The IR-Side of Positivity Bounds

Abstract

We show how calculable IR loop effects impact positivity bounds in Effective Field Theories with causal and unitary UV completions. We identify infrared singularities which appear in dispersion relations at $|t|\lesssim m^2$. In the massless limit, they weaken two-sided bounds based on crossing symmetry, such as the lower bound on the amplitude for Galileon scattering. For amplitudes that are analytic in $s$ even for large negative $t$, i.e. $|t|\gg m^2$, we propose a new simple analytic approach to dispersive bounds, which are instead insensitive to the singularities, and explicitly compute the finite contributions from loops. Finally we show that the singularity do not affect the bounds based on smearing in impact parameter.

10 pages, 4 figures; v2: table added, matches journal version

References in corpus (12)

• Causality, Analyticity and an IR Obstruction to UV Completion
• Sharp Boundaries for the Swampland
• Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
• Symmetries, Sum Rules and Constraints on Effective Field Theories
• Falsifying Models of New Physics Via WW Scattering
• Into the EFThedron and UV constraints from IR consistency
• Rigorous Bounds on Light-by-Light Scattering
• Dispersion Relation Bounds for pi pi Scattering
• Natural Selection Rules: New Positivity Bounds for Massive Spinning Particles
• Positivity bounds in the Standard Model effective field theory beyond tree level
• Gravitational Causality and the Self-Stress of Photons
• Four-fermion operators at dimension 6: dispersion relations and UV completions