electroweak baryogenesis: electric dipole moments, the lhc, and the sign of the baryon asymmetry...
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Electroweak Baryogenesis:Electroweak Baryogenesis:Electric dipole moments, the LHC, and the sign of Electric dipole moments, the LHC, and the sign of
the baryon asymmetrythe baryon asymmetry
Sean Tulin (Caltech)Sean Tulin (Caltech)Collaborators:Collaborators:
Daniel ChungDaniel Chung
Bjorn GarbrechtBjorn Garbrecht
Michael Ramsey-MusolfMichael Ramsey-Musolf
(NPAC UW-Madison)(NPAC UW-Madison)
Summary of this talkSummary of this talk
1.1. Review electroweak baryogenesis Review electroweak baryogenesis Basic pictureBasic picture Requirements for it to workRequirements for it to work
2.2. EWB in the MSSMEWB in the MSSM What is neededWhat is needed Sign of the baryon Sign of the baryon
asymmetryasymmetry
Sign of Sign of EDMsEDMs
Stop/sbottom Stop/sbottom mass spectrummass spectrum
Universe made Universe made of matterof matter
Supersymmetry is super-great!Supersymmetry is super-great!
+
The minimal supersymmetric standard model (MSSM):
+
Coupling unificationCoupling unificationHierarchy problemHierarchy problem
Dark matterDark matter Stringy motivationStringy motivation
Electroweak Baryogenesis PictureElectroweak Baryogenesis PictureWe want to explain
PDG
Dunkley et al [WMAP5]
Sakharov conditions:Sakharov conditions:
1.1. Baryon number violationBaryon number violation
2.2. C- and CP-violationC- and CP-violation
3.3. Departure from Departure from thermal equilibriumthermal equilibrium
95% C.L.
based on dynamics during the electroweak phase transition.
Electroweak sphalerons
complex phases
1st order phase transition
Electroweak Baryogenesis PictureElectroweak Baryogenesis Picture
Higgs potentialHiggs potentialV( )
T > Tc T = Tc
T =0
First order electroweak phase transition during the early universe
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 PictureElectroweak Baryogenesis Picture
electroweak sphaleron
Three Steps:Three Steps:
1. Nucleation and expansion of 1. Nucleation and expansion of bubbles of broken EW symmetrybubbles of broken EW symmetry
2. CP-violating interactions at 2. CP-violating interactions at bubble wall induces charge bubble wall induces charge density, diffusing outside bubbledensity, diffusing outside bubble
3. Sphalerons convert LH 3. Sphalerons convert LH asymmetry into B asymmetryasymmetry into B asymmetry
diffusion
moving bubble wall
CPCP
Cohen, Kaplan, Nelson, 1992-1994; Huet, Nelson, 1996
Quark
num
ber
densi
ty
electroweak sphaleron
Three Steps:Three Steps:
1. Nucleation and expansion of 1. Nucleation and expansion of bubbles of broken EW symmetrybubbles of broken EW symmetry
2. CP-violating interactions at 2. CP-violating interactions at bubble wall induces charge bubble wall induces charge density, diffusing outside bubbledensity, diffusing outside bubble
3. Sphalerons convert LH 3. Sphalerons convert LH asymmetry into B asymmetryasymmetry into B asymmetry
diffusion
moving bubble wall
CPCP
Cohen, Kaplan, Nelson, 1992-1994; Huet, Nelson, 1996
Quark
num
ber
densi
ty
Electroweak Baryogenesis PictureElectroweak Baryogenesis Picture
4. Baryon asymmetry 4. Baryon asymmetry captured by expanding bubblecaptured by expanding bubble
Requirements for electroweak Requirements for electroweak baryogenesis to workbaryogenesis to work
Given a model of electroweak symmetry breaking (e.g. the standard model), what is required?
Two requirements:Two requirements:
1.1. Sufficient CP-violation to explain observed nSufficient CP-violation to explain observed nBB
2.2. A A strongstrong first-order electroweak phase transition 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 requirementselectroweak baryogenesis requirementsRequirement #1: sufficient CP-violationRequirement #1: sufficient CP-violation
Need to have “sufficient” CP-violation to produce the Need to have “sufficient” CP-violation to produce the observed baryon asymmetryobserved baryon asymmetry
1.1. Solve Boltzmann equations for particles species in the Solve Boltzmann equations for particles species in the plasma, with background of expanding bubble of broken EW plasma, with background of expanding bubble of broken EW symmetrysymmetry
diffusiondiffusion collisionscollisions CP-violating CP-violating sourcesource
nnii = number density for = number density for particles — antiparticlesparticles — antiparticles
stolen from Bjorn Garbrechtstolen from Bjorn Garbrecht
electroweak baryogenesis requirementselectroweak baryogenesis requirementsRequirement #1: sufficient CP-violationRequirement #1: sufficient CP-violation
Need to have “sufficient” CP-violation to produce the Need to have “sufficient” CP-violation to produce the observed baryon asymmetryobserved baryon asymmetry
1.1. Solve Boltzmann equations for particles species in the Solve Boltzmann equations for particles species in the plasma, with background of expanding bubble of broken EW plasma, with background of expanding bubble of broken EW symmetrysymmetry
diffusiondiffusion collisionscollisions CP-violating CP-violating sourcesource
nnii = number density for = number density for particles — antiparticlesparticles — antiparticles
weak weak sphaleronsphaleron
collision collision factorfactor
2. Take left-handed fermion charge n2. Take left-handed fermion charge nLL and compute baryon asymmetry and compute baryon asymmetry
Baryon asymmetryBaryon asymmetry
CP-violating CP-violating sourcesource
collision collision factorfactor
1.1. MagnitudeMagnitude of the baryon asymmetry depends on: of the baryon asymmetry depends on:
KKCC: depends on large fraction of MSSM spectrum: depends on large fraction of MSSM spectrum
CP-violating source: depends on only a few parameters, but CP-violating source: depends on only a few parameters, but still much theoretical uncertaintystill much theoretical uncertainty
2. 2. SignSign of baryon asymmetry of baryon asymmetry
Depends on CP-violating phase and relatively few other Depends on CP-violating phase and relatively few other parametersparameters
Collision factorCollision factorWhat interactions in the plasma are in chemical equilibrium? What interactions in the plasma are in chemical equilibrium? (i.e. fast compared to diffusion time scale)(i.e. fast compared to diffusion time scale)
Previous lore:Previous lore:
1.1. Gauge/gaugino interactionsGauge/gaugino interactions
2.2. Top yukawa interactionsTop yukawa interactions
3.3. Strong sphaleronsStrong sphalerons
diffusion
ttLL
ttLL
ttRR
ttRR
~~
~~
nnLL
left-handed left-handed fermion density fermion density
Cohen, Kaplan, Nelson, 1992-1994; Huet, Nelson, 1996
Collision factorCollision factorWhat interactions in the plasma are in chemical equilibrium? What interactions in the plasma are in chemical equilibrium? (i.e. fast compared to diffusion time scale)(i.e. fast compared to diffusion time scale)
Previous lore:Previous lore:
1.1. Gauge/gaugino interactionsGauge/gaugino interactions
2.2. Top yukawa interactionsTop yukawa interactions
3.3. Strong sphaleronsStrong sphalerons
Cohen, Kaplan, Nelson, 1992-1994; Huet, Nelson, 1996
Cirigliano, Lee, Ramsey-Musolf, S.T. (2006)
Next, use Next, use nnii = k = kii ii
Then can express Then can express nnLL = K = KCC n nHH where K where KCC given in terms of k given in terms of kii’s’s~~
Collision factorCollision factorWhat interactions in the plasma are in chemical equilibrium? What interactions in the plasma are in chemical equilibrium? (i.e. fast compared to diffusion time scale)(i.e. fast compared to diffusion time scale)
Previous lore:Previous lore:
1.1. Gauge/gaugino interactionsGauge/gaugino interactions
2.2. Top yukawa interactionsTop yukawa interactions
3.3. Strong sphaleronsStrong sphalerons
Cohen, Kaplan, Nelson, 1992-1994; Huet, Nelson, 1996
New Results:New Results:
4. Bottom yukawa interactions4. Bottom yukawa interactions
5. Tau yukawa interactions (lepton-driven EWB)5. Tau yukawa interactions (lepton-driven EWB)
Chung, Garbrecht, Ramsey-Musolf, S.T. (2008)
Cirigliano, Lee, Ramsey-Musolf, S.T. (2006)
Collision factorCollision factorWhen are bottom Yukawa interactions important?When are bottom Yukawa interactions important?
Chung, Garbrecht, Ramsey-Musolf, S.T. (in prep)
Time scale for bottom Time scale for bottom Yukawa interactions vs. Yukawa interactions vs. diffusion time scalediffusion time scale
onlyonly
Collision factorCollision factorWith bottom Yukawa interactions, KWith bottom Yukawa interactions, KCC simplifies greatly: simplifies greatly:
nnLL = K = KCC n nHH~~
Conversion factor for Higgsinos into LH quarks (3Conversion factor for Higgsinos into LH quarks (3rdrd gen) gen)
kkii = k = kii(m(mii/T) largest for small m/T) largest for small mii
KKCC = 0 for = 0 for
KKCC < 0 for < 0 for
KKCC > 0 for > 0 for
Sign of KSign of KCC (and, in part, n (and, in part, nBB) ) determined by whether RH determined by whether RH stop or sbottom is lighterstop or sbottom is lighter
Chung, Garbrecht, Ramsey-Musolf, S.T. (2008)
Also, KC -> 0 forAlso, KC -> 0 for
Collision factorCollision factorWith bottom Yukawa interactions, KWith bottom Yukawa interactions, KCC simplifies greatly: simplifies greatly:
nnLL = K = KCC n nHH~~
Physical reason for this effect Physical reason for this effect
Which effect wins depends on which degrees of freedom are Which effect wins depends on which degrees of freedom are lighterlighter
Chung, Garbrecht, Ramsey-Musolf, S.T. (2008)
Focus on case where RH stop < 120 GeV (i.e. MSSM)
p p
Good: Light stop means large Good: Light stop means large production cross sectionproduction cross section
*
Stop at the LHCStop at the LHC
Decay products: (assume m < 120 GeV)
stable (on collider time scales)
only if
CHAMP searches imply CDF 2007
1.
2. 115 GeV115 GeV
Stop at the LHCStop at the LHC
Light RH stop at the LHC
p p
Good: Light stop means large Good: Light stop means large production cross sectionproduction cross section
*
Decay products: (assume m < 120 GeV)
tends to dominate for
Hikasa, Kobayashi (1987)
Hiller, Nir (2008)
4.
3.
Stop at the LHCStop at the LHC
Light RH stop at the LHC
Low energy QCD (~50 GeV)
p p
Good: Light stop means large Good: Light stop means large production cross sectionproduction cross section
cMissing energy
Bad: Difficult to Bad: Difficult to observe at LHC!observe at LHC!
*
/g Better: radiative decayBetter: radiative decay
(signal: missing energy (signal: missing energy + high p+ high pTT jet or photon) jet or photon)Carena, Freitas, Wagner (2008)
Light RH stop at the LHC
Stop at the LHCStop at the LHC
Radiative stop decay:“LSP”
dominant
Signal: Signal:
high Phigh PTT jet + E jet + ET T + + soft charm jets (tough)soft charm jets (tough)
Light stop window for strong 1st order phase transition
Carena, Freitas, Wagner (2008)
Baryon asymmetryBaryon asymmetry
CP-violating CP-violating sourcesource
collision collision factorfactor
CP-violating source:CP-violating source:
Two-flavor oscillation problem (a la neutrino oscillations) but with a Two-flavor oscillation problem (a la neutrino oscillations) but with a spacetime dependent Hamiltonian mass matrixspacetime dependent Hamiltonian mass matrix
What parameters govern the sign of the CP-violating source?What parameters govern the sign of the CP-violating source?
relevant phasesrelevant phases
Carena, Quiros, Seco, Wagner Carena, Quiros, Seco, Wagner (2000)(2000)
Lee, Cirigliano, Ramsey-Musolf Lee, Cirigliano, Ramsey-Musolf (2004)(2004)
Carena, Moreno, Quiros, Seco, Wagner Carena, Moreno, Quiros, Seco, Wagner (2002)(2002)
Konstandin, Prokopec, Schmidt, Seco Konstandin, Prokopec, Schmidt, Seco (2005)(2005)
CP-violating sourceCP-violating sourceVarious results:Various results:
plotted vs. plotted vs. ,,for Mfor M22 = 200 GeV = 200 GeV
andand
CP-violating sourceCP-violating sourceHow does an expanding bubble of broken EW symmetry produce a How does an expanding bubble of broken EW symmetry produce a CP-asymmetry of particles vs antiparticles?CP-asymmetry of particles vs antiparticles?
Two-flavor oscillation problem (a la neutrino oscillations) but Two-flavor oscillation problem (a la neutrino oscillations) but with a spacetime dependent Hamiltonian H(t)with a spacetime dependent Hamiltonian H(t)
V(t)V(t) V(t)V(t)**
particlesparticlesanti-particlesanti-particles
V(t) rotates flavor states into mass eigenstates
(Consider simplified case where Hamiltonian only depends on t)
Full treatment requires non-equilibrium, finite temp field theoryFull treatment requires non-equilibrium, finite temp field theory
Quick & dirty explanation: (using elementary QM)Quick & dirty explanation: (using elementary QM)
CP-violating sourceCP-violating source
Schrödinger Eqn: Schrödinger Eqn: (flavor basis)(flavor basis) = L, R= L, R
flavor statesflavor states
Evolution of states:Evolution of states:
Then rotate to mass basisThen rotate to mass basis
Schrödinger Eqn is nowSchrödinger Eqn is now
wherewhere
Similarly for anti-Similarly for anti-particle statesparticle states
CP-violating sourceCP-violating sourceEvolution of states:Evolution of states:
Amplitude for mass state |j> to be in flavor state |Amplitude for mass state |j> to be in flavor state |> after time > after time tt
CP-violating source:CP-violating source:
Initial condition:Initial condition:
Begin with plasma in equilibrium: ensemble of mass basis Begin with plasma in equilibrium: ensemble of mass basis states with weightstates with weight
CP-violating sourceCP-violating sourceCP-violating source:CP-violating source:
wherewhere
Conclusions:Conclusions:
1.1. Need two nearly degenerate states — otherwise small Need two nearly degenerate states — otherwise small and source washed out by oscillationsand source washed out by oscillations
2.2. Need spacetime-dependent phase in mixing matrixNeed spacetime-dependent phase in mixing matrix
3.3. States not too heavy compared to temp T — otherwise States not too heavy compared to temp T — otherwise Boltzmann suppressedBoltzmann suppressed
CP-violating sourceCP-violating sourceExample:Example:
CP-violating source from Higgsino/Wino oscillations. CP-violating source from Higgsino/Wino oscillations.
Flavor states Flavor states
Carena, Quiros, Seco, Wagner Carena, Quiros, Seco, Wagner (2000)(2000)
Lee, Cirigliano, Ramsey-Musolf Lee, Cirigliano, Ramsey-Musolf (2004)(2004)
Carena, Moreno, Quiros, Seco, Wagner Carena, Moreno, Quiros, Seco, Wagner (2002)(2002)
Konstandin, Prokopec, Schmidt, Seco Konstandin, Prokopec, Schmidt, Seco (2005)(2005)
CP-violating sourceCP-violating sourceVarious results:Various results:
plotted vs. plotted vs. ,,for Mfor M22 = 200 GeV = 200 GeV
andand
Implications for EDMsImplications for EDMs
Two-loop EDMs are irreducible:Two-loop EDMs are irreducible:
Recently computed in full by Li et al (2008)
Two possible CP-violating phases Two possible CP-violating phases that could drive baryogenesis in that could drive baryogenesis in MSSM also give rise to EDMsMSSM also give rise to EDMs
Suppose EDM measured. What are implications for EWB?Suppose EDM measured. What are implications for EWB?
1.1. Assume same phase for both baryon asymmetry and EDMAssume same phase for both baryon asymmetry and EDM
2.2. Assume one-loop EDMs suppressed (heavy 1st/2nd gen Assume one-loop EDMs suppressed (heavy 1st/2nd gen sfermions)sfermions)
CP-violating phaseCP-violating phase
Li, Profumo, Ramsey-Musolf (2008)
Sign of two-loop EDMs mostly correlated wrt CP-violating phases!Sign of two-loop EDMs mostly correlated wrt CP-violating phases!
positive contributionspositive contributions
negative contributionsnegative contributions
Current EDM constraintsCurrent EDM constraintselectron EDMelectron EDM neutron EDMneutron EDM
ExcludeExcluded d
Li et al (2008)
Future EDM searches Future EDM searches
Very exciting!Very exciting!
Future EDM Future EDM measurements measurements will improve will improve sensitivities bysensitivities by orders of orders of magnitude.magnitude.
Future EDM constraintsFuture EDM constraintselectron EDMelectron EDM neutron EDMneutron EDM
ExcludeExcluded d
ddee < 3x10 < 3x10-30-30 e cm e cm ddnn < 1x10 < 1x10-28-28 e cm e cm
Baryogenesis Baryogenesis curves made curves made with most with most optimistic optimistic estimatesestimates
Li et al (2008)
ConclusionsConclusionsSign of baryon asymmetry may be the easiest consistency check for Sign of baryon asymmetry may be the easiest consistency check for electroweak baryogenesis in the MSSMelectroweak baryogenesis in the MSSM
Under simplest assumptions (EDM and EWB determined by same Under simplest assumptions (EDM and EWB determined by same phase), sign of baryon asymmetry determined by:phase), sign of baryon asymmetry determined by:
• Collision factor KCollision factor KCC: depends on whether RH stop or sbottom is : depends on whether RH stop or sbottom is heavierheavier
• Sin of CP-violating phaseSin of CP-violating phase
Generalization beyond the MSSM?Generalization beyond the MSSM?
same collision factorsame collision factor
unknown if EDMs correlate with CP-violating phaseunknown if EDMs correlate with CP-violating phase
-25 -20 -15 -10 -5
-5
5
10
15
20
CP-violating sourceCP-violating source
Discrepency in treatment of diffusion Discrepency in treatment of diffusion
Konstandin et al (2005)Cirigliano, Lee, Ramsey-Musolf, S.T. (2006)
nnBB/s =/s = 3 x (nB/s)WMAP x sin nnBB/s =/s = x (nB/s)WMAP x sin 30
nnHH ~~nnHH ~~