The fractions of non-prompt (i.e. originating from beauty-hadron decays) D$^0$ and D$^+$ mesons with respect to the inclusive yield are measured as a function of the charged-particle multiplicity in proton$-$proton collisions at a centre-of-mass energy of $\sqrt{s} = 13$ TeV with the ALICE detector at the LHC. The results are reported in intervals of transverse momentum ($p_{\rm T}$) and integrated in the range $1 < p_{\rm T} < 24$ GeV/$c$. The fraction of non-prompt D$^0$ and D$^+$ mesons is found to increase slightly as a function of $p_{\rm T}$ in all the measured multiplicity intervals, while no significant dependence on the charged-particle multiplicity is observed. In order to investigate the production and hadronisation mechanisms of charm and beauty quarks, the results are compared to PYTHIA 8 as well as EPOS 3 and EPOS 4 Monte Carlo simulations, and to calculations based on the colour glass condensate including three-pomeron fusion.
Differential cross sections are presented for the prompt and non-prompt production of the hidden-charm states $X(3872)$ and $\psi(2S)$, in the decay mode $J/\psi \pi^+\pi^-$, measured using 11.4 fb$^{-1}$ of $pp$ collisions at $\sqrt{s} = 8$ TeV by the ATLAS detector at the LHC. The ratio of cross-sections $X(3872)/\psi(2S)$ is also given, separately for prompt and non-prompt components, as well as the non-prompt fractions of $X(3872)$ and $\psi(2S)$. Assuming independent single effective lifetimes for non-prompt $X(3872)$ and $\psi(2S)$ production gives $R_B = \frac{\mathcal{B}(B \rightarrow X(3872)\textrm{ + any}) \mathcal{B}(X(3872 \rightarrow J/\psi\pi^+\pi^-)}{\mathcal{B}(B \rightarrow \psi(2S)\textrm{ + any}) \mathcal{B}(\psi(2S) \rightarrow J/\psi\pi^+\pi^-)} = (3.95 \pm 0.32 \mathrm{(stat)} \pm 0.08\mathrm{(sys)}) \times 10^{-2}$, while separating short- and long-lived contributions, assuming that the short-lived component is due to $B_c$ decays, gives $R_B = (3.57 \pm 0.33\mathrm{(stat)} \pm 0.11\mathrm{(sys)}) \times 10^{-2}$, with the fraction of non-prompt $X(3872)$ produced via $B_c$ decays for $p_\mathrm{T}(X(3872)) > 10$ GeV being $(25 \pm 13\mathrm{(stat)} \pm 2\mathrm{(sys)} \pm 5\mathrm{(spin)})\%$. The distributions of the dipion invariant mass in the $X(3872)$ and $\psi(2S)$ decays are also measured and compared to theoretical predictions.
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