This paper presents a first‑principles approach to a long‑standing problem in quantum chromodynamics (QCD): how to compute inclusive P‑wave heavy quarkonium decays into light hadrons. Inclusive decay widths measure how often a particle decays into any set of light hadrons. The authors combine lattice QCD with a low‑energy effective theory called potential nonrelativistic QCD (pNRQCD) to make these decay rates calculable from the fundamental theory of quarks and gluons.

At leading order in an expansion in the heavy‑quark velocity, the authors show that all nonperturbative effects — except for the square of the derivative of the quarkonium wavefunction at the origin — are captured by a single universal number. That number is a moment of a two‑point chromoelectric correlator, which is a measure of how the chromoelectric field (the gluon analogue of the electric field) at one point in space and time is correlated with the field at another point. The paper reports the first determination of this moment from a lattice QCD calculation.

The lattice calculation was done in the quenched approximation, which omits the effects of virtual light quark–antiquark pairs (sea quarks). The lattice result was converted into the widely used modified minimal subtraction scheme (MSbar) by applying the gradient flow, a smoothing technique that helps define and renormalize field correlators on the lattice. The computed moment was then combined with known short‑distance coefficients from perturbation theory and the wavefunction‑derivative factor to produce decay widths.

When they put the pieces together, the authors find that their framework reproduces the observed widths of the charmonium P‑wave states called chi_cJ(1P). At the same time, the same method gives predictions for the analogous bottomonium P‑wave states chi_bJ(nP), whose inclusive hadronic widths have not all been measured. The approach is presented as general: it can be extended to other inclusive decays and to production of ordinary or exotic hadrons.