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 ChungBjorn GarbrechtBjorn GarbrechtMichael Ramsey-MusolfMichael Ramsey-Musolf

(NPAC UW-Madison)(NPAC UW-Madison)

Summary of this talkSummary of this talk1.1. 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 symmetry2. CP-violating interactions at 2. CP-violating interactions at bubble wall induces charge bubble wall induces charge density, diffusing outside bubbledensity, diffusing outside bubble3. Sphalerons convert LH 3. Sphalerons convert LH asymmetry into B asymmetryasymmetry into B asymmetrydiffusion

moving bubble wall

CPCP

Cohen, Kaplan, Nelson, 1992-1994; Huet, Nelson, 1996

Quar

k nu

mbe

r den

sity

electroweak sphaleron

Three Steps:Three Steps:1. Nucleation and expansion of 1. Nucleation and expansion of bubbles of broken EW symmetrybubbles of broken EW symmetry2. CP-violating interactions at 2. CP-violating interactions at bubble wall induces charge bubble wall induces charge density, diffusing outside bubbledensity, diffusing outside bubble3. Sphalerons convert LH 3. Sphalerons convert LH asymmetry into B asymmetryasymmetry into B asymmetrydiffusion

moving bubble wall

CPCP

Cohen, Kaplan, Nelson, 1992-1994; Huet, Nelson, 1996

Quar

k nu

mbe

r den

sity

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 SMMay 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 spectrumCP-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 asymmetryDepends 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 interactions2.2. Top yukawa interactionsTop yukawa interactions3.3. 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 lighterChung, 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 20071.

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 oscillations2.2. Need spacetime-dependent phase in mixing matrixNeed spacetime-dependent phase in mixing matrix3.3. 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 EDM2.2. 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 contributionsnegative 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 MSSMUnder 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 factorunknown 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 ~~