  Collider experiments often exploit information about the quantum numbers of
final state hadrons to maximize their sensitivity, with applications ranging
from the use of tracking information (electric charge) for precision jet
substructure measurements, to flavor tagging for nucleon structure studies. For
such measurements, perturbative calculations in terms of quarks and gluons are
insufficient, and non-perturbative track functions describing the energy
fraction of a quark or gluon converted into a subset of hadrons (e.g., charged
hadrons) must be incorporated. Unlike fragmentation functions, track functions
describe correlations between hadrons and therefore satisfy complicated
non-linear evolution equations whose structure has so far eluded calculation
beyond the leading order. In this Letter, we develop an understanding of track
functions and their interplay with energy flow observables beyond the leading
order, allowing them to be used in state-of-the-art perturbative calculations
for the first time. We identify a shift symmetry in the evolution of their
moments that fixes their structure, and we explicitly compute the evolution of
the first three moments at next-to-leading order, allowing for the description
of up to three-point energy correlations. We then calculate the two-point
energy correlator on charged particles at $O(\alpha_s^2)$, illustrating
explicitly that infrared singularities in perturbation theory are absorbed by
moments of the track functions and also highlighting how these moments
seamlessly interplay with modern techniques for perturbative calculations. Our
results extend the boundaries of traditional perturbative QCD, enabling
precision perturbative predictions for energy flow observables sensitive to the
quantum numbers of hadronic states.
