Measurement of the Shape of the b Quark Fragmentation Function Using Charmed Mesons in Proton-Proton Collisions at a Center of Mass-Energy of 13 TeV

In this analysis we present the first results of the measurement of the shape parameter r$_{b}$ in the Lund-Bowler fragmentation function for the b quark in a $t$$\bar{t}$ environment. The analysis uses charmed mesons produced in the leptonic decays of $t$$\bar{t}$ at $\sqrt{s}$ = 13 TeV in the CMS detector using the full 2016 dataset with an integrated luminosity of 35.9 fb$^{-1}$. The charged particle decays of J/$\psi$ $\rightarrow$ $\mu$$^{+}$$\mu$$^{-}$ and D$^{0}$ $\rightarrow$ K$\pm$$\mu$$\mp$ are used as proxies for the parent b quark via the ratio x$_{B}$(the $p$$_{T}$ of the charmed meson divided by the $\sum$E$p$$_{T}^{ch}$ of all charged particles in the jet containing the meson) to measure the shape parameter r$_{b}$. The shape parameter r$_{b}$ is measured to be r$_{b}$ = 0.841$\pm$0.014(stat)$\pm$0.010 (syst)$_{+0.033}^{-0.026}$(FSR).