Automatic Calculation of supersymmetric Renormalization Group Equations and Self Energies

Abstract

SARAH is a Mathematica package for studying supersymmetric models. It calculates for a given model the masses, tadpole equations and all vertices at tree-level. Those information can be used by \SARAH to write model files for CalcHep/CompHep or FeynArts/FormCalc. In addition, the second version of SARAH can derive the renormalization group equations for the gauge couplings, parameters of the superpotential and soft-breaking parameters at one and two-loop level. Furthermore, it calculates the one-loop self energies and the one-loop corrections to the tadpoles. SARAH can handle all N=1 SUSY models whose gauge sector is a direct product of SU(N) and U(1) gauge groups. The particle content of the model can be an arbitrary number of chiral superfields transforming as any irreducible representation with respect to the gauge groups. To implement a new model, the user has just to define the gauge sector, the particle, the superpotential and the field rotations to mass eigenstates.

32 pages, some typoes corrected, matches published version

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Cited by in corpus (317)

• SARAH 4: A tool for (not only SUSY) model builders
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• FlexibleSUSY -- A spectrum generator generator for supersymmetric models
• Reconciling EFT and hybrid calculations of the light MSSM Higgs-boson mass
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• Lepton flavor violation in low-scale seesaw models: SUSY and non-SUSY contributions
• FlexibleSUSY 2.0: Extensions to investigate the phenomenology of SUSY and non-SUSY models
• Next-to-Minimal SOFTSUSY
• A global fit of the MSSM with GAMBIT
• NMSSMCALC: A Program Package for the Calculation of Loop-Corrected Higgs Boson Masses and Decay Widths in the (Complex) NMSSM
• Constraining the Natural MSSM through tunneling to color-breaking vacua at zero and non-zero temperature
• Stability of the CMSSM against sfermion VEVs
• GM2Calc: Precise MSSM prediction for $(g-2)$ of the muon
• A superspace module for the FeynRules package
• Combined collider constraints on neutralinos and charginos
• The generalised NMSSM at one loop: fine tuning and phenomenology
• Higgs-mass predictions in the MSSM and beyond
• Dirac Gauginos and the 125 GeV Higgs
• PyR@TE: Renormalization Group Equations for General Gauge Theories
• Enhanced $h\to \gamma \gamma$ rate in MSSM singlet extensions
• Improved predictions for intermediate and heavy Supersymmetry in the MSSM and beyond
• Precise Higgs mass calculations in (non-)minimal supersymmetry at both high and low scales
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• Decays of the neutral Higgs bosons into SM fermions and gauge bosons in the $\mathcal{C}\mathcal{P}$-violating NMSSM
• Generic calculation of two-body partial decay widths at the full one-loop level
• Analysis of the NMSSM Higgs Boson Masses at One-Loop Level
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• On the two-loop corrections to the Higgs masses in the NMSSM
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• Explaining the Lepton Non-universality at the LHCb and CMS from a Unified Framework
• Higgs Boson Masses in the Complex NMSSM at One-Loop Level
• Running soft parameters in SUSY models with multiple U(1) gauge factors
• Beyond the Minimal Supersymmetric Standard Model: from theory to phenomenology
• A Review of Higgs Mass Calculations in Supersymmetric Models
• Mass spectrum of the minimal SUSY B-L model
• On two-loop corrections to the Higgs trilinear coupling in models with extended scalar sectors
• Revisiting RGEs for general gauge theories
• Completing the scalar and fermionic Universal One-Loop Effective Action
• A unified leptoquark model confronted with lepton non-universality in $B$-meson decays
• A stable Higgs portal with vector dark matter
• Dark matter scenarios in the minimal SUSY B-L model
• Supersymmetric and non-supersymmetric models without catastrophic Goldstone bosons
• Exploring the Higgs Sector of a Most Natural NMSSM and its Prediction on Higgs Pair Production at the LHC
• Non-universal gaugino masses and fine tuning implications for SUSY searches in the MSSM and the GNMSSM
• Precise Predictions for the Higgs-Boson Masses in the NMSSM
• Calculating the renormalisation group equations of a SUSY model with Susyno
• Revisiting fine-tuning in the MSSM
• Maxi-sizing the trilinear Higgs self-coupling: how large could it be?
• Enhancing lepton flavour violation in the supersymmetric inverse seesaw beyond the dipole contribution
• Two-loop RGEs with Dirac gaugino masses
• The Higgs mass in the CP violating MSSM, NMSSM, and beyond
• Higgs mass predictions of public NMSSM spectrum generators
• Enhanced diphoton rates at Fermi and the LHC
• Exploring the CP-violating NMSSM: EDM Constraints and Phenomenology
• SpecBit, DecayBit and PrecisionBit: GAMBIT modules for computing mass spectra, particle decay rates and precision observables
• How arbitrary are perturbative calculations of the electroweak phase transition?
• Leading two-loop corrections to the Higgs boson self-couplings in models with extended scalar sectors
• The Constrained Minimal Dirac Gaugino Supersymmetric Standard Model
• "L=R" - $U(1{)}_R$ as the Origin of Leptonic 'RPV'
• Vacuum stability and supersymmetry at high scales with two Higgs doublets
• Gravitational Wave Signals of Pseudo-Goldstone Dark Matter in the ${\mathbb{Z}}_3$ Complex Singlet Model
• Higgs mass prediction in the MSSM at three-loop level in a pure $\overline{\text{DR}}$ context
• Strong first-order phase transitions in the NMSSM --- a comprehensive survey
• $E_6$ Inspired SUSY Benchmarks, Dark Matter Relic Density and a 125 GeV Higgs
• Avoiding the Goldstone Boson Catastrophe in general renormalisable field theories at two loops
• Hefty MSSM-like light Higgs in extended gauge models
• Leading two-loop corrections to the Higgs boson masses in SUSY models with Dirac gauginos
• Phenomenology of the minimal supersymmetric $U(1{)}_{B-L}\times U(1{)}_R$ extension of the standard model
• Generalizing the Scotogenic model
• $(\mathbf{g}-2{)}_{\mathbf{e},\mathbf{\mu }}$ in an extended inverse type-III seesaw
• Probing the Heavy Neutrinos of Inverse Seesaw Model at the LHeC
• Exploring the Higgs sector of the MRSSM with a light scalar
• Phenomenology of the inflation-inspired NMSSM at the electroweak scale
• R-Parity Violation at the LHC
• Precise prediction for the Higgs-Boson Masses in the $\mu \nu$SSM with three right-handed neutrino superfields
• Induced Electroweak Symmetry Breaking and Supersymmetric Naturalness
• The light CP-even MSSM Higgs mass resummed to fourth logarithmic order
• Two loop electroweak corrections to $\bar{B}\to X_s\gamma$ and $B_s^0\to {\mu }^{+}{\mu }^{-}$ in the B-LSSM
• New bounds on trilinear R-parity violation from lepton flavor violating observables
• Invisible Higgs Decay in a Supersymmetric Inverse Seesaw Model with Light Sneutrino Dark Matter
• Precise calculation of the W boson pole mass beyond the Standard Model with FlexibleSUSY
• New constraints on extended Higgs sectors from the trilinear Higgs coupling
• Enhancing $h\to \gamma \gamma$ with staus in SUSY models with extended gauge sector
• Lepton-flavor violation and two loop electroweak corrections to $(g-2{)}_{\mu }$ in the B-L symmetry SSM
• Higgs-Boson Masses and Mixing Matrices in the NMSSM: Analysis of On-Shell Calculations
• Muon g-2 and related phenomenology in constrained vector-like extensions of the MSSM
• Improved bounds on ${\mathbb{Z}}_3$ singlet dark matter
• On the MSSM Higgsino mass and fine tuning
• Non-Standard Higgs Decays in U(1) Extensions of the MSSM
• Sneutrino Dark Matter in Low-scale Seesaw Scenarios
• High scale impact in alignment and decoupling in two-Higgs doublet models
• Precision tools and models to narrow in on the 750 GeV diphoton resonance
• Squark production in R-symmetric SUSY with Dirac gluinos: NLO corrections
• Confronting the Galactic Center Gamma Ray Excess With a Light Scalar Dark Matter
• Dark matter scenarios in a constrained model with Dirac gauginos
• The Di-Photon Excess in a Perturbative SUSY Model
• The Higgs sector of the minimal SUSY $B-L$ model
• Proposal for generalised Supersymmetry Les Houches Accord for see-saw models and PDG numbering scheme
• Dark matter and LHC phenomenology in a left-right supersymmetric model
• Conservative upper limits on WIMP annihilation cross section from Fermi-LAT γ-rays
• Enhancing $l_i\to 3l_j$ with the $Z^0$-penguin
• Reopen parameter regions in Two-Higgs Doublet Models
• Soft masses in SUSY SO(10) GUTs with low intermediate scales
• Electron and muon magnetic moments and implications for dark matter and model characterisation in non-universal $U(1{)}^{\prime }$ supersymmetric models
• Two-loop analysis of classically scale-invariant models with extended Higgs sectors
• Lepton Flavor Violation in the singlet-triplet scotogenic model
• Dark Matter in a Constrained $E_6$ Inspired SUSY Model
• LHC and lepton flavour violation phenomenology of a left-right extension of the MSSM
• N-loop running should be combined with N-loop matching
• On the maximal diphoton width
• Extending the Universal One-Loop Effective Action by Regularization Scheme Translating Operators
• Focus Point Supersymmetry in Extended Gauge Mediation
• A precision study of the fine tuning in the DiracNMSSM
• Doubly-charged Higgs and vacuum stability in left-right supersymmetry
• En-gauging Naturalness
• Stability of R parity in supersymmetric models extended by U(1)_{B-L}
• Mass Spectrum and Higgs Profile in BLSSM
• Phenomenology of Light Sneutrino Dark Matter in cMSSM/mSUGRA with Inverse Seesaw
• Perspectives for Detecting Lepton Flavour Violation in Left-Right Symmetric Models
• Perturbativity Constraints in BSM Models
• Improved unitarity constraints in Two-Higgs-Doublet-Models
• Two-loop Higgs mass calculation from a diagrammatic approach
• Implications of gauge kinetic mixing on Z' and slepton production at the LHC
• Collider phenomenology of a unified leptoquark model
• The THDMa revisited
• Generalized Soft Breaking Leverage for the MSSM
• Two-loop Prediction of the Anomalous Magnetic Moment of the Muon in the Two-Higgs Doublet Model with GM2Calc 2
• Probing Non-holomorphic MSSM via precision constraints, dark matter and LHC data
• Explaining a CMS $eejj$ Excess With $\mathcal{R}-$parity Violating Supersymmetry and Implications for Neutrinoless Double Beta Decay
• Automatised matching between two scalar sectors at the one-loop level
• Top quark decays with flavor violation in the B-LSSM
• The $S3$ Symmetric Model with a Dark Scalar
• Two-loop mass splittings in electroweak multiplets: winos and minimal dark matter
• Resonant Slepton Production Yields CMS $eejj$ and $ejj$ Missing $p_T$ Excesses
• Impact of LHC data on muon $g-2$ solutions in vector-like extension of the Constrained MSSM
• LHC limits on gluinos and squarks in the minimal Dirac gaugino model
• The GAMBIT Universal Model Machine: from Lagrangians to Likelihoods
• The Supersymmetric Standard Models with a Pseudo-Dirac Gluino from Hybrid $F-$ and $D-$Term Supersymmetry Breakings
• Lepton portal dark matter at muon colliders: Total rates and generic features for phenomenologically viable scenarios
• Z' mass limits and the naturalness of supersymmetry
• Has the Origin of the Third-Family Fermion Masses been Determined?
• Neutrino masses, vacuum stability and quantum gravity prediction for the mass of the top quark
• Constraining Electroweakinos in the Minimal Dirac Gaugino Model
• Computing Tools for Effective Field Theories
• Singlet-Doublet Dirac Dark Matter and Neutrino Masses
• Constraints on $Z^{\prime }$ solutions to the flavor anomalies with trans-Planckian asymptotic safety
• Electroweak baryogenesis and electron EDM in the B-LSSM
• Phenomenological consistency of the singlet-triplet scotogenic model
• Inert doublet as multicomponent dark matter
• Precise prediction for the W boson mass in the MRSSM
• The Higgsploding Universe
• The Order $\mathcal{O}({\alpha }_t{\alpha }_s)$ Corrections to the Trilinear Higgs Self-Couplings in the Complex NMSSM
• On-Shell neutral Higgs bosons in the NMSSM with complex parameters
• Light lepton portal dark matter meets the LHC
• $B_{s,d}^0\to \mu \bar{\mu }$ and $B\to X_s\gamma$ in the R-parity violating MSSM
• Unitarity constraints in triplet extensions beyond the large s limit
• Dark matter candidates in the constrained Exceptional Supersymmetric Standard Model
• A $\mu$-$\tau$-philic scalar doublet under $Z_n$ flavor symmetry
• Two-Loop $\mathcal{O}({\alpha }_t^2)$ Corrections to the Neutral Higgs Boson Masses in the CP-Violating NMSSM
• The Higgs Mass in the MSSM at two-loop order beyond minimal flavour violation
• Updating Bounds on $R$-Parity Violating Supersymmetry from Meson Oscillation Data
• FlexibleDecay: An automated calculator of scalar decay widths
• Confronting SUSY models with LHC data via electroweakino production
• On the two-loop corrections to the Higgs mass in trilinear R-parity violation
• Exploring Non-Holomorphic Soft Terms in the Framework of Gauge Mediated Supersymmetry Breaking
• Relaxing LHC constraints on the $W_R$ mass
• Dark matter and lepton flavour phenomenology in a singlet-doublet scotogenic model
• Supersoft Supersymmetry, Conformal Sequestering, and Single Scale Supersymmetry Breaking
• Is the CMS eejj excess a hint for light supersymmetry?
• Precise determination of the Higgs mass in supersymmetric models with vectorlike tops and the impact on naturalness in minimal GMSB
• Analytical two-loop soft mass terms of sfermions in Extended GMSB models
• Naturalness of scale-invariant NMSSMs with and without extra matter
• The NMSSM with F-theory unified boundary conditions
• Gauge Dependences of Higher-Order Corrections to NMSSM Higgs Boson Masses and the Charged Higgs Decay $H^{\pm }\to W^{\pm }{h}_i$
• Next-to-Leading Order NMSSM Decays with CP-odd Higgs Bosons and Stops
• Higgs Mass and Muon $g-2$ Anomaly in MSSM with Gauge-Gravity hybrid Mediation
• Dark Matter versus h into gamma gamma and h into gamma Z with supersymmetric triplets
• One-Loop Corrections to the Two-Body Decays of the Neutral Higgs Bosons in the Complex NMSSM
• Electroweak Corrections to Dark Matter Direct Detection in a Vector Dark Matter Model
• A Lepton-specific Universal Seesaw Model with Left-Right Symmetry
• SO(10) inspired gauge-mediated supersymmetry breaking
• Full 1-loop calculation of BR$(B_{s,d}^0\to \ell \bar{\ell })$ in models beyond the MSSM with SARAH and SPheno
• How robust are particle physics predictions in asymptotic safety?
• Computer tools in particle physics
• Direct detection of pseudo-Nambu-Goldstone dark matter in a two Higgs doublet plus singlet extension of the SM
• One-loop Corrections to the Higgs Boson Invisible Decay in the Dark Doublet Phase of the N2HDM
• Decoupling of heavy sneutrinos in low-scale seesaw models
• munuSSM: A python package for the $\mu$-from-$\nu$ Supersymmetric Standard Model
• Interpreting 95 GeV di-photon/$b\bar{b}$ excesses as a lightest Higgs boson of the MRSSM
• Quasi Yukawa Unification and Fine-Tuning in U(1) Extended SSM
• FeynOnium: Using FeynCalc for automatic calculations in Nonrelativistic Effective Field Theories
• Higgs boson decays with lepton flavor violation in the $B-L$ symmetric SSM
• Sparticle Spectroscopy and Dark Matter in a $U(1{)}_{B-L}$ extension of MSSM
• The Trilinear Higgs Self-Couplings at $\mathcal{O}({\alpha }_t^2)$ in the CP-Violating NMSSM
• Supersymmetry with a Sister Higgs
• Revisiting (s)neutrino dark matter in natural SUSY
• Bilinear R-parity violating supersymmetry under the light of neutrino oscillation, higgs and flavor data
• Fermionic triplet dark matter in an $SO(10)$-inspired left right model
• Comparison of the EFT Hybrid and Three-Loop Fixed-Order Calculations of the Lightest MSSM Higgs Boson Mass
• From the unification scale to the weak scale: A self consistent supersymmetric Dine-Fischler-Srednicki-Zhitnitsky axion model
• Lepton Flavor Violation in a $Z^{\prime }$ model for the $b\to s$ anomalies
• The Supersymmetric R-Parity Violating Dine-Fischler-Srednicki-Zhitnitsky Axion Model
• Exploring Charge and Color Breaking vacuum in Non-Holomorphic MSSM
• Confronting the coloured sector of the MRSSM with LHC data
• One-loop Corrections to the Higgs Boson Invisible Decay in a Complex Singlet Extension of the SM
• Electroweak corrections to the fermionic decays of heavy Higgs states
• Exploring collider aspects of a neutrinophilic Higgs doublet model in multilepton channels
• Pitfalls of iterative pole mass calculation in electroweak multiplets
• Two-loop matching of renormalizable operators: general considerations and applications
• Leading two-loop corrections to the Higgs di-photon decay in the Inert Doublet Model
• The Ultraviolet Landscape of Two-Higgs Doublet Models
• Theoretical Constraints on Supersymmetric Models: Perturbative Unitarity vs. Vacuum Stability
• Spontaneous Charge Breaking in the NMSSM - Dangerous or not?
• The Muon Magnetic Moment and Physics Beyond the Standard Model
• A constrained supersymmetric left-right model
• The Constrained NMSSM with right-handed neutrinos
• Resurrecting light stops after the 125 GeV Higgs in the baryon number violating CMSSM
• ewN2HDECAY - A program for the Calculation of Electroweak One-Loop Corrections to Higgs Decays in the Next-to-Minimal Two-Higgs-Doublet Model Including State-of-the-Art QCD Corrections
• Higgs boson mass and high-luminosity LHC probes of supersymmetry with vectorlike top quark
• Anomaly-free axion dark matter in three Higgs doublet model and its phenomenological implications
• Naturalness, dark matter, and the muon anomalous magnetic moment in supersymmetric extensions of the standard model with a pseudo-Dirac gluino
• Partially composite supersymmetry
• Supersymmetric type-III seesaw: lepton flavour violation and LHC phenomenology
• The Singlet Extended Standard Model in the Context of Split Supersymmetry
• Interpretation of 95 GeV Excess within the Georgi-Machacek Model in Light of Positive Definiteness Constraints
• Exploring the supersymmetric U(1)${}_{B-L}\times$ U(1)${}_R$ model with dark matter, muon $g-2$ and $Z^{\prime }$ mass limits
• Least Fine-Tuned U(1) Extended SSM
• Color-octet scalars in Dirac gaugino models with broken $R$ symmetry
• Supersymmetric mass spectra and the seesaw scale
• Electric dipole moments of neutron and heavy quarks in the B-L symmetric MSSM
• Charged Higgs in MSSM and Beyond
• (O)Mega Split
• 750 GeV Diphotons from Supersymmetry with Dirac Gauginos
• Long Dead Winos
• 3HDM with $\Delta (27)$ symmetry and its phenomenological consequences
• A Large Muon EDM from Dark Matter
• Non-Holomorphic Soft-Term Contributions to the Higgs-Boson Masses in the Feynman Diagrammatic Approach
• The Two Scales of New Physics in Higgs Couplings
• Whac-a-constraint with anomaly-free dark matter models
• Phenomenology of extended multiHiggs doublet models with $S_4$ family symmetry
• Leptophobic $Z^{\prime }$ bosons in the secluded UMSSM
• Natural Supersymmetry and Dynamical Flavour with Metastable Vacua
• Same-sign trilepton signal for stop quark in the presence of sneutrino dark matter
• Expectation management
• A New Tool for the study of the CP-violating NMSSM
• Validity of the CMSSM interpretation of the diphoton excess
• Higher Order Corrections to the Trilinear Higgs Self-Couplings in the Real NMSSM
• Constrained Dirac gluino mediation
• Probing intractable beyond-standard-model parameter spaces armed with Machine Learning
• Dark matter and Collider signals in supersymmetric $U(1{)}^{\prime }$ models with non-universal $Z^{\prime }$ couplings
• Neutralino Dark Matter in Gauge Mediation After Run I of LHC and LUX
• xSLHA: an Les Houches Accord reader for Python and Mathematica
• External leg corrections as an origin of large logarithms
• Higgs-mass prediction in the NMSSM with heavy BSM particles
• Naturalness and a light $Z^{\prime }$
• Probing Relatively Heavier Right-Handed Selectron at the CEPC, $\mathbf{FC}{\mathbf{C}}_{\mathbf{ee}}$ and ILC
• Lepton flavor violation beyond the MSSM
• Probing Type-I 2HDM light Higgs in the top-pair-associated diphoton channel
• A Potentially Detectable Gamma-Ray Line in the Fermi Galactic Center Excess -- In Light of One-Step Cascade Annihilations of Secluded (Vector) Dark Matter via the Higgs Portal
• Global fits of SUSY at future Higgs factories
• Impact of one-loop corrections to trilinear scalar couplings on di-Higgs production in the RxSM
• Constraining sleptons at the LHC in a supersymmetric low-scale seesaw scenario
• Soft Gamma Rays from Heavy WIMPs
• The Higgs mass and the scale of SUSY breaking in the NMSSM
• Prospects of Indirect Detection for the Heavy S3 Dark Doublet
• Non-minimal flavour violation in $A_4\times SU(5)$ SUSY GUTs with smuon assisted dark matter
• Constraining flavour-universal nonstandard interactions and superweak extension of the standard model
• Hiding the little hierarchy problem in the NMSSM
• Dilaton domination in the MSSM and its singlet extensions
• Family Non-Universal U(1)${}^{\prime }$ Model with Minimal Number of Exotics
• Enhanced lepton flavour violation in the supersymmetric inverse seesaw
• Data-driven analysis of a SUSY GUT of flavour
• Radiative corrections to the $\mathrm{S},\mathrm{T},\mathrm{U}$ parameters and their impact on the $W$ boson mass in the 331 model
• Dirac dark matter, neutrino masses, and dark baryogenesis
• Squark production with R-symmetry beyond NLO at the LHC
• On the On-Shell Renormalization of Fermion Masses, Fields, and Mixing Matrices at 1-loop
• Illuminating Stealth Scenarios at the LHC
• A closer look at non-decoupling D-Terms
• ARGES -- Advanced Renormalisation Group Equation Simplifier
• Radiative Muon Mass Models and $(g-2{)}_{\mu }$
• Supersymmetry - When Theory Inspires Experimental Searches
• The Two Scales of New Physics in Loop-Induced Higgs Couplings
• Reinterpretation of ATLAS 8 TeV searches for Natural SUSY with a $R$-Sneutrino LSP
• Higgs Mass Predictions in the CP-Violating High-Scale NMSSM
• Markov Chain Monte Carlo analysis to probe trilinear $R$-parity violating SUSY scenarios and possible LHC signatures
• Resolving a challenging supersymmetric low-scale seesaw scenario at the ILC
• Triplet fermion WIMP dark matter in the general supersymmetric Georgi-Machacek model
• Electric dipole moments from the perspective of a scalar triplet and singlet extension of the MSSM: A study of neutrons, electrons, mercury, and b and c quarks
• Probing the Supersymmetric Grand Unified Theories at the Future Proton-Proton Colliders and Hyper-Kamiokande Experiment
• One-loop Corrections to the Two-Body Decays of the Charged Higgs Bosons in the Real and Complex NMSSM
• Features of electroweak symmetry breaking in five dimensional SUSY models
• Phenomenological consequences of Higgs inflation in the NMSSM at the electroweak scale
• Scherk-Schwarz orbifolds at the LHC
• $e^{+}{e}^{-}\to hhZ$ in the B-L symmetric SSM
• Lepton dark matter portal in the inert Zee model
• Dark matter in a SUSY left-right model
• Hybrid Anomaly and Gravity Mediation for Electroweak Supersymmetry
• Feasibility to probe the dynamical scotogenic model at the LHC
• Positive definiteness constraints of effective scalar potential in Georgi-Machacek Model
• New physics effects on the $W$-boson mass from a doublet extension of the SM Higgs sector
• One-loop corrections to light neutrino masses in gauged U(1) extensions of the standard model
• The THDMa revisited -- A preview
• Can SUSY relax LNV constraints coming from loop corrections to light neutrino masses on the low-scale Seesaw?
• Natural Supersymmetry and Unification in Five Dimensions
• Review of Calculators for BSM Higgs bosons
• Refining two-loop corrections to trilinear Higgs couplings in the Two-Higgs-Doublet Model
• Investigating a strong first-order electroweak phase transition in the RxSM at future linear $e^{+}{e}^{-}$ colliders and LISA