Positively Identifying HEFT or SMEFT

Abstract

We establish the bounds on Wilson coefficients of the Higgs effective field theory (HEFT) mandated by unitarity and analyticity. These positivity constraints can be projected into the space of the standard model effective field theory (SMEFT) as HEFT$\,\supset\,$SMEFT. Doing so reveals a subspace allowed by the HEFT but forbidden by SMEFT positivity, thereby identifying a region that could herald the use of the wrong EFT rather than a pathological UV. Restricting to custodial symmetric dimension-eight Higgs operators, there is a unique pair within the SMEFT where this concept can be sharply realized and is already being probed at colliders.

Figures (2)

• Figure 1: Positivity bounds for the HEFT projected into the two-dimensional space spanned by the custodial symmetric SMEFT. Applying positivity to the SMEFT directly restricts the allowable EFTs to live in the light blue region. If the Higgs sector is instead described by the HEFT, this region is enlarged to include the region shown in orange: a unique region within which new physics could emerge as indicating a breakdown of the SMEFT rather than violation of analyticity or unitarity. ATLAS measurements constrain these coefficients to within the yellow lines ATLAS:2023sua. We justify these partitions in the present Letter.
• Figure 2: A perspective on the projection of the HEFT to the SMEFT. Beyond the SMEFT plane shown in Fig. \ref{['fig:proj']}, we have included the additional dimension $d_3$ of the HEFT; we continue to marginalize over $d_{1,2}$. The space permitted by HEFT positivity bounds---that is, where there exist some $d_{1,2}$ such that a given point $(C_+,C_\times,d_3)$ complies with the HEFT positivity bounds---is to the right of the hatched light orange contour. The contour provides an indication of how the HEFT can enlarge the allowed parameters to the orange region, and in dark gray we illustrate the projection to the SMEFT.