1. The Electroweak Phase Transition within natural GNMSSM models Presenter: Christopher Harman Supervisor: Dr. Stephan Huber University of Sussex Image courtesy of: http://www.symmetrymagazine.org/art icle/october-2012/what-else-could-the- higgs-be http://www.symmetrymagazine.org/art icle/october-2012/what-else-could-the- higgs-be

2. What is supersymmetry? SUSY STAN SUPERSYMMETRY INVARIANT THEORY

3. What is supersymmetry? SUSY STAN SUPERSYMMETRY INVARIANT THEORY

4. What is natural supersymmetry? FESTIVE EDITION

5. What is natural supersymmetry? natural unnatural

6. What is natural supersymmetry? natural unnatural excluded

7. What is the MSSM? MSSM: Minimal Supersymmetric Standard Model Motivation: To address deviations (?) and physics not addressed by the Standard Model Theory: A type II 2HDM with supersymmetry invariance at the high-scale and soft SUSY broken terms to describe the low energy scales

8. What is the NMSSM? NMSSM: Next-to-MSSM Motivation: To resolve the μ-problem Theory: Include a singlet chiral superfield into the Higgs sector of the MSSM

9. GNMSSM: Generalised NMSSM Motivation: Include all possible renormalisable terms in the superpotential What is the GNMSSM? Not in the scale-invariant NMSSM

10. Aim of the project

12. The (effective) potential is given by with CP violating phases ``switched off’’. It contains the following free parameters The one loop zero temperature potential

13. Parameter point scan

14. Randomly assign a (natural) value Parameter point scan

15. Randomly assign a (natural) value Ensure: 1.No linear term in S at the zero field value 2.Zero field minimum and EW broken minimum are degenerate (CHOICE!) Parameter point scan

16. Randomly assign a (natural) value Ensure: 1.No linear term in S at the zero field value 2.Zero field minimum and EW broken minimum are degenerate (CHOICE!) Record parameter points satisfying certain criteria, e.g.: stable potential, physical masses. Parameter point scan

17. At tree level At tree level, we find but this is insufficient for a 125 GeV Higgs… … go to one-loop level!

18. Aim of the project

20. Parameter point scan

21. Choose a specific stop structure: 1.No gauge eigenstate mixing: 2.Stop soft mass deviation: Parameter point scan

22. Choose a specific stop structure: 1.No gauge eigenstate mixing: 2.Stop soft mass deviation: Assign a value to Δm 3 and scan over natural values of m Q3 until a 125 GeV Higgs is obtained Parameter point scan

23. Parameter point scan (two distinct potential shapes) TYPE 1 Tree 1 loop

24. Parameter point scan (two distinct potential shapes) TYPE 1 1 loop

25. Parameter point scan (two distinct potential shapes) TYPE 2 Tree 1 loop

26. Parameter point scan (two distinct potential shapes) TYPE 2 1 loop

27. Aim of the project

29. One loop finite temperature potential Include to the potential the following term: We implement this into our program and obtain values for the critical temperature and critical VEV by numerical means

30. One loop level (finite temperature) We implement this into our program and obtain values for the critical temperature and critical VEV by numerical means Tree 1 loop (0T) 1 loop (finite T) TYPE 1 TYPE 2

31. Aim of the project

34. Outlook CONCLUSIONS: Can have a 125 GeV Higgs in the GNMSSM EWPT is found to be rather strongly first order for around 200 natural parameter points FUTURE WORK: Relax some of our choices: – Tree-level minima degeneracy (A λ choice); – No stop mixing (A t choice); – Stop soft mass deviation (Δm 3 choice) Repeat the analysis

35. Thank you! S. Martin, A SUSY Primer: http://arxiv.org/abs/hep-ph/9709356http://arxiv.org/abs/hep-ph/9709356 U. Ellwanger, The NMSSM: http://arxiv.org/abs/arXiv:0910.1785http://arxiv.org/abs/arXiv:0910.1785 G. Ross et al., The GNMSSM at one loop: fine tuning and phenomenology G. Anderson and L. Hall, The Electroweak phase transition and baryogenesis

36. Gauge eigenstate basis: Mass eigenstate basis: CP-even part CP-odd part Charged part The tree-level potential

37. One-loop level (zero temperature) Green – Exact solution with degenerate stops Red – Naïve solution with non-degenerate stops

38. One-loop level (finite temperature) Include to the potential the following term: Piece-wise analytic function can be constructed

39. Finite temperature potential (analytic)

40. Parameter scan statistics Models with an unstable singlet potential only: 17.9477 % Models with at least one unphysical mass only: 6.40353 % Models with both of the above issues: 73.7124 % Models with none of the above issues: 1.93641 % Runs:20192Successes:20192