The Electroweak Phase Transition within natural GNMSSM models

Presenter: Christopher HarmanSupervisor: Dr. Stephan Huber

University of Sussex

Image courtesy of: http://www.symmetrymagazine.org/article/october-2012/what-else-could-the-higgs-be

What is supersymmetry?

SUSYSUSYSTANSTAN

SUPERSYMMETRY INVARIANT THEORYSUPERSYMMETRY INVARIANT THEORY

What is supersymmetry?

SUSYSUSY

STANSTAN

SUPERSYMMETRY INVARIANT THEORYSUPERSYMMETRY INVARIANT THEORY

What is natural supersymmetry?

FESTIVE EDITIONFESTIVE 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 ModelTheory: 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-problemTheory: 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

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) valueEnsure: 1.No linear term in S at the zero field value2.Zero field minimum and EW broken minimum are degenerate (CHOICE!)

Parameter point scan

Randomly assign a (natural) valueEnsure: 1.No linear term in S at the zero field value2.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

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 Δm3 and scan over natural values of mQ3 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

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

Aim of the project

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 (Aλ choice);– No stop mixing (At choice);– Stop soft mass deviation (Δm3 choice)

•Repeat the analysis

Thank you!

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

• Gauge eigenstate basis:

• Mass eigenstate basis:CP-even partCP-even part CP-odd partCP-odd part

Charged partCharged part

The tree-level potential

One-loop level (zero temperature)Green – Exact solution with degenerate stopsRed – 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: 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: 20192 Successes: 20192