iv. edms & the origin of matter

• The cosmic baryon asymmetry

• Electroweak baryogenesis

• Electric dipole moments

IV. EDMs & the Origin of Matter

Baryon asymmetry of the universe:

Cosmic Energy Budget

Baryons

Dark Matter

Dark Energy

Stars, planets, humans…

Matter & Cosmic History

After inflation: equal amounts of matter and antimatter

Quarks & gluons become protons, neutrons….

qqq p, n… e+ + e- q + q

p, n, e- become light elements & later stars, galaxies…

np d +

How did we get something from nothing?

Baryon asymmetry of the universe:


Baryons

Dark Matter

Dark Energy

Stars, planets, humans…

Explaining non-zero B requires CP-violation and a scalar sector beyond those of the Standard Model (assuming inflation set B=0)

Leptogenesis: discover the ingredients: LN- & CP-violation in neutrinos

Weak scale baryogenesis: test experimentally: EDMs & Higgs Boson Searches

€

rE

€

rd = d

r S

€

νEDM = −d

r S ⋅

r E

h

T-odd , CP-odd by CPT theorem

€

rE

€

rd = d

r S

€

νEDM = −d (−

r S ) ⋅

r E

h


€

νEDM = −d

r S ⋅

r E

h


€

rE

€

rd = d

r S

€

rB

€

νEDM = −d

r S ⋅(−

r E )

h


€

rE

€

rd = d

r S

€

rB


Big Bang Nucleosynthesis:

Light element abundances depend on YB

p, n, e- become light elements & later stars, galaxies…

np d +

BBN and YB

QuickTime™ and a decompressor

are needed to see this picture.




Cosmic Microwave Bcknd:

Shape of anisotropies depends on YB

Last scattering: imperfect black body

CMB and YB



Baryogenesis: Ingredients

Anomalous B-violating processes

Prevent washout by inverse processes

Sakharov Criteria

• B violation

• C & CP violation

• Nonequilibrium dynamics

Sakharov, 1967

EW Baryogenesis: Standard Model

Weak Scale Baryogenesis

• B violation



Sakharov, 1967

Anomalous Processes

Different vacua: (B+L)= NCS€

Aλ

Kuzmin, Rubakov, Shaposhnikov McLerran,…

Sphaleron Transitions€

W

€

W

€

JμB

€

qL

EW Baryogenesis: Standard Model


• B violation



Sakharov, 1967€

mt4

MW4

mb4

MW4

mc2

MW2

ms2

MW2

≈ 3 ×10−13

€

J = s12 s13 s23c12c132 c23sinδ13

= (2.88 ± 0.33) ×10−5

?

φ

?

φ

?

F

?

F

Increasing mh

1st order 2nd order

• CP-violation too weak• EWPT too weak

Shaposhnikov

Baryogenesis: New Electroweak Physics


• B violation



Sakharov, 1967

?

ϕ new

?

φ(x)

Unbroken phase

Broken phaseCP Violation

Topological transitions

1st order phase transition

?

?

e -?

ψnew

?

ϕ new

?

ϕ new

€

g

€

ϕ

€

g€

€

€

e+

€

e−

€

Z 0

€

Z 0€

ϕ• Is it viable?• Can experiment constrain it?• How reliably can we compute it?

Quantum Transport

CPV

Chem Eq

R-M et al

• Is it viable?• Can experiment constrain it?• How reliably can we compute it?

Theoretical Issues:Strength of phase transition (Higgs sector) Bubble dynamics (numerical)Transport at phase boundary (non-eq QFT)EDMs: many-body physics & QCD

Systematic baryogenesis: SD equations + power counting

Veff (ϕ,T): Requirements on Higgs sector extensions & expt’l probes

EWSB: Higgs?

• SM “background” well below new CPV expectations

• New expts: 102 to 103 more sensitive

• CPV needed for BAU?



LEPEWWGLEP Exclusion Non-SM Higgs(es) ?

EW Precision Data: 95% CL (our fit-GAPP)

Electroweak Phase Transition & Higgs

?

φ

?

φ

?

F

?

F1st order 2nd orderLEP EWWG

Increasing mh

mh>114.4 GeV

or ~ 90 GeV (SUSY)

Computed ESM : mH < 40 GeV

Need

So that sphaleron is not too fast

EMSSM ~ 10 ESM : mH < 120 GeV€

ϕ

€

ϕ

€

˜ t

€

+LStop loops in VEff

Light RH stop w/ special


?

φ

?

φ

?

F

?

F

Increasing mH

1st order 2nd orderLEP EWWG

mh>114.4 GeV

or ~ 90 GeV (SUSY)


Need

So that sphaleron is not too fastNon-doublet Higgs (w / wo SUSY)

€

S

€

ϕ

Mixing€

S

€

ϕ

€

S

Decay

€

e+

€

e−

€

Z 0

€

Z 0

€

ϕ

€

S

sin2

Can an augmented Higgs sector

• Generate a strong 1st order EWPT ?

• Allow for a heavier SM-like Higgs than in the MSSM ?

• Alleviate the tension between direct Higgs search bounds and the EWPO ?

• Be discovered at the LHC ?

Can its necessary characteristic probed at the LHC and a future e+e- collider ?


?

φ

?

φ

?

F

?

F

Increasing mH

1st order 2nd orderLEP EWWG

mh>114.4 GeV

or ~ 90 GeV (SUSY)


Need

So that sphaleron is not too fastNon-doublet Higgs (w / wo SUSY)

€

S

€

ϕ

Mixing€

S

€

ϕ

€

S

Decay

B.R. reduction

Reduced SM Higgs branching ratios

Unusual final states

€

S

€

ϕ

€

S€

b

€

b

€

μ+

€

μ−

mH

O’Connell, R-M, Wise



• B violation



Sakharov, 1967

?

ϕ new

?

φ(x)

Unbroken phase





90’s: Cohen, Kaplan, Nelson Joyce, Prokopec, Turok

Theoretical Issues:Strength of phase transition (Higgs sector) Bubble dynamics (expansion rate)Transport at phase boundary (non-eq QFT)EDMs: many-body physics & QCD

?

?

e -?

ψnew

?

ϕ new

?

ϕ new

“Gentle” departure from equilibrium & scale hierarchyCirigliano, Lee, R-M,Tulin

Systematic Baryogenesis I

Goal: Derive dependence of YB on parameters Lnew systematically (controlled approximations)

Parameters in LnewBubble & PT dynamics

CPV phases

Departure from equilibrium

• Earliest work: QM scattering & stat mech

• New developments: non-equilibrium QFT

Systematic Baryogenesis

Unbroken phase


Broken phase

1st order phase transition ?

φ(x)

€

∂B

∂t− D∇ 2ρ B = −ΓWS FWS (x) nL (x) + Rρ B[ ]

FWS (x)->0 deep inside bubble

nL produced in wall & diffuses in front

Cohen, Kaplan, Nelson Joyce, Prokopec, Turok

“snow”

€

W

€

W

€

JμB

€

qL

Systematic Baryogenesis

€

∂ni

∂t− D∇ 2ni = S n j ,T,ϕ , ˜ M ( )

Quantum Transport Equation

Unbroken phase


Broken phase

1st order phase transition ?

φ(x)

= +

+

+ …

€

˜ G

€

˜ G 0

€

˜ G 0

€

˜ G 0

€

˜ Σ

Schwinger-Dyson Equations

Riotto Carena et al Lee, Cirigliano, Tulin, R-M

Compute from first principles given Lnew

Quantum Transport & Baryogenesis

Particle Propagation: Beyond familiar (Peskin) QFT

€

0IN

€

0OUT

LI

Assumptions: 1. Evolution is adiabatic2. Spectrum is non-degenerate3. Density is zero

?

ϕ new

?

φ(x)

Electroweak Baryogenesis 1. Evolution is non-adiabatic: vwall > 0 -> decoherence

2. Spectrum is degenerate: T > 0 -> Quasiparticles mix

3. Density is non-zero

Generalized Green F’ns • Spectral degeneracies• Non-adiabaticity

LI

€

0IN

€

0OUT

€

˜ G (x,y) = Pϕ a (x)ϕ b* (y) τ ab =

G t (x,y) −G<(x,y)

G>(x, y) −G t (x,y)

⎡

⎣ ⎢

⎤

⎦ ⎥

€

ˆ O (x) = ρ nn ' nn

∑ SI [ϕ ]T ˆ O (x) SI [ϕ ]{ } n'+-

Non-equilibrium T>0 Evolution

= + + …

€

˜ G

€

˜ G 0+

€

˜ G 0

€

˜ G 0

€

˜ Σ

Scale Hierarchy

T > 0: Degeneracies

€

q

€

q

€

gM(T)

P(T)

vW > 0: Non-adiabaticity

vW

Time Scales

Plasma time:

P ~ 1/ P

Decoherence time:

d ~ 1/vW k)

€

˜ t L

e.g., particle in an expanding box

Quantum Decoherence

L L L

€

ψn0(x) = An sin kn x

€

kn =nπ

L €

ψn0 ψ n

2

€

L + ΔL( ) L

n=1

n=2

n=3

k = kEFF( ,Lw)

Quantum Transport & Baryogenesis

?

ϕ new

?

φ(x)

Electroweak Baryogenesis 1. Evolution is non-adiabatic: vwall > 0 -> decoherence

2. Spectrum is degenerate: T > 0 -> Quasiparticles mix

3. Density is non-zero

Scale Hierarchy:

Fast, but not too fast

Hot, but not too hot

Dense, but not too dense

d = vw (k / << 1

p = p / << 1

μ = μ / T << 1

Work to lowest, non-trivial order in ’s

Error is O () ~ 0.1

Cirigliano, Lee, R-M

Systematically derive transport eq’s from Lnew

Competing Dynamics

CPV

Ch eq

Cirigliano, Lee,Tulin, R-M

Quantum Transport Equations

= + + …

€

˜ G

€

˜ G 0+

€

˜ G 0

€

˜ G 0

€

˜ Σ

Expand in d,p,μ

Currents

CP violating sources Links CP violation in Higgs

and baryon sectors

Chiral Relaxation

Strong sphalerons

Producing nL = 0

• SCPV

• M , H , Y , SS

€

∂Xμ jμ (X) = d3z dz0 Σ>(X,z) G<(z, X) − G>(X,z) Σ<(z, X) +L[ ]

−∞

X 0∫∫Approximations

• Neglect O() terms

• Others under scrutiny

R-M, Chung, Tulin, Garbrecht, Lee, Cirigliano

From S-D Equations:

• SCPV

• M , H , Y …

Riotto, Carena et al, R-M et al, Konstandin et al

R-M et al

Objectives:

• Determine param dep of SCPV and all s and not just that of SCPV

• Develop general methods for any model with new CPV

• Quantify theor uncertainties

• Y >> other rates? (No)

• Majorana fermions ? (densities decouple)

• Particle-sparticle eq?

• Density indep thermal widths?

Illustrative Study: MSSM

Neutralino Mass Matrix

M1

-μ

M2

-mZ cos sin W mZ cos cos W

mZ sin sin W -mZ sin sin W 0

0

0

0

-μ

-mZ cos sin W mZ cos cos W

mZ sin sin W -mZ sin sin WMN =

Chargino Mass Matrix

M2

μMC =

cos2mW

sin2mWT << TEW : mixing

of H,W to ~ ~ ~ ~

T ~TEW : scattering

of H,W from

background field

~~

?

ϕ new

?

φ(x)

€

q , ˜ W , ˜ B , ˜ H u,d

T ~ TEW

CPV

Resonant CPV: M1,2 ~ μ



• B violation



Sakharov, 1967

?

ϕ new

?

φ(x)

Unbroken phase





90’s: Cohen, Kaplan, Nelson Joyce, Prokopec, Turok

Theoretical Issues:Strength of phase transition (Higgs sector) Bubble dynamics (expansion rate)Transport at phase boundary (non-eq QFT)EDMs: many-body physics & QCD

?

?

e -?

ψnew

?

ϕ new

?

ϕ new

Elementary particle EDMs: N>>1

Engel,Flambaum, Haxton, Henley, Khriplovich,Liu, R-M

Many-body EDMs:

EDMs: New CPV?

• SM “background” well below new CPV expectations

• New expts: 102 to 103 more sensitive

• CPV needed for BAU?

EDMs: Complementary Searches

€

€

f

€

˜ χ 0

€

˜ f

€

˜ f

€

g

€

q

€

˜ χ 0

€

˜ q

€

˜ q

Electron

Improvements of 102 to 103

Neutron

€

€

f

€

˜ χ 0

€

˜ f

€

˜ f

Neutral Atoms

€

g

€

q

€

˜ χ 0

€

˜ q

€

˜ q

Deuteron€

g

€

q

€

˜ χ 0

€

˜ q

€

˜ q

€

N

€

e−

QCD

QCD

QCD

€

π

€

+L

€

€

n€

p

€

π−

€

π−

€

π

€

+L

Classification of CP-odd operators at 1GeV

Dimension 4:

Dimension “6”:

Dimension “8”:

Effective field theory is used to provide a model-independent parametrization of CP-violating operators at 1GeV

Courtesy A. Ritz

Courtesy A. Ritz

Fundamental CP phases

Origin of the EDMs

TeV

Energy

QCD

nuclear

atomic

pion-nucleon coupling ( )

EDMs of paramagnetic atoms ( )

EDMs of diamagnetic atoms ( )

Neutron EDM ( )

Effective CPV Operators

EDMs: Theory

€

g

€

q

€

˜ χ 0

€

˜ q

€

˜ q

€

€

f

€

˜ χ 0

€

˜ f

€

˜ f

Electron

Improvements of 102 to 103

Neutron

€

€

f

€

˜ χ 0

€

˜ f

€

˜ f

Neutral Atoms

€

g

€

q

€

˜ χ 0

€

˜ q

€

˜ q

Deuteron€

g

€

q

€

˜ χ 0

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˜ q

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˜ q

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N

€

e−

QCD

QCD

QCD

€

π

€

+L

€

€

n€

p

€

π−

€

π−

€

π

€

+L

Nuclear Schiff Moment

Nuclear EDM: Screened in atoms

Neutron EDM from LQCD:

Two approaches:

• Expand in & average over topological sectors (Blum et al, Shintani et al)

• Compute E for spin up/down nucleon in background E field (Shintani et al)

mN=2.2 GeV

QCD SR (Pospelov et al)

Hadronic couplings

Pospelov et al:

PCAC + had models & QCD SR

ChPT for dn: van Kolck et al

Schiff Screening

Atomic effect from nuclear finite size: Schiff moment

EDMs & Schiff Moments I





Courtesy C.P. Liu

EDMs & Schiff Moments II

€

€

f

€

˜ χ 0

€

˜ f

€

˜ f

€

g

€

q

€

˜ χ 0

€

˜ q

€

˜ q

One-loop

EDM: q, l, n… Chromo-EDM: q, n…€

π

€

+L

Dominant in nuclei & atoms

Engel & de Jesus: Reduced isoscalar sensitivity ( QCD )

Schiff Moment in 199Hg Nuclear & hadron structure !

Liu et al: New formulation of Schiff operator

+ …

New nuclear calc’s needed !

EDMs in SUSY I

€

€

f

€

˜ χ 0

€

˜ f

€

˜ f

€

g

€

q

€

˜ χ 0

€

˜ q

€

˜ q

One-loop


π

€

+L


With a universality assumption, 2 new physical CP-odd phases

EDMS in SUSY II

• E.G. MSSM: In general, the MSSM contains many new parameters, including multiple new CP-violating phases, e.g.

Complex CP-odd phase

• EG:1-loop EDM contribution:

[Ellis, Ferrara & Nanopoulos ‘82]

M ~ sfermion massCourtesy A. Ritz

Current Limits on de:

μ ~ 10-3 at one loop

“SUSY CP Problem”

EDMs & Baryogenesis: One Loop

€

g

€

q

€

˜ χ 0

€

˜ q

€

˜ q

€

€

f

€

˜ χ 0

€

˜ f

€

˜ f ?

ϕ new

?

φ(x)

€

q , ˜ W , ˜ B , ˜ H u,d

T ~ TEW

Resonant Non-resonantCirigliano, Lee, Tulin, R-M

Future de dn dA

EDMs in SUSY III

€

€

f

€

˜ χ 0

€

˜ f

€

˜ f

€

g

€

q

€

˜ χ 0

€

˜ q

€

˜ q

One-loop


π

€

+L


Two-loop

EDM only: no chromo-EDM

€

g€

g

€

g

Weinberg: small matrix el’s

Decouple in large limit

Baryogenesis: EDMs & Colliders





Cosmology LHC EDMs

Theory

Theory

SUSY Baryogenesis: EDMs & Colliders I

baryogenesis

Present de

LEP II excl

LHC reach

QuickTime™ and aTIFF (Uncompressed) decompressor


Prospective dn

Cirigliano, Profumo, R-M

€

€

f

€

˜ χ 0

€

˜ f

€

˜ f

One loop EDMS

• ϕCPV tiny: EWB & SUSY CP prob

• suppress with heavy sfermions

• two-loop de , dn but tiny dA

SUSY Baryogenesis: EDMs & Colliders II



Transport, Spectrum, & EDMs QuickTime™ and a decompressor




Stronger limits on ϕCPV for light squarks (one-loop regime)



Chung, Garbrecht, R-M, Tulin

Light LH squarks Heavy RH squarks

Heavy LH squarks Light RH squarks

Knowledge of spectrum needed (LHC)

“Superequilibrium” ?

SUSY Baryogenesis: EDMs & Colliders III



Higgs Boson Masses



Limits on ϕCPV for depend on Higgs mass & tan



Larger YB for light Higgses



Li, Profumo, RM

Vanishing EDMs due to cancellations, even at small mA

Need knowledge of spectrum (LHC) & tan (gμ-2)

The Origin of Matter & Energy

Beyond the SM SM symmetry (broken)

Electroweak symmetry breaking: Higgs ?


?

Baryogenesis: When? CPV? SUSY? Neutrinos?

Leptogenesis: discover the ingredients: LN- & CP-violation in neutrinos

Weak scale baryogenesis: test experimentally: EDMs

Baryogenesis: Ingredients

€

Tr ˆ ρ ˆ H , t( ) ˆ B [ ] = 0€

ˆ H , ˆ C [ ] = 0

€

ˆ H , ˆ C ̂ P [ ] = 0,

€

Tr e−β ˆ H ˆ B ( ) = 0

€

ˆ H , ˆ C ̂ P ˆ T [ ] = 0

• B violation



Sakharov, 1967

Sakharov Criteria

Non-equilibrium Quantum Field Theory

Closed Time Path (CTP) Formulation

€

ˆ O (x) = ρ nn ' nn

∑ SI T ˆ O (x) SI{ } n'

€

SI = T exp i d4 x LI∫( )

Conventional, T=0 equilibrium field theory:

€

nn' →δn 0 δn ' 0

€

ˆ O (x) → 0 SI T ˆ O (x) SI{ } 0

Non-equilibrium Quantum Field Theory

Two assumptions: • Non-degenerate spectrum• Adiabatic switch-on of LI

LI

€

ˆ O (x) =n

∑ 0 SI n n T ˆ O (x) SI{ } 0

€

→ 0 SI 0 0 T ˆ O (x) SI{ } 0 =0 T ˆ O (x) SI{ } 0

0 SI 0

€

0IN

€

0OUT

iv. edms & the origin of matter

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