Beyond MSSM Baryogenesis Kfir Blum and Yosef Nir

Beyond MSSM Baryogenesis Kfir Blum and Yosef Nir, Phys. Rev. D 78: 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, mh<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 100 -300 Ge. V

6 (B)MSSM Electroweak Baryogenesis Observable: Baryon Asymmetry of the Universe (BAU)

7 Electro. Weak Baryo. Genesis (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 ≈ 6 x 10 -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

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: • Effective cubic term - parameterize by E: λ = effective quartic coupling: • With a light : …Observe:

12 BMSSM EWPT • 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 Te. V hierarchy problem exponentially worse! BMSSM solution: Keep mh fixed by ε term EWBG window hierarchy-free * Latest: M. Carena, G. Nardini, M. Quiros, C. E. M. Wagner, ar. Xiv: 0809. 3760 [hep-ph] and ref. Therein

13 BMSSM higgs & stops

14 Conclusions & Outlook Conclusions: • BMSSM: Effective action approach to MSSM extensions at the few Te. V scale. Impact on higgs sector captured by dim. 5 operators • Little hierarchy problem ameliorated DST, Phys. Rev. D 76: 095004, 2007 • EWBG significantly more natural BN, Phys. Rev. D 78: 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