Measurement of f(c→D∗+X), f(b→D∗+X) and Γcc¯/Γhad using D∗± mesons

TLDR: In this article, a combination of several charm quark tagging methods based on fully and partially reconstructed mesons, and a bottom tag based on identified muons and electrons, was found to be the hadronisation fractions of charm and bottom quarks into hadronic mesons.

Abstract: The production rates of \({\rm D}^{*\pm}\) mesons in charm and bottom events at centre-of-mass energies of about 91 GeV and the partial width of primary \({\rm c\bar c}\) pairs in hadronic \({\rm Z}^0\) decays have been measured at LEP using almost 4.4 million hadronic \({\rm Z}^0\) decays collected with the OPAL detector between 1990 and 1995. Using a combination of several charm quark tagging methods based on fully and partially reconstructed \({\rm D}^{*\pm}\) mesons, and a bottom tag based on identified muons and electrons, the hadronisation fractions of charm and bottom quarks into \({\rm D}^{*\pm}\) mesons have been found to be \(\) The fraction of \({\rm c\bar c}\) events in hadronic \({\rm Z}^0\) decays, \(\Gamma_{\rm c\bar c}/\Gamma_{\rm had}=\Gamma({\rm Z}^0\to{\rm c\bar c}) / \Gamma({\rm Z}^0\to\rm hadrons)\), is determined to be \(\) In all cases the first error is statistical, and the second one systematic. The last error quoted for \(\Gamma_{\rm c\bar c}/\Gamma_{\rm had}\) is due to external branching ratios.

Figures

Figure 1: Distributions of the difference ∆M = M∗ − M0 reconstructed in the four different D∗+ channels. The arrows indicate the selected signal region. (a) 3-prong decay mode, (b) the two semileptonic modes combined, (c) the satellite decay mode, and (d) the 5-prong decay mode. The points with error bars are the signal candidates. Superimposed in each case (line histogram) are the background estimator distributions, normalised to the upper sidebands in ∆M .

Table 3: List of systematic errors relevant in the determination of the rate of D∗+ mesons produced in Z0 → cc and in Z0 → bb events, the total multiplicity of D∗+ mesons in Z0 decays, and the mean scaled energy. For the error of the mean scaled energy only errors which are larger than 0.001× 10−3 are listed separately, otherwise the total contribution from a class of errors is given. A sign in front of an error indicates the direction of change under a positive change of the variable. The last three errors from the flavour separation include the contribution from the same sources through the D∗+ reconstruction. Note that all flavour separation errors are anti-correlated between the charm and the bottom result.

Figure 5: Spectrum of the squared transverse momentum of double tagged candidates after applying all cuts of the (a) signal candidates, reconstructed with opposite charges in both jets. The non-charm component is indicated by the hatched area; (b) lepton-tagged candidates. The points are the data and the lines the results of the fit; (c) background candidates, reconstructed in ∆M sidebands.

Figure 4: Efficiency corrected yield of D∗+ mesons as a function of the scaled energy xD∗+ , 1/NhaddND∗+/dxD∗+ , for all candidates (filled points with error bars) reconstructed in the decay D∗+ → D0π+,D0 → K−π+, and the charm component after flavour separation (solid line). The open points are the bottom component, and the dashed line represents the result of the fit. Also shown is the predicted contribution from gluon splitting events (hatched area). The reconstruction is only done for xD∗+ > 0.2, as indicated by the solid vertical line.

Table 1: List of selection cuts used in the D∗+ reconstruction. Note that both the scaled energy xD∗+ and the mass M0 are effective quantities, calculated from the reconstructed tracks only. The exact meaning of the different quantities is explained in the text.

Figure 2: Distributions of the different tag-variables used in the flavour separation. Shown are the data distribution after background subtraction (points with error bars), the equivalent Monte Carlo distribution for all candidates (open histogram) and the predicted charm component (hatched histogram). Shown are the (a) decay length significance in the jet with the exclusive D∗+ candidate; (b) decay length significance in the jet opposite the exclusive D∗+ candidate; (c) distribution of the neural network based on jet-shape variables, and (d) distribution of the hemisphere charge.

Full text

arXiv:hep-ex/9708021v1 16 Aug 1997
EUROPEAN LABORATORY FOR PARTICLE PHYSICS
CERN-PPE/97-093
18-July-1997
Measurement of
f(c → D
∗+
X), f(b → D
∗+
X) and
Γ
c¯c
/Γ
had
using D
∗±
Mesons
THE OPAL COLLABORATION
Abstract
The production rates of D
∗±
mesons in charm and bottom events at centre-of-mass energies
of about 91 GeV and the partial width of primary c
c pairs in hadronic Z
0
decays have
been measured at LEP using almost 4.4 million hadronic Z
0
decays collected with the
OPAL detector between 1990 and 1995. Using a combination of several charm quark
tagging methods based on fully and partially reconstructed D
∗±
mesons, and a bottom
tag based on identified muons and electrons, the hadronisation fractions of charm and
bottom quarks into D
∗±
mesons have been found to be
f (b → D
∗+
X) = 0.173 ± 0.016 ± 0.012 and f (c → D
∗+
X) = 0.222 ± 0.014 ± 0.014 .
The fraction of c
c events in hadr on ic Z
0
decays, Γ
c
c
/Γ
had
= Γ(Z
0
→ c
c)/Γ(Z
0
→ hadrons),
is determined to be
Γ
c
c
/Γ
had
= 0.180 ± 0.011 ± 0.012 ± 0.006 .
In all cases the first err or is s tatistical, and the second one systematic. The last error
quoted for Γ
c
c
/Γ
had
is due to external branching ratios.
Submitted to Zeitschrift f¨ur Physik C

THE OPAL COLLABORATION
K. Ackerstaff
8
, G. Alexander
23
, J. Allison
16
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5
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9
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,
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2
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,
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3
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16
,
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1
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20
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23
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8
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14
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,
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27
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34
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2
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20
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8
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8
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10
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2
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6
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13
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17
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4
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15
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22
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2
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1

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T¨orne
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8
1
School of Physics and Space Research, University of Birmingham, Birmingham B15 2TT, UK
2
Dipartimento di Fisica dell’ Universit`a di Bologna and INFN, I-4012 6 Bologna, Italy
3
Physikalisches Institut, Universit¨at Bonn, D-53115 Bonn, Germany
4
Department of Physics, University of California, Riverside CA 92521, USA
5
Cavendish Laboratory, Cambridge CB3 0HE, UK
6
Ottawa-Carleton Institute for Physics, D epartment of Physics, Carleton University, Ottawa,
Ontario K1S 5B6, Canada
7
Centre for Research in Particle Physics, Carleton University, Ot t awa, Ontario K1S 5B6,
Canada
8
CERN, European Organisation for Particle Physics, CH-1211 Geneva 23, Switzerland
9
Enrico Fermi Institute and Department of Physics, University of Chicago, Chicago IL 60 637,
USA
10
Fakult¨at f¨ur Physik, Albert Ludwigs Universit¨at, D-79104 Freiburg, Germany
11
Physikalisches Institut, Universit¨at Heidelberg, D-69120 Heidelberg, Germany
12
Indiana University, Department of Physics, Swain Hall West 117 , Bloomington IN 47405,
USA
13
Queen Mary and Westfield College, University of London, London E1 4NS, UK
14
Technische Hochschule Aachen, III Physikalisches Institut, Sommerfeldstrasse 26-28, D-52056
Aachen, Germany
15
University College London, London WC1E 6BT, UK
16
Department of Physics, Schuster Laborato r y, The University, Manchester M13 9PL, UK
17
Department of Physics, University of Maryland, College Park, MD 20742, USA
18
Laboratoire de Physique Nucl´eaire, Universit´e de Montr´eal, Montr´eal, Quebec H3C 3J7,
Canada
19
University of Oregon, Department of Physics, Eugene OR 97403, USA
20
Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, UK
22
Department of Physics, Technion-Israel Institute of Technology, Haifa 320 00, Israel
23
Department of Physics and Astronomy, Tel Aviv University, Tel Aviv 699 78, Israel
24
International Centre for Elementary Particle Physics and Department of Physics, University
of Tokyo, Tokyo 113, and K obe University, Kobe 657, Japan
25
Brunel University, Uxbridge, Middlesex UB8 3PH, UK
26
Particle Physics Department, Weizmann Institute of Science, Rehovot 7610 0, Israel
27
Universit¨at Hamburg/DESY, II Institut f¨ur Experimental Physik, Notkestrasse 85, D-22607
Hamburg, Germany
28
University of Victoria, Department of Physics, P O Box 3055, Victoria BC V8W 3P6, Canada
29
University of British Columbia, Department o f Physics, Vancouver BC V6T 1Z1, Canada
2

30
University of Alberta, Department of Physics, Edmonton AB T6G 2J1, Canada
31
Duke University, Dept of Physics, Durham, NC 27708-0305, USA
32
Research Institute for Particle and Nuclear Physics, H-1525 Budapest, P O Box 49, Hungary
33
Institute of Nuclear Research, H- 4001 Debrecen, P O Box 51, Hungary
34
Ludwigs-Maximilians-Universit¨at M¨unchen, Sektion Physik, Am Coulombwall 1, D-85748
Garching, Germany
a
and at TRIUMF, Vancouver, Canada V6T 2A3
b
and Royal Society University Research Fellow
c
and Institute of Nuclear Resear ch, Debrecen, Hungary
d
and Department of Experimental Physics, Lajos Kossuth University, Debrecen, Hungary
e
and Department of Physics, New York University, NY 1003, USA
3

1 Introduction
The production of heavy quarks in the decay of the Z
0
boson and their hadronisation have been
the subject of considerable interest over the last few years. In particular the fractions with which
the Z
0
boson decays into quark pairs of flavour q have been studied extensively in Z
0
→ b
b
decays [1–4], in Z
0
→ c
c decays [5–8] a nd in light flavour events [9]. The fraction of bb events
in Z
0
decays has been measured with very good precision. To achieve this goal, very efficient
and pure bottom tag ging methods have been developed, resulting in samples of events that are
nearly free of non-bottom backgrounds. Significantly fewer and less precise measurements exist
of the equivalent quantity for c
c events or for light flavour events. In particular the selectio n of
a pure c
c sample has met with many difficulties, and the efficiencies and purities achieved by
charm tags are inferior to those for bottom tags. The reason for this is that charmed hadrons
are lighter and shorter lived than bottom hadro ns, and are similar enough to most light hadrons
to make a separation very difficult. However, the precise knowledge of the partial widths for
different flavours constitutes an important test of the predictions of the Standard Model, since
in lowest-order Born approxima tion the partia l Z
0
decay width to q
q, Γ
qq
, is related to the
coupling constants of the vect or and axial vector current, g
q
V
and g
q
A
:
Γ
q
q
= N
q
c
G
µ
m
3
Z
6π
√
2
((g
q
V
)
2
+ (g
q
A
)
2
) . (1)
Here G
µ
is the Fermi decay constant and m
Z
the Z
0
mass. The f actor N
q
c
= 3 denotes the
number of colours. Higher order electroweak and QCD corrections to the Z
0
propagator and q
q
vertex that modify Γ
qq
essentially cancel in the ratio Γ
qq
/Γ
had
except in the case of Z
0
→ bb,
where a small dependence o n the Higgs mass and on the precise value of the top quark mass
is introduced. The ratio Γ
q
q
/Γ
had
therefore is the preferred measurable quantity, for which
precise predictions exist in the context of the Standard Model for the quark flavours u,d,s and
c, almost independent of unknown quantities.
In this paper a measurement of the fraction of primary c
c pairs produced in the decays
of Z
0
bosons is presented. At the same time t he hadronisation fractions f (c → D
∗+
X) and
f (b → D
∗+
X) are measured. The analysis is based on the identification of charged D
∗±
mesons,
electrons and muons.
The hadronisation fractions f (c → D
∗+
X) and f (b → D
∗+
X) are measured using a double
tagging technique. To determine f (c → D
∗+
X), charged D
∗±
mesons are sought in both event
hemispher es
1
. The hadronisation fraction f (b → D
∗+
X) is determined in events tagged by a
hard lepton in one hemisphere and a D
∗±
in the other hemisphere. Comparing the number of
such double tagged events with the number of singly reconstructed D
∗±
mesons or leptons, the
hadronisation f ractions can be extracted with minimal model dependence and without explicit
knowledge of the D
∗±
or lepton reconstruction efficiencies.
The ratio o f the charm partial width to the total hadronic width, Γ
c
c
/Γ
had
, is determined
from the hadronisation f raction f (c → D
∗+
X) and from a measurement of the total production
rate of D
∗±
mesons in Z
0
→ c
c events, Γ
c
c
/Γ
had
·f (c → D
∗+
X). This rate is measured in this paper
using a particularly well understood D
∗±
decay mode, the decay
2
D
∗+
→ D
0
π
+
, D
0
→ K
−
π
+
.
Both the measurement of the hadronisation fraction and the measurement of Γ
c
c
/Γ
had
rely
heavily on the reconstruction of D
∗+
mesons using two different techniques. Therefore the
1
The plane separating the two hemispheres in an event is defined perpendicular to the thrust axis of the
event.
2
Charge conjugation is assumed throughout this paper.
4

Frequently asked questions

Q1. What is the general strategy for the measurement of the hadronisation fractions?

The general strategy for the measurement of the hadronisation fractions is that a charm or bottom enriched sample is selected by applying the high purity charm or bottom tag to one hemisphere of the event, and then searching for D∗+ mesons in the opposite hemisphere using the more efficient, less pure tag. 

Q2. What is the resolution of secondary vertices?

The resolution of secondary vertices depends on the fraction of tracks which use measurements from the silicon micro-vertex detector. 

Q3. How is the influence of the detector resolution on the tagging variables studied in Monte Carlo?

The influence of the detector resolution on the tagging variables is studied in Monte Carlo by varying the resolutions in the tracking system by ±10% relative to values that optimally describe the data. 

Q4. How many D mesons are observed in the decay of charm events?

From the number of D∗± mesons observed in the decay D∗+ → D0π+, D0 → K−π+ the multiplicity of D∗+ mesons in hadronic Z decays is measured to ben̄Z0→D∗+X = 0.1854 ± 0.0041 ± 0.0059 ± 0.0069 . 

Q5. What is the contribution of the hemisphere charge to the exclusively tagged sample?

The total contribution of these events to the exclusively tagged sample is found to be (0.2±0.1)%, where the error quoted is only due to Monte Carlo statistics. 

Q6. How much error is the rate of partially reconstructed mesons?

In total the relative error of the rate of partially reconstructed D∗+ mesons contributing to the signal is estimated to be 22% of the rate of partially reconstructed mesons, which contributes an error of 1.5% to the total rate measurement.• 

Q7. How is the cosine of the polar angle of the thrust axis with respect?

To ensure that the event is mostly contained in the sensitive detector volume, the absolute value of the cosine of the polar angle of the thrust axis with respect to the beam direction, | cos θthrust|, has to be smaller than 0.9. 

Q8. How many tagged electrons and muons do not originate in bottom decays?

The number of tagged electron and muon candidates is determined to be 43 579, of which 4445 ± 64 do not originate in bottom decays. 

Q9. What is the shape of the p2t signal in bottom events?

The shape of the p2t signal in bottom events is determined in data from the lepton-slow pion double tagged sample, which is about 90% pure in bottom decays. 

Q10. What is the product branching ratio in bottom events?

In bottom events the product branching ratio is determined to beΓbb/Γhad · f (b → D∗+X) B(D∗+ → D0π+) B(D0 → K−π+) = (1.334 ± 0.049) × 10−3 . 

Q11. What is the efficiency to select an event of flavour q using the pure tag?

Neglecting for simplicity any background from other flavours, the number of events of flavour q is given byNtag1 ∼ Γqq Γhad f (q → D∗+X) ǫtag1 , (2)where ǫtag1 is the efficiency to select an event of flavour q using the pure tag. 

Q12. What is the function that describes the partial decay of the satellite?

The other decays contributing to the partially reconstructed sample are described by an additional exponential function, added to the parametrisation of the satellite decay. 

Q13. How is the multiplicity of charm decays in the Monte Carlo?

The multiplicity for heavy flavour decays in the Monte Carlo has been varied by reweighting simulated events,corresponding to the current experimental bounds of ±0.2 tracks for charm decays, and ±0.35 tracks for bottom decays [16]. 

Q14. How is the contribution from fakes measured in the sideband sample?

The absolute contribution from the fakes is obtained by rescaling the fitted fake contribution by the ratio α of the number of background candidates in the sideband sample to that in the signal sample. 

Q15. What is the average scaled energy of D+ mesons in charm decays?

From the shape of the fragmentation function the average mean scaled energy xD∗+ of D∗+ mesons in charm decays is determined to be 〈xD∗+〉c = 0.515 ± 0.002 ± 0.009 . 

Q16. How many times has the lifetime of the charmed hadrons been varied independently?

The lifetimes of the weakly-decaying charmed hadrons D0 and D+ has been varied independently by ±0.004 ps for the D0, and ±0.015 ps for the D+ [22], corresponding to a total error of 0.4%.• 

Q17. How much error is there due to mixing in the neutral B sector?

The uncertainty due to mixing in the neutral B sector has been studied by varying the effective mixing parameter χeff within its error, or 0.5% of the final result.– 

Q18. what is the preferred measurable quantity for the quark flavours u,d,s?

The ratio Γqq/Γhad therefore is the preferred measurable quantity, for which precise predictions exist in the context of the Standard Model for the quark flavours u,d,s and c, almost independent of unknown quantities.