Measurement of the shape of the b quark fragmentation function using charmed mesons produced inside b jets from $\mathrm{t}\bar{\mathrm{t}}$ pair decays

A determination of the shape parameter of the Lund-Bowler fragmentation function for b quarks is presented. The analysis uses charm mesons produced inside b jets from $\mathrm{t}\bar{\mathrm{t}}$ pair decays in a data sample collected by the CMS experiment at the LHC at $\sqrt{s}=13~\mathrm{TeV}$, corresponding to an integrated luminosity of $35.9~\mathrm{fb}^{-1}$. Samples of D$^{0}$ and J/$\psi$ mesons are reconstructed from the decays D$^{0} \to$ K$^{\pm} \pi^{\mp}$and J/$\psi \to \mu^{+}\mu^{-}$ using charged particle track information. The reconstructed mesons are used as proxies for their parent B hadrons. The corresponding $x_{b}$ distributions, where $x_{b}$ is the fraction of the total transverse momentum of the charged constituents of the jet carried by the charm meson, are fitted to extract the value of the fragmentation function shape parameter, $r_{b}$. A value of $r_{b}= 0.858 \pm 0.037 (\mathrm{stat}) \pm 0.031 (\mathrm{syst})$ is obtained. This is the first measurement of the b quark fragmentation function in $\mathrm{t}\bar{\mathrm{t}}$ events at the LHC, and significantly improves the experimental constraints on the shape of the function. From a comparison with results at the Z pole in e$^{+}$e$^{-}$ data, no evidence for an environmental dependence of the fragmentation function is observed.