Measurement of low p_{T} D^{+} meson production cross section at CDF
1. Fermilab
2. University of Oxford
3. INFN and Università degli studi di Bologna
4. INFN  sede di Pisa
5. Cern
We report on a measurement of cross section for D^{+} mesons whose p_{T} extends down to 1.5 GeV/c, a range still unexplored in protonantiproton collisions.The
measurement is conducted as a function of meson transverse momentum
using D^{+}→
K^{}π^{+}π^{+} decays
reconstructed in the full CDF Run II data set. Events are collected
through minimal, if any, requirements on the event features, thus reducing biases to the physics properties of the
collected charm decays. The sample is divided into subsamples according to the D^{+}candidate p_{T} (p_{T} bins). In each, we apply a datadriven optimization
of the offine selection and perform a twodimensional simultaneous fit of the resulting distributions of K^{}π^{+}π^{+}
mass and D^{+} impactparameter, the minimum transverse distance between the D^{+} trajectory and the beam. The fit determines, for each p_{T} bin, the signal yield of D^{+} candidates genuinely produced in the
protonantiproton interaction or originated from excited charm resonances (primary D^{+}) by statistically subtracting D^{+} candidates originated from
bhadron decays (secondary D^{+}). Each primary yield is combined with corresponding reconstruction and selection effciencies derived using simulation to determine the differential cross section. Chargeconjugate decays are implied throughout. The cross section σ_{i}, averaged
in each p_{T} bin i and integrated in the range y<1 (where y = 0.5 ln[(E + p_{z})/(Ep_{z})] and E and p_{z} are charm meson energy and longitudinal momentum, respectively)
is determined using the following equation:
where N_{i} is the observed number of primary D^{+} and D mesons in each p_{T} bin. The factor 1/2 is included because both D^{+} and D^{} mesons contribute to N_{i} and we
report results solely for D^{+}, assuming flavorsymmetric hadroproduction of charm quarks in the strong interaction.
The integrated
luminosity ∫ Ldt is
normalized to
an inelastic protonantiproton cross section of σ = 60.7 ± 2.4 mb and ε_{i} is the
global detection, reconstruction, and selection efficiency. The
branching fraction B is taken from
the PDG .
The differential cross section is averaged in each p_{T} bin and integrated over the D^{+} rapidity interval
y < 1.
The total cross section is σ(D^{+};
p_{T} > 1.5 GeV/c;
y < 1) = 71.9± 6.8 ± 9.3 μb where the first contribution to the uncertainty is statistical
and the second systematic. The results agree with earlier
determinations at higher transverse momenta. While the
measurements agree with theoretical predictions within
the uncertainties, there is a systematic variation
suggesting that theoretical cross section as a function of
transverse momentum is in need of further refinement
taking into account these results.
The complete analysis is described in CDF public note 11199.
List of public plots
INVARIANTMASS AND IMPACTPARAMETER

Figure 1: Twodimensional fit in the (m, d_{0})space for p_{T}(D^{+}) in 1.52.5 GeV/c.

Figure 2: Twodimensional fit in the (m, d_{0})space for p_{T}(D^{+}) in 2.53.5 GeV/c.

Figure 3: Twodimensional fit in the (m, d_{0})space for p_{T}(D^{+}) in 3.54.5 GeV/c.

Figure 4: Twodimensional fit in the (m, d_{0})space for p_{T}(D^{+}) in 4.56.5 GeV/c.

Figure 5: Twodimensional fit in the (m, d_{0})space for p_{T}(D^{+}) in 6.514.5 GeV/c.
CROSS SECTION

Figure 6: D^{+} production cross section, averaged in p_{T}bins and integrated over y< 1, as a function of p_{T}(D^{+}) bins in both data and FONLL prediction. The measurement point is displayed at the p_{T} pointvalue at which the theoretical cross section equals the observed value of the p_{T}averaged crosssection. The point values are 1.99, 2.97, 3.97, 5.37, and 9.14 GeV/c, as determined using the theoretical prediction.

Figure 7: D^{+} production cross section as a function of p_{T}(D^{+}) bins for both the current and 2003 CDF results. The current measurement is averaged in p_{T}bins and integrated over y< 1, while the 2003 result is a p_{T}point cross section and and integrated over y< 1. For the current result the measurement point is displayed at the mean p_{T} point of the bin.

Figure 8: D^{+} production cross section as a function of p_{T}(D^{+}) bins for both the current and 2003 CDF results after the theory scaling. For the current result the measurement point is displayed at the p_{T} pointvalue at which the cross section equals the observed value of the p_{T}averaged crosssection. The point values are 1.99, 2.97, 3.97, 5.37, and 9.14 GeV/c, as determined using the theoretical prediction.
ADDITIONAL MATERIAL

Figure 9: Invariant K^{}π^{+}π^{+} mass before the optimization.

Figure 10: Signal and sideband defintion.

Figure 11: Impactparameter distribution before (left) and after (right) the sidebands subtraction for p_{T}(D^{+}) in 1.52.5 GeV/c.

Figure 12: Conditionalsilicon efficiency in both data and MC for the J/ψ sample (left) and the π_{soft} (right) sample.

Figure 13: Production cross section for even and odd subsamples.

Figure 14: Conditionalsilicon efficiency as a function of cotθ for the J/ψ sample.

Figure 15: Conditionalsilicon efficiency for π in D^{+}MC and in D^{*}data (left). (η,z_{0})map for the π_{soft} dataset (right).

Figure 16: Fit to the p_{T}efficiency of the J/ψ and π_{soft} for the first (left) and second (right) time periods.

Figure 17: Fit to the p_{T}efficiency of the J/ψ and π_{soft} for the third (left) and fourth (right) time periods.

Figure 18: Fit to the p_{T}efficiency of the J/ψ and π_{soft} for the fifth time period.

Figure 19: Correlation study in both MC and data for the J/ψ sample: conditional silicon efficiency for the second muon when the first one is already detected by the COT.
List of public tables

Table I: Results of the 2Dfit for the five p_{T}(D^{+})bins.

Table II: Reconstruction efficiency as a function of p_{T}(D^{+}).

Table III: Scale factors for control samples.

Table IV: Correction factors for the five p_{T}(D^{+})bins.

Table V: Corrected reconstruction efficiency for the five p_{T}(D^{+})bins with the CF method.

Table VI: Summary of systematic uncertainties. When parenthes are present, the number in (out of) parenthesis refer to the contribution to the even (odd) sample.

Table VII: Differential crosssection results for D^{+} and D^{} separately.

Table VIII: Differential crosssection results for two separate data types, those resulting from the zero–bias (ZB) and minimumbias (MB) online triggers.

Table IX: Present CDF differential crosssection measurement, averaged in p_{T}bins and integrated over y< 1, compared to the thoeretical prediction.

Table X: Previously published CDF differential crosssection measurement, p_{T}point and and integrated over y< 1, compared to the thoeretical prediction.

Table XI: Comparison between the previous and the present CDF measurement over the range 1.5  14.5 GeV/c for the current measurement and over the range 6.0  20.0 GeV/c for the 2003 result.