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 v~mSUSY

• Regard EWSB as a consequence of supersymmetry breaking

• EW symmetry and hierarchy “protected” by supersymmetry

3

Origin of Hierarchy

• v<<MPl because v~mSUSY<<MPl

• Why mSUSY<<MPl?

• 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, can’t analyze with Seibergian techniques “non-calculable”

(Affleck-Dine-Seiberg)

• Add one 10, make it massive and decouple

• When M10=0, moduli space spanned by 161610, 102, generically SO(10)SO(7)

€

W =Λ21/5

(16 ⋅16 ⋅10)2 /5

• SO(7) gaugino condensation generates dynamical superpotential

• Add W=M10102, lifts moduli space, breaks SUSY

• Decouple 10 smoothly(HM)

5

Izawa-Yanagida-Intriligator-Thomas model

• Sp(Nc) gauge theory with Nf=Nc+1

• Quantum modified moduli space

Pf M = 2Nf for mesons Mij=QiQj

• Add superpotential with singlets Sij

W=Sij QiQj forces Mij=0

• 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

i=2Fi0or a D-component of a vector superfield

V=2D0• 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:

m, m2iji*j, Aijkjjk, Bijjj, Cij

• Dark horse terms (not always allowed):

j*jk, j, ij

9

Spurion operators

• Spurion z =i/M=2Fi/M generates soft terms• M is the “mediation scale” where the effects of SUSY

breaking are communicated

m d2 z c W W

m2iji*j d4 z*z ciji*j

Aijkjjk d2 z cijkjjk

Bijjj d2 z cijjj

Cij d2 z cij

• 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

_

€

δ12d

( )RR

< 0.04mSUSY

500GeV

δ12d

( )RR

δ12d

( )LL

< 0.001mSUSY

500GeV

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

13

Gravity Mediation

14

Supergravity

• Specify Kähler potential K and superpotential W

• Minimal supergravity

K=|z|2+ i|i|2 W=Wh(z)+Wo()

• SUSY broken if Fz=zW*+Wz 0, W 0

Universal scalar mass, trilinear couplings etc

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

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

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

m2iji*j d4 z*z cij i*j

• 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

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 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)

22

Dine-Nelson-Shirman model

• Messenger sector• a pair charged under

messenger U(1) • NF pairs of F+F* (5+5*)

under SU(5) SU(3)SU(2)U(1)

W=S+SFF*+S3

• 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 FS>

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

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

• The only communication of SUSY breaking is through the auxiliary component of F

d4 * * d2 (M • Scale d4 * d2 ( M 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

(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 -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 ~v

U(1)-breaking scale• Can be made calculable within the same universality class

by (1) additional flavor >>v or (2) additional color&flavor <<v to show D0

• Can be used to generate right-handed neutrino mass(Harnik, HM, Pierce)

36

SUSY spectra

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)

– mu:mc:mt ~ md2:ms

2:mb2

~ me2:m

2:m2 ~4: 2 :1

Mu ~

ε4 ε3 ε2

ε3 ε2 ε

ε2 ε 1

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ,Md~

ε3 ε3 ε3

ε2 ε2 ε2

ε ε ε

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ,Ml~

ε3 ε2 ε

ε2 ε2 ε

ε3 ε2 ε

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

40

Not bad!

• mb~ m, ms ~ m, md ~ me @MGUT

• mu:mc:mt ~ md2:ms

2:mb2 ~ me

2:m2:m

2

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?

e μ τ( )

big big small

big big big

big big big

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

νe

νμ

ντ

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

Δmsolar2

Δmatm2 ~0.01– 0.2

42

Is There A StructureIn Neutrino Masses & Mixings?

• Monte Carlo random complex 33 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 don’t 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

• sin2213 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-Mann–Okubo!

• Need to know SUSY masses

M ˜ Q 2 ~M ˜ L

2 ~

1 ε ε2

ε 1 ε

ε2 ε 1

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

46

To Figure It Out…

• Models differ in flavor quantum number assignments

• Need data on sin2213, 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 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

48

Barbieri, Hall, Strumia

49

More Fossils:Quark Flavor Violation

• Now also large mixing between and

– (, bR) and ( , sR) unified in SU(5)

– Doesn’t show up in CKM matrix

– But can show up among squarks

– CP violation in Bs mixing (BsJ )

– Addt’l CP violation in penguin bs (Bd 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