Sum rules in the standard model effective field theory from helicity amplitudes

Abstract

The dispersion relation of an elastic 4-point amplitude in the forward direction leads to a sum rule that connects the low energy amplitude to the high energy observables. We perform a classification of these sum rules based on massless helicity amplitudes. With this classification, we are able to systematically write down the sum rules for the dimension-6 operators of the Standard Model Effective Field Theory (SMEFT), some of which are absent in previous literatures. These sum rules offer distinct insights on the relations between the operator coefficients in the EFT and the properties of the full theory that generates them. Their applicability goes beyond tree level, and in some cases can be used as a practical method of computing the one loop contributions to low energy observables. They also provide an interesting perspective for understanding the custodial symmetries of the SM Higgs and fermion sectors.

Natural selection rules: new positivity bounds for massive spinning particles

“…(4.12) with growth N UV = 1/2 (where we are not distinguishing between t and s). This high-energy behaviour has been discussed also in [5,8,93], and includes for instance tree-level UV completions with no t-channel exchange. Such a "super-Froissart" convergence would imply that, Super-Froissart:…”

“…Furthermore, note that since this interaction has mass dimension < 8, the forward-limit positivity bound A (2) > 0 cannot constrain λ 7 (assuming a local, Froissart-bounded, UV completion). However, following the example of [8,93] and assuming a super-Froissart boundedness (4.13), we can apply the positivity bound (4.21) with N = 0 s-derivatives (since α = 2N because |h u | + |h s | min = 1 and N = N in this example). This gives the bound,…”

Causality, unitarity and symmetry in effective field theory

“…Examination of UV completions may provide insight into this. Some discussion of dimension 6 operators has recently been given in [15,[64][65][66], although conclusions drawn for the IR interactions have been predicated on assumptions about the amplitudes having extra-friendly high-energy scaling.…”

Positivity bounds on Minimal Flavor Violation

“…This property has had a variety of applications, from pion physics [2,3] to Quantum Gravity [4] and to the derivation of the a-theorem [5], see also [6] and references therein. Recently, efforts have been made to constrain the coefficients in the SMEFT expansion [7,8], particularly regarding vector boson scattering [9][10][11] (see also refs. [12][13][14][15][16][17][18][19] for recent developments).…”