High precision heavy-boson-jet substructure with energy correlators

Energy-correlator-based jet substructure has gained significant attention in recent years. One of the notable applications has been the study of multi-scale jets, where distinct physical scales manifest as features localised in different angular regions of the correlator. In this article, we present the first high-precision study of energy correlators on the simplest multi-scale jets: heavy boson jets. In such systems, the boson mass $M$ introduces an additional scale, generating a sharp peak at angles $\sim M/p_T^{\rm jet}$. We show that this feature can be computed directly by boosting the EEC spectrum measured in $e^+e^- \rightarrow {\rm hadrons}$ at the $Z$ pole. We identify that the peak arises from boosting the well-studied Sudakov factorisation governing the back-to-back limit of the two-point correlator. As a result, the feature is controlled by Sudakov resummation, not a Breit-Wigner-like structure in the $Z$ decay, and is therefore calculable with exceptional precision. We provide predictions at N$^3$LL$'$ accuracy for both $pp$ $Z$-tagged jets and $e^+e^-$ di-$Z$ production, and compare them to Herwig and Pythia simulations, finding close agreement. We also demonstrate that the boosted-$Z$ spectrum can be constructed directly by boosting OPAL measurements at the $Z$ pole. In this light, energy-correlator jet substructure on the hadronic decays of heavy bosons at the LHC provide access to clean, lepton-collider-like measurements across a wide range of effective centre-of-mass energies set by the boson jet transverse momentum.