Flexible SUSY Spectrum generation for SUSY and nonSUSY

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

Flexible. Tools [PA, M. Bach, D. Harries, J. H. Park, T. Steudtner, D. Stöckinger, A. Voigt, J. Ziebell] Aim: create precise computational tools for phenomenology in most or all BSM models Process 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

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

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

Flexible. SUSY https: //flexiblesusy. hepforge. org/ [PA, J. H. Park, D. Stöckinger, A. Voigt CPC 190 (2015) 139 -172] • Precision corrections for spectrum generators known in general form • Exploit this abstraction to aid theory and phenomenology. SARAH Flexible. SUSY Feynman rules, RGEs, Self Energies, tadpoles. . . [F. Staub] C++ code, fast, modular, adaptable, reliable. • Many prebuilt spectrum generators: MSSM, NMSSM, USSM, E 6 SSM. . . (No SARAH / MATHEMATICA dependence) https: //flexiblesusy. hepforge. org/models. html • Web interface (go play): https: //flexiblesusy. hepforge. org/online. php

Flexible. SUSY is precise • Flexible. SUSY spectrum generators are as precise as leading public spectrum generators for MSSM and NMSSM: SOFTSUSY, SPheno, SUSPECT, NMSSMTools. . . • 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 • Neutral Higgs can get two loop corrections (optional): (files from Pietro Slavich) (N)MSSM zero momentum [G. Degrassi, P. Slavich Nucl. Phys. B 825, 119] MSSM parts zero momentum • one loop self energies use via iteration (optional): diagonalise for eigenvalues

Higgs Mass in NMSSM Default Flexible. SUSY closely matched to SOFTSUSY Flexible. SUSY and SOFTSUSY agree more closely than most spectrum generators Flexible. SUSY and other NMSSM Spectrum generators were compared here: [F. Staub, PA, U. Ellwanger, R. Grober, M. Muhlleitner, P. Slavich , A. Voigt, ar. Xiv: 1507. 05093 [hep-ph]. ]

Flexible. SUSY is fast • Smart linear algebra package (Eigen 3) • Multi-threading CMSSM run-time comparison

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

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

Flexible. SUSY 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 gauge coupling unification OR Tau-bottom Yukawa unification OR Fixed scale entered as input parameter • Choose EWSB output parameters Common MSSM choice • Select EWSB solvers (FPI vs gsl Broyden, Newton etc) Default setting is to try all, starting with FPI • Build tower of effective field theories C++ code level only so far

A Flexible Future

A Flexible Future • Flexible. BSM available: now (v 1. 1. 0+) Flexible. SUSY now works for non-SUSY models as well. Very similar to SUSY structure but parameters, RGEs and shifts to pole used. 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: • 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

A Flexible Future • Flexible. SAS (Dylan Harries) auto generation available: October Flexible. SUSY has been designed to allow new boundary-value problem solvers Semi-Analytic Solver Use semi-analytic solutions for running masses at EWSB scale Coefficients depend only on dimensionless couplings Rewrite EWSB in terms of universal (m, M, A) parameters Now the EWSB outputs may include universal parameters set at the high scale. This makes it possible to find solutions in the CNMSSM, CE 6 SSM. EXTRACT SUSY ITERATION FIND SEMI-ANALYTIC COEFFICIENTS EWSB ITERATION POLE MASSES

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

A Flexible Future • Flexible. CPV available: now (v 1. 1. 0+) Flexible. SUSY can now generate models with complex parameters. Includes two loop RGEs, one loop self energies and correct mass eigenstates for the CPV version. • Flexible. MW (Markus Bach) available: October 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. • Flexible. AMU (Jobst Ziebell) available: October Calculation of new physics contributions to g-2 specialised to the user chosen model GM 2 Calc which has latest two-loop corrections specialised to MSSM will be released very soon. • Flexible 2 LHiggs (Tom Steudtner) available: October An effective field theory calculation of the two-loop Higgs mass for a generic model • Flexible. Decay (Dylan Harries, Markus Bach ) available: some time next year Calculate BRs for Higgs and new BSM states • Flexible. Tower available: some time next year Automatically generate matching between two BSM models and tower of effective field theories

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

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Flexible. SUSY 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

Flexible. SUSY is adpaptable Object orientation modularity Replaceable/extendable/reusable components: • RGEs • Self energies • Tadpoles • Mass matrices • RGE + BC solver: ü two scale fixed point iteration ü 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. . .

Minimality is not required by fundamental motivations of SUSY Just needs SUSY + little hierarchy problem can be improved • Large Hierarchy Problem • Gauge Coupling Unification • Dark Matter candidate Just depends on incomplete SU(5) Multiplets (Higgs fields) Appropriate LSP from Z 2 symmetry • Explaining the matter-antimatter asymmetry Can have extra contributions • Radiative EWSB Need large Yukawas to drive soft terms negative

Many tools exist to help study the MSSM quickly and precisely 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

Beyond 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

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