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We report on a measurement of the $D^{+}$-meson production cross section as afunction of transverse momentum ($p_T$) in proton-antiproton ($p\bar{p}$)collisions at 1.96 TeV center-of-mass energy, using the full data set collectedby the Collider Detector at Fermilab in Tevatron Run II and corresponding to 10fb$^{-1}$ of integrated luminosity. We use $D^{+} \to K^-\pi^+\pi^+$ decaysfully reconstructed in the central rapidity region $|y|<1$ with transversemomentum down to 1.5 GeV/$c$, a range previously unexplored in $p\bar{p}$collisions. Inelastic $p\bar{p}$-scattering events are selected online usingminimally-biasing requirements followed by an optimized offline selection. The$K^-\pi^+\pi^+$ mass distribution is used to identify the $D^+$ signal, and the$D^+$ transverse impact-parameter distribution is used to separate promptproduction, occurring directly in the hard scattering process, from secondaryproduction from $b$-hadron decays. We obtain a prompt $D^+$ signal of 2950candidates corresponding to a total cross section $\sigma(D^+, 1.5 < p_T <14.5~\mbox{GeV/}c, |y|<1) = 71.9 \pm 6.8 (\mbox{stat}) \pm 9.3(\mbox{syst})~\mu$b. While the measured cross sections are consistent withtheoretical estimates in each $p_T$ bin, the shape of the observed $p_T$spectrum is softer than the expectation from quantum chromodynamics. Theresults are unique in $p\bar{p}$ collisions and can improve the shape anduncertainties of future predictions.

Measurement of the $D^+$-meson production cross section at low transverse momentum in $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV