Spinning Sum Rules for the Dimension-Six SMEFT

Abstract

We construct new dispersive sum rules for the effective field theory of the standard model at mass dimension six. These spinning sum rules encode information about the spin of UV states: the sign of the IR Wilson coefficients carries a memory of the dominant spin in the UV completion. The sum rules are constructed for operators containing scalars and fermions, although we consider the dimension-six SMEFT exhaustively, outlining why equivalent relations do not hold for the remaining operators. As with any dimension-six dispersive argument, our conclusions are contingent on the absence of potential poles at infinity, so-called boundary terms, and we discuss in detail where these are expected to appear. There are a number of phenomenological applications of spinning sum rules, and as an example we explore the connection to the Peskin-Takeuchi parameters and, more generally, the set of oblique parameters in universal theories.

51 pages, 1 figure

References in corpus (11)

• Causality, Analyticity and an IR Obstruction to UV Completion
• A custodial symmetry for Zbb
• The Minimal Set of Electroweak Precision Parameters
• Infrared Consistency and the Weak Gravity Conjecture
• Symmetries, Sum Rules and Constraints on Effective Field Theories
• Positivity of Curvature-Squared Corrections in Gravity
• Falsifying Models of New Physics Via WW Scattering
• Positivity Constraints for Pseudo-linear Massive Spin-2 and Vector Galileons
• Dispersion Relation Bounds for pi pi Scattering
• The Other Fermion Compositeness
• Causal vs. Analytic constraints on anomalous quartic gauge couplings

Cited by in corpus (3)

• Building blocks of the flavourful SMEFT RG
• Amplitude's positivity vs. subluminality: Causality and Unitarity Constraints on dimension 6 & 8 Gluonic operators in the SMEFT
• Positivity bounds at one-loop level: the Higgs sector