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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.
- D0 -> K-pi+
- D*+ -> D0pi+, D0 -> K-pi+
- D+ -> K-pi+pi+
- Ds+ -> phi pi+, phi -> K+K-
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
Confirmed trigger tracks:
- >= 25 axial COT hits
- >= 25 stereo COT hits
- >= 3 SVX phi side hits on different layers (except D*+ slow pion)
- pT >= 0.5 GeV/c
- |z0| <= 47.25cm
- SVX fiducial: at R=10.645 cm |z| <= 47.25 cm
- COT fiducial: at R=133 cm |z| <= 155 cm
Two trigger tracks are called a ``trigger pair'' if they satisfy:
- the track is matched with an SVT track;
- pT >= 2.0 GeV/c (offline and SVT)
- 120 µm <= |d0| <= 1 mm (offline and SVT)
- the track enters and leaves the same mechanical SVX barrel.
- the two tracks have opposite charge
- pT1+pT2 >=5.5 GeV/c (offline and SVT)
- 2° <= |phi1-phi2| <= 90°
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
- the K- pi+ pair is a trigger pair
- Lxy(D0) >= 500 µm;
- opposite sign impact parameters
- |z0(K-)-z0(pi+)| <= 5 cm
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)).
- A D0 candidate with |m(Kpi)-m(D0)|<= 3 sigma m(D0)
- no SVX requirement for the soft pion;
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.
- a trigger pair amongst the D+ decay daughters
- Lxy(D+) >= 800 µm
- |Dz| <= 5cm between any two tracks
- chi2 <= 30 for the three track vertex fit
- Dm (=m(Kpipi)-m(Kpi)) >= 0.18GeV/c2, where m(Kpi) is the invariant mass of the trigger pair.
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.
- the K-pi+ pair form a trigger pair;
- 1.00 GeV/c2 <= m(K+K-) <= 1.04 GeV/c2
- Lxy(Ds+) >= 500 µm
- |Dz| <= 5 cm between any two tracks
- chi2 <= 30 for the three track vertex fit
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.
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.
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%.
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
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.
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 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.
- sigma(D0, pT >= 5.5 GeV) = 13.3±0.2±1.5µb
(when comparing with D*+ and D+, use: sigma(D0, pT >= 6.0 GeV) = 9.3±0.1±1.1µb)
- sigma(D*+, pT >= 6.0GeV) = 5.2±0.1±0.8µb
- sigma(D+, pT >= 6.0 GeV) = 4.3±0.1±0.7µb
- sigma(Ds, pT >= 8.0 GeV) = 0.75±0.05±0.22µb
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
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
- M. Cacciari and P. Nason, "Charm cross sections for the Tevatron RunII"
JHEP 0309, 006 (2003).
This is a Fixed Order Next-to-Leading Log (FONNL) calculation.
is publicly available.
Non-perturbative effects in charm hadronization are taking into account
using recent ALEPH data (R. Barate et al., "Study of charm production in Z decays"
- B.A. Kniehl, private communication.
Their calculation employs the method described in
B.A. Kniehl, G. Kramer, B. Potter,
Nucl.Phys. B597, 337-369 (2001).
The cross section has only been calculated for the D*+ cross section.
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.
This value agrees with the ALEPH measurement: PV=0.595±0.045.
(R. Barate et al., "Study of charm production in Z decays"
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.