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IV. EDMs & the Origin of Matter
•
The cosmic baryon asymmetry
•
Electroweak baryogenesis
•
Electric dipole moments
Cosmic Energy Budget
Dark Matter
Baryons
Stars, planets, humans…
Dark Energy
Baryon asymmetry of the universe:
Matter & Cosmic History
How did we get something
from nothing?
After inflation:
equal amounts
of matter and
antimatter
e+ + eq+ q


Quarks &
gluons become
protons,
neutrons….
qqq
p, n…
p, n, ebecome light
elements &
later stars,
galaxies…
np
d+

E B
d  dS

dddS(S
S (E
E)E E
)
EDM






EDM
EDM
EDM
hhh
Cosmic Energy Budget
Dark Matter
Baryons
T-odd , CP-odd
by CPT theorem
Leptogenesis:
discover
Stars, planets, humans…
the ingredients: LN- & CPviolation in neutrinos
Weak scale baryogenesis:
test
experimentally:
EDMs
Dark
Energy
& Higgs Boson Searches
Baryon asymmetry of the universe:
Explaining non-zero rB requires CP-violation
and a scalar sector beyond those of the
Standard Model (assuming inflation set rB=0)
Matter & Cosmic History
Big Bang Nucleosynthesis:
Light element abundances
depend on YB
p, n, ebecome light
elements &
later stars,
galaxies…
np
d+
BBN and YB
QuickTime™ and a
decompressor
are needed to see this picture.
QuickTime™ and a
decompressor
are needed to see this picture.
Matter & Cosmic History
Cosmic Microwave Bcknd:
Shape of anisotropies
depends on YB
Last 
scattering:
imperfect
black body
CMB and YB
QuickTime™ and a
decompressor
are needed to see this picture.
Baryogenesis: Ingredients
Sakharov Criteria
Anomalous B-violating processes
• B violation
• C & CP violation
• Nonequilibrium
dynamics
Sakharov, 1967
Prevent washout by inverse processes
EW Baryogenesis: Standard Model
Weak Scale Baryogenesis
Anomalous Processes
• B violation
• C & CP violation
J B
• Nonequilibrium
dynamics
A
qL

Sakharov, 1967
W

W
Different vacua: D(B+L)= DNCS

Kuzmin, Rubakov, Shaposhnikov
McLerran,…


Sphaleron Transitions
EW Baryogenesis: Standard Model
Shaposhnikov
2
J  s12 s13 s23 c12 c13
c 23 sin 13
 (2.88  0.33) 105
Weak Scale Baryogenesis
mt4 mb4 mc2 ms2
13

3
10
MW4 MW4 MW2 MW2
• B violation
• C & CP violation
• Nonequilibrium
dynamics


F
F
1st order
2nd order
Sakharov, 1967



• CP-violation too weak
• EWPT too weak
Increasing mh



Quantum Transport
CPV
Baryogenesis: New Electroweak Physics
Chem Eq
Systematic baryogenesis: SD
equations + power counting
R-M et al
Unbroken phase
Weak Scale Baryogenesis
Veff (,T): Topological
Requirements
on Higgs
• B violation
transitions
• C & CP violation
• Nonequilibrium
dynamics
(x)
new
sector extensions & expt’l probes
Broken phase
1st order phase transition


Sakharov, 1967
Theoretical
Issues:
Strength of phase transition (Higgs

new
sector)• •Bubble
dynamics
(numerical)
viable?
gIsIsititviable?

e

Transport
at
phase
boundary
(non-eq
• •Can
Canexperiment
experiment
constrain
constrain
it?
it? QFT)

e
g
 
EDMs:
&compute
QCD

 physics
• many-body
•How
Howreliably
reliably
can
canwe
we
computeit?
it?
e

CP Violation
new



0
Z
new
Z0




EWSB: Higgs?
EW Precision Data:
95% CL (our fit-GAPP)
• SM “background”
well below new
CPV expectations
• New expts: 102 to
103 more sensitive
• CPV needed for
BAU?
QuickTime™ and a
decompressor
are needed to see this picture.
LEP Exclusion
Non-SM Higgs(es) ?
LEPEWWG
Electroweak Phase Transition & Higgs
F
F
1st order
2nd order

Need


Increasing mh

Stop loops
in VEff
LEP EWWG

t˜




EMSSM ~ 10
 ESM : m
H < 120 GeV

Light RH stop w/ special
So that Gsphaleron is not too fast
mh>114.4 GeV
ComputedorESM
: mGeV
~ 90
H < 40 GeV
(SUSY)

S


Electroweak Phase Transition & Higgs
e
e




Z0

F
sin2q
Z0


F
1st order
2nd order

LEP EWWG
Need


Can an augmented Higgs sector
Increasing mH
• Generate 
a strong 1st order EWPT
?

•Non-doublet
Allow for a heavier
SM-like
Higgs
Higgs
(w
/
wo
than in the MSSM ? SUSY)
S
• Alleviate
the tension
between
directS


Higgs search bounds and the
S
EWPO ?

• Be discovered
at the LHCMixing
?
Decay



Can its necessary
characteristic probed at

the LHC and a future e+e- collider ?
So that Gsphaleron is not too fast
mh>114.4 GeV
ComputedorESM
: mGeV
~ 90
H < 40 GeV
(SUSY)
Reduced SM Higgs branching ratios
Electroweak Phase Transition & Higgs
B.R.
reduction
F
F
1st order
2nd order
LEP EWWG
mH
Unusual final states


S


b

S






Increasing
m
H


Need
b

O’Connell,
 R-M, Wise
 (w / wo SUSY)
Non-doublet Higgs
S


S
S


Decay


So that Gsphaleron is not too fast
mh>114.4 GeV
Mixing

ComputedorESM
: mGeV
~ 90
H < 40 GeV
(SUSY)
Baryogenesis: New Electroweak Physics
90’s:
Weak Scale Baryogenesis
• B violation
Cohen, Kaplan, Nelson
Joyce, Prokopec, Turok
Unbroken phase
Topological transitions
• C & CP violation
• Nonequilibrium
dynamics
(x)
new
Broken phase
1st order phase transition


CP Violation
Sakharov, 1967
Theoretical
Issues:
new
Strength of phase transition (Higgs
“Gentle” departure
from
equilibrium&

sector) •Bubble
dynamics (expansion rate)
Is it viable?
new
scale hierarchy
Transport
at
phase
boundary
(non-eq
QFT)
• Can experiment constrain it?
Lee,
Cirigliano,
new

R-M,Tulin
EDMs: many-body
physics
& QCD

• How reliably
can we
compute it?
e


Systematic Baryogenesis I
Goal: Derive dependence of YB on parameters
Lnew systematically (controlled approximations)
Parameters in Lnew
CPV phases
Bubble & PT
dynamics
Departure from equilibrium
• Earliest work: QM scattering & stat mech
• New developments: non-equilibrium QFT
Systematic Baryogenesis
Unbroken phase
(x)
Topological transitions
“snow”
Broken phase
1st order phase transition
Cohen, Kaplan,
Nelson
Joyce, Prokopec,
Turok
nL produced in wall
& diffuses in front
rB
 D 2 rB  GW S FW S (x)nL (x)  RrB 
t
FWS (x)->0 deep inside bubble
J B
qL

W

W
Systematic Baryogenesis
Riotto
Carena et al
Lee, Cirigliano,
Tulin, R-M
Unbroken phase
(x)
Topological transitions
Compute from first
principles given Lnew
Broken phase

1st order phase transition
ni
˜
 D 2 ni  Sn j ,T,, M
t
Quantum Transport Equation
G˜ 0


G˜


=
˜

G˜ 0

G˜ 0
+
+
+…
Schwinger-Dyson Equations
Quantum Transport & Baryogenesis
Electroweak Baryogenesis
new


(x)
1.
Evolution is non-adiabatic:
vwall > 0 -> decoherence
2.
Spectrum is degenerate:
T > 0 -> Quasiparticles mix
Density is non-zero
3.
ParticlePropagation: Beyond familiar (Peskin) QFT
0
LI
IN
Assumptions:
1.
2.
3.
Evolution is adiabatic

Spectrum is non-degenerate
Density is zero
0
OUT
Non-equilibrium T>0 Evolution
Generalized Green F’ns
0
• Spectral degeneracies
• Non-adiabaticity
0
IN
LI

˜

˜0 O
Oˆ (x) G˜  rnn'G˜ 0n SI [ G]T
ˆ (x)G˜ 0SI [ ]n'
=
n



+ -



G˜ (x, y)  P a (x) *b (y)  ab
+
+
G t (x, y) G (x, y)
  

t
G (x, y) G (x, y)
+…
OUT
Scale Hierarchy
T > 0: Degeneracies
g
q
q
Time Scales
M(T)
GP(T)
P ~ 1/GP


Plasma time:
vW > 0: Non-adiabaticity

t˜L
vW
Decoherence time:
d ~ 1/vW k)
e.g., particle in an
expanding box
Quantum Decoherence
L DL
L
 (x)  An sin kn x
0
n

n
kn 
L
 n
0
n
k = kEFF(,Lw)
2
n=1
n=2

n=3
L  DL
L
Quantum Transport & Baryogenesis
Electroweak Baryogenesis
new
(x)
1.
Competing
Evolution
Dynamics
is non-adiabatic:
vwall > 0 -> decoherence
CPV
2. Spectrum is degenerate:
T > 0 -> Quasiparticles mix
Ch
eq
3. Density is non-zero
Cirigliano, Lee,Tulin, R-M


Scale Hierarchy:
Fast, but not too fast
Systematically derive
transport eq’s from Lnew
ed = vw (k / w<< 1
Hot, but not too hot
ep = Gp / w<< 1
Dense, but not too dense
e = / T << 1
Work to lowest, nontrivial order in e’s
Error is O (e) ~ 0.1
Cirigliano, Lee, R-M
Quantum Transport Equations

˜

0X 0
0
3

˜ 0
˜
˜
˜
G
G
G
G
Approximations
j (X)  d z dz  (X,z) G (z,X)  G (X,z)  (z,X)  + …
• Neglect


+0 
O(e3)
terms
=

X 





• Others under scrutiny
R-M, Chung, Tulin,
Garbrecht, Lee,
Cirigliano
• GY >> other rates? (No)
• Majorana fermions ?
(densities decouple)
• Particle-sparticle eq?
• Density indep thermal
widths?
Currents
+

From S-D Equations:
Expand
in ed,p,
• SCPV
Chiral
Producing
Relaxation
Riotto,
CarenanLet=al,0R-M et al,
Konstandin et al
• SCPV
• G M , GH , GY …
R-M et al
Strong
sphalerons
Objectives:
• GM , GH , GY , GSS
• Determine param dep of SCPV
and all Gs and not just that of SCPV
• Develop general
methods for any
CP violating
model with new CPV
Links CP violation in Higgs
sources
and baryon sectors • Quantify theor uncertainties
Illustrative Study: MSSM
Chargino Mass Matrix
CPV
MC =
new
background field
m W 2 cos b
M2
mW 2 sin b


Neutralino Mass Matrix

T << TEW : mixing
~ ~
~0
of H,W to c~,c
˜ u,d
q , W˜ , B˜ , H
M1
MN =
T ~TEWT: ~
scattering
TEW
~) ~
of(xH,W
from
0
Resonant CPV:
M1,2 ~ 
0
-mZ cos bsin qW
mZ cos bcos qW
M2
mZ sin bsin qW
-mZ sin bsin qW
-mZ cos bsin qW
mZ cos bcos qW
0
-
mZ sin bsin qW
-mZ sin bsin qW
-
0

Baryogenesis: New Electroweak Physics
90’s:
Weak Scale Baryogenesis
• B violation
Cohen, Kaplan, Nelson
Joyce, Prokopec, Turok
Unbroken phase
Topological transitions
• C & CP violation
• Nonequilibrium
dynamics
Sakharov, 1967
(x)
new
Broken phase
1st order phase transition


CP Violation
Elementary particle
EDMs: N>>1
Theoretical Issues:
new
Strength of phase transition (Higgs
Many-body EDMs:
Engel,Flambaum,
sector) •Bubble
dynamics (expansion rate)

Is it viable?
new
Haxton, Henley,
Transport
at phase
boundary
(non-eq
• Can
experiment
constrain
it? QFT)
new R-M
Khriplovich,Liu,
 
EDMs: many-body
physics
& QCD
• How reliably
can we
compute it?
e


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˜
Electron

˜0
c
f˜



Improvements
of 102 to 103
f


f˜

˜0
c
Neutron


˜0
c
f˜



g
p

q˜

f


q˜
q
QCD





˜
c
0
N
e



g
q

˜
c



g
q˜
q





q˜
0


QCD


Deuteron

q˜


n

q˜
Neutral
Atoms



QCD


Classification of CP-odd operators at 1GeV
Effective field theory is used to provide a model-independent
parametrization of CP-violating operators at 1GeV
Dimension 4:
Dimension “6”:
Dimension “8”:
Courtesy A. Ritz
Origin of the EDMs
Energy
TeV
Fundamental
CP phases
Effective CPV
Operators
QCD
pion-nucleon
coupling (
)
nuclear
atomic
EDMs of
paramagnetic
atoms (
)
Neutron
EDM ( )
EDMs of
diamagnetic
atoms (
)
Courtesy A. Ritz
Schiff
Screening
Hadronic
couplings
EDMs: Theory
Nuclear Schiff Moment
f˜
Electron
Improvements
of 102 to 103

˜0
c
Pospelov et al:
PCAC + had
models & QCD SR
Atomic effect from
nuclear finite size:
Schiff moment
Nuclear
EDM:for
Screened
in
atoms
ChPT
dn: van
Kolck
et al
f˜

f




f˜

˜0
c
Neutron



g

q
QCD
mN=2.2 GeV
q˜
˜
c
0
N
e
• Expand in q& average over
 et al,
topological sectors (Blum
Shintani et al)
Deuteron
• Compute
DE for spin up/down
nucleon in background E field
(Shintani et al)




g
q

˜
c
g
q˜

QCD
al)
q SR (Pospelov et QCD







q˜
0


QCD




n
q˜







p
q˜

f
  
Neutron EDM from LQCD:
Neutral
Atoms
Two
approaches:
˜0
c
f˜


q˜


EDMs & Schiff Moments I
QuickTime™ and a
decompressor
are needed to see this picture.
QuickTime™ and a
decompressor
are needed to see this picture.
Courtesy C.P. Liu
EDMs & Schiff Moments II
One-loop
f˜
˜0
c


q˜

f˜


f
 q, l, n…
EDM:

˜0
c

q˜
q
 
Chromo-EDM:
q, n…


Schiff Moment in 199Hg


g
Dominant in
 & atoms
nuclei
Nuclear
New
nuclear
& hadron
calc’sstructure
needed !
Liu et al: New formulation of Schiff operator
+…
Engel & de Jesus: Reduced isoscalar sensitivity ( qQCD )
EDMs in SUSY I
One-loop
f˜
˜0
c


q˜

f˜


f
 q, l, n…
EDM:

˜0
c


g
q˜
q
 
Chromo-EDM:
q, n…



Dominant in
 & atoms
nuclei
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
Current Limits on de:
With a universality assumption, 2 new
-3 at one loop
q ~ 10phases
physical CP-odd
• EG:1-loop EDM contribution:
“SUSY CP Problem”
[Ellis, Ferrara &
Nanopoulos ‘82]
M ~ sfermion mass
Courtesy A. Ritz
EDMs & Baryogenesis: One Loop
f˜
q˜
˜
c
0

g
q˜


˜
c
0




new

f˜

q
(x)


f
˜,B
˜,H
˜ u,d
q,W



Future
de dn dA
Cirigliano, Lee,
Tulin, R-M
Resonant
Non-resonant
T ~ TEW
EDMs in SUSY III
Decouple in large
One-loop
f˜
˜0
c


q˜

˜0
c
f˜

f
 q, l, n…
EDM:


limit

q˜
q
 
Chromo-EDM:
q, n…


Dominant in
 & atoms
nuclei
Two-loop
g

EDM only: no chromo-EDM


g
g

g
Weinberg: small matrix el’s

Baryogenesis: EDMs & Colliders
Theory
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Cosmology
LHC
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Theory
EDMs
SUSY Baryogenesis: EDMs & Colliders I
One loop EDMS
baryogenesis
f˜
˜0
c


LHC reach
LEP II excl
Present de

f˜
f

• CPV
tiny: EWB

& SUSY CP prob
• suppress with
heavyProspective
sfermions d
n
• two-loop de , dn
but tiny dA
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Cirigliano, Profumo, R-M
SUSY Baryogenesis: EDMs & Colliders II
Transport, Spectrum, & EDMs
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“Superequilibrium” ?
Knowledge of spectrum
needed (LHC)
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Light LH squarks
Heavy RH squarks
Heavy LH squarks
Light RH squarks
Chung, Garbrecht,
R-M, Tulin
Stronger limits on CPV for light
squarks (one-loop regime)
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SUSY Baryogenesis: EDMs & Colliders III
Larger YB for light
Higgses
Higgs Boson Masses
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Li, Profumo, RM
Vanishing EDMs due
to cancellations, even
at small mA
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Need
of spectrum
Limitsknowledge
on CPV for depend
on
(LHC)
tanb&(g
Higgs &
mass
tan
b
-2)
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The Origin of Matter & Energy
Electroweak symmetry
breaking: Higgs ?
Leptogenesis: discover
the ingredients: LN- & CPviolation in neutrinos
Baryogenesis: When?
CPV? SUSY? Neutrinos?
?
Weak scale
baryogenesis: test
experimentally: EDMs
Beyond the SM
SM symmetry (broken)
Cosmic Energy Budget
Baryogenesis: Ingredients
Hˆ , Cˆ  0 , Hˆ , Cˆ Pˆ  0
Sakharov Criteria
  
ˆ Hˆ ,t Bˆ  0
Tr r
• B violation
• C & CP violation


• Nonequilibrium
dynamics
Sakharov, 1967


Hˆ , Cˆ Pˆ Tˆ  0


Tr e

 b Hˆ

Bˆ  0
Non-equilibrium Quantum Field Theory
Closed Time Path (CTP) Formulation
Oˆ (x)   rnn' n SI TOˆ (x) SI n'
n

SI  T exp i  d 4 x LI


Conventional, T=0 equilibrium field theory:

rnn'  n0 n'0
Oˆ (x)  0 SI TOˆ (x) SI 0

Non-equilibrium Quantum Field Theory
Two assumptions:
0
• Non-degenerate spectrum
• Adiabatic switch-on of LI
0
IN
LI
Oˆ (x)  

0 SI n n TOˆ (x) SI 0
n

ˆ (x) S 0 
 0 SI 0 0 TO
I
ˆ (x) S 0
0 TO
I
0 SI 0
OUT