# Supersymmetry, the Baryon Asymmetyry and the Origin of Mass

BaryogenesisBaryogenesis andand NewNew PhysicsPhysics atat thethe WeakWeak ScaleScale

C.E.M. Wagner

Argonne National Laboratory EFI, University of Chicago

SLAC Summer Institute, SLAC, August 11, 2004 TheThe PuzzlePuzzle ofof thethe MatterMatter--AntimatterAntimatter asymmetryasymmetry

Anti-matter is governed by the same interactions as matter.

Observable Universe is composed of matter.

Anti-matter is only seen in cosmic rays and particle physics accelerators

The rate observed in cosmic rays consistent with secondary emission of antiprotons n P ≈ 10 − 4 n P BaryonBaryon--AntibaryonAntibaryon asymmetryasymmetry

Baryon Number abundance is only a tiny fraction of other relativistic species n B ≈ 6 10−10 nγ

But in early universe baryons, antibaryons and photons were equally abundant. What explains the above ratio ?

Explanation: Baryons and Antibaryons annihilated very efficiently. No net baryon number if B would be conserved at all times.

What generated the small observed baryon-antibaryon asymmetry ? ElectroweakElectroweak BaryogenesisBaryogenesis ElectroweakElectroweak BaryogenesisBaryogenesis inin thethe StandardStandard ModelModel

SM fufills the Sakharov conditions:

Baryon number violation: Anomalous Processes

CP violation: Quark CKM mixing

Non-equilibrium: Possible at the electroweak phase transition. BaryonBaryon NumberNumber ViolationViolation atat finitefinite TT

At zero T baryon number violating processes highly suppressed

At finite T, only Boltzman suppression ⎛ E ⎞ 8π v ⎜ sph ⎟ E ∝ Γ(∆B≠0)∝AT exp⎜− ⎟ sph g ⎝ T ⎠

Baryon Number violating processes unsuppressed at high temperatures, but suppressed at temperatures below the electroweak phase transition.

Anomalous processes violate both baryon and lepton number, but preserve B – L. Relevant for the explanation of the Universe baryon asymmetry. BaryonBaryon NumberNumber GenerationGeneration

From weak scale mass particle decay: Difficult, since non-equilibrium condition is satisfied for small couplings, for which CP- violating effects become small (example: resonant leptogenesis).

Baryon number violating processes out of equilibrium in the broken phase if phase transition is sufficiently strongly first order : Baryon asymmetry generation at the electroweak phase transition (Electroweak Baryogenesis). BaryonBaryon AsymmetryAsymmetry PreservationPreservation

If Baryon number generated at the electroweak phase transition, n n (T ) ⎛ 1016 ⎛ E (T )⎞ ⎞ B B c ⎜ ⎜ sph c ⎟ ⎟ = exp ⎜ − exp ⎜ − ⎟ ⎟ s s ⎝ Tc (GeV) ⎝ Tc ⎠ ⎠

Baryon number erased unless the baryon number violating processes are out of equilibrium in the broken phase.

Therefore, to preserve the baryon asymmetry, a strongly first order phase transition is necessary: v(T ) c > 1 Tc ElectroweakElectroweak PhasePhase TransitionTransition Higgs Potential Evolution in the case of a first order Phase Transition

v(Tc )

FiniteFinite TemperatureTemperature HiggsHiggs PotentialPotential

D receives contributions at one-loop proportional to the sum of the couplings of all bosons and fermions squared, and is responsible for the phenomenon of symmetry restoration

E receives contributions proportional to the sum of the cube of all light boson particle couplings m2 v(Tc ) E H ≈ , with λ ∝ 2 Tc λ v Since in the SM the only bosons are the gauge bosons, and the quartic coupling is proportional to the square of the Higgs mass,

v(Tc ) > 1 implies mH < 40 GeV. Tc If the Higgs Boson is created , it will decay rapidly into other particles At LEP energies mainly into pairs of b quarks

One detects the decay products of the Higgs and the Z bosons

LEP Run is over

• No Higgs seen with a mass below 114 GeV • But, tantalizing hint of a Higgs with mass about 115 -- 116 GeV (just at the edge of LEP reach) Electroweak Baryogenesis in the SM is ruled out ElectroweakElectroweak BaryogenesisBaryogenesis

andand

NewNew PhysicsPhysics atat thethe WeakWeak ScaleScale Supersymmetry fermionsfermions bosonsbosons electronelectron sselectronelectron quarkquark ssquarkquark photphotinoino photonphoton gravitgravitinoino gravitongraviton

Photino, Zino and Neutral Higgsino: Neutralinos

Charged Wino, charged Higgsino: Charginos

Particles and Sparticles share the same couplings to the Higgs. Two superpartners of the two quarks (one for each chirality) couple strongly to the Higgs with a Yukawa coupling of order one (same as the top-quark Yukawa coupling) WhyWhy SupersymmetrySupersymmetry ??

Helps to stabilize the weak scale—Planck scale hierarchy

Supersymmetry algebra contains the generator of space-time translations. Necessary ingredient of theory of quantum gravity.

Minimal supersymmetric extension of the SM : Leads to Unification of gauge couplings.

Starting from positive masses at high energies, electroweak symmetry breaking is induced radiatively.

3B+L+2S If discrete symmetry, P = (-1) is imposed, lightest SUSY particle neutral and stable: Excellent candidate for cold Dark Matter. Supersymmetry at colliders Gluino production and decay: Missing Energy Signature

Supersymmetric Particles tend to be heavier if they ~χ 0 carry color charges. 1

Particles with large Yukawas tend to be lighter. ~χ 0 Charge-less particles 1 tend to be the lightest ones.

¾ Lightest supersymmetric particle = Excellent Cold dark matter candidate. PreservationPreservation ofof thethe BaryonBaryon AsymmetryAsymmetry

EW Baryogenesis requires new boson degrees of freedom with strong couplings to the Higgs.

Supersymmetry provides a natural framework for this scenario.

Relevant SUSY particle: Superpartner of the top

Each stop has six degrees of freedom (3 of color, two of charge) and coupling of order one to the Higgs g 3 h 3 E = w + t ≈ 8 E SUSY 4π 2π SM m2 v(Tc ) E H Since ≈ , with λ ∝ 2 Tc λ v

Higgs masses up to 120 GeV may be accomodated ConstraintsConstraints onon thethe StopStop SectorSector

The top quark has two supersymmetric partners, one for each chirality (left and right).

One of the stops has to be light, in order to make the phase transitioin strongly first order

Second stop needs to be heavier than about 1 TeV in order to make the Higgs mass larger than the current bound, of about 114 GeV.

Upper bound on the Higgs imposed by the requirement of the preservation of the baryon asymmetry. LightLight Stops:Stops: MotivationMotivation

In low energy supersymmetry models, light stops are induced as a consequence of large mixing or large negative radiative effects.

They are required for the realization of the mechanism of electroweak baryogenesis in the MSSM

Signatures of a light stop at the Tevatron collider depend strongly on the chargino and neutralino spectrum as well as on the nature of supersymmetry breaking StopStop massmass matrixmatrix

Radiative corrections affect mostly the hierarchy of diagonal masses in stop mass matrix

2 2 ⎡mQ + mt mt (At − µ cotanβ )⎤ M 2 = ⎢ ⎥ 2 2 ⎣⎢mt (At − µ cotanβ ) mU + mt ⎦⎥

Stop mixing induced by off-diagonal elements in stop mass matrix

In supersymmetric theories, two Higgs doublet superfields necessary to cancel anomalies and give masses to all fermions

v 2 tanβ = with v i the v..e v.of the two Higgs fields v 1 HiggsHiggs andand StopStop MassesMasses MSSM: Limits on the Stop and Higgs Masses to preserve the baryon asymmetry

Suficciently strong first order phase transition to preserve generated baryon asymmetry: • Higgs masses up to 120 GeV

• The lightest stop must have a mass below the top quark mass.

Moderate values of tanβ, tanβ ≥ 5 preferred in order to raise the Higgs LEP Excluded boson mass.

M. Carena, M. Quiros, C.W. ExperimentalExperimental TestsTests ofof ElectroweakElectroweak BaryogenesisBaryogenesis inin thethe MSSMMSSM Experimental Tests of Electroweak Baryogenesis and Dark Matter

• Higgs searches beyond LEP:

1. Tevatron collider may test this possibility: 3 sigma evidence with about 4 fb−1 Discovery quite challenging, detecting a signal will mean that the Higgs has relevant strong (SM-like) couplings to W and Z Maximal mixing scenario

2. A definitive test of this scenario will come at the LHC with the first 30 fb − 1 of data

qq → qqV*V* → qqh with h →τ +τ − TevatronTevatron StopStop ReachReach whenwhen twotwo bodybody decaydecay channelchannel isis dominantdominant

Main signature:

2 or more jets plus missing energy

2 or more Jets with ET > 15 GeV

Missing ET > 35 GeV

Demina, Lykken, Matchev,Nomerotsky ‘99 StopStop--NeutralinoNeutralino MassMass Difference:Difference: InformationInformation fromfrom thethe CosmosCosmos

If the neutralino provides the observed dark matter relic density, then it must be stable and lighter than the light stop.

Relic density is inversely proportional to the neutralino annihilation cross section.

If only stops, charginos and neutralinos are light, there are three main annihilation channels:

1. Coannihilation of neutralino with light stop or charginos: Small mass differences. 2. s-channel annihilation via light CP-even Higgs boson 3. s-channel annihilation via heavy CP-even Higgs boson and CP-odd Higgs boson Relic density is inversely proportional to the thermally averaged ~ 0 ~ 0 χ χ annihilation cross section σ v

~ 0 χ f h,H,A,Z

χ~ 0 f

If any other SUSY particle has mass close to the neutralino LSP, it may substantially affect the relic density via co-annihilation χ~ 0 χ~0 w w if stops NLSP t χ~ + neutralino-stop ~ t b ~ co-annihilation t b RelicRelic DensityDensity valuesvalues (WMAP)(WMAP)

hh=0.71=0.71±±0.040.04 2 ΩΩMhh =0.135=0.135±±0.0090.009

2 ΩΩBhh =0.0224=0.0224±±0.00090.0009 ΩΩtot=1.02=1.02±±0.020.02 DarkDark MatterMatter andand ElectroweakElectroweak BaryogenesisBaryogenesis

M 21≈=2 M , tanβ 10 Three interesting regions with neutralino relic density compatible with WMAP obs. 2 (green areas) σ si =1 E - 07 σ si =1 E - 08 0.095 < ΩCDMh < 0.129

1. Mass difference about 20-30 GeV neutralino-stop co-annihilation

m~0 =160 GeV 1 χ 3 140 2. s-channel neutralino annihilation via mh m 0 ≈ χ~ 2 120 light Higgs boson

m~t =164 GeV 169 174 2 3. Annihilation via Z boson exchange and chargino coannihilation

M. Carena, C. Balazs and C.W. 04 HeavyHeavy HiggsHiggs massmass EffectsEffects

tan β =10

mA = 300 GeV mA = 200 GeV

σ si =1 E - 07 σ si =1 E - 08

σ si =1 E - 07

σ si =1 E - 08

• Larger neutralino-proton scattering cross sections!

Balazs, Carena, C.W. TevatronTevatron stopstop searchessearches andand darkdark mattermatter constraintsconstraints

Carena, Balazs and C.W. ‘04

20 fb −1

Searches for light stops difficult in stop-neutralino 4 fb −1 coannihilarion region. 2 fb −1 LHC will have equal difficulties. Searches become easier at a Linear Collider ! Baryon Asymmetry Generation CPCP--ViolatingViolating SourcesSources CPCP--ViolatingViolating SourcesSources

Chiral charges are induced by the passage of the wall of the expanding true – vacuum bubbles. ~ γ i

New sources of CP violation from the sfermion sector

Generation of the baryon asymmetry: Charginos with masses

µ and M2 play most relevant role.

CP-violating Sources depend on arg()µ M 2 Higgs profile depends on the mass of the heavy Higgs bosons. tanβ = 10 We plot for maximal mixing: within uncertainties, values of preferred sin φµ ≥ 0.05

Gaugino and Higgsino masses of the order of the weak scale highly preferred

Large CP-odd Higgs mass values are acceptable

M.Carena, Quiros,. Seco and C.W.‘02 Baryon Asymmetry Dependence on the Chargino Mass Parameters

tanβ = 10 Results for maximal CP violation

Gaugino and Higgsino masses of the order of the weak scale highly preferred

M.Carena, M.Quiros, M. Seco and C.W. ‘02 Baryon Asymmetry Enhanced for M2 = | µ | Even for large values of the CP-odd Higgs mass, acceptable values obtained for phases of order one. ElectricElectric DipoleDipole MomentsMoments

Sizeable phases in the mu-parameter may induce large electron and neutron electric dipole moments.

Dipole moments suppressed for large values of the first and second generation sfermion masses, which we assume to be of about a few TeV.

Two-loop effects still present, of the size of present experimental bounds on these quantities. Pilaftsis, Chang et al ‘02

Two-loop effects suppressed for larger values of the CP-odd Higgs mass. ElectroweakElectroweak BaryogenesisBaryogenesis inin thethe nMSSMnMSSM

MinimalMinimal ExtensionExtension ofof thethe MSSM:MSSM: AddAdd aa singletsinglet chiralchiral superfield,superfield, SS MinimalMinimal ExtensionExtension ofof thethe MSSMMSSM Dedes et al. , Panagiotakopoulos, Pilaftsis’01

R R Superpotential restricted by Zo 5 r Z 7 symmetries

2 m12 WS=+λ HH Sy+QHU 12 λ t2

No cubic term. Tadpole of order cube of the weak scale, instead

Discrete symmetries broken by tadpole term, induced at the sixth loop level. Scale stability preserved

Similar superpotential appears in Fat-Higgs models at low energies Harnik et al. ’03, G. Kribs’ talk

2 2 2 2 22 Vmsoft =++1 H1 m2 H2 mS S+( ts S+h..c)

++()aSλ H12H h..c CP-Violating Sources

In the nMSSM, the chargino sector is the same as in the MSSM. Hence, sources of CP-violation are preserved.

Difference in Higgs sector: Large tan β values are no longer necessary, implying an enhancement of the sources compared to the MSSM.

In addition, new sources may arises from the additional parameters of the theory. In general, we expect smaller bounds on the CP- violating phases than in the MSSM. MinimizationMinimization ConditionsConditions

Mass parameters may be replaced as a function of doublet Higgs fields by means of the minization conditions

2 2 2 2 gg2 + 1 2 2 2 2 mm=−()+avtanβλ− ((vv−+)v+v) 1 12 λ S 4 1 2 1 2

2 2 2 2 gg2 + 1 2 2 2 2 mm=−()+avcotanβλ+ ((vv−+)v+v) 2 12 λ S 4 1 2 1 2

2 vv12 tS mas =− λ − v S v S CharginoChargino andand NeutralinoNeutralino SpectrumSpectrum

We impose the unification condition on gaugino masses and allow non-vanishing phases for them.

Chargino and neutralino masses are governed by the size of the parameter λ and the singlet v.e.v.

Chargino spectrum similar to the MSSM, with µ ↔ − λ v S

⎡M2sinβ M⎤ ⎢ 2W⎥ M = ⎢ ⎥ χ + ⎢ ⎥ − ⎣⎢ 2cosβλMWSv ⎦⎥ NeutralinoNeutralino spectrumspectrum

Neutralino spectrum more complex. Gaugino masses may have phases

⎡ M 1 ••••⎤ ⎢ ⎥ 0M••• ⎢ 2 ⎥

M 0 = ⎢−•cosββs WZM cos c WZM 0 •⎥ χ ⎢ ⎥ • ⎢ sinββs WZM sin c WZM λv S 0 ⎥ ⎢ ⎥ ⎣ 00λλv21v0⎦

For M 1 > 100 GeV, lightest neutralino is approximately given by

2vλ sin β x v S m12= 2with x = ()1t++anβ x v 1 Values of λ vs tan β

Low values of tan β restricted by top-Yukawa perturbative limit.

Perturbative limit

Menon,Morrissey,C.W.’04 UpperUpper boundbound onon NeutralinoNeutralino MassesMasses

Values of neutralino masses below dotted line consistent with perturbativity constraints.

MaximumMaximum value of Lightest neut. mass

Perturbative limit

Menon,Morrissey,C.W.’04 Electroweak Phase Transition

2 2 2 v1 Defining φβ=+HH1 2 , tan= v 2 ElectroweakElectroweak BaryogenesisBaryogenesis

Due to the presence of tree-level trilinear terms, first order transition may be achieved even if stops are heavy

One can solve the finite temperature minimization conditions including only the dominant loop effects, to show that

2 1 λ tS =−≥ D ~ 2 maS λ cosββsin 1 λ mS mS ~ where λ 2 is the effective quartic coupling of the SM-like Higgs, is a necessary, but not sufficient, condition to obtain a first order trans.

2 In general, this demands the value of m S to be not too large ParametersParameters withwith stronglystrongly firstfirst orderorder transitiontransition

Values constrained by perturbativity up to the GUT scale.

All dimensionful parameters Maximum value of singlet varied up to 1 TeV mass

Small values of the singlet mass parameter selected

Menon,Morrissey,C.W.’04 ParametersParameters leadingleading toto stronglystrongly firstfirst orderorder transitiontransition

Larger values of λ allowed

Menon,Morrissey,C.W.’04 HiggsHiggs SpectrumSpectrum

New CP-odd and CP-even Higgs fields induced by singlet field 2 (mass controled by m S )

They mix with standard CP-even and CP-odd states in a way proportional to λ and a λ

Values of λ restricted to be lower than 0.8 in order to avoid Landau-pole at energies below the GUT scale.

As in the NMSSM, upper bound on Higgs that couples to weak bosons,

Extra tree-level term helps in avoiding LEP bounds.

2 22 222 m h ≤+M Z cos βλv sin 2β+loop corrections Espinosa,Quiros;Kane et al. LightLight HiggsHiggs bosonboson massesmasses

MaS==900GeV v −300GeV 13/ aλ ==350GeV tS 150GeV λ = 07.

Menon,Morrissey,C.W.’04 LightLight HiggsHiggs bosonboson massesmasses

M9aS= 00GeVv= − 300GeV 13/ aλ ==350GeV tS 150GeV tanβ= 2 DarkDark MatterMatter

Apart from satisfying the conditions for the realization of the electroweak baryogenesis scenario, the model may lead to an acceptable relic density

Interesting: The R-symmetries lead to the cancellation of all dominant baryon and lepton number violating operators (act like R-Parity)

Non-renormalizable operators still exist, but proton stability ensured and neutralino lifetime longer than the age of the Universe, so far 14 the relevant scale of operators is larger than Λ≥10 GeV RelicRelic DensityDensity

Dark Matter Relic Density depends crucially on neutralino mass and composition

We assumed all squarks and sleptons to be heavier than 300 GeV, playing no relevant role in annihilation cross sections

Since lightest neutralinos are lighter than 70 GeV, Z-pole s-channel annihilation cross section is most relevant in determining the final relic density

The presence of three light Higgs bosons also plays a role, when the neutralino masses are close to the resonance region RelicRelic DensityDensity andand ElectroweakElectroweak BaryogenesisBaryogenesis

Region of neutralino masses selected when perturbativity constraints are impossed. Z-boson and Higgs boson contributions shown to guide the eye.

Z-width constraint

Menon,Morrissey,C.W.’04 RelicRelic DensityDensity andand ElectroweakElectroweak BaryogenesisBaryogenesis

Neutralino masses for larger values of λ

Z-width constraint

Menon,Morrissey,C.W.’04 PhenomenologicalPhenomenological PropertiesProperties

If perturbative consistency up to the GUT scale is demanded, lightest neutralino mass is below M2Z /

This has relevant implications for Higgs physics : Due to the smallness of the bottom-quark Yukawa coupling, light Higgs bosons tend to decay into neutralinos

LEP constraints on CP-even Higgs boson masses still strong, due to a relevant coupling of these to the Z-gauge boson

Searches at the Tevatron and the LHC should proceed via the invisible channels ParticleParticle SpectraSpectra forfor representativerepresentative pointspoints

Charginos and Neutralinos at the reach of the Tevatron or the LHC. Lightest Neutralino mostly singlino. CompositionComposition ofof HiggsHiggs andand neutralinoneutralino statesstates

In order, the neutral Bino, Wino, Higgsinos and Singlino components of the lightest neutralino (1 to 5). In order, the neutral Higgs doublet and singlet components of the lightest scalar and pseudoscalar Higgs states. HiggsHiggs SearchesSearches

Invisibly decaying Higgs may be searched for at the LHC in the Weak Boson Fusion production channel. Defining σ ()WBF η =→BR(.H inv ) σ ()WBF SM

The value of η varies between 0.5 and 0.9 for the lightest CP- even Higgs boson. Minimal luminosity required to exclude (discover) such a Higgs boson, with mass lower than 130 GeV:

1.2 fb −−1 8 fb 1 LL==, 95% ηη2 5σ 2

Lightest CP-odd and heavier CP-even has much larger singlet component. More difficult to detect. ConclusionsConclusions

Electroweak Baryogenesis in the MSSM demands a light Higgs, with mass lower than 120 GeV and a stop lighter than the top-quark.

Dark Matter : Even lighter neutralinos. If coannihilation channel relevant, searches for stops at hadron colliders difficult.

nMSSM provides an attractive phenomenological scenario that solves the µ problem without the usual domain wall problem

Dark Matter and Electroweak Baryogenesis rely on the same fields

Interesting phenomenological properties: Light charginos and neutralinos and, possibly, invisibly decaying Higgs bosons Some other subjects LeptogenesisLeptogenesis Heavy, right-handed neutrinos decay out-of-equilibrium

CP violating phases appear in the interference between the tree-level and one-loop amplitudes.

Majorana fermions have extra physical phases. Two generations of neutrinos would be sufficient for the mechanism to work

Detailed calculation shows that lightest right handed neutrino mass 10 should be M1~10 GeV to obtain proper baryon asymmetry.

Leptogenesis may work even in the absence of supersymmetry. (In SUSY reheating temperatures of the order of dangerous, since they lead to overproduction of gravitinos). DirectDirect DarkDark MatterMatter DetectionDetection E T at colliders important evidence of DM candidate, but, stability of LSP on DM time scales cannot be chekced at colliders

Neutralino DM is searched for in neutralino-nucleon scattering exp. detecting elastic recoil off nuclei EDELWEISS 03

CDMS L E ZEPLIN upper bounds on ~P Spin independent cross sections t excl.

−8 XENON Next few years: σ SI ≈10 pb −10 Ultimate goal: σ SI ≈10 pb

small σ si for large µ : co-annihilation and h-resonant regions Balazs, MC, Wagner ’04 tan β EffectsEffects onon thethe relicrelic densitydensity Main effect is via the coupling of the heavy Higgs A,H to bottom quarks • annihilation cross section grows quadratically with tan β

σ si =1 E - 07 • For sufficiently small heavy Higgs masses and large tan beta: σ si =1 E - 08

mA ≈ 250 − −300 GeV tan β ≈ 50 can have dramatic cosequences on the allowed region of parameter space

( m A ≈ 200 GeV can make the relic density too small over most of the space) tan β = 50

mA = 300 GeV

Balazs, Carena, C.W. ‘04