model

• Sp(Nc) gauge theory with NfNc1
• Quantum modified moduli space
• Pf M L2Nf for mesons MijQiQj
• Add superpotential with singlets Sij
• WSij QiQj forces Mij0
• Contradiction ? no SUSY vacua

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

7
Spurion

• Supersymmetry is broken either by an F-component
  of a chiral superfield
• fiq2Fi?0
• or a D-component of a vector superfield
• Vq2D?0
• Once they are frozen at their expectation values,
  they can be viewed as spurions of supersymmetry
  breaking order parameters

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
• mll, m2ijfifj, Aijkfjfjfk, Bijfjfj, Cifj
• Dark horse terms (not always allowed)
• fjfjfk, lyj, yiyj

9
Spurion operators

• Spurion z fi/Mq2Fi/M generates soft terms
• M is the mediation scale where the effects of
  SUSY breaking are communicated
• m ll ?d2q z c Wa Wa
• m2ijfifj ?d4q zz cijfifj
• Aijkfjfjfk ?d2q z cijkfjfjfk
• Bijfjfj ?d2q z cijfjfj
• Cifj ?d2q z cifj
• Coefficients c are random at this point

10
Supersymmetric flavor problem

• Random SUSY breaking excluded by FCNC constraints
• Consider scalar down quarks
• Take the off-diagonal terms to be perturbation

11
Supersymmetric flavor problem

• Random SUSY breaking excluded by FCNC constraints
• Want a reason why off-diagonal terms are
  suppressed

_
K0
K0
12
Two possible directions

• Develop a theory of flavor that predicts not only
  the pattern of Yukawa matrices (masses, mixings),
  but also soft masses
• Develop a theory of mediation mechanism of
  supersymmetry breaking that predicts
  (approximately) flavor-blind soft masses

13
Gravity Mediation
14
Supergravity

• Specify Kähler potential K and superpotential W
• Minimal supergravity
• Kz2?ifi2 WWh(z)Wo(f)
• SUSY broken if FzzWWz?0, W?0
• ?Universal scalar mass, trilinear couplings etc

15
Lore

• Got universal scalar mass!
• Of course, because gravity doesnt 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

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 isnt
• 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

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
• m2ijfifj ?d4q zz cij fifj
• Phenomenogically disaster

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

19
Flavor-blind Mediation Mechanisms

• Gauge Mediation
• Gaugino Mediation
• Anomaly Mediation

20
Gauge Mediation
21
Dine-Nelson-Shirman model

• Dynamical supersymmetry breaking sector
• Take SU(5) with 105
• (non-calculable DSB model
• add massive 55 and can show DSB HM)
• break it to SU(4)?U(1) with non-anomalous global
  U(1)m
• (624-31-8)1 (4-114)-3
• W 4-1 4-3 14 14 14 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)

22
Dine-Nelson-Shirman model

• Messenger sector
• a pair f? charged under messenger U(1)
• NF pairs of FF (55) under SU(5)
  ?SU(3)?SU(2)?U(1)
• Wl1Sff-l2SFFl3S3
• f? 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 FF
• Ml2ltSgt, MBl2ltFSgt

23
Dine-Nelson-Shirman model

• Because FF 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

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

25
Direct Gauge Mediation

• Too many sectors to worry about!

• DSB sector Sp(4) with 5 flavors charged under
  SU(5) (HM)

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

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

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

29
Weyl compensator formalism

• Conformal Supergravity fixed by Weyl
  compensator F
• The only communication of SUSY breaking is
  through the auxiliary component of Fq2F
• ?d4q FF ff ?d2q F3 (M f2l f3)
• Scale f?f/F
• ?d4q ff ?d2q (F M f2l f3)
• Only dimensionful parameters acquire SUSY
  breaking
• Massless theory ? no SUSY breaking

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 m
• (Boyda, HM, Pierce)
• Regulator receives SUSY breaking
• SUSY breaking induced by regulator effect anomaly

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 b-functions anomalous dimensions
• (Giudice, Luty, HM, Rattazzi)
• (Boyda, HM, Pierce)
• SUSY breakings always stay on the RGE trajectory

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

33
Viable UV-insensitiveAnomaly 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)

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)

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 Lv U(1)-breaking scale
• Can be made calculable within the same
  universality class by (1) additional flavor Lgtgtv
  or (2) additional colorflavor Lltltv to show D?0
• Can be used to generate right-handed neutrino
  mass
• (Harnik, HM, Pierce)

36
SUSY spectra
37
Models of Flavor
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

39
Broken Flavor Symmetry

• Flavor symmetry broken by a VEV ???0.02
• SU(5)-like
• 10(Q, uR, eR) (2, 1, 0)
• 5(L, dR) (1, 1, 1)
• mumcmt md2ms2mb2 me2mm2mt2 ?4 ?2 1

40
Not bad!

• mb mt, ms mm, md me _at_MGUT
• mumcmt md2ms2mb2 me2mm2mt2

41
New Data from Neutrinos

• Neutrinos are already providing significant new
  information about flavor symmetries
• If LMA, all mixing except Ue3 large
• Two mass splittings not very different
• Atmospheric mixing maximal
• Any new symmetry or structure behind it?

42
Is There A StructureIn Neutrino Masses Mixings?

• Monte Carlo random complex 3?3 matrices with
  seesaw mechanism
• (Hall, HM, Weiner Haba, HM)

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 dont distinguish 3
  neutrinos.

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
• sin22q13 just below the bound
• Ideal for VLBL experiments
• Wants globalization!

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-MannOkubo!
• Need to know SUSY masses

46
To Figure It Out

• Models differ in flavor quantum number
  assignments
• Need data on sin22q13, 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

47
More FossilsLepton 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(t?mg), B(m?eg), m?e at interesting (or
  too-large) levels

48
Barbieri, Hall, Strumia
49
More FossilsQuark Flavor Violation

• Now also large mixing between nt and nm
• (nt, bR) and (nm , sR) unified in SU(5)
• Doesnt show up in CKM matrix
• But can show up among squarks

• CP violation in Bs mixing (Bs?J/y f)
• Addtl CP violation in penguin b?s (Bd?f Ks)
• (Chang, Masiero, HM)

50
Conclusions

• Dynamical supersymmetry breaking successfully
  produces hierarchy
• Various mediation mechanisms
• Gravity mediation flavor symmetry
• Gauge mediation
• Anomaly mediation
• Gaugino mediation