Inclusive $J/\psi$ and $\psi (2S)$ production from $b$-hadron decay in $p\overline{p}$ and $pp$ collisions

We study the inclusive production of $J/\psi$ and $\psi (2S)$ mesons originating from the decays of bottom-flavored hadrons produced in $p\overline{p}$ collisions at the Fermilab Tevatron and in $pp$ collisions at the CERN LHC. We work at next-to-leading order in the general-mass variable-flavor-number scheme implemented with nonperturbative fragmentation functions fitted to $e^{+}{e}^{-}$ data of inclusive $b$-hadron production exploiting their universality. The three-momentum distributions of the charmonia used were extracted from $B$-decay data in the framework of nonrelativistic-QCD factorization. Comparing the theoretical predictions thus obtained with transverse-momentum distributions measured by the CDF II, ALICE, ATLAS, CMS, and LHCb collaborations, we find excellent overall agreement as for both absolute normalization and line shape, which provides a nontrivial test of the general-mass variable-flavor-number scheme over wide ranges of center-of-mass energy, transverse momentum, and rapidity.

Figure 1

The inclusive cross sections of nonprompt $J/\psi$ hadroproduction measured by CDF II [10] in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ and by CMS [12, 13], LHCb [14], ATLAS [16], and ALICE [17] in $pp$ collisions at $\sqrt{s}=7\mathrm{TeV}$ are compared with NLO GM-VFNS predictions, whose default values and error bands are indicated by the solid and dashed lines, respectively. In frame (a), the result obtained by replacing the total $B\to J/\psi +X$ three-momentum distribution in the default evaluation by a delta function in $z$ peaking at $⟨z⟩=0.6$ [2] and normalized to the total $B\to J/\psi +X$ branching fraction, 1.12% [2], is represented by the dotted line.

Figure 2

The inclusive cross sections of nonprompt $\psi (2S)$ hadroproduction measured by CDF II [11] in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ and by CMS [13] and LHCb [15] in $pp$ collisions at $\sqrt{s}=7\mathrm{TeV}$ are compared with NLO GM-VFNS predictions, whose default values and error bands are indicated by the solid and dashed lines, respectively.