The Minimal Supersymmetric Standard Model

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Table of contents

Introduction
1 The Higgs boson and Physics beyond the Standard Model
1.1 The Standard Model and the Higgs sector
1.1.1 Mass terms of gauge bosons and fermions
1.1.2 Electroweak Symmetry Breaking and the Brout-Englert-Higgs mechanism
1.1.3 Electroweak gauge xing
1.1.4 The Higgs sector at tree-level and beyond
1.1.5 The Goldstone Boson Catastrophe in the Standard Model
1.2 Going beyond the Standard Model
1.2.1 The hierarchy problem
1.2.2 The stability of the electroweak vacuum
1.2.3 Building models beyond the Standard Model
1.3 Supersymmetry
1.3.1 Some basics of SUSY
1.3.1.1 Fermions in two-component notation
1.3.1.2 Supersymmetry, the SUSY algebra and its representations
1.3.1.3 Superspace formalism and superelds
1.3.1.4 Superpotential and supersymmetric Lagrangians
1.3.1.5 R-symmetry
1.3.2 SUSY breaking
1.3.3 The hierarchy problem and Supersymmetry
1.3.4 Minimal models
1.3.4.1 The Minimal Supersymmetric Standard Model
1.3.4.2 The Higgs sector of the MSSM
1.3.4.3 Gauginos in the MSSM
1.3.4.4 Shortcomings of the MSSM
1.3.4.5 The Next-to-Minimal Supersymmetric Standard Model
1.3.4.6 The Higgs sector of the NMSSM
1.3.5 Dirac gaugino models
1.3.5.1 Extended Supersymmetry and supersoft SUSY breaking
1.3.5.2 A brief overview of Dirac gaugino models
1.3.5.3 Some aspects of the phenomenology of Dirac gaugino models
1.3.5.4 Properties of the adjoint scalars
1.3.5.5 Gluino masses and couplings
1.3.5.6 The MDGSSM and the MRSSM
1.4 Non-supersymmetric extensions of the Standard Model
1.4.1 Singlet extensions of the Standard Model
1.4.2 Two-Higgs-Doublet Models
1.4.3 The Georgi-Machacek model
2 Precision calculations of the Higgs boson mass
2.1 Measurements of the Higgs mass
2.2 Scalar mass calculations
2.2.1 Regularisation and renormalisation schemes
2.2.2 Calculations beyond leading order and choice of inputs
2.2.3 Dierent types of mass calculations
2.2.3.1 Fixed-order calculations
2.2.3.2 The eective eld theory approach
2.3 State-of-the-art of Higgs mass calculations
2.3.1 Real and complex MSSMs
2.3.1.1 Fixed-order results
2.3.1.2 EFT and hybrid results
2.3.2 Supersymmetric models beyond the MSSM
2.3.3 Non-supersymmetric models
2.4 Calculations in generic theories
2.4.1 Notations for general eld theories
2.4.2 Two-loop neutral scalar masses in generic theories
2.4.3 The SARAH/SPheno framework
2.4.3.1 Analytic calculations with SARAH 87
2.4.3.2 Interfaces with SPheno and other HEP codes
2.4.3.3 Numerical set-up of the spectrum calculation
3 Leading two-loop corrections to the Higgs boson masses in SUSY models with Dirac gauginos
3.1 Two-loop corrections in the eective potential approach
3.1.1 General results
3.1.2 Two-loop top/stop contributions to the eective potential
3.1.3 Mass corrections in the MDGSSM
3.1.4 Mass corrections in the MRSSM
3.1.5 On-shell parameters in the top/stop sector
3.1.6 Obtaining the O(bs) corrections
3.1.7 Simplied formulae
3.1.7.1 Common SUSY-breaking scale
3.1.7.2 MRSSM with heavy Dirac gluino
3.2 Numerical examples
3.2.1 An example in the MDGSSM
3.2.2 An example in the MRSSM
3.3 Conclusions
4 Avoiding the Goldstone Boson Catastrophe in general renormalisable eld theories at two loops
4.1 The Goldstone Boson Catastrophe and resummation
4.1.1 Abelian Goldstone model
4.1.2 Goldstone bosons in general eld theories
4.1.3 Small m2 G expansion of the eective potential for general theories
4.2 Removing infra-red divergences in the minimum condition
4.2.1 All-scalar diagrams
4.2.1.1 Elimination of the divergences by method (i)
4.2.1.2 Elimination of the divergences by method (ii)
4.2.1.3 Elimination of the divergences by setting the Goldstone boson on-shell
4.2.2 Diagrams with scalars and fermions
4.2.3 Diagrams with scalars and gauge bosons
4.2.4 Total tadpole
4.3 Mass diagrams in the gaugeless limit
4.3.1 All-scalar terms
4.3.1.1 Goldstone shifts
4.3.1.2 Momentum-regulated diagrams
4.3.2 Fermion-scalar diagrams
4.4 Self-consistent solution of the tadpole equations
4.5 Conclusions
5 Supersymmetric and non-supersymmetric models without catastrophic Goldstone bosons
5.1 The Goldstone Boson Catastrophe and its solutions
5.1.1 Previous approaches in SARAH
5.1.2 On-shell Goldstone bosons, consistent tadpole solutions, and the implementation in SARAH
5.2 Standard Model
5.2.1 A rst comparison of our results with existing calculations
5.2.2 A detailed comparative study of SPheno and SMH results
5.2.3 Momentum dependence
5.3 The NMSSM
5.4 Split SUSY
5.5 Two-Higgs-Doublet Model
5.5.1 The alignment in Two-Higgs-Doublet Models
5.5.2 Renormalisation scale dependence of the Higgs mass computed with SPheno
5.5.3 Quantum corrections to the alignment limit
5.5.4 Perturbativity constraints
5.6 Georgi-Machacek Model
5.7 Conclusions
6 Matching and running
6.1 Matching and Running
6.1.1 Renormalisation Group Equations
6.1.2 Matching
6.2 Models and results
6.2.1 Singlet Extension
6.2.2 Singlet Extension with an additional Z2 symmetry
6.2.2.1 Analytical approximation
6.2.2.2 Numerical study
6.2.3 Vector-like quarks and stability of the SM
6.2.4 Two-Higgs Doublet model
6.3 Conclusions
Conclusion
A Derivatives of the two-loop eective potential in models with Dirac gauginos
B Denitions and expansions of loop functions
B.1 Loop functions
B.1.1 Denition of loop functions
B.1.1.1 One-loop functions
B.1.1.2 Two-loop functions
B.1.2 Small m2 G expansion
B.2 Diagrams regulated by momentum
B.2.1 Limits of the Z and U functions
B.2.2 Limits of the M function
B.3 Additional expressions for ~ V (x; 0; z; u)
B.3.1 Integral representation
C Consistent solution of the tadpole equations with shifts to fermion masses
Bibliography