Towards the QED beta function and renormalons at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>1</mml:mn><mml:mo stretchy="false">/</mml:mo><mml:msubsup><mml:mi>N</mml:mi><mml:mi>f</mml:mi><mml:mn>2</mml:mn></mml:msubsup></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>1</mml:mn><mml:mo stretchy="false">/</mml:mo><mml:msubsup><mml:mi>N</mml:mi><mml:mi>f</mml:mi><mml:mn>3</mml:mn></mml:msubsup></mml:math>
Nicola Andrea Dondi, Gerald V. Dunne, Manuel Reichert, Francesco Sannino
Abstract
We determine the $1/{N}_{f}^{2}$ and $1/{N}_{f}^{3}$ contributions to the QED beta function stemming from the closed set of nested diagrams. At the order of $1/{N}_{f}^{2}$, we discover a new logarithmic branch cut closer to the origin when compared to the $1/{N}_{f}$ results. The same singularity location appears at $1/{N}_{f}^{3}$, and these correspond to a UV renormalon singularity in the finite part of the photon two-point function.
Topics & Concepts
RenormalonFunction (biology)SingularityOrder (exchange)PhysicsLogarithmMathematical physicsMathematicsParticle physicsGeometryMathematical analysisBiologyFinanceEconomicsQuantum chromodynamicsEvolutionary biologyBlack Holes and Theoretical PhysicsParticle physics theoretical and experimental studiesQuantum Chromodynamics and Particle Interactions