Electroweak Baryogenesis:
Electric dipole moments, the LHC, and the sign of
the baryon asymmetry
Sean Tulin (Caltech)
Collaborators:
Daniel Chung
Bjorn Garbrecht
Michael Ramsey-Musolf
(NPAC UW-Madison)
Summary of this talk
1. Review electroweak baryogenesis


Basic picture
Requirements for it to work
2. EWB in the MSSM


What is needed
Sign of the
baryon asymmetry
Sign of
EDMs
Universe made
of matter
Stop/sbottom
mass spectrum
Supersymmetry is super-great!
The minimal supersymmetric standard model (MSSM):
+
Coupling unification
Hierarchy problem
+
Dark matter
Stringy motivation
Electroweak Baryogenesis Picture
PDG
We want to explain
95% C.L.
Dunkley et al
[WMAP5]
based on dynamics during the electroweak phase transition.
Sakharov conditions:
1. Baryon number violation
Electroweak sphalerons
2. C- and CP-violation
3. Departure from
thermal equilibrium
complex phases
1st order phase
transition
Electroweak Baryogenesis Picture
First order electroweak phase transition during the early universe
V(
)
Higgs potential
T > Tc
f = (f1, f2, ...)
T = Tc
T =0
High T: EW symmetry
restored from thermal
corrections to Higgs potential
Low T: EW symmetry broken
At critical temp Tc, degenerate minima. Just below Tc, quantum
tunneling from
to
bubble nucleation!
Electroweak Baryogenesis Picture
Cohen, Kaplan, Nelson, 1992-1994;
Huet, Nelson, 1996
Three Steps:
moving
bubble
wall
CP
Quark number density
diffusion
1. Nucleation and expansion of
bubbles of broken EW symmetry
2. CP-violating interactions at
bubble wall induces charge
density, diffusing outside bubble
3. Sphalerons convert LH
asymmetry into B asymmetry
electroweak
sphaleron
Electroweak Baryogenesis Picture
Cohen, Kaplan, Nelson, 1992-1994;
Huet, Nelson, 1996
Three Steps:
moving
bubble
wall
1. Nucleation and expansion of
bubbles of broken EW symmetry
2. CP-violating interactions at
bubble wall induces charge
density, diffusing outside bubble
4. Baryon asymmetry
3. Sphalerons
captured by expanding
bubble convert LH
CP
Quark number density
diffusion
asymmetry into B asymmetry
electroweak
sphaleron
Requirements for electroweak
baryogenesis to work
Given a model of electroweak symmetry breaking (e.g. the
standard model), what is required?
Two requirements:
1. Sufficient CP-violation to explain observed nB
2. A strong first-order electroweak phase
transition
Neither satisfied in the SM
May be satisfied in the MSSM, or in extensions of MSSM (e.g. NMSSM)
RH stop < 125 GeV, LH stop > 6.5 TeV (to avoid color-breaking
phase transition) in MSSM Carena, Nardini, Quiros, Wagner, 2008
electroweak baryogenesis requirements
Requirement #1: sufficient CP-violation
Need to have “sufficient” CP-violation to produce the
observed baryon asymmetry
1. Solve Boltzmann equations for particles species in the
plasma, with background of expanding bubble of broken
EW symmetry
diffusion
ni = number density for
particles — antiparticles
collisions
CP-violating
source
stolen from Bjorn Garbrecht
electroweak baryogenesis requirements
Requirement #1: sufficient CP-violation
Need to have “sufficient” CP-violation to produce the
observed baryon asymmetry
1. Solve Boltzmann equations for particles species in the
plasma, with background of expanding bubble of broken
EW symmetry
ni = number density for
particles — antiparticles
diffusion
collisions
CP-violating
source
2. Take left-handed fermion charge nL
and compute baryon asymmetry
weak
sphaleron
collision
factor
Baryon asymmetry
collision
factor
CP-violating
source
1. Magnitude of the baryon asymmetry depends on:
KC: depends on large fraction of MSSM spectrum
CP-violating source: depends on only a few parameters, but
still much theoretical uncertainty
2. Sign of baryon asymmetry
Depends on CP-violating phase and relatively few other
parameters
Collision factor
What interactions in the plasma are in chemical equilibrium?
(i.e. fast compared to diffusion time scale)
Previous lore:
Cohen, Kaplan, Nelson, 1992-1994;
Huet, Nelson, 1996
1. Gauge/gaugino interactions
2. Top yukawa interactions
3. Strong sphalerons
tL
~
tR
diffusion
tL
~
tR
nL
left-handed
fermion density
Collision factor
What interactions in the plasma are in chemical equilibrium?
(i.e. fast compared to diffusion time scale)
Previous lore:
Cohen, Kaplan, Nelson, 1992-1994;
Huet, Nelson, 1996
1. Gauge/gaugino interactions
2. Top yukawa interactions
Cirigliano, Lee, Ramsey-Musolf, S.T. (2006)
3. Strong sphalerons
Next, use ni = ki mi
Then can express nL = KC n~
H where KC given in terms of ki’s
Collision factor
What interactions in the plasma are in chemical equilibrium?
(i.e. fast compared to diffusion time scale)
Previous lore:
Cohen, Kaplan, Nelson, 1992-1994;
Huet, Nelson, 1996
1. Gauge/gaugino interactions
2. Top yukawa interactions
Cirigliano, Lee, Ramsey-Musolf, S.T. (2006)
3. Strong sphalerons
New Results:
Chung, Garbrecht, Ramsey-Musolf, S.T. (2008)
4. Bottom yukawa interactions
5. Tau yukawa interactions (lepton-driven EWB)
Collision factor
When are bottom Yukawa interactions important?
Time scale for bottom
Yukawa interactions vs.
diffusion time scale
only
Chung, Garbrecht, Ramsey-Musolf, S.T. (in prep)
Collision factor
With bottom Yukawa interactions, KC simplifies greatly:
nL = KC nH~
Conversion factor for Higgsinos into LH quarks (3rd gen)
ki = ki(mi/T) largest for small mi
KC = 0 for
KC < 0 for
KC > 0 for
Sign of KC (and, in part, nB)
determined by whether RH
stop or sbottom is lighter
Chung, Garbrecht, Ramsey-Musolf, S.T. (2008)
Also, KC -> 0 for
Collision factor
With bottom Yukawa interactions, KC simplifies greatly:
nL = KC nH~
Physical reason for this effect
Chung, Garbrecht, Ramsey-Musolf, S.T. (2008)
Which effect wins depends on which degrees of freedom are
lighter
Stop at the LHC
*
Focus on case where RH
stop < 120 GeV (i.e. MSSM)
p
p
Good: Light stop means large
production cross section
Decay products: (assume m
1.
stable (on collider time scales)
CHAMP searches imply
2.
< 120 GeV)
only if
CDF 2007
115 GeV
Stop at the LHC
*
Light RH stop at the LHC
p
p
Good: Light stop means large
production cross section
Decay products: (assume m
< 120 GeV)
tends to dominate for
3.
4.
Hikasa, Kobayashi
(1987)
Hiller, Nir (2008)
Stop at the LHC
*
Light RH stop at the LHC
p
p
Good: Light stop means large
production cross section
Missing
energy
Bad: Difficult to
observe at LHC!
c
Low energy QCD
(~50 GeV)
g/g
Better: radiative decay
(signal: missing energy
+ high pT jet or photon)
Carena, Freitas, Wagner (2008)
Stop at the LHC
Light RH stop at the LHC
Carena, Freitas, Wagner (2008)
Radiative stop decay:
“LSP”
Signal:
high PT jet + ET
+ soft charm jets (tough)
Light stop window for
strong 1st order
phase transition
dominant
Baryon asymmetry
collision
factor
CP-violating
source
CP-violating source:
Two-flavor oscillation problem (a la neutrino oscillations) but with a
spacetime dependent Hamiltonian mass matrix
relevant phases
What parameters govern the sign of the CP-violating source?
CP-violating source
Various results:
plotted vs. m,
for M2 = 200 GeV
Lee, Cirigliano, Ramsey-Musolf
(2004)
Carena, Quiros, Seco, Wagner
(2000)
and
Carena, Moreno, Quiros, Seco, Wagner
(2002)
Konstandin, Prokopec, Schmidt, Seco
(2005)
CP-violating source
How does an expanding bubble of broken EW symmetry produce a
CP-asymmetry of particles vs antiparticles?
Full treatment requires non-equilibrium, finite temp field theory
Quick & dirty explanation: (using elementary QM)
Two-flavor oscillation problem (a la neutrino oscillations) but
with a spacetime dependent Hamiltonian H(t)
particles
V(t)
V(t)*
anti-particles
V(t) rotates flavor states into mass eigenstates
(Consider simplified case where Hamiltonian only depends on t)
CP-violating source
Evolution of states:
Schrödinger Eqn:
(flavor basis)
flavor states
a, b = L, R
Then rotate to mass basis
Schrödinger Eqn is now
where
Similarly for antiparticle states
CP-violating source
Evolution of states:
Amplitude for mass state |j> to be in flavor state |a> after time t
Initial condition:
Begin with plasma in equilibrium: ensemble of mass basis
states
with weight
CP-violating source:
CP-violating source
CP-violating source:
where
Conclusions:
1. Need two nearly degenerate states — otherwise small q
and source washed out by oscillations
2. Need spacetime-dependent phase in mixing matrix
3. States not too heavy compared to temp T — otherwise
Boltzmann suppressed
CP-violating source
Example:
CP-violating source from Higgsino/Wino oscillations.
Flavor states
CP-violating source
Various results:
plotted vs. m,
for M2 = 200 GeV
Lee, Cirigliano, Ramsey-Musolf
(2004)
Carena, Quiros, Seco, Wagner
(2000)
and
Carena, Moreno, Quiros, Seco, Wagner
(2002)
Konstandin, Prokopec, Schmidt, Seco
(2005)
Implications for EDMs
Suppose EDM measured. What are implications for EWB?
1. Assume same phase for both baryon asymmetry and EDM
2. Assume one-loop EDMs suppressed (heavy 1st/2nd gen
sfermions)
Two-loop EDMs are irreducible:
Two possible CP-violating phases
that could drive baryogenesis in
MSSM also give rise to EDMs
Recently computed in
full by Li et al (2008)
CP-violating phase
Sign of two-loop EDMs mostly correlated wrt CP-violating phases!
positive contributions
negative contributions
Li, Profumo, Ramsey-Musolf (2008)
Current EDM constraints
electron EDM
neutron EDM
Excluded
Li et al (2008)
Future EDM searches
Very exciting!
Future EDM
measurements
will improve
sensitivities by
orders of
magnitude.
Future EDM constraints
electron EDM
neutron EDM
Excluded
de < 3x10-30 e cm
dn < 1x10-28 e cm
Li et al (2008)
Baryogenesis
curves made
with most
optimistic
estimates
Conclusions
Sign of baryon asymmetry may be the easiest consistency check for
electroweak baryogenesis in the MSSM
Under simplest assumptions (EDM and EWB determined by same
phase), sign of baryon asymmetry determined by:
• Collision factor KC: depends on whether RH stop or sbottom is
heavier
• Sin of CP-violating phase
Generalization beyond the MSSM?
same collision factor
unknown if EDMs correlate with CP-violating phase
CP-violating source
20
15
10
n~
H
n~
H
5
-25
-20
-15
-10
-5
-5
Cirigliano, Lee, Ramsey-Musolf, S.T. (2006)
nB/s = 30 x (nB/s)WMAP x sin fM2m
Discrepency in treatment of diffusion
Konstandin et al (2005)
nB/s = 3 x (nB/s)WMAP x sin fM2m