Guises and Disguises of Quadratic Divergences

Abstract

In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale $\lambda$. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.

arXiv commentAccepted for publication at Annals of Physics

References in corpus (38)

• Verifiable Radiative Seesaw Mechanism of Neutrino Mass and Dark Matter
• Hidden Local Symmetry at Loop -- A New Perspective of Composite Gauge Boson and Chiral Phase Transition
• Resolving the Constrained Minimal and Next-to-Minimal Supersymmetric Standard Models
• Implications of the 125 GeV Higgs boson for scalar dark matter and for the CMSSM phenomenology
• When radiative corrections are finite but undetermined
• Physical (ir)relevance of ambiguities to Lorentz and CPT violation in QED
• Higgs and Supersymmetry
• Bare Higgs mass at Planck scale
• Anthropic considerations in multiple domain theories and the scale of electroweak symmetry breaking
• A New Probe of Naturalness
• QED with minimal and nonminimal couplings: on the quantum generation of Lorentz violating terms in the pure photon sector
• Chiral Anomaly and CPT invariance in an implicit momentum space regularization framework
• Revisiting the Naturalness Problem -- Who is afraid of quadratic divergences? --
• Gauge invariance and the CPT and Lorentz violating induced Chern-Simons-like term in extended QED
• Criteria for Natural Hierarchies
• Radiative symmetry breaking at the Fermi scale and flat potential at the Planck scale
• On the Veltman Condition, the Hierarchy Problem and High-Scale Supersymmetry
• Consistency Relations for an Implicit n-dimensional Regularization Scheme
• Systematic Implementation of Implicit Regularization for Multi-Loop Feynman Diagrams
• Consistent Momentum Space Regularization/Renormalization of Supersymmetric Quantum Field Theories: The 3-loop beta function for the Wess-Zumino Model
• Implicit Regularization and Renormalization of QCD
• (Un)determined finite regularization dependent quantum corrections: the Higgs decay into two photons and the two photon scattering examples
• On Quadratic Divergences and the Higgs Mass
• Regularization Independent Analysis of the Origin of Two Loop Contributions to N=1 Super Yang-Mills Beta Function
• Implicit regularization beyond one loop order: gauge field theories
• Arbitrary parameters in implicit regularization and democracy within perturbative description of 2-dimensional gravitational anomalies
• Effective multi-quark interactions with explicit breaking of chiral symmetry
• Momentum routing invariance in Feynman diagrams and quantum symmetry breakings
• Light Quark Masses in Multi-Quark Interactions
• Effective Chiral Meson Lagrangian For The Extended Nambu-Jona-Lasinio Model
• Conductivity of Coulomb interacting massless Dirac particles in graphene: Regularization-dependent parameters and symmetry constraints
• Remark on the subtractive renormalization of quadratically divergent scalar mass
• Systematization of Basic Divergent Integrals in Perturbation Theory and Renormalization Group Functions
• On the equivalence between Implicit Regularization and Constrained Differential Renormalization
• How to preserve symmetries with cut-off regularized integrals?
• Naturalness and theoretical constraints on the Higgs boson mass
• Strong dynamics behind the formation of the $125$ GeV Higgs boson
• Cancelling Quadratic Divergences Without Supersymmetry

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• One-loop conformal anomaly in an implicit momentum space regularization framework
• Supercurrent anomaly and gauge invariance in N=1 supersymmetric Yang-Mills theory
• Gauge and Poincare properties of the UV cutoff and UV completion in quantum field theory
• Dimensional Regularization in Quantum Field Theory with Ultraviolet Cutoff
• Infrared Subtleties and Chiral Vertices at NLO: An Implicit Regularization Analysis
• Dimensional regularization is generic