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Year: 2013
Measurement of the fragmentation fraction ratio fs/fd and its dependence on
B meson kinematics
LHCb Collaboration; et al; Bernet, R; Müller, K; Steinkamp, O; Straumann, U; Vollhardt, A
Abstract: The relative production rate of B0s and B 0 mesons is determined with the hadronic decays
B0s→D−s�+ and B 0 → D − K +. The measurement uses data corresponding to 1.0 fb−1 of pp collisions
at a centre-of-mass energy of s√=7 TeV recorded in the forward region with the LHCb experiment. The
ratio of production rates, f s /f d , is measured to be 0.238 ± 0.004 ± 0.015 ± 0.021, where the first
uncertainty is statistical, the second systematic, and the third theoretical. This is combined with a
previous LHCb measurement to obtain f s /f d = 0.256 ± 0.020. The dependence of f s /f d on the
transverse momentum and pseudorapidity of the B meson is determined using the decays B0s→D−s�+
and B 0 → D −�+. There is evidence for a decrease with increasing transverse momentum, whereas the
ratio remains constant as a function of pseudorapidity. In addition, the ratio of branching fractions of
the decays B 0 → D − K + and B 0 → D −�+ is measured to be 0.0822 ± 0.0011 (stat) ± 0.0025 (syst).
DOI: https://doi.org/10.1007/JHEP04(2013)001
Posted at the Zurich Open Repository and Archive, University of Zurich
ZORA URL: https://doi.org/10.5167/uzh-92008
Published Version
Originally published at:
LHCb Collaboration; et al; Bernet, R; Müller, K; Steinkamp, O; Straumann, U; Vollhardt, A (2013).
Measurement of the fragmentation fraction ratio fs/fd and its dependence on B meson kinematics. Journal
of High Energy Physics, 2013:1.
DOI: https://doi.org/10.1007/JHEP04(2013)001
Published for SISSA by
Springer
Received: January 23, 2013
Accepted: March 18, 2013
Published: April 2, 2013
The LHCb collaboration
E-mail: [email protected]
Abstract: The relative production rate of Bs0 and B 0 mesons is determined with the
hadronic decays Bs0 → Ds− π + and B 0 → D− K + . The measurement uses data corre√
sponding to 1.0 fb−1 of pp collisions at a centre-of-mass energy of s = 7 TeV recorded
in the forward region with the LHCb experiment. The ratio of production rates, fs /fd ,
is measured to be 0.238 ± 0.004 ± 0.015 ± 0.021, where the first uncertainty is statistical,
the second systematic, and the third theoretical. This is combined with a previous LHCb
measurement to obtain fs /fd = 0.256 ± 0.020. The dependence of fs /fd on the transverse
momentum and pseudorapidity of the B meson is determined using the decays Bs0 → Ds− π +
and B 0 → D− π + . There is evidence for a decrease with increasing transverse momentum,
whereas the ratio remains constant as a function of pseudorapidity. In addition, the ratio
of branching fractions of the decays B 0 → D− K + and B 0 → D− π + is measured to be
0.0822 ± 0.0011 (stat) ± 0.0025 (syst).
Keywords: Hadron-Hadron Scattering, Branching fraction, B physics, Flavor physics
ArXiv ePrint: 1301.5286
Open Access, Copyright CERN,
for the benefit of the LHCb collaboration
doi:10.1007/JHEP04(2013)001
JHEP04(2013)001
Measurement of the fragmentation fraction ratio
fs/fd and its dependence on B meson kinematics
Contents
1
2 Detector and software
2
3 Event selection
3
4 Event yields
4
5 Systematic uncertainties
7
6 Results
8
7 Conclusions
10
The LHCb collaboration
13
1
Introduction
The ratio of fragmentation fractions fs /fd quantifies the relative production rate of Bs0
mesons with respect to B 0 mesons. Knowledge of this quantity is essential when determining any Bs0 branching fraction at the LHC. The measurement of the branching fraction
of the rare decay Bs0 → µ+ µ− [1] is the prime example where a precise measurement of
fs /fd is crucial for reaching the highest sensitivity in the search for physics beyond the
Standard Model. The branching fractions of a large number of B 0 and B + decays have
been measured to high precision at the B factories [2], but no Bs0 branching fraction is yet
known with sufficiently high precision to be used as a normalisation channel.
The relative production rates of b hadrons are determined by the fragmentation fractions fu , fd , fs , fc and fΛ , which describe the probability that a b quark will hadronize into
a Bq meson (where q = u, d, s, c), or a b baryon, respectively1 . The ratio of fragmentation
fractions fs /fd has been previously measured at LHCb with hadronic [3] and semileptonic
decays [4], and the resulting values were combined [4].
In this paper, the ratio of fragmentation fractions fs /fd is determined using Bs0 →
Ds− π + and B 0 → D− K + decays collected in pp collisions at a centre-of-mass energy of
√
s = 7 TeV, with data corresponding to an integrated luminosity of 1.0 fb−1 recorded
with the LHCb detector. Since the framework of factorization is well applicable to these
decays [5], their ratio of branching fractions is theoretically well understood [6] and their
1
Charge conjugation is implied throughout this paper.
–1–
JHEP04(2013)001
1 Introduction
relative decay rates can be used to determine the ratio of fragmentation fractions for Bs0
and B 0 mesons through
fs
B(B 0 → D− K + ) DK NDs π
=
fd
B(Bs0 → Ds− π + ) Ds π NDK
Vus 2 fK 2 τB 0 1 B(D− → K + π − π − ) DK NDs π
= ΦPS ,
Vud fπ
τBs0 Na NF B(Ds− → K + K − π − ) Ds π NDK
(1.1)
2
Detector and software
The LHCb detector [12] is a single-arm forward spectrometer covering the pseudorapidity
range 2 < η < 5, designed for the study of particles containing b or c quarks. The detector
includes a high precision tracking system consisting of a silicon-strip vertex detector surrounding the pp interaction region, a large-area silicon-strip detector located upstream of
a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-strip
detectors and straw drift tubes placed downstream. Data are taken with both magnet
polarities. The combined tracking system has momentum resolution ∆p/p that varies from
–2–
JHEP04(2013)001
where N corresponds to a signal yield, corresponds to a total efficiency, τBs0 /τB 0 =
0.984 ± 0.011 [7] corresponds to the ratio of lifetimes and B(D− → K + π − π − ) = (9.14 ±
−
0.20)% [8] and B(Ds− → K + K − π − ) = (5.50 ± 0.27)% [9] correspond to the D(s)
meson
branching fractions. The factor Na = 1.00 ± 0.02 accounts for the ratio of non-factorizable
0 → D − form factors [11], and
corrections [10], NF = 1.092 ± 0.093 for the ratio of B(s)
(s)
ΦPS = 0.971 for the difference in phase space due to the mass differences of the initial and
final state particles. The numerical values used for the CKM matrix elements are |Vus | =
0.2252, |Vud | = 0.97425, and for the decay constants are fπ = 130.41 MeV, fK = 156.1 MeV,
with negligible uncertainties, below 1% [2]. The measurement is not statistically limited by
the size of the B 0 → D− K + sample , and therefore the theoretically less clean B 0 → D− π +
decays, where exchange diagrams contribute to the total amplitude, do not contribute to
the knowledge of fs /fd .
The ratio of fragmentation fractions can depend on the centre-of-mass energy, as well
0 meson, as was studied previously at LHCb with partially
as on the kinematics of the B(s)
reconstructed B decays [4]. The dependence of the ratio of fragmentation fractions on
0 meson is determined using
the transverse momentum pT and pseudorapidity η of the B(s)
fully reconstructed B 0 → D− π + and Bs0 → Ds− π + decays. Since it is only the dependence
that is of interest here, the more abundant B 0 → D− π + decay is used rather than the
B 0 → D− K + decay. The B 0 → D− K + and B 0 → D− π + decays are also used to determine
their ratio of branching fractions, which can be used to quantify non-factorizable effects in
such heavy-to-light decays [10].
The paper is organised as follows: the detector is described in section 2, followed
by the event selection and the relative selection efficiencies in section 3. The fit to the
mass distributions and the determination of the signal yields are discussed in section 4.
The systematic uncertainties are presented in section 5, and the final results are given in
section 6.
3
Event selection
The three decay modes, B 0 → D− π + , B 0 → D− K + and Bs0 → Ds− π + , are topologically
very similar and can therefore be selected using the same event selection criteria, thus
0 candidates are reconstructed
minimizing efficiency differences between the modes. The B(s)
−
from a D(s)
candidate and an additional pion or kaon (the “bachelor” particle), with the
−
D(s) meson decaying to K + π − π − (K + K − π − ).
0 and D − masses,
After the trigger selection, a loose preselection is made using the B(s)
(s)
lifetimes and vertex qualities. A boosted decision tree (BDT) [21] is used to further separate
signal from background. The BDT is trained on half the Bs0 → Ds− π + data sample. The
0 impact parameter χ2 , the pointing angle of the
most discriminating variables are the B(s)
0
B(s) candidate to the primary vertex and the pT of the tracks. A cut value for the BDT
output variable was chosen to optimally reduce the number of combinatorial background
events, retaining approximately 84% of the signal events.
−
The D(s)
candidates are identified by requiring the invariant mass under the K + π − π −
(K + K − π − ) hypothesis to fall within the selection window 1844–1890 (1944–1990) MeV/c2 .
The relative efficiency of the selection procedure is evaluated for all decay modes using
simulated events, generated with the appropriate Dalitz plot structures [22, 23]. Since the
analysis is only sensitive to relative efficiencies, the impact of any discrepancy between
data and simulation is small.
2
Impact parameter (IP) is defined as the transverse distance of closest approach between the track and
a primary interaction.
–3–
JHEP04(2013)001
0.4% at 5 GeV/c to 0.6% at 100 GeV/c, and impact parameter2 resolution of 20 µm for tracks
with high transverse momentum. Charged hadrons are identified using two ring-imaging
Cherenkov detectors.
The trigger [13] consists of a hardware stage, based on information from the calorimeter
and muon systems, followed by a software stage which applies a full event reconstruction.
The events used in this analysis are selected at the hardware stage by requiring a cluster in
the calorimeters with transverse energy larger than 3.6 GeV. The software stage requires
a two-, three- or four-track secondary vertex with a high sum of the pT of the tracks and
a significant displacement from the primary pp interaction vertices (PVs). At least one
track should have pT greater than 1.7 GeV/c, track fit χ2 over the number of degrees of
freedom less than two, and IP χ2 with respect to the associated primary interaction greater
than sixteen. The IP χ2 is defined as the difference between the χ2 from the vertex fit of
the associated PV reconstructed with and without the considered track. A multivariate
algorithm is used for the identification of the secondary vertices consistent with the decay
of a b hadron.
In the simulation, pp collisions are generated using Pythia 6.4 [14] with a specific
LHCb configuration [15]. Decays of hadronic particles are described by EvtGen [16],
whilst final state radiation is generated using Photos [17]. The interaction of the generated
particles with the detector and its response are implemented using the Geant4 toolkit [18,
19] as described in ref. [20].
4
Event yields
The relative yields of the three decay modes are determined from unbinned extended maxi0 candidates as shown
mum likelihood fits to the mass distributions of the reconstructed B(s)
in figure 1. In order to achieve the highest sensitivity, the sample is separated according
to the two magnet polarities, allowing for possible differences in PID performance and in
running conditions. A simultaneous fit to the two magnet polarities is performed for each
decay mode, with the peak position and width of each signal shared between the two.
The signal mass shape is described by a Gaussian distribution with power-law tails on
either side to model the radiative tail and non-Gaussian detector effects. It consists of a
Crystal Ball function [24]

(m−µ)2
m−µ


for
> −α
 e− 2σ2 ,
σ
−n
fleft (m, α, n, µ, σ) = N · n n
n
m−µ
m−µ
2


· e−|α| /2 ·
−|α|−
, for
≤ −α

|α|
|α|
σ
σ
(4.1)
and a second, similar but mirrored, function to describe the right tail, resulting in the
signal mass shape f2CB (m) = fleft (m) + fright (m). The parameters of the tails are obtained
from simulated events. The mean µ and the width σ of the Gaussian distribution are equal
in both Crystal Ball functions, and are allowed to vary in the fit. The parameter N is a
normalisation factor.
Three classes of background are considered in the fit: fully reconstructed decays where
at least one track is misidentified, partially reconstructed decays with or without misidentified tracks and combinatorial background. The shapes of the invariant mass distributions
for the partially reconstructed decays are taken from large samples of simulated events. The
main sources are B 0 → D− ρ+ and B 0 → D∗− π + (K + ) for the B 0 → D− π + (K + ) sample,
and Bs0 → Ds− ρ+ and Bs0 → Ds∗− π + for the Bs0 → Ds− π + sample.
–4–
JHEP04(2013)001
The final Bs0 → Ds− π + , B 0 → D− π + and B 0 → D− K + event samples are obtained
after particle identification (PID) criteria, based on the difference in log-likelihood between
the kaon and pion hypotheses (DLL). The PID performance as a function of pT and η of
the track is estimated from data using a calibration sample of approximately 27 million
D∗− → D0 (K + π − )π − decays, which are selected using kinematic criteria only. A cut
on the bachelor particle is placed at DLL(K − π)< 0 to select the Bs0 → Ds− π + and
B 0 → D− π + event samples and at DLL(K − π)> 5 to select the B 0 → D− K + sample.
These requirements have an average efficiency of 85.5% and 73.0% respectively with a
misidentification probability of 8.81% and 2.77%. The Ds− → K + K − π − decay is further
distinguished from D− → K + π − π − decays by imposing DLL(K − π)> 5 on the kaon
candidate with the same charge as the D meson, whilst the DLL criteria for the π − and
−
K + are identical between D− and Ds− and are used to discriminate D(s)
decays from
−
background. The total (PID and invariant mass) efficiency to select the D (Ds− ) particle
is 84.6% (78.5%) with a misidentification probability of 4.57% (0.77%).
Candidates / ( 5 MeV/ c2)
12000
8000
−
B 0→ D K +
0
−
Λb → Λc π +
*
−
B 0 → D π+
−
B 0→ D ρ+
Combinatorial
6000
4000
2000
1000
5200
5400
5600
5800
m(D−π+) [MeV/ c2]
LHCb
(b)
−
B 0→ D K +
800
*−
B 0→ D K +
600
B 0→ D K *+
400
B 0→ D ρ+
−
−
−
B 0 → D π+
200
0
2000
Combinatorial
5200
5400
5600
5800
−
m(D K +) [MeV/ c2]
LHCb
(c)
−
B 0s → Ds π+
0
−
B → Ds π+
1500
−
B 0→ D π +
0
Λb→
B 0s →
B 0s →
1000
500
−
Λc π+
*−
Ds π+
−
Ds ρ+
Combinatorial
0
5200
5400
5600
5800
m(D−s π+) [MeV/ c2]
Figure 1. Invariant mass distributions of (a) B 0 → D− π + (b) B 0 → D− K + and (c) Bs0 → Ds− π +
candidates. The solid line is the result of the fit and the dotted line indicates the signal. The
stacked background shapes follow the same top-to-bottom order in the legend and the plot. The Bs0
0
and Λb backgrounds in the B 0 → D− π + mass distribution are invisibly small. The resulting signal
yields are listed in table 1. For illustration purposes the figures include events from both magnet
polarities, although they are fitted separately as described in the text.
–5–
JHEP04(2013)001
Candidates / ( 5 MeV/ c2)
−
B 0 → D π+
−
B 0s → Ds π+
10000
0
5000
Candidates / ( 5 MeV/ c2)
LHCb
(a)
Signal
B0 →
Yield
D− π+
106 197 ± 344
B 0 → D− K +
Bs0 →
Ds− π +
7 664 ± 99
17 419 ± 155
Table 1. Yields obtained from the fits to the invariant mass distributions.
–6–
JHEP04(2013)001
The invariant mass distributions of the misidentified decays are affected by the PID
criteria. The shapes are obtained from simulated events, with the appropriate mass hypothesis applied. The distribution is then reweighted in a data-driven way, according to the
particle identification cut efficiency obtained from the calibration sample, which is strongly
dependent on the momentum of the particle.
Despite the small π → K misidentification probability of 2.8%, the largest misidentified
background in the B 0 → D− K + sample originates from Cabibbo-favoured B 0 → D− π +
decays where the bachelor pion is misidentified as a kaon. The shape of this particular
misidentified decay is determined from data using a high purity sample of B 0 → D− π +
decays (see figure 1(a)), obtained by selecting events in a narrow mass window 5200–
5340 MeV/c2 . The yield of this prominent peaking background is allowed to vary in the
fit and is found to be consistent with the expected yield based on the B 0 → D− π + signal
yield and the misidentification probability. The contamination of B 0 → D− π + events
in the Bs0 → Ds− π + sample can be caused by the misidentification of either pion from
the D− decay. The misidentification probability is 2.0% (3.2%) for the higher (lower)
pT pion. After selecting the Ds− candidate within the mass window around the nominal
Ds− mass [2], the number of misidentified pions is reduced to 0.75% (0.02%). The yield
of this background is constrained in the fit, based on the B 0 → D− π + signal yield, the
misidentification probability and their associated uncertainties.
0
+
The yield of Λb → Λ−
c π decays is allowed to vary in the fit. The cross-feeds from
B 0 → D− K + and Bs0 → Ds− π + events in the B 0 → D− π + signal is small, and are constrained to their respective predicted yields. In addition, a contribution from the rare
B 0 → Ds− π + decay is expected with a yield of 3.3% compared to the Bs0 → Ds− π + signal,
and is accounted for accordingly.
The combinatorial background consists of events with random pions and kaons, forming
a fake D− or Ds− candidate, as well as real D− or Ds− mesons, that combine with a random
pion or kaon. The combinatorial background is modelled with an exponential shape.
The results of the fits are presented in figure 1, and the corresponding signal yields
are listed in table 1. The total yields of the decays B 0 → D− π + and B 0 → D− K +
are used to determine the ratio of their branching fractions, while the event yields of
the decays Bs0 → Ds− π + and B 0 → D− K + are used to measure the average ratio of
fragmentation fractions.
The dependence of the relative b-hadron production fractions as a function of the
0 meson is studied in the ranges 2.0 <
transverse momentum and pseudorapidity of the B(s)
η < 5.0 and 1.5 < pT < 40 GeV/c, using B 0 → D− π + and Bs0 → Ds− π + decays. The
Source
(%)
0.7
2.0
1.2
1.0
1.0
0.7
0.5
0.8
0.4
3.1
Bs0→Ds− π +
B 0→D− K +
0.7
2.0
1.1
1.0
1.5
1.0
0.6
1.0
—
3.4
(%)
Bs0→Ds− π +
B 0→D− π +
(%)
2.0 − 2.9
0.8
1.2
1.5
1.1
0.8
[correl.]
[correl.]
[correl.]
3.2 − 3.8
Table 2. Systematic uncertainties for the measurement of the corrected ratio of event yields used
for the measurements of fs /fd and the relative branching fraction of B 0 → D− K + . The systematic
uncertainty in pT and η bins is shown as a range in the last column, and the total systematic
uncertainty is the quadratic sum of the uncorrelated uncertainties. The systematic uncertainties on
the ratio of B 0 → D− π + and Bs0 → Ds− π + yields that are correlated among the bins do not affect
the dependence on pT or η, and are not accounted for in the total systematic uncertainty.
event sample is subdivided in 20 bins in pT and 10 bins in η, with the bin sizes chosen to
obtain approximately equal number of events per bin. The fitting model for each bin is
the same as that for the integrated samples, apart from the treatment of the exponent of
the combinatorial background distribution, which is fixed to the value obtained from the
fits to the integrated sample.
5
Systematic uncertainties
The systematic uncertainties on the measurement of the relative event yields of the B 0 →
D− π + , B 0 → D− K + and Bs0 → Ds− π + decay modes are related to trigger and offline
selection efficiency corrections, particle identification calibration and the fit model.
The response to charged pions and kaons of the hadronic calorimeter used at the
hardware trigger level has been investigated. As the hardware trigger mostly triggers on
the high-pT bachelor, a systematic uncertainty of 2% is assigned to the ratio of trigger
efficiencies for the decays B 0 → D− K + and B 0 → D− π + , estimated from dedicated studies
with D∗− → D0 (K + π − )π − decays. This uncertainty is assumed to be uncorrelated between
the individual bins in the binned analysis.
The relative selection efficiencies from simulation are studied by varying the BDT
criterion, changing the signal yields by about ±25%. The variation of the relative efficiency
is 1.0% which is assigned as systematic uncertainty.
The uncertainty on the PID efficiencies is estimated by comparing, in simulated events,
the results obtained using the D∗− calibration sample to the true simulated PID perfor-
–7–
JHEP04(2013)001
Detector acceptance
and reconstruction
Hardware trigger efficiency
Offline selection
BDT cut
PID selection
Comb. background
Signal shape (tails)
Signal shape (core)
Charmless background
Total
B 0→D− π +
B 0→D− K +
6
Results
The relative signal yields of the decays B 0 → D− π + , B 0 → D− K + and Bs0 → Ds− π +
are used to determine the branching fraction of the decay B 0 → D− K + , and the ratio of
fragmentation fractions fs /fd .
The efficiency corrected ratio of B 0 → D− K + and B 0 → D− π + signal yields results in
the ratio of branching fractions
B B 0 → D− K +
= 0.0822 ± 0.0011 (stat) ± 0.0025 (syst).
B (B 0 → D− π + )
–8–
JHEP04(2013)001
mance on the signal decays. The corresponding uncertainty ranges from 1.0% to 1.5% for
the different measurements.
The exponent of the combinatorial background distribution is allowed to vary in the fits
to the B 0 → D− π + and Bs0 → Ds− π + mass distributions. By studying D− π − and D− K −
combinations, it is suggested that the value of the exponent is smaller for the B 0 → D− K +
decays than for the B 0 → D− π + decays, and therefore in the fit to the B 0 → D− K +
candidates the exponent is fixed to half the value found in the fit to the B 0 → D− π + sample.
The uncertainty on the signal yields due to the shape of the combinatorial background
is estimated by reducing the exponent to half its value in the fits to the B 0 → D− π +
and Bs0 → Ds− π + mass distributions, and by taking a flat background for the fit to the
B 0 → D− K + mass distribution. An uncertainty of 1.0% (0.7%) is assigned to the relative
B 0 → D− K + and Bs0 → Ds− π + (B 0 → D− π + ) yields.
The tails of the signal distributions are fixed from simulation due to the presence of
large amounts of partially reconstructed decays in the lower sidebands. The uncertainty on
the signal yield is estimated by varying the parameters that describe the tails by 10%. The
uncertainty from the shape of the central peak is taken from a fit allowing for two different
widths for the Crystal Ball functions in eq. 4.1, leading to a 1.0% (0.8%) uncertainty on
the relative B 0 → D− K + and Bs0 → Ds− π + (B 0 → D− π + ) yields.
The contribution of charmless B decays without an intermediate D meson is ignored
in the fit. To evaluate the systematic uncertainty due to these decays, the B mass spectra
for candidates in the sidebands of the D mass distribution are examined. A contribution
of 0.4% relative to the signal yield is found in the B 0 → D− π + decay mode, and no
contribution is seen in the other modes. For the B 0 → D− π + decay mode no correction is
applied and the full size is taken as an uncertainty. No systematic uncertainty is assigned
for the other decay modes.
The various sources of the systematic uncertainty that contribute to the uncertainties
on the ratios of signal yields are listed in table 2. No uncertainty is associated to the
0
+
Λb → Λ−
c π background, as the yield is allowed to vary in the fit. Other cross checks, like
0
+
varying the B 0 → Ds− π + yield in the Bs0 → Ds− π + fit or including Λb → Λ−
c K in the
0
−
+
B → D K fit, show a negligible effect on the signal yields.
All systematic variations are also performed in bins, and the corresponding relative
changes in the ratio of yields have been quantified. Variations showing correlated behaviour
do not affect the slope and are therefore not considered further.
0.35
d
(a)
fs f
LHCb
/
/
fs f
d
0.35
0.3
0.3
0.25
0.25
0.2
0
10000
20000
30000
0.2
40000
p (B) [MeV/ c]
(b)
2
LHCb
3
4
5
η(B)
Figure 2. Ratio of fragmentation fractions fs /fd as functions of (a) pT and (b) η. The errors on the
data points are the statistical and uncorrelated systematic uncertainties added in quadrature. The
solid line is the result of a linear fit, and the dashed line corresponds to the fit for the no-dependence
hypothesis. The average value of pT or η is determined for each bin and used as the center of the
bin. The horizontal error bars indicate the bin size. Note that the scale is zero suppressed.
This is combined with the world average branching fraction B B 0 → D− π + = (26.8 ±
1.3) × 10−4 [2], to give
B B 0 → D− K + = (2.20 ± 0.03 ± 0.07 ± 0.11) × 10−4 ,
where the first uncertainty is statistical, the second is systematic and the last is due to the
uncertainty on the B 0 → D− π + branching fraction.
The ratio of fragmentation fractions is determined from the efficiency corrected event
yields. The ratio of efficiencies is 0.913 ± 0.027. This results in
fs
1
= (0.261 ± 0.004 ± 0.017) ×
fd
Na NF
= 0.238 ± 0.004 ± 0.015 ± 0.021 ,
where the first uncertainty is statistical, the second is systematic containing the sources
listed in table 2 as well as errors from external measurements, and the third is theoretical,
due to the knowledge of Na and NF . The last source is dominated by the uncertainty on
the form factor ratio.
This measurement supersedes and is in agreement with the previous determination with
hadronic decays [3]. It also agrees with the previous measurement based on semileptonic
decays [4]. The two independent results are combined taking into account the various
−
sources of correlated systematic uncertainties, notably the D(s)
branching fractions and
0
B(s) lifetimes, to give
fs
= 0.256 ± 0.020,
fd
which supersedes the previous measurement from LHCb.
–9–
(6.1)
JHEP04(2013)001
T
The value of fs /fd in bins of pT or η is determined using the Bs0 → Ds− π + and B 0 →
D− π + decay modes and is presented in figure 2. A linear χ2 fit gives
fs /fd (pT ) = (0.256 ± 0.020) + (−2.0 ± 0.6) × 10−3 / GeV/c × (pT − hpT i)
fs /fd (η) = (0.256 ± 0.020) + (0.005 ± 0.006) × (η − hηi),
7
Conclusions
The relative production rate of Bs0 and B 0 mesons is determined using the hadronic decays
Bs0 → Ds− π + and B 0 → D− K + resulting in fs /fd = 0.238 ± 0.004(stat) ± 0.015(syst) ±
0.021(theo). This value is consistent with a previous LHCb measurement based on semileptonic decays, with which it is averaged to obtain fs /fd = 0.256 ± 0.020. The ratio of
fragmentation fractions fs /fd is determined as a function of the transverse momentum
0 meson, and a variation consistent with a linear depenand pseudorapidity of the B(s)
0 meson is observed, with a significance
dence on the transverse momentum of the the B(s)
of three standard deviations. In addition, the ratio of branching fractions of the decays
B 0 → D− K + and B 0 → D− π + is measured to be 0.0822 ± 0.0011 (stat) ± 0.0025 (syst).
Acknowledgments
We express our gratitude to our colleagues in the CERN accelerator departments for the
excellent performance of the LHC. We thank the technical and administrative staff at the
LHCb institutes. We acknowledge support from CERN and from the national agencies:
CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC (China); CNRS/IN2P3 and Region
Auvergne (France); BMBF, DFG, HGF and MPG (Germany); SFI (Ireland); INFN (Italy);
FOM and NWO (The Netherlands); SCSR (Poland); ANCS/IFA (Romania); MinES,
Rosatom, RFBR and NRC “Kurchatov Institute” (Russia); MinECo, XuntaGal and GENCAT (Spain); SNSF and SER (Switzerland); NAS Ukraine (Ukraine); STFC (United Kingdom); NSF (USA). We also acknowledge the support received from the ERC under FP7.
The Tier1 computing centres are supported by IN2P3 (France), KIT and BMBF (Germany), INFN (Italy), NWO and SURF (The Netherlands), PIC (Spain), GridPP (United
Kingdom). We are thankful for the computing resources put at our disposal by Yandex
LLC (Russia), as well as to the communities behind the multiple open source software
packages that we depend on.
Open Access. This article is distributed under the terms of the Creative Commons
Attribution License which permits any use, distribution and reproduction in any medium,
provided the original author(s) and source are credited.
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JHEP04(2013)001
with hpT i = 10.4 GeV/c and hηi = 3.28. The data points are normalised with a scale factor
to match the average value of 0.256. The uncertainty associated to this parameter is taken
from eq. 6.1, whilst the error from the fit is 0.003 for both pT and η.
The p-value for this linear fit is found to be 0.16 (0.87) for pT (η). The observed slope
0 meson deviates from zero with
for the dependence on the transverse momentum of the B(s)
a significance of three standard deviations. No indication of a dependence on η(B) is found.
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Centro Brasileiro de Pesquisas Fı́sicas (CBPF), Rio de Janeiro, Brazil
Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
Center for High Energy Physics, Tsinghua University, Beijing, China
LAPP, Université de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France
Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France
CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
LPNHE, Université Pierre et Marie Curie, Université Paris Diderot, CNRS/IN2P3, Paris, France
Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
School of Physics, University College Dublin, Dublin, Ireland
Sezione INFN di Bari, Bari, Italy
Sezione INFN di Bologna, Bologna, Italy
Sezione INFN di Cagliari, Cagliari, Italy
Sezione INFN di Ferrara, Ferrara, Italy
Sezione INFN di Firenze, Firenze, Italy
Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
Sezione INFN di Genova, Genova, Italy
Sezione INFN di Milano Bicocca, Milano, Italy
Sezione INFN di Roma Tor Vergata, Roma, Italy
Sezione INFN di Roma La Sapienza, Roma, Italy
Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Kraków, Poland
AGH University of Science and Technology, Kraków, Poland
National Center for Nuclear Research (NCBJ), Warsaw, Poland
Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele,
Romania
Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia
Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN), Moscow, Russia
Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State University, Novosibirsk,
Russia
Institute for High Energy Physics (IHEP), Protvino, Russia
Universitat de Barcelona, Barcelona, Spain
Universidad de Santiago de Compostela, Santiago de Compostela, Spain
European Organization for Nuclear Research (CERN), Geneva, Switzerland
Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
Physik-Institut, Universität Zürich, Zürich, Switzerland
Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam, The
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Università di Bari, Bari, Italy
Università di Bologna, Bologna, Italy
Università di Cagliari, Cagliari, Italy
Università di Ferrara, Ferrara, Italy
Università di Firenze, Firenze, Italy
Università di Urbino, Urbino, Italy
Università di Modena e Reggio Emilia, Modena, Italy
Università di Genova, Genova, Italy
Università di Milano Bicocca, Milano, Italy
Università di Roma Tor Vergata, Roma, Italy
Università di Roma La Sapienza, Roma, Italy
Università della Basilicata, Potenza, Italy
LIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
Hanoi University of Science, Hanoi, Viet Nam
Massachusetts Institute of Technology, Cambridge, MA, United States
– 16 –
JHEP04(2013)001
51
NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine
University of Birmingham, Birmingham, United Kingdom
H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom
Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
Department of Physics, University of Warwick, Coventry, United Kingdom
STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom
School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom
Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
Imperial College London, London, United Kingdom
School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom
Department of Physics, University of Oxford, Oxford, United Kingdom
Syracuse University, Syracuse, NY, United States
Pontifı́cia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated
to2
Institut für Physik, Universität Rostock, Rostock, Germany, associated to11
Institute of Information Technology, COMSATS, Lahore, Pakistan, associated to53
University of Cincinnati, Cincinnati, OH, United States, associated to53