Inclusive P-wave Quarkonium Decay Widths from Lattice QCD and pNRQCD

Abstract

Inclusive hadronic decay widths remain a long-standing challenge for first-principles QCD. We present a framework combining lattice QCD with strongly-coupled potential nonrelativistic QCD (pNRQCD) to compute inclusive P-wave heavy quarkonium decays to light hadrons. At leading order in the velocity expansion, all nonperturbative effects, apart from the square of the derivative of the wavefunction at the origin, are encoded in a single universal moment of the two-point chromoelectric correlator, which we determine for the first time from a quenched lattice QCD calculation matched to $\overline{\mathrm{MS}}$ via the gradient flow. Combined with perturbative short-distance coefficients and the square of the derivative of the wavefunction at the origin, our result reproduces the observed $χ_{cJ}(1P)$ widths and, at the same time, provides predictions for the unmeasured $χ_{bJ}(nP)$ widths. The framework extends naturally to inclusive decays and production of ordinary and exotic hadrons.