Blessed plots for 'Measurement of the Direct Charm Meson Production Cross Section at CDF'

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Large samples of fully reconstructed charm mesons have been observed in the early CDFII data with the Silicon Vertex Trigger (SVT). We reconstruct charm mesons in the following modes:
We count the number of signal events, determine the fraction of direct charm (i.e. not from B-decay), measure the reconstruction and trigger efficiencies, use the luminosity measurement from the CLC, divide by the PDG2002 branching ratios and calculate the cross sections.

Signal peaks

Data sample

The data used in this analysis cover run 138809 to 142206, which have been collected by CDF in February and March 2002. The data were reconstructed with version 4.3.1 of the CDF offline reconstruction program (dataset hbhd01 and gcrs01). The complete good run list is given in the appendix of CDFnote 6165. The corresponding integrated luminosity is 5.801 pb-1.

Track selection criteria

All tracks: Confirmed trigger tracks: Two trigger tracks are called a ``trigger pair'' if they satisfy:

Reconstruction of D0 -> K- pi+

The signal is modeled as a single Gaussian, plus a first order polynmial for the combinatorial background. The auto-reflection is modeled with a wide Gaussian at the same mean value as the D0 signal Gaussian, and the number of events is constrained to be equal to the D0 event number. The ratio of the widths of the auto-reflection and the signal are determined using tagged D0's from D*+ decay in each pT bin (see CDFnote6018).
Note 1: In the shaded plots, the yellow shading corresponds to the combinatoric background and the green shading corresponds to the auto-reflection background.
Note 2: In the D0 reconstruction we do not reject a candidate if it is also compatible with a D*+. Thus, the D0 (and D+) cross sections that we measure include feeddown from D*'s.

Reconstruction of D*+ -> D0pi+

The D*+ signal is modeled as a double Gaussian with the same mean and a the background parametrized as A*sqrt(Dm-mpi) * exp(B*(Dm-mpi)).

Reconstruction of D+ -> K-pi+pi+

We extract the number of D+ mesons using a double Gaussian for the signal and a linear function for the background.

Reconstruction of Ds -> phi pi+, phi -> K+K-

To extract the signal number, we use two Gaussian functions, one for the D+ and the other for the Ds+, plus a linear background.

Direct Charm Fraction

We use the impact parameter of reconstructed charm mesons to distinguish directly produced charm from secondary charm, originating from B decay. Due to the transverse kick in the decay of B hadrons, secondary charm mesons may not point back to the primary vertex. We fit the impact parameter distribution of the reconstructed charm mesons with a direct component and a secondary component taking into account the resolution on the measured impact parameter, measured using Ks -> pi pi in the two-track hadronic data.

Charm Meson Trigger and Reconstruction Efficiency

Thanks to the high efficiency and purity of COT tracking at CDF, we can use the measured COT tracks as a denominator to measure the efficiency of trigger tracks reconstructed by the XFT and SVT, and to measure the efficiency of finding hits in the silicon detector. The direct charm meson efficiencies are then calculated using a parametrized detector Monte Carlo simulation.

XFT Efficiency

The single-track XFT efficiency is measured using minimum bias data. The offline track is matched with an XFT track by requiring the difference between their curvatures and track azimuthal angles at COT super layer 6 to satisfy |curvXFT-curvoffline| <= 2x10-4 cm-1 and |phiXFT-phioffline| <= 15mrad.

We find the XFT efficiency high (>95%) for all pT and see a reduced efficiency when a track intersects one of the COT wire spacers: NB: This XFT efficiency refers to the early data which was taken in "2-miss" mode. From Run 152630 (Oct 9, 2002) onwards, CDF implemented "1-miss" mode, resulting in a somewhat lower efficiency.

SVT Efficiency

Unlike the XFT efficiency, the SVT efficiency is not close to unity and is a complicated function of various track parameters. Moreover, the SVT configuration went through several changes which affected the efficiency. We factorize the SVT efficiency as a pT dependent part, a part that depends on z and cot(theta) and a map of z and phi that is measured store-by store. NB: Since we use COT tracks as a denominator, the SVT efficiency includes cracks, incomplete coverage, single-hit SVX efficiencies etc. The intrinsic SVT efficiency for tracks that have 4 SVX hits in the same wedge has been measured to be about 80% for the data considered here, and has in the meanwhile improved to about 90%.

Two-track efficiencies

The efficiency for two tracks to be both reconstructed by the SVT depends strongly on the kinematics and geometry of the two-track pair. For example, if the opening angle is large, the two tracks go through different SVT wedges, and the efficiencies have little correlation. For small opening angles, the two tracks have a higher probability to go through the same wedge, and the efficiencies are strongly correlated, typically resulting in a higher two-track efficiency. This correlation can be fully accounted for if the single-track SVT efficiency is known as a function of all track parameters. In reality a few simplifying assumptions had to be made and the binning of each variable can not be too fine because of the limited available statistics. Therefore, we expect to underestimate the correlation of the SVT efficiency of two-track combinations. In order to correct for the this effect, we artificially introduce an additional correlation of 0.10 for the efficiency of two tracks if they pass through the same SVX wedge. After introducing this additional correlation, the two-track efficiency calculated from the parametrized SVT efficiency agrees better with the direct measurement.

Reweighting the MC

We do not expect that the pT spectrum from MC is a priori correct, since large discrepancies in the pT spectrum are typical for heavy flavor production models. We compare the pT distribution of charm mesons in data and MC, and make a parametrization of the data/MC ratio. After applying this ratio as a reweight factor to the MC events, the pT spectrum of the MC matches well the data, and no second iteration is needed.

Efficiency curves

We calculate the D meson trigger and reconstruction efficiency as the probability to pass the trigger and reconstruction simulation and offline selection criteria:

Data/MC comparisons

Data/MC comparison of the liftime distributions

The trigger requirements of an impact parameter larger than 120 µm has the effect of strongly sculpting the ct distribution. We verify that we describe this well by comparing the ct distributions of the charm signals between data and MC:

Data/MC comparison of decay angle distributions

Another interesting distribution is the decay angle of the pi+ in the center of mass frame of the D*+. This distribution is very sensitive to the tracking efficiency close to the 500 MeV/c pT threshold. We also do a data/MC comparison of the decay angle between the D0 flight direction and the K- in the center of mass frame of the D0. For this comparison we use D0's from D*+ decay, since for the inclusive D0 decays the auto-reflection gives a strong bias to this distribution. Note the asymmetry: the trigger efficiency for kaons boosted backward is higher than for pions boosted backward.

Dalitz structure of the D+ -> K-pi+pi+ decay

We found that the efficiency of reconstructing a D+ is strongly non-uniform over the allowed Dalitz phase space. In the MC, we use the E691 fit of the D+ -> K-pi+pi+ decay, and find that it describes the data qualitatively well:

Cross section results

Results for the integrated cross section

We calculate the integrated cross section in every bin i as follows:


where Ni is the signal yield, fD,i the direct fraction, L the luminosity, epsi the efficiency, and Br the PDG 2002 branching ratio of the charm meson to the final state. The factor ½ is included because we have counted both C=1 and C=-1 states, while we quote the cross section for C=1 states only.
Summing over all bins, we find the following values for the integrated cross section: where the first error is statistical and the second systematic. The systematic errors include the uncertainty from the branching ratios, from the luminosity measurement, from the signal extraction, from the direct fraction measurement and from the efficiency calculation. All cross sections refer to the rapidity range |Y|<=1.
See also the following table with more details of the integrated cross section (plain text version).

Results for the differential cross sections

We determine the differential cross sections in the center of each bin. For that, we divide the integral cross section by the bin size, and apply a bin center correction, that accounts for non-linear changes of the cross section inside the bin.
The results are shown in a table of the differential cross section (plain text version).

Comparison with NLO calculations

We compare the measurements to two theoretical calculations: We overlay the calculation with the measurement: The inner bars represent the statistical uncertainties; the outer bars are the quadratic sums of the statistical and systematic uncertainties. Note that the systematic uncertainties are fully correlated between pTbins and partially correlated between the different charm species. The solid curves are the theoretical predictions from Cacciari and Nason The dashed curve shown with the D*+ cross section is the theoretical prediction from Kniehl. The yellow(grey) error band from the theory curve corresponds to the maximum variation from changing the renormalization scale and the factorization scales between 0.5 and 2.0 times the default scale (mT for Cacciari, Nason, 2mT for Kniehl, where mT=sqrt(pT2+mc2).)

Data and theory are better compared by looking at the ratio:

Ratio of Vector to Pseudoscalar production

This analysis was blessed at the 10/2/2003 B Meeting, it is described in CDF Note 6623.
We measure PV, the fraction of charm mesons produced as a vector meson: PV=V/(P+V)=D*/(D+D*). Since we cannot reconstruct D*0 at CDF, this analysis assumes isospin symmetry, which predicts that the D*0 and D*+ cross sections are equal, and that the D0 and D+ cross sections excluding the feeddown from D* are equal.

Since we cannot reconstruct charm mesons down to zero transverse momentum, we measure PV for pT>=6GeV/c. We use a Monte Carlo (reweighted in pT to match the measured spectrum) to correct for the loss of transverse momentum in the decay of a D* to a D. Correlations between systematic uncertainties are taken into account. We measure: This value agrees with the ALEPH measurement: PV=0.595±0.045. (R. Barate et al., "Study of charm production in Z decays" Eur.Phys.J.C16:597-611,2000)

The measurement of the D0, D+ and D*+ cross sections allows an additional cross check: According to isospin symmetry, the difference in the measured D0 and D+ cross sections is entrirely due to the different feeddown from D*. This can be expressed in measurable quantities as u=(sigma(D0)-sigma(D+))/sigma(D*)*(f(D*->D0) - f(D*->D+))=1. We measure for this quantity: which is consistent with the expected value of 1.0.