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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
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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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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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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Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections associated with dim 6 term