P--wave quarkonia in jets at the LHC

We present the first systematic theoretical study of the production of P-wave charmonium states χcJ and bottomonium states χbJ(nP) within jets at the LHC using the fragmenting jet function framework at next-to-leading order in αₛ. Our calculation resums both collinear DGLAP logarithms and threshold double logarithms in the fragmentation functions and accounts for feeddown contributions from higher quarkonium states. We observe a notable contrast between the charmonium and bottomonium sectors. For χbJ(nP), the normalized momentum-fraction distributions exhibit a nearly universal shape, with remarkably weak dependence on the choice of long-distance matrix element sets, the radial excitation ($n=1,2,3$), and the total angular momentum ($J=0,1,2$). We attribute this universality to the overwhelming dominance of the ³S₁[8] fragmentation channel, while feeddown contributions from higher bottomonium states remain small. In contrast, the shape of χcJ distributions exhibits a stronger dependence on the matrix-element set, reflecting the different relative contributions of the ³S₁[8] and ³PJ[1] channels. We provide predictions for the χcJ and χbJ(nP) distributions for the CMS and LHCb kinematic selections across a range of jet transverse momenta. We also compare our predictions with {Pythia}~8 simulations for selected P-wave quarkonium states.