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A measurement of vector boson ($V$) production in conjunction with a$D^{*}(2010)^+$ meson is presented. Using a data sample corresponding to $9.7\,{\rm fb}^{-1}$ of ^Mproton-antiproton collisions at center-of-mass energy$\sqrt{s}=1.96\rm~ TeV$ produced by the Fermilab Tevatron, we reconstruct$V+D^{*+}$ samples with the CDF~II detector. The $D^{*+}$ is fullyreconstructed in the $D^{*}(2010)^+ \rightarrow D^{0}(\to K^-\pi^+)\pi^+$ decaymode. This technique is sensitive to the associated production of vector bosonplus charm or bottom mesons. We measure the ratio of production cross sections$\sigma(W+D^{*})/\sigma(W)$ = $[1.75\pm 0.13 {\rm (stat)}\pm 0.09 {\rm(syst)}]\% $ and $\sigma(Z+D^{*})/\sigma(Z)$ = $[1.5\pm 0.4 {\rm (stat)} \pm0.2 {\rm (syst)}]\% $ and perform a differential measurement of$d\sigma(W+D^{*})/dp_T(D^{*})$. Event properties are utilized to determine thefraction of $V+D^{*}(2010)^+$ events originating from different productionprocesses. The results are in agreement with the predictions obtained with the{\sc pythia} program, limiting possible contribution from non-standard-modelphysics processes.

Measurement of vector boson plus $D^{*}(2010)^+$ meson production in $\bar{p}p$ collisions at $\sqrt{s}=1.96\, {\rm TeV}$