S-Wave and P-Wave $B_c$ Meson Production at Hadron Colliders by Heavy Quark Fragmentation

We compute model-independently the production rates and transverse momentum spectra for the $B_c$ mesons in various spin-orbital states ($n\,^1S_0$, $n\,^3S_1$, $n\,^1P_1$, and $n\,^3P_J\,(J=0,1,2)$ ) at hadron colliders via the direct fragmentation of the bottom antiquark and via the Altarelli-Parisi-induced gluon fragmentation. Since all the radially and orbitally excited states below the $BD$ flavor threshold will decay, either electromagnetically, hadronically, or a combination of both, into the pseudoscalar ground state $1\,^1S_0$, they all contribute significantly to the inclusive $B_c$ meson production.