Spinning Sum Rules for the Dimension-Six SMEFT

Understand

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.