EFT at JADE: a case study

As we use the standard model effective field theory to search for signs of new physics beyond the direct reach of the LHC, we often wonder what we may learn from the effective field theory, and what it would look like to make a discovery via effective field theory. This article presents a case study that provides some answers to these questions. We apply the low-energy effective field theory to $e^+e^- \to μ^+μ^-$ data below the Z boson mass from the JADE experiment at DESY. The low-energy effective field theory allows the observation of physics beyond QED in the JADE data and furthermore, by matching the Wilson coefficients to the electroweak theory, a rough measurement of the masses of the W and Z bosons is possible. The ability to make this rough measurement challenges the conventional wisdom that an observation of new physics via EFT tells us nothing about the nature of that new physics. A measurement of this quality would have been sufficient to guide the construction of colliders such as the super proton-antiproton synchrotron or the large electron-positron collider, and so we anticipate that a discovery of new physics via effective field theory at the LHC would be similarly sufficient to guide the construction of future colliders.

💡 Research Summary

The paper presents a pedagogical case study that demonstrates how low‑energy effective field theory (LEFT) can be used to extract meaningful information about physics beyond the Standard Model (SM) from data that lie well below the electroweak scale. The authors focus on the historic JADE experiment at DESY, which measured the differential cross‑section for the process e⁺e⁻ → μ⁺μ⁻ at centre‑of‑mass energies of 13.8, 22.0, 34.4 and 42.4 GeV—energies far below the Z‑boson pole. The JADE data have already been corrected for QED effects up to order α³, so the authors treat the remaining measurements as tree‑level observables that can be described by QED plus possible contributions from higher‑dimensional operators.

The theoretical framework starts from the Standard Model Effective Field Theory (SMEFT). By integrating out the heavy W, Z, Higgs and top fields, one obtains the low‑energy effective theory (LEFT) appropriate for the JADE kinematic regime. Although LEFT contains thousands of operators, the authors systematically reduce the basis to those that (i) contribute at tree level to e⁺e⁻ → μ⁺μ⁻, (ii) preserve CP, and (iii) are non‑vanishing in the SM. This leaves only four dimension‑six four‑fermion operators, conventionally denoted C_LL, C_RR, C_LR and C_RL. Their linear combinations X ≡ Re