The TeraZ Mirage: New Physics Lost in Blind Directions

TL;DR

The paper tackles whether precision EWPOs at the Z-pole, interpreted through SMEFT, can uncover BSM physics or whether blind directions in the SMEFT space substantially limit indirect searches. It combines a bottom-up EWPO fit with mappings to UV completions and analyzes RG evolution and one-loop matching, including three illustrative multi-field UV scenarios. The authors find that many blind directions persist even after RG running and finite one-loop corrections, indicating that TeraZ alone cannot fully constrain the SMEFT parameter space. They argue for complementary high-energy collider programs, such as FCC-hh, to access the remaining degenerate directions and achieve a more complete exploration of UV physics.

Abstract

The next generation of high-luminosity electron-positron colliders, such as FCC-ee and CEPC operating at the $Z$ pole (TeraZ), is expected to deliver unprecedented precision in electroweak measurements. These precision observables are typically interpreted within the Standard Model Effective Field Theory (SMEFT), offering a powerful tool to constrain new physics. However, the large number of independent SMEFT operators allows for the possibility of blind directions, parameter combinations to which electroweak precision data are largely insensitive. In this work, we demonstrate that such blind directions are not merely an artefact of agnostic effective field theory scans, but arise generically in realistic ultraviolet completions involving multiple heavy fields. We identify several concrete multi-field extensions of the Standard Model whose low-energy SMEFT projections align with known blind subspaces, and show that these persist even after accounting for renormalisation group evolution and finite one-loop matching effects. Our analysis shows that TeraZ will set a new benchmark in precision for indirect searches, but fully probing the space of possible ultraviolet physics requires moving towards a high energy hadron collider. Later FCC-ee runs at higher centre-of-mass energies, together with the FCC-hh, will provide the necessary complementary probes, enabling a far more complete exploration of the SMEFT parameter space.

Figures (10)

• Figure 1: Examples of EWPO bounds at 3 $\sigma$ on four-fermion regions involving $c_{uu}$. The orange area enclosed by a solid line includes leading-log RGEs, while we integrate RGEs numerically in the green area enclosed by the dashed line.
• Figure 2: Regions in the space of $c_{ud}^{(1)}$, $c_{qd}^{(1)}$, $c_{qq}^{(1)}$, $c_{qu}^{(1)}$ and $c_{qq}^{(3)}$ excluded by EWPOs at $3\,\sigma$. The orange region enclosed by the solid line includes only leading-log RGE effects, while we numerically integrate the RGEs to obtain the green region enclosed by the dashed line.
• Figure 3: Regions in the space of $c_{eu}$, $c_{lu}$, $c_{qe}$ and $c_{lq}^{(1)}$ excluded by EWPO at $3\,\sigma$. The orange region enclosed by the solid line includes only leading-log RGE effects, while we numerically integrate the RGEs to obtain the green one enclosed by the dashed line.
• Figure 4: Sensitivity of EWPO to different single-scalar extensions of the SMEFT as a function of their only coupling to the SM. The solid (dash) line includes tree-level and leading-log RGE (RGE resummation and finite one-loop matching corrections).
• Figure 5: Tree-level and one-loop diagrams contributing to four-fermion interactions.