Beyond MSSM Baryogenesis Kfir Blum and Yosef Nir, Phys.Rev.D78:035005,2008

2 (B)MSSM Higgs and stop masses (Un-)Observable: Higgs boson mass

3 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

4 BMSSM higgs sector I MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings Same feature responsible for the tree level relation, m h <m Z, 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 = )

5 BMSSM higgs sector II In the scalar potential, leading BMSSM contribution is Light higgs mass shifted  Stops can go light! Both at GeV

6 (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 ~10 2 sec old - Relative magnitude of Doppler peaks in CMBR temperature anisotropies, measured by WMAP from photons released when the universe was ~10 5 sec old - Both methods agree on η ≈ 6x 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

8 Effective potential

9 EWPT I

10 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

11 EWPT III Condition to avoid sphaleron wash-out: With a light : …Observe: Effective cubic term - parameterize by E: λ = effective quartic coupling:

12 BMSSM EWPT * Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner, arXiv: [hep-ph] and ref. Therein λ ~ m h bound from below by experimental limit on higgs mass EWBG window in MSSM *: - Make as light as possible to enhance potential barrier - Keep m h fixed by making very massive MSSM window  heavy stop at several TeV  hierarchy problem exponentially worse! BMSSM solution: Keep m h fixed by ε term  EWBG window hierarchy-free

13 BMSSM higgs & stops

14 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

15 Xtras

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

17 BMSSM higgsinos Chargino-chargino-scalar-scalar terms and modifications to the mass matrices exist as well