Track impact parameter ($d_0$) resolution in the transverse plane($r\phi$ direction) as a function of $\pt$ comparing data and simulation. This resolution includes the uncertainty in the primary vertex position, which is reconstructed excluding the track being probed.

Invariant mass distributions for $\Dzero$ (top) and $\Dplus$ (middle) candidates, and mass difference distribution for $\Dstar$ candidates (bottom), for three $\pt$ intervals. The curves show the fit functions as described in the text. The values of mean ($\mu$) and width ($\sigma$) of the signal peakare reported (for $\Dzero$ and $\Dplus$ they are expressed in $\gev/c^2$)

Acceptance $\times$ efficiency for $\Dzero$, $\Dplus$, and $\Dstar$ mesons, as a function of $\pt$ (see text for details).

Left: prompt fraction $f_{\rm prompt}$ of the $\Dzero$ raw yield as a function of $\pt$, for the two FONLL-based methods (solid: central value, from Eq.2; dashed: alternative method, from Eq.4) and for the impact parameter fit method (circles); the boxes show the envelope of the uncertainty bands of the two FONLL-based methods; the error bars show the total uncertainty from the impact parameter fit, including the statistical and systematic contributions Right: an example of $\Dzero$ meson impact parameter distribution in the transverse plane, for $2< \pt< 3 \gev/c$; the distribution is background-subtracted and fitted with the two-component function for prompt and feed-down contributions, as described in the text; the resulting prompt fraction, impact parameter resolution for prompt mesons, and $\chi^2$/(number of degrees of freedom) of the fit are given; the inset, with linear scale, shows also the negative entries, resulting from the background subtraction.
\begin{align*} (2)   f_{\rm prompt}=1-(N^{\rm D^\pm from B raw}/N^{\rm D^\pm raw}) \end{align*} \begin{align*} (4)   f_{\rm prompt}= \left( 1+ \frac{({\rm Acc}\times\epsilon)_\text{feed-down} }{({\rm Acc}\times\epsilon)_{\rm prompt} } \frac{\left.\frac{{\rm d}\sigma_{\rm FONLL}^{\rm D^+ from B}}{{\rm d}\pt}\right|_{|y|< 0.5}}{\left.\frac{{\rm d}\sigma_{\rm FONLL}^{\rm D^+}}{{\rm d}\pt}\right|_{|y|< 0.5}}\right)^{-1}\, \end{align*}

$\pt$-differential inclusive cross section for prompt $\Dzero$, $\Dplus$, and$\Dstar$ mesons in pp collisions at $\sqrts=7 $TeV compared with FONLL and GM-VFNS  theoretical predictions. The symbols are positionedhorizontally at the centre of each $\pt$ interval. The normalization uncertainty is not shown (3.5\% from the minimum-bias cross section plus the branching ratio uncertainties, as of Table 2).