Dispersion relation bounds forππscattering

2008/01/31 by Aneesh V. Manohar, A. V. Manohar, Vicent Mateu +1 · 8 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-ph

paper · pdf · doi:10.1103/physrevd.77.094019

published as Phys.Rev.D77:094019,2008 · 12 pages, 8 figures. Two references added, a few minor changes. Published version

openalex publication_date 2008/05/22 · arxiv created 2008/05/26 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Axiomatic principles such as analyticity, unitarity, and crossing symmetry constrain the second derivative of the \ensuremathπ\ensuremathπ scattering amplitudes in some channels to be positive in a region of the Mandelstam plane. Since this region lies in the domain of validity of chiral perturbation theory, we can use these positivity conditions to bound linear combinations of l₁ and l₂. We compare our predictions with those derived previously in the literature using similar methods. We compute the one-loop \ensuremathπ\ensuremathπ scattering amplitude in the linear sigma model (LSM) using the MS scheme, a result hitherto absent in the literature. The LSM values for l₁ and l₂ violate the bounds for small values of m_\ensuremathσ/m_\ensuremathπ. We show how this can occur, while still being consistent with the axiomatic principles.

Citations

• The axial vector current in beta decay
• Structure of Phenomenological Lagrangians. I

Cited by

• Partial Waves for Multipositivity
• Aspects of the low-energy constants in the chiral Lagrangian for charmed mesons
• Natural Selection Rules: New Positivity Bounds for Massive Spinning Particles
• Remarks on analyticity and unitarity in the presence of a strongly interacting light Higgs
• Generalized elastic positivity bounds on interacting massive spin-2 theories
• New phenomenological and theoretical perspective on anomalous ZZ and Zγ processes
• Symmetries, sum rules and constraints on effective field theories
• Convex Geometry Perspective on the (Standard Model) Effective Field Theory Space

Related

• Determination of Chiral Perturbarion Theory low energy constants from a precise description of pi-pi scattering threshold parameters
• Recent developments in chiral perturbation theory
• Chiral-dispersive calculations of pion-pion scattering confront experiment
• Pion-pion scattering amplitude. III. Improving the analysis with forward dispersion relations and Roy equations
• The ππ scattering amplitude in chiral perturbation theory