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

What is supersymmetry? SUSY STAN SUPERSYMMETRY INVARIANT THEORY

What is supersymmetry? SUSY STAN SUPERSYMMETRY INVARIANT THEORY

What is natural supersymmetry? FESTIVE EDITION

What is natural supersymmetry? natural unnatural

What is natural supersymmetry? natural unnatural excluded

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

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

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

Aim of the project

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

Parameter point scan

Randomly assign a (natural) value Parameter point scan

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

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

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

Aim of the project

Parameter point scan

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

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

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

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

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

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

Aim of the project

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

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

Aim of the project

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

Thank you! S. Martin, A SUSY Primer: U. Ellwanger, The NMSSM: G. Ross et al., The GNMSSM at one loop: fine tuning and phenomenology G. Anderson and L. Hall, The Electroweak phase transition and baryogenesis

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

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

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

Finite temperature potential (analytic)

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