Causality, Unitarity and Symmetry in Effective Field Theory

Abstract

Sum rules in effective field theories, predicated upon causality, place restrictions on scattering amplitudes mediated by effective contact interactions. Through unitarity of the $S$-matrix, these imply that the size of higher dimensional corrections to transition amplitudes between different states is bounded by the strength of their contributions to elastic forward scattering processes. This places fundamental limits on the extent to which hypothetical symmetries can be broken by effective interactions. All analysis is for dimension $8$ operators in the forward limit. Included is a thorough derivation of all positivity bounds for a chiral fermion in $SU(2)$ and $SU(3)$ global symmetry representations resembling those of the Standard Model, general bounds on flavour violation, new bounds for interactions between particles of different spin, inclusion of loops of dimension $6$ operators and illustration of the resulting strengthening of positivity bounds over tree-level expectations, a catalogue of supersymmetric effective interactions up to mass dimension $8$ and $4$ legs and the demonstration that supersymmetry unifies the positivity theorems as well as the new bounds.

arXiv comment~50 pages v2: Improved discussion and use of discrete symmetries, some corrections and clarifications, some other minor improvements. v3: Corrected sign error in isospin projectors and resulting bounds (no qualitative changes to the extent investigated), minor improvements in exposition and typing errors corrected

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• Bounding Violations of the Weak Gravity Conjecture
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• Positivity Bounds without Boosts
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• Building blocks of the flavourful SMEFT RG
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• Positivity Bounds on Massive Vectors
• Multipositivity Bounds for Scattering Amplitudes
• Positivity Bounds in Scalar Effective Field Theories at One-loop Level
• Positively Identifying HEFT or SMEFT
• Characterising Dark Matter-induced neutrino potentials
• Causality constraints on nonlinear supersymmetry
• Positivity in Amplitudes and Quantum Entanglement
• Positivity bounds in scalar-QED EFT at one-loop level