A bstract Within the framework of nonrelativistic QCD (NRQCD) factorization, and based on the Collins-Soper operator definition of fragmentation functions, we present a systematic calculation of the fragmentation functions for a heavy quark fragmenting into color-singlet P -wave quarkonium states. After reproducing and confirming the known leading-order results, we further compute the relativistic corrections up to order O (v²) O v 2. Our analysis applies both to quarkonium systems composed of heavy quarks with the same flavor and to B c -type mesons formed by heavy quarks of different flavors. Numerical results show that, for all color-singlet P -wave channels, the O (v²) O v 2 relativistic corrections give sizable negative contributions over most of the momentum-fraction z region. We further compute inclusive cross sections for P -wave quarkonium plus charmed hadrons in e + e − annihilation via the single photon process up to O (v²) O v 2 by applying our obtained fragmentation functions, and the resulting predictions are consistent with the full fixed-order results in the high-energy region.
Cui et al. (2026) studied this question.