Leading Infrared Logarithms from Unitarity, Analyticity and Crossing

Abstract

We derive non-linear recursion equations for the leading infrared logarithms in massless non-renormalizable effective field theories. The derivation is based solely on the requirements of the unitarity, analyticity and crossing symmetry of the amplitudes. That emphasizes the general nature of the corresponding equations. The derived equations allow one to compute leading infrared logarithms to essentially unlimited loop order without performing a loop calculation. For the implementation of the recursion equation one needs to calculate tree diagrams only. The application of the equation is demonstrated on several examples of effective field theories in four and higher space-time dimensions.

12 pages

References in corpus (5)

• Leading Logarithms in the Massive O(N) Nonlinear Sigma Model
• Chiral Logarithms Tamed
• Chiral logarithms to five loops
• Leading Chiral Logarithms for Pion Form Factors to Arbitrary Number of Loops
• Large-N Summation of Chiral Logs for Generalized Parton Distributions

Cited by in corpus (19)

• On the running of the gravitational constant
• S-matrix Bootstrap for Effective Field Theories: Massless Pions
• Running couplings and operator mixing in the gravitational corrections to coupling constants
• The Massive O(N) Non-linear Sigma Model at High Orders
• Leading logarithms in the anomalous sector of two-flavour QCD
• Leading logarithms in N-flavour mesonic Chiral Perturbation Theory
• RG Equations and High Energy Behaviour in Non-Renormalizable Theories
• Leading infrared logarithms for sigma-model with fields on arbitrary Riemann manifold
• Leading logarithms for the nucleon mass
• Chiral Perturbation Theory Reflections on Effective Theories of the Standard Model
• Exact summation of leading infrared logarithms in 2D effective field theories
• Leading Logarithms of the Two Point Function in Massless O(N) and SU(N) Models to any Order from Analyticity and Unitarity
• Non-analytic terms of string amplitudes from partial waves
• UV Divergences, RG Equations and High Energy Behaviour of the Amplitudes in the Wess-Zumino Model with Quartic Interaction
• Quasi-Renormalizable Quantum Field Theories
• Leading chiral logarithms for the nucleon mass
• Leading logarithms for mesons and nucleons
• Status of Chiral Meson Physics
• Exact summation of leading logs around $T\bar{T}$ deformation of $O(N+1)$-symmetric 2D QFTs