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Supersymmetry

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Supersymmetry

Hitoshi Murayama

Taiwan Spring School

March 29, 2002

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

- v<<MPl because v~mSUSY<<MPl
- Why mSUSY<<MPl?
- Idea: dimensional transmutation
- SUSY broken by strong gauge dynamics with
- “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)

SO(7) gaugino condensation generates dynamical superpotential

Add W=M10102, lifts moduli space, breaks SUSY

Decouple 10 smoothly(HM)

- Sp(Nc) gauge theory with Nf=Nc+1
- Quantum modified moduli space
Pf M = L2Nffor mesons Mij=QiQj

- Add superpotential with singlets Sij
W=Sij QiQjforces Mij=0

- Contradiction no SUSY vacua

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

- Supersymmetry is broken either by an F-component of a chiral superfield
fi=q2Fi0

or a D-component of a vector superfield

V=q2D0

- Once they are frozen at their expectation values, they can be viewed as spurions of supersymmetry breaking order parameters

- Purpose of supersymmetry is to protect hierarchy
- Arbitrary terms in Lagrangian that break supersymmetry reintroduce power divergences
- “Soft supersymmetry breaking” classified:
mll, m2ijfi*fj, Aijkfjfjfk, Bijfjfj, Cifj

- Dark horse terms (not always allowed):
fj*fjfk, lyj, yiyj

- Spurion z =fi/M=q2Fi/M generates soft terms
- M is the “mediation scale” where the effects of SUSY breaking are communicated
m ll = d2q z c Wa Wa

m2ijfi*fj = d4q z*z cijfi*fj

Aijkfjfjfk = d2q z cijkfjfjfk

Bijfjfj = d2q z cijfjfj

Cifj = d2q z cifj

- Coefficients c are random at this point

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

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

_

K0

K0

- 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

- Specify Kähler potential K and superpotential W
- Minimal supergravity
K=|z|2+i|fi|2W=Wh(z)+Wo(f)

- SUSY broken if Fz=zW*+Wz0, W0
Universal scalar mass, trilinear couplings etc

- 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

- 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

- 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
m2ijfi*fj = d4q z*z cijfi*fj

- Phenomenogically disaster

- 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

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)

Messenger sector

a pair f charged under messenger U(1)

NF pairs of F+F* (5+5*) under SU(5) SU(3)SU(2)U(1)

W=l1Sf+f-+l2SFF*+l3S3

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 F+F*

M=l2<S>, MB=l2<FS>

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

- 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

Too many sectors to worry about!

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

(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

- 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

(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

- Conformal Supergravity “fixed” by Weyl compensator F
- The only communication of SUSY breaking is through the auxiliary component of F=q2F
d4q F*Ff*f +d2q F3(M f2+l f3)

- Scale ff/F
d4q f*f +d2q (FM f2+l f3)

- Only dimensionful parameters acquire SUSY breaking
- Massless theory no SUSY breaking

- 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

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

- 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

Add U(1)B-L and U(1)YD-terms

Three SUSY-breaking parameters now

Can show that UV-insensitive

(Arkani-Hamed, Kaplan, HM, Nomura)

- 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)

- 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 L~v U(1)-breaking scale
- Can be made calculable within the same universality class by (1) additional flavor L>>v or (2) additional color&flavor L<<v to show D0
- Can be used to generate right-handed neutrino mass
(Harnik, HM, Pierce)

Models 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

- 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:ms2:mb2~ me2:mm2:mt2 ~4: 2:1

- mb~ mt, ms ~ mm, md ~ me @MGUT
- mu:mc:mt~ md2:ms2:mb2~ me2:mm2:mt2

- 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?

- Monte Carlo random complex 33 matrices with seesaw mechanism
(Hall, HM, Weiner; Haba, HM)

- 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.

- Reasonable

- 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!

- 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

- 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

- 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(tmg), B(meg), me at interesting (or too-large) levels

Barbieri, Hall, Strumia

Now also large mixing between nt and nm

(nt, bR) and (nm , sR) unified in SU(5)

Doesn’t show up in CKM matrix

But can show up among squarks

CP violation in Bs mixing (BsJ/y f)

Addt’l CP violation in penguin bs (Bdf Ks)

(Chang, Masiero, HM)

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