Nucleon Energy Correlators for the Odderon

We investigate the T-odd nucleon energy correlator (NEC) at small $x$ and establish its connection with the spin-dependent odderon. Probing the T-odd NEC involves measuring a single transverse spin asymmetry (SSA) for the energy pattern in the target fragmentation region in deep inelastic scattering. We find that while the inclusive energy pattern results in a vanishing SSA, a nonzero SSA emerges when restricting the measurement to charged hadrons, which are directly measured in tracking detectors. To describe this effect, we introduce the track-based NEC and evaluate its small-$x$ limit from fracture functions using the energy sum rule. The resulting SSA exhibits an opposite sign between positively and negatively charged hadrons, providing a clear experimental signature of the odderon. Furthermore, by incorporating charge weighting into the NEC, we construct a C-odd tag in the final state, eliminating potential contamination from C-even gluonic contributions. Our results demonstrate that these track-based energy-pattern observables offer a clean and sensitive probe for unveiling odderon dynamics at the future electron-ion collider.