Nucleon energy correlators for the odderon

We investigate the T-odd nucleon energy correlator (NEC) at small- <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>x</a:mi> </a:math> 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- <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>x</c:mi> </c:math> 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 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>C</e:mi> </e:math> -odd tag in the final state, eliminating potential contamination from <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mi>C</g:mi> </g:math> -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.