2021/08/31 by Ahmadullah Zahed
Mathematics · Physics and Astronomy · #Amplitude #Black Holes and Theoretical Physics #Crossing #Dispersion (optics) #Dispersion relation #Function (biology) #Geometry #Isospin #Mathematical analysis #Mathematical physics #Mathematics #Particle physics #Particle physics theoretical and experimental studies #Physics #Pion #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Scattering amplitude #Symmetry (geometry) #hep-ph #hep-th #math-ph #math.MP
paper · pdf · doi:10.1007/jhep12(2021)036
v2:29 pages, 3 figures, version to appear in JHEP
arxiv created 2021/11/23 · openalex publication_date 2021/12/07 · arxiv updated 2021/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A bstract This paper presents the fascinating correspondence between the geometric function theory and the scattering amplitudes with O ( N ) global symmetry. A crucial ingredient to show such correspondence is a fully crossing symmetric dispersion relation in the z -variable, rather than the fixed channel dispersion relation. We have written down fully crossing symmetric dispersion relation for O ( N ) model in z -variable for three independent combinations of isospin amplitudes. We have presented three independent sum rules or locality constraints for the O ( N ) model arising from the fully crossing symmetric dispersion relations. We have derived three sets of positivity conditions. We have obtained two-sided bounds on Taylor coefficients of physical Pion amplitudes around the crossing symmetric point (for example, π + π − → π 0 π 0 ) applying the positivity conditions and the Bieberbach-Rogosinski inequalities from geometric function theory.