1. Spectrum generation for SUSY and non-SUSY extensions of the Standard Model FlexibleSUSY Peter Athron, Jae-hyeon Park, Dominik Stöckinger, Alexander Voigt Markus Bach, Dylan Harries, Tom Steudtner, Jobst Ziebell

2. FlexibleTools Aim: create precise computational tools for phenomenology in most or all BSM models Build general algorithms with flexibility in mind Specialise to specific user specified model and generate C++ implementation Allow flexible adaption at every level: adapt model input, shape tool structure, adapt generated code, configure options via input Process [PA, M.Bach, D.Harries, J.H.Park, T.Steudtner, D.Stöckinger, A.Voigt, J.Ziebell]

3. Spectrum generators boundary-value solver High-scale Boundary condition Low-scale Boundary condition Output Pole masses, mixing angles / matrices, couplings Components RGEs Self energies Mass matrices EWSB equations Tadpoles corrections

4. FlexibleSUSY Precision corrections for spectrum generators known in general form Exploit this abstraction to aid theory and phenomenology. SARAH Feynman rules, RGEs, Self Energies, tadpoles... [F. Staub] FlexibleSUSYC++ code, fast, modular, adaptable, reliable. https://flexiblesusy.hepforge.org/ [PA, J.H.Park, D.Stöckinger, A.Voigt CPC 190 (2015) 139-172]

5. FlexibleSUSY Precision corrections for spectrum generators known in general form Exploit this abstraction to aid theory and phenomenology. SARAH Feynman rules, RGEs, Self Energies, tadpoles... [F. Staub] FlexibleSUSYC++ code, fast, modular, adaptable, reliable. https://flexiblesusy.hepforge.org/ [PA, J.H.Park, D.Stöckinger, A.Voigt CPC 190 (2015) 139-172]

7. FlexibleSUSY Precision corrections for spectrum generators known in general form Exploit this abstraction to aid theory and phenomenology. SARAH Feynman rules, RGEs, Self Energies, tadpoles... [F. Staub] FlexibleSUSYC++ code, fast, modular, adaptable, reliable. Many prebuilt spectrum generators: MSSM,NMSSM,USSM,E6SSM... (No SARAH / MATHEMATICA dependence) https://flexiblesusy.hepforge.org/models.html https://flexiblesusy.hepforge.org/ [PA, J.H.Park, D.Stöckinger, A.Voigt CPC 190 (2015) 139-172] Web interface (go play): https://flexiblesusy.hepforge.org/online/online.php

8. Neutral Higgs can get two loop corrections (optional): (files from Pietro Slavich) FlexibleSUSY is precise Full three family two loop RGEs Full one loop self energies for all states and mass mixing Pure QCD two loop corrections for running top/bottom (N)MSSM zero momentum MSSM parts zero momentum [G.Degrassi, P.Slavich Nucl.Phys. B 825, 119 ] one loop self energies use via iteration (optional): diagonalise for eigenvalues FlexibleSUSY spectrum generators are as precise as leading public spectrum generators for MSSM and NMSSM: SOFTSUSY, SPheno, SUSPECT, NMSSMTools...

9. FlexibleSUSY and other NMSSM Spectrum generators were compared here: Default FlexibleSUSY closely matched to SOFTSUSY FlexibleSUSY and SOFTSUSY agree more closely than most spectrum generators Higgs Mass in NMSSM [F.Staub, PA, U.Ellwanger, R.Grober, M.Muhlleitner, P.Slavich, A.Voigt, arXiv:1507.05093 [hep-ph].]

10. FlexibleSUSY is fast Smart linear algebra package (Eigen3) Multi-threading CMSSM run-time comparison

11. Advantages: fast, finds solutions for most points in many models. FlexibleSUSY is adaptable boundary-value solver High-scale Boundary condition Low-scale Boundary condition Two-scale fixed point iteration Apply boundary conditions Solve EWSB Calculate tadpoles

12. START Apply boundary conditions ITERATION Calculate pole masses and mixings CONVERGENCE Tree level EWSB Two-scale fixed point iteration Solve EWSB Calculate tadpoles

13. FlexibleSUSY is adaptable Two-scale boundary solver may be set in non-standard ways: Specify your own high scale boundary conditions Define the high scale, with fixed number or analytic condition Choose EWSB output parameters Select EWSB solvers (FPI vs gsl Broyden, Newton etc) gauge coupling unification OR Tau-bottom Yukawa unification OR Fixed scale entered as input parameter Common MSSM choice Default setting is to try all, starting with FPI Build tower of effective field theoriesC++ code level only so far

14. A Flexible Future

15. FlexibleBSM available: now (v1.1.0+) FlexibleSUSY now works for non-SUSY models as well. Default executable is based on two-scale solver shaped using the model file Beyond this the C++ code may be adapted or used as a library of C++ routines, you can exploit routines to: Very similar to SUSY structure but parameters, RGEs and shifts to pole used. Solve EWSB Extract DRbar / MSbar parameters Calculate tree level mass eigenstates Calculate Pole mass eigenstates using one loop self energies Run DRbar / MSbar parameters with 2 loop RGEs Usage examples: Calculate spectrum where some SUSY partners are very heavy and a non-SUSY model is used as a low energy effective theory (e.g. Split-SUSY) Study vacuum stability in the model

16. A Flexible Future FlexibleSAS (Dylan Harries ) auto generation available: October FlexibleSUSY has been designed to allow new boundary-value problem solvers Semi-Analytic Solver Use semi-analytic solutions for running masses at EWSB scale Now the EWSB outputs may include universal parameters set at the high scale. This makes it possible to find solutions in the CNMSSM, CE6SSM. SUSY ITERATION FIND SEMI-ANALYTIC COEFFICIENTS EWSB ITERATION EXTRACT POLE MASSES Rewrite EWSB in terms of universal (m, M, A) parameters Coefficients depend only on dimensionless couplings

17. Semi-analytic fixed point iteration Fit semi-analytic coefficients SUSY ITERATION Set high-scale soft parameter Solve EWSB Calculate tadpoles SUSY ITERATION FIND SEMI-ANALYTIC COEFFICIENTS EWSB ITERATION EXTRACT FIND SEMI-ANALYTIC COEFFICIENTS EWSB ITERATION POLE MASSES START

18. A Flexible Future FlexibleCPV available: now (v1.1.0+) FlexibleSUSY can now generate models with complex parameters. Includes two loop RGEs, one loop self energies and correct mass eigenstates for the CPV version. FlexibleMW New calculation of muon decay to be implemented. Allows us to use most precise inputs and make MW a prediction, which can be used in precision tests. FlexibleAMU Calculation of new physics contributions to g-2 specialised to the user chosen model (Markus Bach) available: October (Jobst Ziebell) available: October Flexible2LHiggs (Tom Steudtner) available: October An effective field theory calculation of the two-loop Higgs mass for a generic model GM2Calc which has latest two-loop corrections specialised to MSSM will be released very soon. FlexibleDecay (Dylan Harries, Markus Bach ) available: some time next year Calculate BRs for Higgs and new BSM states FlexibleTower available: some time next year Automatically generate matching between two BSM models and tower of effective field theories

19. Conclusions FlexibleSUSY creates spectrum generators and library of routines for SUSY and non-SUSY models FlexibleSUSY spectrum generators are:fast, adaptable, reliable, easy to use Go to the FlexibleSUSY website now: https://flexiblesusy.hepforge.org/ Download it, build it, adapt it and let us know what you think of it! Many new extensions including EFT 2-loop Higgs calculation, new boundary-value solvers, complex parameters New FlexibleTools including FlexibleDecay and FlexibleAMU

20. The End

21. Backup slides

22. FlexibleSUSY is adpaptable Spectrum generator may be adapted at: Meta-code level Change particle content, gauge structure, mixing, etc Change boundary conditions Change EWSB output parameters Change algorithm Build effective tower of different models Generated code (C++) level Replace components Extend components (i.e. add new corrections) Use components in your own code Replace algorithm Build effective tower of different models

23. FlexibleSUSY is adpaptable Object orientationmodularity Replaceable/extendable/reusable components: RGEs Self energies Tadpoles Mass matrices RGE + BC solver: two scale fixed point iteration Lattice method, semi-analytic solver, shooting method. linear algebra package SUSY or soft breaking parameter objects Passarino-veltman functions I am sure there are more if you are smart...

24. Minimality is not required by fundamental motivations of SUSY Large Hierarchy Problem Gauge Coupling Unification Dark Matter candidate Explaining the matter-antimatter asymmetry Radiative EWSB Just needs SUSY + little hierarchy problem can be improved Just depends on incomplete SU(5) Multiplets (Higgs fields) Appropriate LSP from Z2 symmetry Can have extra contributions Need large Yukawas to drive soft terms negative

25. But non-minimal models can solve problems with the MSSM mu problem little hierarchy problem Explaining the matter-antimatter asymmetry Flavour physics problems boredom: exciting new phenomenology Many tools exist to help study the MSSM quickly and precisely

26. Beyond SUSY SUSY models are not the only possibility (sorry SUSY 2015) Higgs extensions (scalar singlet, two Higgs doublet, triplet Higgs) Dark matter models (non-SUSY) Extra dimensions Composite Higgs (non-SUSY) GUT models Family symmetry models

27. The End