Download - 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:
Cosmic Energy Budget
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
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rE
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rd = d
r S
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νEDM = −d
r S ⋅
r E
h
T-odd , CP-odd by CPT theorem
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rE
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rd = d
r S
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νEDM = −d (−
r S ) ⋅
r E
h
T-odd , CP-odd by CPT theorem
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νEDM = −d
r S ⋅
r E
h
T-odd , CP-odd by CPT theorem
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rE
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rd = d
r S
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rB
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νEDM = −d
r S ⋅(−
r E )
h
T-odd , CP-odd by CPT theorem
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rE
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rd = d
r S
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rB
Matter & Cosmic History
Big Bang Nucleosynthesis:
Light element abundances depend on YB
p, n, e- become light elements & later stars, galaxies…
np d +
BBN and YB
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Matter & Cosmic History
Cosmic Microwave Bcknd:
Shape of anisotropies depends on YB
Last scattering: imperfect black body
CMB and YB
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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
• C & CP violation
• Nonequilibrium dynamics
Sakharov, 1967
Anomalous Processes
Different vacua: (B+L)= NCS€
Aλ
Kuzmin, Rubakov, Shaposhnikov McLerran,…
Sphaleron Transitions€
W
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W
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JμB
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qL
EW Baryogenesis: Standard Model
Weak Scale Baryogenesis
• B violation
• C & CP violation
• Nonequilibrium dynamics
Sakharov, 1967€
mt4
MW4
mb4
MW4
mc2
MW2
ms2
MW2
≈ 3 ×10−13
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J = s12 s13 s23c12c132 c23sinδ13
= (2.88 ± 0.33) ×10−5
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φ
?
φ
?
F
?
F
Increasing mh
1st order 2nd order
• CP-violation too weak• EWPT too weak
Shaposhnikov
Baryogenesis: New Electroweak Physics
Weak Scale Baryogenesis
• B violation
• C & CP violation
• Nonequilibrium dynamics
Sakharov, 1967
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ϕ new
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φ(x)
Unbroken phase
Broken phaseCP Violation
Topological transitions
1st order phase transition
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e -?
ψnew
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ϕ new
?
ϕ new
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ϕ
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g€
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e+
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e−
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Z 0
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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?
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LEPEWWGLEP Exclusion Non-SM Higgs(es) ?
EW Precision Data: 95% CL (our fit-GAPP)
Electroweak Phase Transition & Higgs
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φ
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φ
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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
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˜ t
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+LStop loops in VEff
Light RH stop w/ special
Electroweak Phase Transition & Higgs
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φ
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φ
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F
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F
Increasing mH
1st order 2nd orderLEP EWWG
mh>114.4 GeV
or ~ 90 GeV (SUSY)
Computed ESM : mH < 40 GeV
Need
So that sphaleron is not too fastNon-doublet Higgs (w / wo SUSY)
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S
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ϕ
Mixing€
S
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ϕ
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S
Decay
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e+
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e−
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Z 0
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Z 0
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ϕ
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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 ?
Electroweak Phase Transition & Higgs
?
φ
?
φ
?
F
?
F
Increasing mH
1st order 2nd orderLEP EWWG
mh>114.4 GeV
or ~ 90 GeV (SUSY)
Computed ESM : mH < 40 GeV
Need
So that sphaleron is not too fastNon-doublet Higgs (w / wo SUSY)
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S
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ϕ
Mixing€
S
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ϕ
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S
Decay
B.R. reduction
Reduced SM Higgs branching ratios
Unusual final states
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ϕ
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b
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b
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μ+
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μ−
mH
O’Connell, R-M, Wise
Baryogenesis: New Electroweak Physics
Weak Scale Baryogenesis
• B violation
• C & CP violation
• Nonequilibrium dynamics
Sakharov, 1967
?
ϕ new
?
φ(x)
Unbroken phase
Broken phaseCP Violation
Topological transitions
1st order phase transition
• Is it viable?• Can experiment constrain it?• How reliably can we compute it?
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
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e -?
ψnew
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ϕ new
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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
Topological transitions
Broken phase
1st order phase transition ?
φ(x)
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∂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”
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W
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W
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JμB
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qL
Systematic Baryogenesis
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∂ni
∂t− D∇ 2ni = S n j ,T,ϕ , ˜ M ( )
Quantum Transport Equation
Unbroken phase
Topological transitions
Broken phase
1st order phase transition ?
φ(x)
= +
+
+ …
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˜ G
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˜ G 0
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˜ G 0
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˜ G 0
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˜ 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
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LI
Assumptions: 1. Evolution is adiabatic2. Spectrum is non-degenerate3. Density is zero
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ϕ new
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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
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˜ 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)
⎡
⎣ ⎢
⎤
⎦ ⎥
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ˆ O (x) = ρ nn ' nn
∑ SI [ϕ ]T ˆ O (x) SI [ϕ ]{ } n'+-
Non-equilibrium T>0 Evolution
= + + …
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˜ G
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˜ G 0+
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˜ G 0
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˜ G 0
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˜ Σ
Scale Hierarchy
T > 0: Degeneracies
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q
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q
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gM(T)
P(T)
vW > 0: Non-adiabaticity
vW
Time Scales
Plasma time:
P ~ 1/ P
Decoherence time:
d ~ 1/vW k)
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˜ t L
e.g., particle in an expanding box
Quantum Decoherence
L L L
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kn =nπ
L €
ψn0 ψ n
2
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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
= + + …
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˜ G
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˜ G 0+
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˜ G 0
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˜ G 0
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˜ 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
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∂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)
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q , ˜ W , ˜ B , ˜ H u,d
T ~ TEW
CPV
Resonant CPV: M1,2 ~ μ
Baryogenesis: New Electroweak Physics
Weak Scale Baryogenesis
• B violation
• C & CP violation
• Nonequilibrium dynamics
Sakharov, 1967
?
ϕ new
?
φ(x)
Unbroken phase
Broken phaseCP Violation
Topological transitions
1st order phase transition
• Is it viable?• Can experiment constrain it?• How reliably can we compute it?
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
?
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e -?
ψnew
?
ϕ new
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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
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Electron
Improvements of 102 to 103
Neutron
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˜ χ 0
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Neutral Atoms
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QCD
QCD
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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
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Electron
Improvements of 102 to 103
Neutron
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˜ χ 0
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Neutral Atoms
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QCD
QCD
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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
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Courtesy C.P. Liu
EDMs & Schiff Moments II
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One-loop
EDM: q, l, n… Chromo-EDM: q, n…€
π
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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
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One-loop
EDM: q, l, n… Chromo-EDM: q, n…€
π
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+L
Dominant in nuclei & atoms
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
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φ(x)
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T ~ TEW
Resonant Non-resonantCirigliano, Lee, Tulin, R-M
Future de dn dA
EDMs in SUSY III
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One-loop
EDM: q, l, n… Chromo-EDM: q, n…€
π
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+L
Dominant in nuclei & atoms
Two-loop
EDM only: no chromo-EDM
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Weinberg: small matrix el’s
Decouple in large limit
Baryogenesis: EDMs & Colliders
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Cosmology LHC EDMs
Theory
Theory
SUSY Baryogenesis: EDMs & Colliders I
baryogenesis
Present de
LEP II excl
LHC reach
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Prospective dn
Cirigliano, Profumo, R-M
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˜ χ 0
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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
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Transport, Spectrum, & EDMs QuickTime™ and a decompressor
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Stronger limits on ϕCPV for light squarks (one-loop regime)
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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
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Higgs Boson Masses
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Limits on ϕCPV for depend on Higgs mass & tan
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Larger YB for light Higgses
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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 ?
Cosmic Energy Budget
?
Baryogenesis: When? CPV? SUSY? Neutrinos?
Leptogenesis: discover the ingredients: LN- & CP-violation in neutrinos
Weak scale baryogenesis: test experimentally: EDMs
Baryogenesis: Ingredients
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Tr ˆ ρ ˆ H , t( ) ˆ B [ ] = 0€
ˆ H , ˆ C [ ] = 0
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ˆ H , ˆ C ̂ P [ ] = 0,
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Tr e−β ˆ H ˆ B ( ) = 0
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ˆ H , ˆ C ̂ P ˆ T [ ] = 0
• B violation
• C & CP violation
• Nonequilibrium dynamics
Sakharov, 1967
Sakharov Criteria
Non-equilibrium Quantum Field Theory
Closed Time Path (CTP) Formulation
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ˆ O (x) = ρ nn ' nn
∑ SI T ˆ O (x) SI{ } n'
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SI = T exp i d4 x LI∫( )
Conventional, T=0 equilibrium field theory:
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nn' →δn 0 δn ' 0
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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
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ˆ O (x) =n
∑ 0 SI n n T ˆ O (x) SI{ } 0
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→ 0 SI 0 0 T ˆ O (x) SI{ } 0 =0 T ˆ O (x) SI{ } 0
0 SI 0
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