Positivity and geometric function theory constraints on pion scattering

Journal Article · Tue Dec 07 00:00:00 EST 2021 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep12(2021)036· OSTI ID:2280632

Zahed, Ahmadullah ^[1]

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1. Indian Institute of Science, Bangalore (India); Stony Brook University

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^– → π⁰π⁰) applying the positivity conditions and the Bieberbach-Rogosinski inequalities from geometric function theory.

• Research Organization: Stony Brook Univ., NY (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: FG02-88ER40388
• OSTI ID: 2280632
• Journal Information: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 12 Vol. 2021; ISSN 1029-8479
• Publisher: Springer Nature
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
effective field theories
field theories in higher dimensions
nonperturbative effects