Flow between extremal one-point energy correlators in QCD

The energy density generated by a vector current is characterized by a single parameter $a_{\mathcal{E}}$ bounded by unitarity to $-1/2 \leq a_{\mathcal{E}} \leq 1$, with extremal values saturated by free theories of different matter content. Through confinement, QCD transmutes fermionic matter into scalars, revealing a nontrivial flow between extremal correlators. We reconstruct this flow using perturbative QCD and chiral perturbation theory. The observable is accessible with currently available experimental data.