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Supersymmetry, the Baryon Asymmetyry and the Origin of Mass

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- is governed by the same as matter.

„ is composed of matter.

„ Anti-matter is only seen in cosmic rays and accelerators

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

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

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

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

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

„ SM fufills the Sakharov conditions:

„ Baryon number violation: Anomalous Processes

„ CP violation: CKM mixing

„ Non-equilibrium: Possible at the electroweak . 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 , but suppressed at temperatures below the electroweak phase transition.

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

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

„ 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 ). 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 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 and squared, and is responsible for the phenomenon of restoration

E receives contributions proportional to the sum of the cube of all light 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 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 At LEP energies mainly into pairs of b

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 fermionsfermions bosonsbosons electronelectron sselectronelectron quarkquark ssquarkquark photphotinoino photonphoton gravitgravitinoino gravitongraviton

Photino, Zino and Neutral :

Charged Wino, charged Higgsino:

Particles and Sparticles share the same couplings to the Higgs. Two of the two quarks (one for each ) 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— scale hierarchy

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

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

„ Starting from positive at high energies, electroweak is induced radiatively.

3B+L+2S „ If discrete symmetry, P = (-1) is imposed, lightest SUSY particle neutral and stable: Excellent candidate for cold . Supersymmetry at 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 -less particles 1 tend to be the lightest ones.

¾ Lightest supersymmetric particle = Excellent 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: 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 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 depend strongly on the and spectrum as well as on the 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 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 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- 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 – bubbles. ~ γ i

New sources of CP violation from the 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 and 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

2 m12 WS=+λ HH Sy+QHU 12 λ t2

„ No cubic term. 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

ƒ 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

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

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

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

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

ƒ 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 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 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 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 to an acceptable relic density

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

„ Non-renormalizable operators still exist, but proton stability ensured and neutralino lifetime longer than the , 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-

„ 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, 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 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 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 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 ). 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- scattering exp. detecting elastic recoil off nuclei EDELWEISS 03

CDMS L E ZEPLIN upper bounds on ~P 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