Four-fermion operators at dimension 6: dispersion relations and UV completions

Abstract

A major task in phenomenology today is constraining the parameter space of SMEFT and constructing models of fundamental physics that the SM derives from. To this effect, we report an exhaustive list of sum rules for 4-fermion operators of dimension 6, connecting low energy Wilson coefficients to cross-sections in the UV. Unlike their dimension 8 counterparts which are amenable to a positivity bound, the discussion here is more involved due to the weaker convergence and indefinite signs of the dispersion integrals. We illustrate this by providing examples with weakly coupled UV completions leading to opposite signs of the Wilson coefficients for both convergent and non-convergent dispersion integrals. We further decompose dispersion integrals under weak isospin and color groups which lead to a tighter relation between IR measurements and UV models. These sum rules can become an effective tool for constructing consistent UV completions for SMEFT following the prospective measurement of these Wilson coefficients.

24 pages

References in corpus (9)

• Causality, Analyticity and an IR Obstruction to UV Completion
• Compilation of low-energy constraints on 4-fermion operators in the SMEFT
• Symmetries, Sum Rules and Constraints on Effective Field Theories
• Natural Selection Rules: New Positivity Bounds for Massive Spinning Particles
• Causality, Unitarity and Symmetry in Effective Field Theory
• Positivity in electron-positron scattering: testing the axiomatic quantum field theory principles and probing the existence of UV states
• Positivity bounds on Minimal Flavor Violation
• Signs, Spin, SMEFT: Sum Rules at Dimension Six
• Sum Rules in the Standard Model Effective Field Theory from Helicity Amplitudes

Cited by in corpus (9)

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• Spinning Sum Rules for the Dimension-Six SMEFT
• UV physics from IR features: new prospects from top flavor violation
• Positivity Bounds in Scalar Effective Field Theories at One-loop Level
• Positivity bounds in scalar-QED EFT at one-loop level
• The IR-Side of Positivity Bounds