First observation of the decay $B^0_s \rightarrow K^{*0} \bar{K]^{*0}$

Abstract

The first observation of the decay $\kstarkstar$ is reported using 35\invpb
of data collected by LHCb in proton-proton collisions at a centre-of-mass
energy of 7 TeV. A total of $49.8 \pm 7.5$ $B^0_s \rightarrow
(K^+\pi^-)(K^-\pi^+)$ events are {observed within $\pm 50 \mevcc$ of the \Bs
mass and $746 \mevcc < m_{K\pi}< 1046 \mevcc$, mostly coming from a resonant
$\kstarkstar$ signal.} The branching fraction and the \CP-averaged \Kstarz
longitudinal polarization fraction are measured to be {$\BR(\kstarkstar) =
(2.81 \pm 0.46 ({\rm stat.}) \pm 0.45 ({\rm syst.}) \pm 0.34\,
(f_s/f_d))\times10^{-5}$} and $f_L = 0.31 \pm 0.12 ({\rm stat.}) \pm 0.04 ({\rm
syst.})$.

Full text

Page 1

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)
LHCb-PAPER-2011-012
CERN-PH-EP-2011-183
November 22, 2011
First observation of the decay B0
s→ K∗0K∗0
The LHCb Collaboration1
Abstract
The first observation of the decay B0
in proton-proton collisions at a centre-of-mass energy of 7 TeV. A total of 49.8 ± 7.5 signal events are
observed, with a significance of 10.9 σ. The branching fraction and the CP-averaged K∗0longitudi-
nal polarization fraction are measured to be B?B0
s→ K∗0K∗0is reported using 35pb−1of data collected by LHCb
s→ K∗0K∗0?
= (2.81 ± 0.46(stat.) ± 0.45(syst.) ±
0.34(fs/fd)) × 10−5and fL= 0.31 ± 0.12(stat.) ± 0.04(syst.).
PACS: 14.40.Nd, 13.25.Hw, 14.40.Be
(Submitted to Physics Letters B.)
1Authors are listed on the following pages.
arXiv:1111.4183v2 [hep-ex] 21 Nov 2011

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1Centro Brasileiro de Pesquisas F´ ısicas (CBPF), Rio de Janeiro, Brazil
2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
3Center for High Energy Physics, Tsinghua University, Beijing, China
4LAPP, Universit´ e de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Universit´ e, Universit´ e Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France
6CPPM, Aix-Marseille Universit´ e, CNRS/IN2P3, Marseille, France
7LAL, Universit´ e Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Universit´ e Pierre et Marie Curie, Universit´ e Paris Diderot, CNRS/IN2P3, Paris, France
9Fakult¨ at Physik, Technische Universit¨ at Dortmund, Dortmund, Germany
10Max-Planck-Institut f¨ ur Kernphysik (MPIK), Heidelberg, Germany
11Physikalisches Institut, Ruprecht-Karls-Universit¨ at Heidelberg, Heidelberg, Germany
12School of Physics, University College Dublin, Dublin, Ireland
13Sezione INFN di Bari, Bari, Italy
14Sezione INFN di Bologna, Bologna, Italy
iii

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15Sezione INFN di Cagliari, Cagliari, Italy
16Sezione INFN di Ferrara, Ferrara, Italy
17Sezione INFN di Firenze, Firenze, Italy
18Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
19Sezione INFN di Genova, Genova, Italy
20Sezione INFN di Milano Bicocca, Milano, Italy
21Sezione INFN di Roma Tor Vergata, Roma, Italy
22Sezione INFN di Roma La Sapienza, Roma, Italy
23Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
24Nikhef National Institute for Subatomic Physics and Vrije Universiteit, Amsterdam, Netherlands
25Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Cracow, Poland
26Faculty of Physics & Applied Computer Science, Cracow, Poland
27Soltan Institute for Nuclear Studies, Warsaw, Poland
28Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania
29Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
30Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
31Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia
32Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN), Moscow, Russia
33Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State University, Novosibirsk, Russia
34Institute for High Energy Physics (IHEP), Protvino, Russia
35Universitat de Barcelona, Barcelona, Spain
36Universidad de Santiago de Compostela, Santiago de Compostela, Spain
37European Organization for Nuclear Research (CERN), Geneva, Switzerland
38Ecole Polytechnique F´ ed´ erale de Lausanne (EPFL), Lausanne, Switzerland
39Physik-Institut, Universit¨ at Z¨ urich, Z¨ urich, Switzerland
40NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
41Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine
42H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom
43Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
44Department of Physics, University of Warwick, Coventry, United Kingdom
45STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
46School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom
47School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom
48Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
49Imperial College London, London, United Kingdom
50School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom
51Department of Physics, University of Oxford, Oxford, United Kingdom
52Syracuse University, Syracuse, NY, United States
53CC-IN2P3, CNRS/IN2P3, Lyon-Villeurbanne, France, associated member
54Pontif´ ıcia Universidade Cat´ olica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to2
aP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia
bUniversit` a di Bari, Bari, Italy
cUniversit` a di Bologna, Bologna, Italy
dUniversit` a di Cagliari, Cagliari, Italy
eUniversit` a di Ferrara, Ferrara, Italy
fUniversit` a di Firenze, Firenze, Italy
gUniversit` a di Urbino, Urbino, Italy
hUniversit` a di Modena e Reggio Emilia, Modena, Italy
iUniversit` a di Genova, Genova, Italy
jUniversit` a di Milano Bicocca, Milano, Italy
kUniversit` a di Roma Tor Vergata, Roma, Italy
iv

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lUniversit` a di Roma La Sapienza, Roma, Italy
mUniversit` a della Basilicata, Potenza, Italy
nLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
oHanoi University of Science, Hanoi, Viet Nam
v

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1. Introduction
The decay B0
Standard Model by loop (penguin) diagrams that
contain a b → s transition. The partial width of the
decay arises from three helicity amplitudes that,
assuming no additional contributions from physics
beyond the Standard Model, are determined by the
chiral structure of the quark operators. Predictions
obtained within the framework of QCD factoriza-
tion [1] are B(B0
for the branching fraction and 0.63+0.42
K∗0longitudinal polarization fraction. Predictions
improve to (7.9+4.3
tively, when experimental input is used from B →
K∗φ [2, 3]. The possibility to use B0
for precision CP-violation studies to determine the
phases βsand γ of the CKM matrix [4] has been
emphasised by several authors [5, 6, 7, 8]. The U-
spin related channel, B0→ K∗0K∗0, a b → d tran-
sition, has been observed by BaBar [9], reporting a
branching fraction of (1.28+0.35
fL= 0.80+0.10
events. An upper limit for the B0
branching fraction of 1.68 × 10−3with 90% con-
fidence level was reported by the SLD experiment
[10].
We present in this letter the first observation
of the B0
at√s = 7 TeV at the LHC. The data were col-
lected during 2010 and corresponds to 35 pb−1
of integrated luminosity. LHCb has excellent ca-
pabilities to trigger and reconstruct beauty and
charm hadrons, and covers the pseudorapidity re-
gion 2 < η < 5. The tracking system consists of a
21 station, 1-metre long array of silicon strip detec-
tors placed within 8 mm of the LHC beams. This
is followed by a four layer silicon strip detector up-
stream of a 4 Tm dipole magnet. Downstream of
the magnet are three tracking stations, each com-
posed of a four-layer silicon strip detector in the
high occupancy region near the beam pipe, and an
eight layer straw tube drift chamber composed of
5 mm diameter straws outside this high occupancy
region. Overall, the tracking system provides an
impact parameter (IP)2resolution of 16 µm + 30
µm/pT(GeV/c), and a momentum resolution σp/p
below 8 per mille up to 100 GeV/c. Two ring imag-
s→ K∗0K∗0is described in the
s→ K∗0K∗0) = (9.1+11.3
−6.8) × 10−6
−0.29for the
−3.9) × 10−6and 0.72+0.16
−0.21, respec-
s→ K∗0K∗0
−0.30±0.11)×10−6and
−0.12±0.06 with a signal yield of 33.5+9.1
−8.1
s→ K∗0K∗0
s → K∗0K∗0decay using pp collisions
2The impact parameter is the distance of closest ap-
proach between a particle’s trajectory and its assumed pro-
duction point.
ing Cherenkov detectors, one upstream of the mag-
net, and a second just downstream of the tracking
stations, together provide a typical kaon identifi-
cation efficiency of 90%. The pion fake rate, over
the momentum range from 3 − 100 GeV/c, is be-
tween 5 and 10 percent. Further downstream is a
Preshower/Scintillating Pad Detector, an electro-
magnetic calorimeter, and a hadronic calorimeter.
The LHCb spectrometer also features a large, five
station muon system used for triggering on and
identifying muons. A more detailed description of
the LHCb detector can be found in [11].
To reduce the data rate from the LHC crossing
rate to about 2 kHz for permanent storage, LHCb
uses a two-level trigger system. The first level of
the trigger, implemented in hardware, searches for
either a large transverse energy (ET) cluster in the
calorimeters (ET > 3.6 GeV is a representative
value during the 2010 run), or a single high trans-
verse momentum (pT) muon or di-muon pair in the
muon stations.
Events passing the hardware trigger are read out
and sent to a large computing farm, where they are
analysed using a software-based trigger [12]. The
first stage of the software trigger relies on the se-
lection of a single track with IP larger than 125
µm, pT> 1.8 GeV/c, p > 12.5 GeV/c, along with
other track quality requirements. Events are subse-
quently analysed by a second software stage, where
the event is searched for 2, 3, or 4-particle vertices
that are consistent with originating from b-hadron
decays. The impact parameter χ2of the selected
tracks (IPχ2), defined as the difference between the
χ2of the primary vertex (PV) built with and with-
out the considered track, is required to be greater
than 16 with respect to any PV. The tracks are also
required to have p > 5 GeV/c and pT> 0.5 GeV/c.
The B0
sdecay vertex must have at least one track
with pT> 1.5 GeV/c, a scalar pTsum of at least
4 GeV/c, and a corrected mass3between 4 and 7
GeV/c2. Additional track and vertex quality cuts
are also applied.
Events with large occupancy are slow to re-
construct and were suppressed by applying global
event cuts to hadronically triggered decays. These
included limits on the number of hits in the track-
ing detectors and scintillating pad detector.
3The corrected mass is related to the invariant mass m,
as mcorr =
the missing momentum transverse to the B0
?m2+ |pTmiss|2+ |pTmiss| , where pTmissis
sdirection.
1

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2. Selection procedure and signal yield
Tosearch for thedecay processB0
s
→
K∗0(K+π−)K∗0(K−π+) we applied a number of
offline selection criteria. When a four-track sec-
ondary vertex is found, the reconstructed momen-
tum of the B0
scandidate is used to calculate the
smallest impact parameter with respect to all pri-
mary vertices in the event. Tracks are required to
have pT> 500 MeV/c, and a large impact parame-
ter (IPχ2> 9) with respect to the PV. The differ-
ence in the natural logarithm of the likelihoods of
the kaon and pion hypotheses must be greater than
2 for K+and K−candidates, and less than 0 for π+
and π−candidates. In addition, the K+π−combi-
nations4must form an acceptable quality common
vertex (χ2/ndf < 9), where ndf is the number of
degrees of freedom in the vertex fit) and must have
an invariant mass within ±150 MeV/c2of the nom-
inal K∗0mass (this is around ±3 times its physi-
cal width [4]). The K∗0and K∗0candidates must
have pT> 900 MeV/c and the distance of closest
approach between their trajectories must be less
than 0.3 mm. The secondary vertex must be well
fitted (χ2/ndf< 5). Finally, the B0
mentum is required to point to the PV.
To improve the signal significance, a multivariate
analysis is used that takes into account the proper-
ties of the B0
as well as those of the background. It is based on
a geometrical likelihood (GL) [13, 14] that uses the
following set of variables (generically called xi) as
input:
scandidate mo-
s→ K∗0(K+π−)K∗0(K−π+) signal,
• B0
to the closest primary vertex.
scandidate impact parameter with respect
• Decay time of the B0
• Minimum impact parameter χ2of the four
tracks with respect to all primary vertices in
the event.
scandidate.
• Distance of closest approach between the two
K∗0trajectories reconstructed from the pion
and kaon tracks.
• pTof the B0
For a given input sample, the above distributions
are converted into a set of uncorrelated, Gaussian-
distributed variables. Two vectors are defined for
scandidate.
4This expression refers hereafter to both charge combi-
nations: K+π−and K−π+.
)
2
c
) (MeV/
+
π
-
K
-π
+
M(K
5000 5200 5400 5600 5800
)
2
c
Events / (30 MeV/
0
5
10
15
20
25
30
35
40
LHCb
Figure 1: Fit to the K+π−K−π+mass distribution of se-
lected candidates. The fit model (dashed pink curve) in-
cludes a signal component that has two Gaussian compo-
nents corresponding to the B0
ground is described as an exponential component (dotted
blue) plus the parametrization indicated in the text (dash-
dotted green).
sand B0decays. The back-
each event indicating its distance to the signal {Si}
and to the background {Bi} hypotheses by means
of χ2
S=
∆χ2= χ2
Bis found to be a good discrim-
inant between the two hypotheses and is used to
construct the GL function in such a way that it
is uniformly distributed in the range [0,1] for sig-
nal events and tends to have low values for the
background.The signal simulation is based on
GEANT4 [15].
The GL selection requirement was determined
by maximising the signal significance. The GL was
trained using a fully reconstructed B0
simulation sample for the signal, and a selected
background sample from the first 2 pb−1of data,
which is not used in the analysis. The requirement
GL>0.24, together with the above selection crite-
ria, resulted in the mass spectrum in Fig. 1 for the
selected K+π−K−π+candidates. It is observed
that the events with masses below the signal re-
gion have on average slightly higher GL values than
those with masses above. This indicates the pres-
ence of a background from partially reconstructed
B decays.
To describe the data, we have used a fit in-
cluding two Gaussian probability density functions
(PDFs) centered at the B0and B0
spectively, a decreasing exponential and the fol-
?S2
iand χ2
S− χ2
B=
?B2
i. The quantity
s→ K∗0K∗0
smasses re-
2

Page 8

Table 1: Fitted values of the model parameters for the mass
spectrum, as described in the text.
number of events for the B0
mass value for the B0
ssignal and σ is the Gaussian width.
The mass difference between B0
nominal value [4]. Nbis the number of background events
in the full mass range (4900-5800 MeV/c2), and cbis the
exponential parameter in the fit. Mp, σp and kp are the
parameters of Eq. (1).Finally, fp is the fraction of the
background associated with Eq. (1).
Ns and Nd are the
sand B0signals, µs is the fitted
sand B0was fixed to its
Parameter
Ns
Nd
µs(MeV/c2)
σ (MeV/c2)
Nb
cb(10−3(MeV/c2)−1)
kp(10−2(MeV/c2)−1)
fp
Mp(MeV/c2)
σp(MeV/c2)
Value
50.1 ± 7.5
11.2 ± 4.3
5362.5 ± 4.8
21.2 ± 3.3
90 ± 10
−3.37 ± 0.55
5.5 ± 5.3
0.06+ 0.24
− 0.05
5170 ± 170
37 ± 23
lowing parametrization for partially reconstructed
B-decays
?
AM?
1 −M?2
M2
p
?
Θ(Mp−M?)e−kp·M?⊗G(M−M?;σp),
(1)
where Θ is the Heaviside-step function, ⊗ rep-
resents the convolution, M?is the variable over
which the convolution integral is calculated, G(M−
M?;σp) is a Gaussian PDF with standard deviation
σpand Mpand kpare free parameters. The fit re-
sults are given in Table 1.
The measured signal yield in a window of
±50MeV/c2around the B0
49.8 ± 7.5(stat.). The width of the B0
good agreement with the LHCb resolution mea-
sured in decays with similar kinematics such as
B0
determined to be 10.9 σ by comparing the log of
the likelihood between the models with and with-
out signal. When doing this test, the mass and
width of the B0
obtained from independent LHCb measurements of
B0
peak at the B0mass, though not significant, is com-
patible with the B0→ K∗0K∗0branching fraction
measured by BaBar [9].
As the K∗0meson is light compared to the B0
meson, the invariant masses of the three-body sys-
smass is NK+π−K−π+ =
speak is in
s→ J/ψφ. The significance of the B0
ssignal was
sand B0mesons were fixed to those
s→ J/ψφ and B0→ J/ψK∗0, respectively. The
s
tems K+K−π±and K+π−π±are rather high,
above those of the charmed hadrons. This kine-
matically excludes the possibility of contamination
from b → c decays with very short charm flight
distance, in particular B0
The background subtracted K+π−mass combi-
nations were studied, within a ±50 MeV/c2window
of the B0
ssignal, by means of a maximum likelihood
fit in the (mK+π−,mK−π+) plane. Three compo-
nents are included in the fit, namely a double Breit-
Wigner distribution describing B0
duction, a symmetrized product of a Breit-Wigner
and a nonresonant linear model adjusted for phase-
space in the K+π−mass, and a double nonreso-
nant component. The fit result, as shown in Fig. 2,
gives (62±18)% K∗0K∗0production. The remain-
der is the symmetrised Breit-Wigner/ nonresonant
model.
The shape of the background mass distribution
was extracted from a fit to the K+π−mass spec-
trum observed in two 400 MeV/c2wide sidebands
below and above the B0
smass. The number of back-
ground events to be subtracted was determined
from the results in Table 1. The sizeable K∗0con-
tribution present in this background was taken into
account.
s→ D−
sπ+.
s→ K∗0K∗0pro-
)
2
c
) (MeV/
π
M(K
8009001000
)
2
c
Entries / ( 30 MeV/
0
10
20
30
LHCb
Figure 2: Background subtracted K+π−and K−π+com-
binations for selected candidates within a ±50 MeV/c2win-
dow of the B0
smass. The solid blue line shows the projection
of the 2D fit model described in the text, indicating the K∗0
K∗0yield (dashed-dotted red line) and a nonresonant com-
ponent (blue dotted line), assumed to be a linear function
times the two-body phase space. The dashed red line indi-
cates the overall B0
s→ K∗0X contribution.
A model for B0
s→ K∗0K∗0(1430), representing
3

Page 9

a broad scalar state interfering with B0
was also studied in the available K+π−mass range
of ±150MeV/c2around the K∗0mass. The small
number of events made it impossible to measure
precisely the size of such a contribution for all val-
ues of the interfering phase. However, for values of
the phase away from π/2 and 3π/2 it was deter-
mined to be below 12%. Further study of this issue
requires a larger data sample.
s→ K∗0K∗0
3. Selection of the control channel
The branching fraction measurement of B0
K∗0K∗0is based upon the use of a normalization
channel with a well measured branching fraction,
and knowledge of the selection and trigger efficien-
cies for both the signal and normalization channels.
We chose B0→ J/ψK∗0, with J/ψ → µ+µ−, for
this purpose. This decay has a similar topology to
the signal, allowing the selection cuts to be har-
monised, and it is copiously produced in the LHCb
acceptance. The presence of two muons in the fi-
nal state means that B0→ J/ψK∗0tends to be
triggered by a muon rather than a hadron, lead-
ing to a higher efficiency than for B0
The differences in the trigger can be mitigated by
only considering B0→ J/ψK∗0candidates where
the trigger decision was not allowed to be based on
muon triggers that use tracks from the decay itself.
The offline selection criteria for B0→ J/ψK∗0
were designed to mimic those of B0
In particular, all cuts related to the B0
inition were kept the same. We also used the same
GL as for the signal.
The overall detection efficiency was factorized as
?sel?trig. The first factor ?selis the probability of
the generated tracks being accepted in the LHCb
angular coverage, reconstructed, and selected. The
second factor ?trigdefines the efficiency of the trig-
ger on the selected events. Both are indicated in
Table 2, as calculated from Monte Carlo simula-
tion, along with the number of selected events.
Note that our measurement depends only on the ra-
tios of efficiencies between signal and control chan-
nels.
The event yield for the selected data was de-
termined from a fit to the J/ψK+π−invariant
mass spectrum as shown in Fig. 3.
a constrained J/ψ mass was used in order to im-
prove the B0mass resolution and therefore back-
ground rejection. The absence of background from
s→
s→ K∗0K∗0.
s→ K∗0K∗0.
svertex def-
In this fit,
)
2
c
) (MeV/
π
K
ψ
M(J/
5000520054005600
)
2
c
Events / ( 24 MeV/
1
10
2
10
3
10
LHCb
Figure 3: Fit to the mass distribution of selected B0→
J/ψK∗0events. The dashed red curve is the Gaussian
component for the B signal.
line accounts for partially reconstructed B → J/ψX (see
Eq. 2).The pink hatched region accounts for B0
J/ψφ contamination, and is parametrized as a sum of two
Crystal-Ball functions [18]. The combinatorial background
is parametrized as an exponential and indicated as a blue
dotted line.
The green dashed-dotted
s
→
B0
lished using the Armenteros-Podolanski plot [16]
for the K∗0kinematics.
a Gaussian signal for the B0meson, a combina-
torial background component parameterized with
an exponential function and an additional compo-
nent to account for partially reconstructed B →
J/ψX [17]. This partially reconstructed compo-
nent can be described as
?
s
→ J/ψφ, with φ → K+K−, was estab-
The fit model includes
ρ(M,M,µ,κ) ∝
e−1
e−1
2(M−M
2(µ−M
κ
)2
if M > µ;
κ
)2+(M−µ)(M−µ)
κ2
if M ≤ µ.
(2)
where the parameters µ, κ and M are allowed to
float. The results of the fit are shown in Table 2.
A small fraction of the selected sample contains
two alternative candidates for the reconstructed
event, which share three of the particles but dif-
fer in the fourth one. Those events, which amount
to 3.8 % (3.7%) in the signal (control) channels,
were retained for the determination of the branch-
ing fraction.
4. Analysis of K∗0polarization
The four-particle K+π−K−π+angular distribu-
tion describing the decay of B0
sinto two vector
4

Page 10

Table 2: Selection and trigger efficiencies obtained from simulation. The observed yield found for the signal and control
channels in the full mass range are also indicated. The efficiency errors are statistical, derived from the size of the simulated
samples.
?sel(%)?trig(%)
Yield
B0
s→ K∗0K∗0
B0→ J/ψK∗0
ratio
0.370 ± 0.005
0.547 ± 0.007
0.678 ± 0.013
37.12 ± 0.39
31.16 ± 0.63
1.191 ± 0.027
42.5 ± 6.7
657 ± 27
0.065 ± 0.011
mesons (K∗0→ K+π−and K∗0→ K−π+) is de-
termined by three transversity amplitudes AL, A?
and A⊥. The relative fraction of these can be deter-
mined from the distribution of the decay products
in three angles θ1, θ2 and ϕ. Here θ1 (θ2) is the
K+(K−) emission angle with respect to the direc-
tion opposite to the B0
rest frame, and ϕ is the angle between the nor-
mals to the K∗0and K∗0decay planes in the B0
rest frame [5]. We will refer generically to the θ
angle from now on, unless differences between θ1
and θ2 become relevant for the discussion. In a
time-integrated and flavour-averaged analysis, and
assuming the B0
smixing phase βs ≈ 0 as in the
Standard Model, the angular distribution is given
by [5, 19]
smeson in the K∗0(K∗0)
s
I(θ1,θ2,ϕ) =
d3Γ
dcosθ1dcosθ2dϕ=
?1
1
ΓL|A?|21
1
ΓH|A⊥|21
ΓL
|AL|2cos2θ1cos2θ2
+
2sin2θ1sin2θ2cos2ϕ
+
2sin2θ1sin2θ2sin2ϕ
1
2√2sin2θ1sin2θ2cosϕ
+
1
ΓL|AL| |A?|cosδ?
?
(3)
We denote the polarization fractions by
fk=
|Ak|2
|AL|2+ |A?|2+ |A⊥|2
and consequently fL+ f?+ f⊥ = 1. No CP vio-
lation in the mixing or in the decay has been con-
sidered. The interference terms related to the A⊥
amplitude, both proportional to sinφs, have been
neglected. ΓL,H are the total widths of the low
and high mass eigenstates of the B0
spectively, and δ?is the phase difference between
,k = L,?,⊥ . (4)
smeson, re-
AL and A?. The total decay width is defined as
Γ = (ΓL+ΓH)/2 and ∆Γ = ΓL−ΓH. Note that as
a consequence of time integration the relative nor-
malization acquired by the CP-even and CP-odd
terms is different. The values ∆Γ = (0.062+0.034
1012s−1and Γ = (0.679+0.012
used.
The detector acceptance is compatible with be-
ing constant in ϕ. In contrast, it has a signifi-
cant dependence on the K∗0polarization angle θ.
The two-dimensional angular acceptance function
?(cosθ1,cosθ2) was studied with a full detector sim-
ulation. It drops to nearly zero asymmetrically as
cosθ1,2 becomes close to ±1, as a consequence of
the minimum p and pT of the tracks imposed by
the reconstruction.
The Monte Carlo simulation of the K∗0accep-
tance was extensively cross-checked using the B0
→ J/ψ K∗0control channel, taking advantage of
the fact that the K∗0polarization in this chan-
nel was measured at the B-factory experiments
[20, 21]. The function ?(cosθ1,cosθ2) has been pro-
jected onto the K∗0and K∗0axes separately, show-
ing no appreciable difference, and a small average
correlation, given the size of the simulated sample.
We have then used the one-dimensional acceptance
?θ(cosθ) as the basis of our analysis, and deter-
mined it in five bins of cosθ. Since the longitudinal
polarization fraction for the B0→ J/ψ K∗0channel
is well measured, a comparison between data and
simulation is possible. Agreement was found in-
cluding variations of the angular distribution with
longitudinal and transverse K∗0momentum. In the
region cosθ > 0.6 these variations were four times
larger than for lower values of cosθ.
The background cosθ distribution was studied in
two 200MeV/c2sidebands, defined below and above
the B0
ssignal region. Like the signal, it showed a
dip close to cosθ = +1 and it was parameterized
as ?θ·(1+β cosθ). A one parameter fit for β gives
the result β = −0.18 ± 0.13.
−0.037)×
−0.011) × 1012s−1[4] were
5

Page 11

An unbinned maximum likelihood fit was then
performed to the data in a ±50 MeV/c2window
around the B0
smass, in the region cosθ < 0.6, ac-
cording to the PDF
F(θ1,θ2,ϕ) = (1 − α)?θ(θ1)?θ(θ2)I(θ1,θ2,ϕ)
+α(1 + β cosθ1)(1 + β cosθ2)?θ(θ1)?θ(θ2).
(5)
The background fraction α was determined from
the fit to the B0
smass spectrum described in Sec.
2. Only three parameters were allowed to vary in
the fit, namely fL, f?and the phase difference δ?.
One-dimensional projections of the fit results are
shown in Fig. 4. The consistency of the measure-
ment in various regions of the K∗0phase space, and
of the impact parameter of the daughter particles,
was checked. The experimental systematic error
on fLwas estimated from the variation of the mea-
surements amongst those regions to be ±0.03.
The acceptance for B0
form as a function of proper decay time due to the
cuts made on the IP of the kaons and pions, and
a small correction to the polarization fractions, of
order 3%, was applied in order to take into account
this effect. It was calculated from the variation in
the measured polarization amplitudes induced by
including a parametrization of the time acceptance
in Eq. 5. Note the different correction sign for each
polarization fraction, as a consequence of the as-
sumption ∆Γ ?= 0.
The sensitivity of the fLmeasurement with re-
spect to small variations of the cosθ distribution
has been tested.These variations could be at-
tributed to experimental errors not accounted for in
the simulation or to interference with other partial
waves in the Kπ system. A high statistics study us-
ing B0→ J/ψ K∗0muon triggers revealed a small
systematic difference between data and simulation
in ?θ(cosθ) as cosθ approaches +1, which was taken
into account as a correction in our analysis. When
this correction in varied by ±100%, fL varies by
±0.02 which we consider as an additional source
of systematic error. The total systematic on fLis
thus ±0.04.
We finally measure the K∗0longitudinal polar-
ization fraction fL= 0.31±0.12(stat.)±0.04(syst.),
as well as the transverse components f?and f⊥. In
the small sample available, the CP-odd component
f⊥appears to be sizeable f⊥= 0.38±0.11(stat.)±
0.04(syst.). A significant measurement of δ?could
not be achieved (δ?= 1.47 ± 1.85).
s→ K∗0K∗0is not uni-
θ
cos
-1-0.8-0.6-0.4-0.20 0.2 0.4 0.60.81
θ
dcos

Γ
1
Γ
d
0
0.2
0.4
LHCb
ϕ
0123456
ϕ
d

Γ
1
Γ
d
0
0.2
0.4
LHCb
Figure 4: cosθ (above) and ϕ (below) acceptance corrected
distributions for events in the narrow window around the
B0
smass. The blue line is the projection of the fit model
given by Eq. 3 for the measured values of the parameters
fL, f?and δ?. The dotted lines indicate ±1σ variation of
the fLcentral value.
As seen in Eq. (3), due to a nonzero ∆Γ time in-
tegration changes the relative proportion between
the various terms of the angular distribution, with
respect to their values at t = 0. If we call f0
polarization fractions we would have measured un-
der the assumption ∆Γ = 0, it can be derived from
Eq. 3 that our measured values are
?
with CP eigenvalue ηk = +1,+1,−1 for k = L,?
,⊥. Given the current knowledge of ∆Γ/Γ [4], the
magnitude of the correction to fkamounts to 4.6%,
and the associated systematic error related to ∆Γ
error is 2.6%, which we have neglected in compar-
ison to other sources.
kthe
fk= f0
k
1 + ηk∆Γ
2Γ
?
(6)
5. Determination of the branching fraction
The results of the previous sections can be
brought together to provide a determination of the
branching fraction of the B0
based upon the use of the normalization channel
B0→ J/ψK∗0through the expression
B?B0
?trig
B0→J/ψK∗0
?trig
B0
×Bvis(B0→ J/ψK∗0) ×fd
s → K∗0K∗0decay
s→ K∗0K∗0?= λfL×
?sel
B0→J/ψK∗0
?sel
B0
s→K∗0K∗0
×
s→K∗0K∗0
×
NB0
NB0→J/ψK∗0
s→K∗0K∗0
fs
×9
4,(7)
6

Page 12

where Bvis(B0→ J/ψK∗0), the visible branching
ratio, is the product B(B0→ J/ψK∗0) × B(J/ψ →
µ+µ−) × B(K∗0→ K+π−). The numerical value
of B(B0→ J/ψK∗0) = (1.33±0.06)×10−3is taken
from the world average in [4], B(J/ψ → µ+µ−) =
0.0593±0.0006 [4] and B(K∗0→ K+π−) = 2/3 [4].
The ratio of b-quark hadronization factors that ac-
counts for the different production rate of B0and
B0
smesons is fs/fd= 0.253 ± 0.031 [22]. The fac-
tor 9/4 is the inverse square of the 2/3 branch-
ing fraction of K∗0→ K+π−.
candidate events in the signal and control channel
data samples are designated by NB0
NB0→J/ψK∗0.
The correction factor λfLis motivated by the fact
that the overall efficiency of the LHCb detector is a
linear function of the K∗0longitudinal polarization
fL. Taking into account the measured value and er-
rors reported in section 4, Monte Carlo simulation
was used to estimate λfL= 0.812 ± 0.059.
We have considered two sources of systematic
uncertainty associated to the ratio of selection ef-
ficiencies. The first source results from discrepan-
cies between data and simulation in the variables
related to track and vertex quality, and the sec-
ond is related to particle identification. A small
difference observed in the average impact parame-
ter of the particles was corrected for by introducing
an additional smearing to the track parameters in
the simulation [23]. While the absolute efficien-
cies vary significantly as a function of vertex reso-
lution, the ratio of efficiencies remains stable. We
have assigned a 2% uncertainty to the ratio, af-
ter comparison between simulation and the B0→
J/ψ K∗0data. The K/π identification efficiency
was determined using a sample of B0→ J/ψ K∗0
events selected without making use of the RICH
detectors. As the signal channel contains one more
kaon than the control channel, a correction factor of
1.098±0.019 was applied to the branching fraction,
and a 2% error was assigned to it. The efficiency of
muon identification agrees with simulation within
1.1% [24]. All these factors are combined to pro-
duce an overall systematic uncertainty of 3.4% in
the ratio of selection efficiencies. The uncertainty
in the background model in the B0
events) contributes an additional systematic error
of 4.7%.
Trigger efficiencies can be determined, for partic-
ular trigger paths in LHCb, using the data driven
algorithm described in [24]. This algorithm could
be applied for the specific hadronic triggers used for
The number of
s→K∗0K∗0 and
smass fit (±2
Table 3:
B?B0
Systematic effect
Trigger efficiency
Global angular acceptance
S-wave fraction
Background subtraction
B0→ J/ψ K∗0and J/ψ → µµ
BR uncertainty
Selection efficiency
Total
Estimated systematic error sources in the
s→ K∗0K∗0?measurement.
Error (%)
11.0
7.2
5.0
4.7
4.6
3.4
15.9
B0→ J/ψ K∗0, but not for the small B0
K∗0signal. The efficiency related to cuts on global
event properties, applied during the 2010 data tak-
ing, is determined from J/ψ minimum bias trig-
gers [24]. The result indicates a trigger efficiency of
(26.8±3.8)%, smaller than the simulation result of
(31.16 ± 0.63)% shown in Table 2. Although these
are consistent within uncertainties, we nonetheless
apply a −9% correction to the ratio of trigger effi-
ciencies between B0→ J/ψ K∗0and B0
channels, taking into account correlations in the
trigger probability. A systematic error of 11% was
assigned to uncertainty on the trigger efficiency, en-
tirely limited by statistics, both in the signal and
control channels. Detector occupancies, estimated
by the average number of reconstructed tracks, are
larger by 10% in the data than in the simulation.
This implies an additional correction of +4.5% to
the ratio of efficiencies, since the control channel is
observed to be more sensitive to occupancy than
the signal channel.
An ∼ 8% S-wave contribution under the K∗0res-
onance in the B0→ J/ψ K∗0channel has been
observed by BaBar [21], and the data in a ±70
MeV/c2mass interval around the K∗0mass [25]
yields a (9.0 ± 3.6)% extrapolation to the ±150
MeV/c2mass window.
doubles for the K∗0K∗0final state, and it may
certainly have a different coupling for both chan-
nels. Our direct measurement reported in section 2
of (19±9)% is still lacking precision to be used for
this purpose. When evaluating the branching frac-
tion, we have assumed a 9% S-wave contribution,
and assigned a systematic error of 50% to this hy-
pothesis. A summary of the various contributions
to the systematic error can be seen in Table 3.
s→ K∗0
s→ K∗0K∗0
The S-wave background
7

Page 13

Our final result is
B(B0
s→ K∗0K∗0) = (2.81 ± 0.46 (stat.)
± 0.45 (syst.)
± 0.34 (fs/fd)) × 10−5.
As we have seen at the end of section 4, unequal
normalization factors arise upon time integration
of individual polarization amplitudes with well de-
fined CP-eigenvalues. This has the interesting im-
plication that the time-integrated flavour-averaged
branching fraction (B1) as determined above can-
not be directly compared with theoretical predic-
tions solely formulated in terms of the decay am-
plitudes AL2+A?2+A⊥2(B0). Meson oscillation
needs to be taken into account, since two distinct
particles with different lifetimes are involved. Ow-
ing to the fact that A⊥is CP-odd, the relationship
between these quantities reads as follows
?
According to our measurements of fL+f?−f⊥, the
correction is small (3% if current values are taken
for ∆Γ), and we do not apply it to our measure-
ment.
B0= B1
1 +∆Γ
2Γ(fL+ f?− f⊥)
?
. (8)
6. Conclusion
The b → s penguin decay B0
has been observed for the first time.
pb−1of pp collisions at 7 TeV centre-of-mass en-
ergy, LHCb has found 49.8 ± 7.5 signal events
in the mass interval ±50MeV/c2around the B0
mass. Analysis of the K+π−mass distributions
shows that most of the signal comes from B0
K∗0K∗0, with some S-wave contribution.
branching fraction has been measured, with the
result B?B0
longitudinal K∗0polarization fraction has also been
measured to be fL= 0.31±0.12(stat.)±0.04(syst.),
as well as the CP-odd component f⊥ = 0.38 ±
0.11(stat.) ± 0.04(syst.).
When we consider our measurement in associa-
tion with that of [9], it is remarkable that the lon-
gitudinal polarization of the K∗0mesons seems to
be quite different between B0
0.31±0.12(stat.)±0.04(syst.)) and B0→ K∗0K∗0
(fL = 0.80+0.10
fact that the two decays are related by a U-spin ro-
tation. However, the ratio of the branching ratios
s
→ K∗0K∗0
Using 35
s
s→
The
s→ K∗0K∗0?
= (2.81 ± 0.46(stat.) ±
0.45(syst.)±0.34(fs/fd))×10−5. The CP-averaged
s→ K∗0K∗0(fL =
−0.12(stat.) ± 0.06(syst.)), despite the
of B0
λ is the Wolfenstein parameter, as expected.
sand B0decays is consistent with 1/λ2where
Acknowledgements
We would like to thank J. Mat´ ıas for useful dis-
cussions.We express our gratitude to our col-
leagues in the CERN accelerator departments for
the excellent performance of the LHC. We thank
the technical and administrative staff at CERN
and at the LHCb institutes, and acknowledge
support from the National Agencies:
CNPq, FAPERJ and FINEP (Brazil); CERN;
NSFC (China); CNRS/IN2P3 (France); BMBF,
DFG, HGF and MPG (Germany); SFI (Ireland);
INFN (Italy); FOM and NWO (The Netherlands);
SCSR (Poland); ANCS (Romania); MinES of Rus-
sia and Rosatom (Russia); MICINN, XuntaGal and
GENCAT (Spain); SNSF and SER (Switzerland);
NAS Ukraine (Ukraine); STFC (United Kingdom);
NSF (USA). We also acknowledge the support re-
ceived from the ERC under FP7 and the Region
Auvergne.
CAPES,
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