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Beyond the MSSM From the little hierarchy problem to the Baryon Asymmetry of the Universe Kfir Blum Advisors: Yossi Nir and Eli Waxman

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Supersymmetry (SUSY) is a great idea It fixes the fine tuning problem MSSM = simplest SUSY extension of SM Higgs sector extremely predictive: more so than in SM! …But it does not completely solve the tuning – little hierarchy problem remains

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The little hierarchy problem MSSM: at classical level, m H < m Z =91 GeV ! LEPII: m H >114 GeV need large quantum corrections; can do with very heavy stops, m st >TeV This implies % tuning If additional DOF heavy M >> m Z, general way to proceed is via effective field theory: Beyond MSSM MSSM aint the whole story (we know this: for one, it isnt enough to break SUSY) Can additional DOF solve little hierarchy problem?

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BMSSM Expand in powers of m/M, m ~ m Z << M Higgs sector: (Approx) SUSY + leading m/M Only two operators ! In the scalar potential: For M < 10 TeV, More than enough to lift m H above LEP at classical level See e.g. Dine, Seiberg & Thomas, Phys.Rev.D76:095004,2007

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BMSSM: Implications for vacuum stability and Cosmology Vacuum stability Dark Matter The electroweak phase transition and electroweak baryogenesis Blum, Delaunay & Hochberg, Phys.Rev.D80:075004,2009 Bernal, Blum, Losada & Nir, JHEP 0908:053,2009 Blum, Delaunay, Losada, Nir, Tulin, Work in progress Bernal, Blum, Losada & Nir, JHEP 0908:053,2009 Blum & Nir, Phys.Rev.D78:035005,2009 MSSM BMSSM

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BMSSM Higgs potential non trivial. Raise m H tunneling problem ? Vacuum stability …SUSY implies: Constraints remain: Must not overcome gauge couplings Upper bound on M

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MSSM BMSSM Baryon Asymmetry of the Universe cannot be solved within SM MSSM EWBG – little hierarchy amplified need m H ~114 GeV, but also light stop other stop very heavy big little hierarchy BMSSM: Can have 2 light stops! No hierarchy New couplings CP violation Spontaneous EWBG BMSSM Electroweak Baryogenesis

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Summary * MSSM little hierarchy problem – due to constrained Higgs sector, solved Beyond-MSSM * Vacuum stability – SUSY renders effective theory simple & consistent * Implications for Cosmology – Natural EW Baryogenesis with 2 light stops – DM scenarios (bulk region reopens) Outlook * Spontaneous EW Baryogenesis * Light stop phenomenology * Microscopic realizations

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Thanks!

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Xtras

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If… BMSSM respects R-parity Approximately SUSY (msoft<<M) SUSY breaking via spurions Pure Higgs: Only 2 new operators! … enough to solve little hierarchy problem

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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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Effective potential

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EWPT I

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EWPT – Barrier Formation 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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BMSSM higgsinos Chargino-chargino-scalar-scalar terms and modifications to the mass matrices exist as well

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Most natural parameter space for MSSM DM: Bino annihilates via light sfermion exchange. Example – mSUGRA Bulk Region. If sfermion spectrum correlated (light sleptons light stops), LEPII kills bulk region, since stops must be heavy. BMSSM Dark Matter BMSSM: m H decoupled from m st efficient sfermion t-channel, bulk region lives Stop co-annihilation region Also: Higgs resonance channel, Modified Higgsino couplings

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