Avoiding the Goldstone Boson Catastrophe in general renormalisable field theories at two loops

Abstract

We show how the infra-red divergences associated to Goldstone bosons in the minimum condition of the two-loop Landau-gauge effective potential can be avoided in general field theories. This extends the resummation formalism recently developed for the Standard Model and the MSSM, and we give compact, infra-red finite expressions in closed form for the tadpole equations. We also show that the results at this loop order are equivalent to (and are most easily obtained by) imposing an "on-shell" condition for the Goldstone bosons. Moreover, we extend the approach to show how the infra-red divergences in the calculation of the masses of neutral scalars (such as the Higgs boson) can be eliminated. For the mass computation, we specialise to the gaugeless limit and extend the effective potential computation to allow the masses to be determined without needing to solve differential equations for the loop functions -- opening the door to fast, infra-red safe determinations of the Higgs mass in general theories.

arXiv comment42 pages, one figure; v2: corrected typos and added explanations

References in corpus (53)

• SARAH 4: A tool for (not only SUSY) model builders
• The Masses of the Neutral CP-even Higgs Bosons in the MSSM: Accurate Analysis at the Two-Loop Level
• Automatic Calculation of supersymmetric Renormalization Group Equations and Self Energies
• SARAH 3.2: Dirac Gauginos, UFO output, and more
• From Superpotential to Model Files for FeynArts and CalcHep/CompHep
• The Standard Model Effective Potential at Two Loops
• On the O(alpha_t^2) two-loop corrections to the neutral Higgs boson masses in the MSSM
• Two-loop effective potential for a general renormalizable theory and softly broken supersymmetry
• QCD Corrections to the Masses of the neutral CP-even Higgs Bosons in the MSSM
• Two-Loop Radiative Corrections to the Lightest Higgs Boson Mass in the Minimal Supersymmetric Model
• On the neutral Higgs boson masses in the MSSM for arbitrary stop mixing
• On the two-loop sbottom corrections to the neutral Higgs boson masses in the MSSM
• Complete Two-loop Dominant Corrections to the Mass of the Lightest CP-even Higgs Boson in the Minimal Supersymmetric Standard Model
• Precise Prediction for the Mass of the Lightest Higgs Boson in the MSSM
• MSSM Lightest CP-Even MSSM Higgs Boson Mass to O(alpha_s alpha_t): the Effective Potential Approach
• On the two-loop Yukawa corrections to the MSSM Higgs boson masses at large tan(beta)
• Light MSSM Higgs boson mass to three-loop accuracy
• Higgs boson mass in supersymmetry to three loops
• High-Precision Predictions for the MSSM Higgs Sector at O(alpha_b alpha_s)
• Two-Loop Effective Potential Calculation of the Lightest CP-Even Higgs-Boson Mass in the MSSM
• On the radiative corrections to the neutral Higgs boson masses in the NMSSM
• Three-loop corrections to the lightest Higgs scalar boson mass in supersymmetry
• TSIL: a program for the calculation of two-loop self-energy integrals
• Two-loop effective potential for the minimal supersymmetric standard model
• Complete two-loop effective potential approximation to the lightest Higgs scalar boson mass in supersymmetry
• Taming Infrared Divergences in the Effective Potential
• Taming the Goldstone contributions to the effective potential
• Two-Loop Higgs mass calculations in supersymmetric models beyond the MSSM with SARAH and SPheno
• Evaluation of two-loop self-energy basis integrals using differential equations
• Consistent Use of Effective Potentials
• Two-loop scalar self-energies in a general renormalizable theory at leading order in gauge couplings
• Strong and Yukawa two-loop contributions to Higgs scalar boson self-energies and pole masses in supersymmetry
• Momentum-dependent two-loop QCD corrections to the neutral Higgs-boson masses in the MSSM
• On the two-loop corrections to the Higgs masses in the NMSSM
• Two-loop QCD corrections to the MSSM Higgs masses beyond the effective-potential approximation
• Gauge-Independent Scales Related to the Standard Model Vacuum Instability
• Three-loop Standard Model effective potential at leading order in strong and top Yukawa couplings
• The Higgs mass in the CP violating MSSM, NMSSM, and beyond
• Higgs mass predictions of public NMSSM spectrum generators
• Symmetry Improved CJT Effective Action
• Four-loop Standard Model effective potential at leading order in QCD
• Leading two-loop corrections to the Higgs boson masses in SUSY models with Dirac gauginos
• Exploring the Higgs sector of the MRSSM with a light scalar
• Interplay of Infrared Divergences and Gauge-Dependence of the Effective Potential
• Dark matter scenarios in a constrained model with Dirac gauginos
• Symmetry-Improved 2PI Approach to the Goldstone-Boson IR Problem of the SM Effective Potential
• The Di-Photon Excess in a Perturbative SUSY Model
• Two-loop Higgs mass calculation from a diagrammatic approach
• Resummation of Goldstone boson contributions to the MSSM effective potential
• Symmetry Improved 2PI Effective Action and the Infrared Divergences of the Standard Model
• The Higgs Mass in the MSSM at two-loop order beyond minimal flavour violation
• On the two-loop corrections to the Higgs mass in trilinear R-parity violation
• Precise determination of the Higgs mass in supersymmetric models with vectorlike tops and the impact on naturalness in minimal GMSB

Cited by in corpus (26)

• Cosmological phase transitions: from perturbative particle physics to gravitational waves
• Higgs-mass predictions in the MSSM and beyond
• Improved predictions for intermediate and heavy Supersymmetry in the MSSM and beyond
• Generic calculation of two-body partial decay widths at the full one-loop level
• On two-loop corrections to the Higgs trilinear coupling in models with extended scalar sectors
• Supersymmetric and non-supersymmetric models without catastrophic Goldstone bosons
• Evaluation of the general 3-loop vacuum Feynman integral
• Leading two-loop corrections to the Higgs boson self-couplings in models with extended scalar sectors
• Effective potential at three loops
• Standard Model parameters in the tadpole-free pure $\overline{\mathrm{MS}}$ scheme
• Higgs alignment from extended supersymmetry
• Two-loop effective potential for generalized gauge fixing
• Two-loop analysis of classically scale-invariant models with extended Higgs sectors
• N-loop running should be combined with N-loop matching
• Perturbativity Constraints in BSM Models
• All two-loop scalar self-energies and tadpoles in general renormalisable field theories
• Matching renormalisable couplings: simple schemes and a plot
• Resummation of Goldstone Infrared Divergences: A Proof to All Orders
• Dilution of dark matter relic density in singlet extension models
• Leading two-loop corrections to the Higgs di-photon decay in the Inert Doublet Model
• The Ultraviolet Landscape of Two-Higgs Doublet Models
• Minima of Classically Scale-Invariant Potentials
• Expectation management
• External leg corrections as an origin of large logarithms
• W boson mass in minimal Dirac gaugino scenarios
• Fighting off field dependence in MSSM Higgs-mass corrections of order ${\alpha }_t{\alpha }_s$ and ${\alpha }_t^2$