Beyond MSSM Baryogenesis

Kfir Blum and Yosef Nir ,

Phys.Rev.D78:035005,2008

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(B)MSSM

Higgs and stop masses

(Un-)Observable: Higgs boson mass

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Higgs and stop masses• In MSSM, LEP bound on higgs boson mass violates tree level prediction

• This implies sizable quantum corrections

• The most important corrections come from top and stop loops

• To satisfy LEP bound, stop masses are pushed high

Little hierarchy problem

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BMSSM higgs sector I• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings

• Same feature responsible for the tree level relation, mh<mZ,

and for its vulnerability to quantum corrections

• Little hierarchy problem avoided if MSSM quartic higgs potential is modified

- Many microscopic extensions do this

- May or may not add light dof to the MSSM particle content

- Here, deal with the second possibility, via effective low-energy action

• BMSSM: Effective lagrangian summarized by adding non-renormalizable

superpotential terms

(DST = )

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BMSSM higgs sector II• In the scalar potential, leading BMSSM contribution is

• Light higgs mass shifted

Stops can go light!

Both at 100-300 GeV21~,~ tt

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(B)MSSM

Electroweak Baryogenesis

Observable: Baryon Asymmetry of the Universe (BAU)

7 ElectroWeak BaryoGenesis (EWBG)

• BAU measured via- Deuterium abundance (D/H), dictated by BBN when the universe was ~102 sec old- Relative magnitude of Doppler peaks in CMBR temperature anisotropies, measured by WMAP from photons released when the universe was ~105 sec old- Both methods agree on η ≈ 6x10-10 with <10% errors

• EWBG: BAU generated during EW Phase Transition (EWPT)- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation

• EWPT Imposes constraints on weak-scale dof: predictive

Object to calculate: Effective scalar potential at finite temperature

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Effective potential

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EWPT I

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EWPT II

• First order: barrier forms between EW breaking and conserving minima

• Barrier height depends on light scalar dof coupling to the higgs field, and on thermal screening

• In SM, only gauge bosons contribute to barrier

• In MSSM, negative soft squared-mass can reduce thermal screening for stops, making them the dominant player by far

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EWPT III

• Condition to avoid sphaleron wash-out:

• With a light :

…Observe:

• Effective cubic term - parameterize by E:

λ = effective quartic coupling:

Rt~

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BMSSM EWPT

* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner, arXiv:0809.3760 [hep-ph] and ref. Therein

• λ ~ mh bound from below by experimental limit on higgs mass

• EWBG window in MSSM *:

- Make as light as possible to enhance potential barrier

- Keep mh fixed by making very massive

• MSSM window heavy stop at several TeV

hierarchy problem exponentially worse!

Rt~

Lt~

BMSSM solution: Keep mh fixed by ε term

EWBG window hierarchy-free

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BMSSM higgs & stops

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Conclusions & Outlook

Conclusions:• BMSSM: Effective action approach to MSSM extensions

at the few TeV scale. Impact on higgs sector captured by dim.5 operators• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007

• EWBG significantly more natural BN, Phys.Rev.D78:035005,2008

To-do list:• Constraints on dim>4 operators

- Stability of scalar potential

- EDMs, EW Precision Tests

• DM implications

• CPV analysis – EDMs, Baryogenesis

• Collider signatures

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Xtras

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Choice of basis

Leading mass shift

Dimension 6 scalar term,

and condition for neglecting it

2-loop thermal corrections associated with dim 6 term

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BMSSM higgsinos

Chargino-chargino-scalar-scalar

terms and modifications to the mass

matrices exist as well