New positivity bounds from full crossing symmetry

Abstract

Positivity bounds are powerful tools to constrain effective field theories. Utilizing the partial wave expansion in the dispersion relation and the full crossing symmetry of the scattering amplitude, we derive several sets of generically nonlinear positivity bounds for a generic scalar effective field theory: We refer to these as the $PQ$, $D^{\mathrm{su}}$, $D^{\mathrm{stu}}$ and ${\bar{D}}^{\mathrm{stu}}$ bounds. While the $PQ$ bounds and $D^{\mathrm{su}}$ bounds only make use of the $s\leftrightarrow u$ dispersion relation, the $D^{\mathrm{stu}}$ and ${\bar{D}}^{\mathrm{stu}}$ bounds are obtained by further imposing the $s\leftrightarrow t$ crossing symmetry. In contradistinction to the linear positivity for scalars, these inequalities can be applied to put upper and lower bounds on Wilson coefficients, and are much more constraining as shown in the lowest orders. In particular we are able to exclude theories with soft amplitude behaviour such as weakly broken Galileon theories from admitting a standard UV completion. We also apply these bounds to chiral perturbation theory and we find these bounds are stronger than the previous bounds in constraining its Wilson coefficients.

39 pages, 8 figures; v2: published in JHEP, various small edits, in particular minor improvement due to use of vanishing odd partial waves

References in corpus (18)

• Resummation of Massive Gravity
• Causality, Analyticity and an IR Obstruction to UV Completion
• Galileon inflation
• DBI and the Galileon reunited
• Effective Field Theories from Soft Limits
• A Periodic Table of Effective Field Theories
• Positivity of Curvature-Squared Corrections in Gravity
• Falsifying Models of New Physics Via WW Scattering
• Gravitational positivity bounds
• Positivity Constraints for Pseudo-linear Massive Spin-2 and Vector Galileons
• Dispersion Relation Bounds for pi pi Scattering
• Carving out the Space of Open-String S-matrix
• Elastic positivity vs extremal positivity bounds in SMEFT: a case study in transversal electroweak gauge-boson scatterings
• The Other Fermion Compositeness
• Positivity in electron-positron scattering: testing the axiomatic quantum field theory principles and probing the existence of UV states
• Goldstones with Extended Shift Symmetries
• Causal vs. Analytic constraints on anomalous quartic gauge couplings
• Road Signs for UV-Completion

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