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Exploring Baryogenesis in the BMSSM Framework: Higgs and Stop Mass Implications

This study delves into the Beyond Minimal Supersymmetric Standard Model (BMSSM), particularly focusing on baryogenesis and the associated mass dynamics of Higgs and stop particles. We highlight how the LEP bound on the Higgs mass suggests significant quantum corrections that push stop masses to high values, leading to the little hierarchy problem. Our analysis includes the effective low-energy action of the BMSSM and its impact on electroweak baryogenesis (EWBG), emphasizing the necessary conditions for generating baryon asymmetry during the electroweak phase transition (EWPT). The connection between light stops, Higgs mass stability, and baryogenesis is also explored.

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Exploring Baryogenesis in the BMSSM Framework: Higgs and Stop Mass Implications

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  1. 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, 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 = )

  5. Stops can go light! Both at 100-300 GeV BMSSM higgs sector II • In the scalar potential, leading BMSSM contribution is • Light higgs mass shifted

  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 ~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

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

  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 TeV •  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, arXiv: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 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

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