Origins of parameters in adimensional models

Abstract

We explore the origins of parameters in adimensional theories -- fundamental theories with no classical massive scales. If the parameters originate as draws from a distribution, it should be possible to write a distribution for them that doesn't depend on or introduce any massive scales. These distributions are the invariant distributions for the renormalization group (RG). If there exist RG invariant combinations of parameters, the RG invariant distributions are specified up to arbitrary functions of the RG invariants. If such distributions can be constructed, adimensional theories could predict the values of their parameters through distributions that are constrained by the RG. If they can't be constructed, the parameters must originate in a different way. We demonstrate the RG invariant distributions in QCD, the Coleman-Weinberg model and a totally asymptotically free theory.

arXiv comment6 pages, 5 figures; minor improvements, matches version accepted for publication

References in corpus (20)

• Agravity
• A solution to the hierarchy problem from an almost decoupled hidden sector within a classically scale invariant theory
• Emergence of the Electroweak Scale through the Higgs Portal
• Quadratic Gravity
• Dynamically Induced Planck Scale and Inflation
• Physical Naturalness and Dynamical Breaking of Classical Scale Invariance
• Towards Completing the Standard Model: Vacuum Stability, EWSB and Dark Matter
• Agravity up to infinite energy
• Consistent Use of Effective Potentials
• Quantum mechanics of 4-derivative theories
• Softened Gravity and the Extension of the Standard Model up to Infinite Energy
• Embedding inflation into the Standard Model - more evidence for classical scale invariance
• On the Quantisation of Complex Higher Derivative Theories and Avoiding the Ostrogradsky Ghost
• The Ostrogradsky instability can be overcome by quantum physics
• Dimensional Transmutation in Gravity and Cosmology
• Interpretation of quantum mechanics with indefinite norm
• Is negative kinetic energy meta-stable?
• Naturalness, Extra-Empirical Theory Assessments, and the Implications of Skepticism
• Experimental validation of nonextensive statistical field theory: applications to manganites
• Radiative Corrections as the Origin of Spontaneous Symmetry Breaking