EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2015-021 LHCb-PAPER-2014-067

Precise measurements of the properties of the $B_{1}(5721)^{0,+}$ and
$B_{2}^{*}(5747)^{0,+}$ states and observation of $B^{+,0}\pi^{-,+}$ mass
structures

The LHCb collaboration†††Authors are listed at the end of this paper.

Invariant mass distributions of $B^{+}\pi^{-}$ and $B^{0}\pi^{+}$ combinations
are investigated in order to study excited $B$ mesons. The analysis is based
on a data sample corresponding to $3.0\mbox{\,fb}^{-1}$ of $pp$ collision
data, recorded by the LHCb detector at centre-of-mass energies of 7 and
$8\mathrm{\,Te\kern-1.00006ptV}$. Precise measurements of the masses and
widths of the $B_{1}(5721)^{0,+}$ and $B_{2}^{*}(5747)^{0,+}$ states are
reported. Clear enhancements, particularly prominent at high pion transverse
momentum, are seen over background in the mass range
$5850$–$6000\mathrm{\,Me\kern-1.00006ptV}$ in both $B^{+}\pi^{-}$ and
$B^{0}\pi^{+}$ combinations. The structures are consistent with the presence
of four excited $B$ mesons, labelled $B_{J}(5840)^{0,+}$ and
$B_{J}(5960)^{0,+}$, whose masses and widths are obtained under different
hypotheses for their quantum numbers.

Published in JHEP

© CERN on behalf of the LHCb collaboration, licence CC-BY-4.0.

##  1 Introduction

The properties of excited $B$ mesons containing a light quark can be described
in the context of heavy quark effective theory (HQET) [1]. Since the mass of
the $b$ quark is much larger than the QCD scale, the Lagrangian can be
expanded in powers of $1/m_{b}$, where the leading term defines the static
limit ($m_{b}\rightarrow\infty$). In the heavy quark approximation, the $B$
mesons are characterised by three quantum numbers: the orbital angular
momentum $L$ (S, P, D for $L=0,1,2$ respectively) of the light quark, its
total angular momentum $j_{q}=|L\pm\frac{1}{2}|$, and the total angular
momentum $J=|j_{q}\pm\frac{1}{2}|$ of the $B$ meson. The spectroscopic
notation has the form $n^{2S+1}L_{J}$, where $S=0$ or $1$ is the sum of the
quark spins and where the quantum number $n$ describes the radial excitations
of the state. The PDG notation [2] (which is used in this paper) has the form
$B_{J}^{(*)}(m)$ or $B_{J}^{(*)}(nL)$, where $m$ is the mass in units of
$\mathrm{\,Me\kern-1.00006ptV}$,111Natural units where $\hbar$ = c = 1 are
used. the $*$ superscript is given to those states with natural spin-parity
$P=(-1)^{J}$ ($J^{P}=0^{+},1^{-},2^{+},...$), and the subscript $J$ is omitted
for pseudoscalar and vector states. A prime may be used to distinguish two
states with the same quantum numbers.

For $L=0$, there are two possible ($J$; $j_{q}$) combinations, both parity-
odd, corresponding to the $B$ meson ground state with $J^{P}=0^{-}$ and to the
excited $B^{*}$ state with $J^{P}=1^{-}$. Higher excitations are collectively
referred to as $B^{**}$ states and decay strongly to lighter $B$ mesons and
pions. For $L=1$ there are four different possible ($J$; $j_{q}$)
combinations, all parity-even. Predictions for the masses of such states and
higher excitations spread over a wide range of values, as shown in Fig. 1 [3,
4, 5, 6, 7, 8, 9, 10].

Figure 1:  Mass predictions of the excited $B$ states [3, 4, 5, 6, 7, 8, 9,
10]. The boxes cover the range of predictions for the masses of each state,
and the red dots indicate the measured values. The horizontal lines correspond
to the $B\pi$ (red) and $B^{*}\pi$ (blue) thresholds.

As can be seen in Fig. 1, the states come in doublets (two values of $J$ for
each $j_{q}$), and within each doublet, one has natural and one unnatural
spin-parity quantum numbers. States with natural spin-parity (except for
$0^{+}$) can decay to both $B\pi$ and $B^{*}\pi$ final states. States with
unnatural spin-parity cannot decay to the pseudoscalar-pseudoscalar $B\pi$
final state due to parity conservation, but may decay to $B^{*}\pi$ (Table 1).
Since the $B^{*}$ meson decays to $B\gamma$, the signature from a doublet of
$B^{**}$ states is given by three peaks in the $B\pi$ mass spectrum (unless
the doublet includes a $0^{+}$ state): one from the natural spin-parity state
decay to $B\pi$, and two from both states decaying to $B^{*}\pi$ with a
missing photon. Due to the missing photon, the peaks from $B^{*}\pi$ decays
are shifted down from the true $B^{**}$ mass by the difference between the
$B^{*}$ and $B$ masses (this feature recently allowed a precise determination
of the $B^{*}-B$ mass difference from the $B^{+}K^{-}$ spectrum [11]).
Depending on the widths of the states and the mass resolution, two or all
three of these peaks may overlap and be hard to distinguish experimentally.
The $B_{0}^{*}$ and $B_{1}^{\prime}$ states are predicted to be very broad [3,
10] since they decay via S-wave (the comparable states in the charm sector
have widths of around $300\mathrm{\,Me\kern-1.00006ptV}$ [2]). However, the
$B_{1}$ and $B_{2}^{*}$ states decay only via D-wave and are predicted [3, 10]
and observed [2] to be much narrower. Higher states such as the $B(2{\rm S})$,
$B^{*}(2{\rm S})$, $B_{2}(1{\rm D})$ and $B_{3}^{*}(1{\rm D})$ are predicted
to have widths in the $100$–$200\mathrm{\,Me\kern-1.00006ptV}$ range [10],
consistent with the recent measurement of the properties of the
$D_{s3}^{*}(1{\rm D})$ state [12, 13].

Table 1:  Allowed decay modes for the excited $B$ states. $J^{P}$ | Allowed decay mode
---|---
|  kk $B\pi$ kk |  kk $B^{*}\pi$ kk
$0^{+}$ | yes | no
$0^{-},1^{+},2^{-},...$ | no | yes
$1^{-},2^{+},3^{-},...$ | yes | yes

In contrast to the situation in the charm sector, there is relatively little
experimental information concerning $B$ meson spectroscopy. The
$B_{1}(5721)^{0}$ and $B_{2}^{*}(5747)^{0}$ states have been observed by the
CDF [14] and D0 [15] experiments, and recently the CDF collaboration has
presented results on the charged isospin partners, together with evidence for
a higher mass resonance [16]. This result has prompted theoretical speculation
about the origin of the new state [17, 18, 19, 20, 21]. While in the $D$ meson
system amplitude analyses of excited states produced in $B$ decays can be used
to determine their spin and parity (see, for example, Refs. [22, 12, 13]), in
the $B$ meson system it is very difficult to assign with certainty quantum
numbers to observed states. The labelling of the states follows the quark-
model expectations for the quantum numbers, which have not been experimentally
verified.

In this paper, the results of a study of $B^{+}\pi^{-}$ and $B^{0}\pi^{+}$
combinations are presented. The inclusion of charge-conjugate processes is
implied throughout. The analysis is based on a data sample corresponding to
$3.0\mbox{\,fb}^{-1}$ of LHC $pp$ collision data recorded with the LHCb
detector at centre-of-mass energies of 7 and $8\mathrm{\,Te\kern-1.00006ptV}$.

The $B$ mesons are reconstructed in the ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}K^{+}$, $\kern 1.99997pt\overline{\kern-1.99997ptD}{}^{0}\pi^{+}$,
$\kern 1.99997pt\overline{\kern-1.99997ptD}{}^{0}\pi^{+}\pi^{+}\pi^{-}$,
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}K^{*0}$, $D^{-}\pi^{+}$ and
$D^{-}\pi^{+}\pi^{+}\pi^{-}$ channels, with subsequent
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}\rightarrow\mu^{+}\mu^{-}$,
$\kern 1.99997pt\overline{\kern-1.99997ptD}{}^{0}\rightarrow K^{+}\pi^{-}\
{\rm and}\ K^{+}\pi^{-}\pi^{+}\pi^{-}$, $D^{-}\rightarrow K^{+}\pi^{-}\pi^{-}$
and $K^{*0}\rightarrow K^{+}\pi^{-}$ decays. The $B$ meson candidates are
required to originate from a primary $pp$ collision vertex (PV), and are
combined with pions originating from the same PV (referred to as “companion
pions”). Both “right-sign” (RS) and “wrong-sign” (WS) combinations are
considered, where the latter are those with quark-content that precludes that
the pair originates from the strong decay of an excited $B$ meson (e.g.
$B^{+}\pi^{+}$) and are used to model the combinatorial background. Excited
$B$ mesons are seen as peaks in the RS invariant mass distributions, and are
fitted with relativistic Breit-Wigner (RBW) functions. An additional very
broad component, observed in the RS and not in the WS combinations, is
referred to as “associated production” (AP) in this paper. The AP contribution
may originate from very broad resonances or from correlated nonresonant
production of $B$ mesons and companion pions in the fragmentation chain.

The remainder of the paper is organised as follows. A brief description of the
LHCb detector is given in Sec. 2. The selection requirements are described in
Sec. 3, the fit model is discussed in Sec. 4, and the nominal fit results are
given in Sec. 5, with the evaluation of the systematic uncertainties in Sec.
6. Interpretation of the results and a summary are given in Sec. 7.

##  2 Detector and dataset

The LHCb detector [23, 24] is a single-arm forward spectrometer covering the
pseudorapidity range $2<\eta<5$, 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 [25] surrounding the $pp$
interaction region, a large-area silicon-strip detector located upstream of a
dipole magnet with a bending power of about $4{\rm\,Tm}$, and three stations
of silicon-strip detectors and straw drift tubes [26] placed downstream of the
magnet. The tracking system provides a momentum measurement with relative
uncertainty that varies from 0.5% at low momentum to 1.0% at
200$\mathrm{\,Ge\kern-1.00006ptV}$, and an impact parameter measurement with
resolution of 20${\,\upmu\rm m}$ for tracks with large momentum transverse to
the beamline ($p_{\rm T}$). Different types of charged hadrons are
distinguished using information from two ring-imaging Cherenkov detectors
[27]. Photon, electron and hadron candidates are identified by a calorimeter
system consisting of scintillating-pad and preshower detectors, an
electromagnetic calorimeter and a hadronic calorimeter. Muons are identified
by a system composed of alternating layers of iron and multiwire proportional
chambers [28]. The trigger [29] consists of a hardware stage, based on
information from the calorimeter and muon systems, followed by a software
stage, which uses information from the vertex detector and tracking system.

In the simulation, $pp$ collisions are generated using Pythia [30] with a
specific LHCb configuration [31]. Decays of hadronic particles are described
by EvtGen [32], in which final-state radiation is generated using Photos [33].
The interaction of the generated particles with the detector, and its
response, are implemented using the Geant4 toolkit [34, *Agostinelli:2002hh]
as described in Ref. [36].

##  3 Event selection

The $B$ meson candidates in each decay mode are reconstructed using a set of
loose selection requirements to suppress the majority of the combinatorial
backgrounds. The selection criteria are similar to those used in previous
analyses of the same channels [37, 38, 39, 40]. The $B^{+}\rightarrow J/\psi
K^{+}$ and $B^{0}\rightarrow J/\psi K^{*0}$ selections require a $B$ candidate
with $\mbox{$p_{\rm T}$}>3\mathrm{\,Ge\kern-1.00006ptV}$ and a decay time of
at least $0.3{\rm\,ps}$. For the other decay modes, the selection explicitly
requires that the software trigger decision is based only on tracks from which
the $B$ meson candidate is formed. No requirement is imposed on how the event
was selected at the hardware trigger stage. Additional loose selection
requirements are placed on variables related to the $B$ meson production and
decay, such as transverse momentum and quality of the track fits for the decay
products, detachment of the $B$ candidate from the PV, and whether the
momentum of the $B$ candidate points back to the PV. Because $B^{0}$ mesons
oscillate, the distinction between RS and WS combinations is clearest at short
$B^{0}$ decay times, and hence only $B^{0}$ candidates with decay time below
$2{\rm\,ps}$ are used in the analysis.

Figure 2:  Mass distributions of the $B^{+}$ and $B^{0}$ candidates
reconstructed through (a) $B^{+}\rightarrow\kern
1.99997pt\overline{\kern-1.99997ptD}{}^{0}(\pi^{+},\pi^{+}\pi^{+}\pi^{-})$,
(b) $B^{+}\rightarrow J/\psi K^{+}$, (c) $B^{0}\rightarrow
D^{-}(\pi^{+},\pi^{+}\pi^{+}\pi^{-})$, and (d) $B^{0}\rightarrow J/\psi
K^{*0}$ decays. The ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$, $\kern
1.99997pt\overline{\kern-1.99997ptD}{}^{0}$ and $D^{-}$ masses are constrained
to their world average values [2]. Results of fits are superimposed for
illustration. The signal (dot-dashed red line) is modelled with a double
Crystal Ball [41] distribution, while the background (dashed black line) is
modelled with a second-order polynomial. The total fit is shown as a solid
blue line.

The mass distributions for the $B^{+}$ and $B^{0}$ candidates are shown in
Fig. 2. Only $B$ meson candidates falling within
$25\mathrm{\,Me\kern-1.00006ptV}$ of the nominal $B$ mass for the decay modes
containing ${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$ mesons, or
$50\mathrm{\,Me\kern-1.00006ptV}$ for the other modes, are selected for
further analysis. Samples of about 1.2 million $B^{0}$ and 2.5 million $B^{+}$
candidates are obtained, with purity depending on decay mode and always larger
than 80%. Each candidate is combined with any track that originates from the
same PV and that is identified as a pion. The particle identification
requirements on the companion pion are chosen to reduce potential backgrounds
from misidentified particles to a level where they can be neglected in the
analysis. Over the momentum range relevant for this analysis, the pion
identification requirements are $81\%$ efficient at identifying pions, while
they have $3.1\%$ and $2.6\%$ probabilities respectively to misidentify a kaon
or a proton as a pion. Since the production of $B^{**0}_{s}$ mesons is likely
to be suppressed relative to the production of $B^{**}$ states, as has been
observed for the ground states [42, 43], these requirements are expected to
reduce background from the decays $B_{s1}(5830)^{0}\rightarrow B^{*+}K^{-}$
and $B_{s2}^{*}(5840)^{0}\rightarrow B^{*+}K^{-}\ {\rm or}\ B^{+}K^{-}$, where
the kaon is misidentified as a pion, to a negligible level.

Further selection requirements are placed on the $B^{**}$ candidate. The
invariant mass and $\chi^{2}/\mathrm{ndf}$ (ndf is the number of degrees of
freedom) of the $B^{**}$ candidate vertex fit are calculated constraining the
$B$ candidates and companion pion to originate from the PV, and also
constraining the known $B$ meson mass, and the masses of intermediate
${J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}$, $\kern
1.99997pt\overline{\kern-1.99997ptD}{}^{0}$ and $D^{-}$ mesons in the $B$
decay. The $\chi^{2}/\mathrm{ndf}$ of the $B^{**}$ candidate vertex fit is
then required to be below $3.5$. In order to reduce combinatorial backgrounds,
the PV associated with the $B^{**}$ candidate is required to have fewer than
75 charged particles associated with it. The angle $\theta$ is required to
satisfy $\cos\theta>-0.5$, where $\theta$ is the angle between the pion in the
$B\pi$ rest frame and the opposite direction of the boost vector from the
$B\pi$ rest frame to the laboratory frame.

Finally, the companion pion is required to have more than ($0.5$)
$5\mathrm{\,Ge\kern-1.00006ptV}$ of (transverse) momentum, while the $B$
candidate is required to have $\mbox{$p_{\rm
T}$}>10\mathrm{\,Ge\kern-1.00006ptV}$ for candidates where the companion pion
has $\mbox{$p_{\rm T}$}>2\mathrm{\,Ge\kern-1.00006ptV}$. In any selected
event, the $B$ candidate can potentially be combined with several different
pions to create $B^{**}$ candidates. The average number of candidates per
selected event is 1.4 and all of them are used for the subsequent analysis.

##  4 Fit model

Figure 3:  Distributions of the $Q$ values of the $B^{**}$ candidates after
the selection for the (top) $B^{+}$ and (bottom) $B^{0}$ candidates. The white
histograms represent the RS combinations, while the overlaid shaded red
histograms represent the WS combinations. The right hand plots are made after
applying an additional requirement of $\mbox{$p_{\rm
T}$}>2\mathrm{\,Ge\kern-1.00006ptV}$ on the companion pion.

The distributions of the mass difference, $Q\equiv m(B\pi)-m(B)-m(\pi)$,
following these selection requirements are shown in Fig. 3 for both RS and WS
$B^{**}$ candidates, where $m_{B}$ and $m_{\pi}$ are the known masses of the
$B$ meson and the pion [2]. All $B$ decay modes are combined in Fig. 3 and in
the subsequent analysis. Two narrow peaks are seen in both $B^{+}\pi^{-}$ and
$B^{0}\pi^{+}$ mass difference distributions, corresponding to the
$B_{1}(5721)^{0,+}\rightarrow B^{*}\pi$ signal overlapping with the
$B_{2}^{*}(5747)^{0,+}\rightarrow B^{*}\pi$ decay, and the
$B_{2}^{*}(5747)^{0,+}\rightarrow B\pi$ decay. In addition, an excess of RS
over WS combinations around $Q\sim 500\mathrm{\,Me\kern-1.00006ptV}$ is
particularly prominent after requiring the companion pion to have
$\mbox{$p_{\rm T}$}>2\mathrm{\,Ge\kern-1.00006ptV}$. This peak could result
from a combination of two heavier $B^{**}$ resonances, consistent with the
expectation that $B^{**}$ states come in doublets, as described in Sec. 1; the
structure is further analysed as described below. Furthermore, a comparison
with the WS distributions shows a very broad excess of RS combinations lying
under the resonances, corresponding to AP as discussed in Sec. 1.

The $Q$-value distributions of $B^{+}\pi^{-}$ and $B^{0}\pi^{+}$ candidates
are fitted independently to determine the masses and widths of the various
resonant signals. In order to increase sensitivity to the parameters of the
high mass states, the fits are performed in three bins of companion pion
$p_{\rm T}$: $0.5<\mbox{$p_{\rm T}$}\leq 1\mathrm{\,Ge\kern-1.00006ptV}$,
$1<\mbox{$p_{\rm T}$}\leq 2\mathrm{\,Ge\kern-1.00006ptV}$ and $\mbox{$p_{\rm
T}$}>2\mathrm{\,Ge\kern-1.00006ptV}$. The fits minimise the total $\chi^{2}$
of the $Q$-value distributions (in bins of width
$1\mathrm{\,Me\kern-1.00006ptV}$) simultaneously for the three companion pion
$p_{\rm T}$ bins.

The combinatorial background shape is obtained from WS combinations. It has
been checked that the WS background consists of purely combinatorial
background by studying $B\pi$ combinations in which a $B$ meson from one event
is combined with a companion pion from another event; consistent shapes are
found. The WS $Q$-value distributions are fitted with piecewise-defined,
smooth polynomial (“spline”) functions. The shape is fixed in the subsequent
fit to the RS distribution, but the yield is allowed to vary.

Resonances are modelled with RBW lineshapes [44], given by

$A_{\rm
RBW}(m)=\frac{\Gamma(m)}{\left(m^{2}-m_{0}^{2}\right)^{2}+m_{0}^{2}\Gamma^{2}(m)}\,,$
(1)

where $m$ is the $B\pi$ invariant mass (which is trivially related to the $Q$
value), $m_{0}$ is the mass value for the resonance222The mass difference
$m_{0}-m(B)-m(\pi)$ is referred to as the mean $\mu$ hereafter. and
$\Gamma(m)$ is the mass dependent width

$\Gamma(m)=\Gamma_{0}\frac{m_{0}}{m}\left(\frac{q(m)}{q(m_{0})}\right)^{2l+1}{\mathcal{F}}_{l}^{2}\,.$
(2)

In the latter equation $\Gamma_{0}$ is the natural width, $q(m)$ is the $B$ or
$\pi$ momentum in the rest frame of the resonance and $l$ is the orbital
angular momentum between the $B$ and $\pi$ mesons. The Blatt-Weisskopf form
factors ${\mathcal{F}}_{l}$ [45, 46] account for the fact that the maximum
angular momentum is limited by the phase-space in the decay. Defining the
dimensionless quantity $z(m)=q^{2}(m)R^{2}$, where $R$ is the effective
radius, ${\mathcal{F}_{l}}$ is defined as

$\displaystyle{\mathcal{F}_{0}}$ $\displaystyle=$ $\displaystyle 1\,,$ (3)
$\displaystyle{\mathcal{F}_{1}}$ $\displaystyle=$
$\displaystyle\sqrt{\frac{1+z(m_{0})}{1+z(m)}}\,,$ (4)
$\displaystyle{\mathcal{F}_{2}}$ $\displaystyle=$
$\displaystyle\sqrt{\frac{\left(z(m_{0})-3\right)^{2}+9z(m_{0})}{\left(z(m)-3\right)^{2}+9z(m)}}\,.$
(5)

Depending on the fit model, the $B^{**}$ resonances are described by five or
six RBW shapes:

  * •

one for the $B_{1}(5721)^{0,+}\rightarrow B^{*}\pi$ feed-down into the left
narrow peak with width, yield, and mean free to vary in the fits;

  * •

one for the $B_{2}^{*}(5747)^{0,+}\rightarrow B\pi$ signal (the right narrow
peak) with width, yield, and mean free to vary in the fits;

  * •

one for the $B_{2}^{*}(5747)^{0,+}\rightarrow B^{*}\pi$ feed-down into the
left narrow peak with width fixed to be the same as that of the
$B_{2}^{*}(5747)^{0,+}\rightarrow B\pi$ signal, mean shifted from the
$B_{2}^{*}(5747)^{0,+}\rightarrow B\pi$ peak by the known $B^{*}-B$ mass
difference, $45.0\pm 0.4$ $\mathrm{\,Me\kern-1.00006ptV}$ [2], and relative
yield in $p_{\rm T}$ bins constrained as described later;

  * •

two (or three) for the higher mass components, with widths, means, and yields
free to vary in the fits (except in the three RBW case, where two of the means
are constrained by the $B^{*}-B$ mass difference).

The alternative descriptions for the higher mass resonances are motivated by
the lack of knowledge of their quantum numbers. As described in Sec. 1, a
doublet of states is expected to give rise to three peaks. For example, for
the $(B(2{\rm S}),B^{*}(2{\rm S}))$ doublet the higher (lower) mass of the
pair has natural (unnatural) spin-parity. The description with three RBW
shapes, two of which are constrained to have means offset by the $B^{*}-B$
mass difference, is therefore a physically motivated choice, obtained by
applying quark-model expectations to the new states. However, there are two
possibilities for this configuration, since it may be either the lower or the
higher of the states that gives rise to two peaks. The alternative, with only
two RBW shapes, is an empirical model, that corresponds to the minimal choice
necessary to obtain a satisfactory description of the data. This is taken as
the default and is referred to hereafter as the empirical model, but results
of alternative fits with three RBW shapes are also presented.

The RBW shapes have several parameters which need to be fixed in the fits, in
particular the spin and effective radius input to the Blatt-Weisskopf form
factors. The $B_{1}(5721)^{0,+}$ and $B_{2}^{*}(5747)^{0,+}$ resonances are
assigned spin 1 and 2, respectively, and are both assumed to decay via D-wave
($l=2$), while the two higher mass resonances are assigned spin 0 ($l=0$) in
the default fit. The effective radius is fixed to
$4\mathrm{\,Ge\kern-1.00006ptV}^{-1}$ [13]. The mass resolution is around
$2\mathrm{\,Me\kern-1.00006ptV}$ which is negligible compared to the natural
widths ($>20\mathrm{\,Me\kern-1.00006ptV}$) of the resonances, and is
therefore not modelled. The variation of the signal reconstruction efficiency
with $Q$ value is described with a fifth-order polynomial function with
parameters determined from simulation. All signal parameters except the yields
are shared between the different $p_{\rm T}$ bins and $B$ meson decay modes,
though the efficiency function is determined independently for each $p_{\rm
T}$ bin.

The AP component is caused by correlations between the $B$ meson and the
companion pion, and as such is not present in either the WS sample or in a
sample obtained by mixing $B$ mesons and pions from different events. As there
is no suitable data control sample from which it can be constrained, it must
be empirically modelled. The AP is modelled by a sixth-order polynomial shape
determined from simulation with an additional broad spin-0 RBW function to
account for possible data-simulation differences. The latter component is
introduced since the modelling of fragmentation effects in the simulation is
expected to be imprecise.

The relative yields of $B_{2}^{*}(5747)^{0,+}\rightarrow B^{*}\pi$ and $B\pi$
in each $p_{\rm T}$ bin are fixed according to the relative efficiencies found
in simulation, so that the relative branching fraction ratios ${\cal
B}(B_{2}^{*}(5747)^{0,+}\rightarrow B^{*}\pi)/{\cal
B}(B_{2}^{*}(5747)^{0,+}\rightarrow B\pi)$ are free parameters of the fits.
The WS and AP yields are freely varied in the fits, independently in each
$p_{\rm T}$ bin. The RBW parameters of the AP shape are also freely varied;
the remaining parameters are fixed to the values obtained from simulation to
avoid instabilities in the fits. The fit procedure is validated using large
ensembles of pseudoexperiments.

##  5 Fit results

The results of the empirical model fits to the $B^{**}$ candidates integrated
over the three $p_{\rm T}$ bins are shown in Fig. 4. The results are also
shown split by $p_{\rm T}$ bin in Fig. 5, where the plots have been zoomed
into the range below $800\mathrm{\,Me\kern-1.00006ptV}$ in order to emphasise
the resonant structures. The results for the parameters of interest are
reported in Table 2.

Table 2:  Results of the fits when two RBW functions are used for the $B_{J}(5840)^{0,+}$ and $B_{J}(5960)^{0,+}$ states (empirical model). The mean $\mu$ of each peak is given together with the width $\Gamma$ and the yield $N_{\textrm{state}}$. The parameters related to the AP and WS components are suppressed for brevity. All uncertainties are statistical only. Units of $\mathrm{\,Me\kern-1.00006ptV}$ for $\mu$ and $\Gamma$ are implied.  Fit parameter | $\phantom{11}B^{+}\pi^{-}$ | $\phantom{11}B^{0}\pi^{+}$
---|---|---
$B_{1}(5721)^{0,+}$ $\mu$ | $263.9\pm 0.7$ | $260.9\pm 1.8$
$B_{1}(5721)^{0,+}$ $\Gamma$ | $\phantom{1}30.1\pm 1.5$ | $\phantom{1}29.1\pm 3.6$
$B_{2}^{*}(5747)^{0,+}$ $\mu$ | $320.6\pm 0.4$ | $318.1\pm 0.7$
$B_{2}^{*}(5747)^{0,+}$ $\Gamma$ | $\phantom{1}24.5\pm 1.0$ | $\phantom{1}23.6\pm 2.0$
$N_{B_{1}(5721)^{0,+}}$ low $p_{\rm T}$ | $14200\pm 1400$ | $3140\pm 750$
$N_{B_{1}(5721)^{0,+}}$ mid $p_{\rm T}$ | $16200\pm 1500$ | $4020\pm 890$
$N_{B_{1}(5721)^{0,+}}$ high $p_{\rm T}$ | $\phantom{1}4830\pm\phantom{1}470$ | $\phantom{1}940\pm 260$
$N_{B_{2}^{*}(5747)^{0,+}}$ low $p_{\rm T}$ | $\phantom{1}7450\pm\phantom{1}420$ | $1310\pm 180$
$N_{B_{2}^{*}(5747)^{0,+}}$ mid $p_{\rm T}$ | $\phantom{1}7600\pm\phantom{1}340$ | $2070\pm 180$
$N_{B_{2}^{*}(5747)^{0,+}}$ high $p_{\rm T}$ | $\phantom{1}1690\pm\phantom{1}130$ | $\phantom{1}640\pm\phantom{1}80$
${\cal B}(B_{2}^{*}(5747)^{0,+}\rightarrow B^{*}\pi)/{\cal B}(B_{2}^{*}(5747)^{0,+}\rightarrow B\pi)$ | $\phantom{1}0.71\pm 0.14$ | $\phantom{1}1.0\pm 0.5$
$B_{J}(5840)^{0,+}$ $\mu$ | $444\pm\phantom{1.}5$ | $431\pm\phantom{.}13$
$B_{J}(5840)^{0,+}$ $\Gamma$ | $127\pm\phantom{.}17$ | $224\pm\phantom{.}24$
$B_{J}(5960)^{0,+}$ $\mu$ | $550.4\pm 2.9\phantom{1.}$ | $545.8\pm 4.1\phantom{1.}$
$B_{J}(5960)^{0,+}$ $\Gamma$ | $\phantom{1}82\pm\phantom{1.}8$ | $\phantom{1}63\pm\phantom{.}15$
$N_{B_{J}(5840)^{0,+}}$ low $p_{\rm T}$ | $3200\pm 1300$ | $1630\pm 970$
$N_{B_{J}(5840)^{0,+}}$ mid $p_{\rm T}$ | $5600\pm 1000$ | $3230\pm 720$
$N_{B_{J}(5840)^{0,+}}$ high $p_{\rm T}$ | $3090\pm\phantom{1}550$ | $2280\pm 450$
$N_{B_{J}(5960)^{0,+}}$ low $p_{\rm T}$ | $3270\pm\phantom{1}660$ | $\phantom{1}610\pm 240$
$N_{B_{J}(5960)^{0,+}}$ mid $p_{\rm T}$ | $4590\pm\phantom{1}610$ | $\phantom{1}910\pm 250$
$N_{B_{J}(5960)^{0,+}}$ high $p_{\rm T}$ | $2400\pm\phantom{1}320$ | $\phantom{1}500\pm 140$

Note that the reported mean values correspond to the peak positions, and do
not include any correction for the $B^{*}-B$ mass difference, but when a state
is assumed to have natural spin-parity, and therefore gives two peaks, the
mass value reported is that of the higher peak. The results are consistent for
the charged and neutral states, as expected since the uncertainties are larger
than isospin splitting effects. The results for the higher mass states depend
on whether they are assumed to have natural or unnatural spin-parity, and the
results with the alternative hypotheses are presented in Table 3. For the
purpose of labelling, and without prejudice on their quantum numbers, the
lower of these states is referred to subsequently as the $B_{J}(5840)^{0,+}$
and the other as the $B_{J}(5960)^{0,+}$ state.

Figure 4:  Result of the fits to the $Q$-value distributions for (top)
$B^{+}\pi^{-}$ and (bottom) $B^{0}\pi^{+}$ candidates. The components are
labelled in the legend. The normalised residuals (pulls) of the difference
between the fit results and the data points, divided by their uncertainties,
are shown underneath each plot.

$1\geq\mbox{$p_{\rm T}$}>0.5$GeV$1\geq\mbox{$p_{\rm T}$}>0.5$GeV
$2\geq\mbox{$p_{\rm T}$}>1$GeV$2\geq\mbox{$p_{\rm T}$}>1$GeV
$\mbox{$p_{\rm T}$}>2$GeV$\mbox{$p_{\rm T}$}>2$GeV

Figure 5:  Result of the fit to (left) $B^{+}\pi^{-}$ and (right)
$B^{0}\pi^{+}$ candidates, split into (top to bottom) low, medium and high
$p_{\rm T}$ bins, with ranges as labelled on the plots. The components are
labelled in the legends. The fit pulls are shown underneath each plot.

The covariance matrix of the empirical model fit is given in Appendix A. For
brevity, the results for the signal yields and for the background parameters
are not reported. The magnitudes of the correlations between the signal
observables and background shapes are smaller than $30\%$. All fits have
acceptable minimum $\chi^{2}$ values.

Table 3:  Results of the fits when the natural spin-parity hypothesis is assigned to (top quadruplet) the $B_{J}(5840)^{0,+}$ state or (bottom quadruplet) the $B_{J}(5960)^{0,+}$ state, so that three RBW shapes are used to model the broad resonances in the fit. The mean $\mu$ of each peak is given together with the width $\Gamma$. All uncertainties are statistical only. Units of $\mathrm{\,Me\kern-1.00006ptV}$ for $\mu$ and $\Gamma$ are implied.  Fit parameter | $B^{+}\pi^{-}$ | $B^{0}\pi^{+}$
---|---|---
$B_{J}(5840)^{0,+}$ $\mu$ | $471\pm 22$ | $455\pm 26$
$B_{J}(5840)^{0,+}$ $\Gamma$ | $107\pm 20$ | $215\pm 27$
$B_{J}(5960)^{0,+}$ $\mu$ | $552\pm\phantom{1}4$ | $547\pm\phantom{1}4$
$B_{J}(5960)^{0,+}$ $\Gamma$ | $\phantom{1}82\pm 10$ | $\phantom{1}61\pm 15$
$B_{J}(5840)^{0,+}$ $\mu$ | $444\pm\phantom{1}5$ | $425\pm 15$
$B_{J}(5840)^{0,+}$ $\Gamma$ | $119\pm 17$ | $229\pm 27$
$B_{J}(5960)^{0,+}$ $\mu$ | $575\pm\phantom{1}6$ | $547\pm\phantom{1}5$
$B_{J}(5960)^{0,+}$ $\Gamma$ | $\phantom{1}56\pm\phantom{1}7$ | $\phantom{1}61\pm 14$

##  6 Systematic uncertainties

Systematic uncertainties are evaluated in a data-driven manner, by varying fit
parameters or configurations from their default values and taking the
difference in the fit results as a systematic uncertainty. Summaries of the
systematic uncertainties are given in Tables 4 and 5 for $B^{+}\pi^{-}$ and
$B^{0}\pi^{+}$ resonances.The total systematic uncertainties on each
individual parameter are obtained by combining all sources in quadrature.

Table 4:  Systematic uncertainties on the results of the fit to the
$B^{+}\pi^{-}$ candidates. Units of $\mathrm{\,Me\kern-1.00006ptV}$ for $\mu$
and $\Gamma$ are implied.

Source | $B_{1}(5721)^{0}$ | $B_{2}^{*}(5747)^{0}$ | $B_{J}(5840)^{0}$ | $B_{J}(5960)^{0}$
---|---|---|---|---
| $\mu$ | $\Gamma$ | BF ratio | $\mu$ | $\Gamma$ | $\mu$ | $\Gamma$ | $\mu$ | $\Gamma$
Total statistical | 0.72 | 1.52 | 0.14 | 0.37 | 1.01 | 4.95 | 16.70 | 2.88 | 7.71
Fit range (high) | 0.33 | 1.30 | 0.06 | 0.08 | 0.37 | 2.20 |  12.90 | 0.52 | 0.26
Fit range (low) | 0.04 | 0.11 | 0.01 | 0.02 | 0.39 | 0.04 |  18.22 | 0.69 | 2.83
$2\mathrm{\,Me\kern-1.00006ptV}$ bins | 0.02 | 0.14 | 0.00 | 0.04 | 0.07 | 1.09 |  10.50 | 0.08 | 1.00
Spline knots | 0.11 | 0.01 | 0.02 | 0.02 | 0.26 | 1.75 |  10.04 | 0.45 | 1.44
Float AP | 0.03 | 0.00 | 0.00 | 0.03 | 0.30 | 1.58 | 10.16 | 0.73 | 4.23
$B_{2}^{*}(5747)^{0}$ rel. eff., low $p_{\rm T}$ | 0.56 | 0.91 | 0.15 | 0.08 | 0.16 | 0.07 |  10.23 | 0.00 | 0.18
$B_{2}^{*}(5747)^{0}$ rel. eff., mid $p_{\rm T}$ | 0.64 | 1.01 | 0.05 | 0.09 | 0.18 | 0.08 |  10.26 | 0.00 | 0.16
$B_{2}^{*}(5747)^{0}$ rel. eff., high $p_{\rm T}$ | 0.20 | 0.37 | 0.03 | 0.02 | 0.07 | 0.02 |  10.00 | 0.01 | 0.09
Eff. variation with $Q$ value | 0.13 | 0.33 | 0.02 | 0.04 | 0.07 | 0.45 |  12.46 | 0.19 | 0.70
Data-simulation reweighting | 0.07 | 0.38 | 0.02 | 0.00 | 0.16 | 1.81 |  12.03 | 0.49 | 0.12
$B$ $p_{\rm T}$ | 0.02 | 0.20 | 0.01 | 0.24 | 0.72 | 3.98 |  13.67 | 1.30 | 4.29
$p_{\rm T}$ binning | 0.90 | 2.45 | 0.24 | 0.06 | 0.39 | 1.49 | 27.77 | 4.20 | 1.47
Fit bias | 0.06 | 0.17 | 0.01 | 0.00 | 0.16 | 0.45 |  15.34 | 0.40 | 2.24
Spin | 0.02 | 0.06 | 0.01 | 0.06 | 0.46 | 1.95 |  13.32 | 0.62 | 3.74
Effective radius | 0.33 | 1.44 | 0.02 | 0.12 | 0.76 | 2.17 |  19.68 | 1.24 | 3.81
$B^{*}-B$ mass | 0.10 | 0.11 | 0.03 | 0.02 | 0.11 | 0.04 |  10.17 | 0.00 | 0.09
$B_{J}(5840)^{0}$ $J^{P}$ | 0.01 | 0.04 | 0.00 | 0.01 | 0.01 | — | — | 1.67 | 0.76
$B_{J}(5960)^{0}$ $J^{P}$ | 0.01 | 0.20 | 0.00 | 0.00 | 0.16 | 0.18 |  18.00 | — | —
Extra state | 0.00 | 0.26 | 0.00 | 0.04 | 0.34 | 1.67 |  10.99 | 0.12 | 2.08
Total systematic | 1.36 | 3.49 | 0.30 | 0.33 | 1.48 | 6.68 | 34.24 | 5.10 | 9.41

Table 5:  Systematic uncertainties on the results of the fit to the
$B^{0}\pi^{+}$ candidates. Units of $\mathrm{\,Me\kern-1.00006ptV}$ for $\mu$
and $\Gamma$ are implied.

Source | $B_{1}(5721)^{+}$ | $B_{2}^{*}(5747)^{+}$ | $B_{J}(5840)^{+}$ | $B_{J}(5960)^{+}$
---|---|---|---|---
| $\mu$ | $\Gamma$ | BF ratio | $\mu$ | $\Gamma$ | $\mu$ | $\Gamma$ | $\mu$ | $\Gamma$
Total statistical | 1.81 | 3.57 | 0.51 | 0.72 | 1.99 | 12.70 | 23.90 | 4.07 | 14.50
Fit range (high) | 0.35 | 0.74 | 0.10 | 0.11 | 0.25 |  11.51 | 12.85 | 0.38 |  10.46
Fit range (low) | 0.64 | 1.13 | 0.13 | 0.06 | 0.13 |  17.85 | 39.71 | 0.14 |  11.44
$2\mathrm{\,Me\kern-1.00006ptV}$ bins | 0.16 | 0.34 | 0.05 | 0.10 | 0.49 |  10.58 |  13.84 | 0.28 |  10.52
Spline knots | 0.30 | 0.08 | 0.07 | 0.03 | 0.22 |  11.94 |  12.64 | 0.25 |  10.25
Float AP | 0.02 | 0.31 | 0.01 | 0.02 | 0.03 |  12.91 |  12.44 | 0.19 |  12.24
$B_{2}^{*}(5747)^{+}$ rel. eff, low $p_{\rm T}$ | 1.50 | 2.14 | 0.43 | 0.12 | 0.49 |  10.15 |  11.63 | 0.02 |  10.03
$B_{2}^{*}(5747)^{+}$ rel. eff, mid $p_{\rm T}$ | 1.55 | 2.26 | 0.53 | 0.12 | 0.51 |  10.29 |  12.03 | 0.04 |  10.15
$B_{2}^{*}(5747)^{+}$ rel. eff, high $p_{\rm T}$ | 0.49 | 0.90 | 0.11 | 0.03 | 0.12 |  10.10 |  10.84 | 0.02 |  10.07
Eff. variation with $Q$ value | 0.07 | 0.27 | 0.02 | 0.03 | 0.10 |  11.65 |  17.28 | 0.16 |  10.94
Data-simulation reweighting | 0.04 | 0.38 | 0.03 | 0.00 | 0.02 |  12.13 |  17.49 | 0.40 |  11.75
$B$ $p_{\rm T}$ | 0.45 | 1.38 | 0.17 | 0.14 | 0.54 |  11.16 |  17.79 | 0.98 |  14.65
$p_{\rm T}$ binning | 1.82 | 1.03 | 0.26 | 0.15 | 1.38 |  10.54 | 55.56 | 0.94 | 11.43
Fit bias | 0.14 | 0.39 | 0.04 | 0.01 | 0.32 |  11.14 |  17.65 | 0.57 |  14.21
Spin | 0.14 | 0.33 | 0.05 | 0.15 | 0.94 |  14.18 | 24.49 | 1.67 |  15.98
Effective radius | 0.70 | 1.48 | 0.12 | 0.19 | 0.29 |  12.82 | 22.15 | 0.39 |  13.76
$B^{*}-B$ mass | 0.21 | 0.06 | 0.07 | 0.01 | 0.15 |  10.32 |  10.48 | 0.03 |  10.07
$B_{J}(5840)^{+}$ $J^{P}$ | 0.00 | 0.05 | 0.00 | 0.03 | 0.15 | — | — | 0.72 |  11.64
$B_{J}(5960)^{+}$ $J^{P}$ | 0.02 | 0.01 | 0.01 | 0.04 | 0.26 |  15.99 |  14.86 | — | —
Extra state | 0.03 | 0.41 | 0.00 | 0.00 | 0.15 |  16.28 | 12.82 | 0.43 |  17.81
Total systematic | 3.10 | 4.28 | 0.79 | 0.40 | 2.07 | 13.70 | 79.82 | 2.52 | 17.18

The covariance matrix of the systematic uncertainties, given in Appendix A, is
computed by considering the correlated effects on the fit parameters of the
systematic uncertainties.

The modelling of the background shapes may depend on the choice of fit range.
The upper and lower edges of the range are varied independently by 20% to
assign systematic uncertainties. Similarly, any dependence of the results on
the choice of bin width is evaluated by repeating the fits with 2 (instead of
1) $\mathrm{\,Me\kern-1.00006ptV}$ binning. Additional uncertainties due to
the background modelling are assigned by varying the spline function used to
describe the WS distribution and by varying parameters of the AP polynomial
function.

The relative efficiencies of the $B_{2}^{*}(5747)$ decays to $B^{*}\pi$ and
$B\pi$ in each of the three $p_{\rm T}$ bins are fixed in the nominal fit.
These are varied independently to assign systematic uncertainties. The
uncertainties in the dependence of the efficiency on $Q$ value are propagated
to the results by repeating the fit after varying, within their errors, the
parameters of the polynomial function used to describe the variation.
Uncertainties are assigned for possible differences between data and
simulation in the efficiency function by reweighting the simulation to match
the $B$ momentum distributions observed in data. Uncertainties are also
assigned to take in account the effect of changing the $\mbox{$p_{\rm
T}$}>3\mathrm{\,Ge\kern-1.00006ptV}$ cut on the $B$ candidate to
$\mbox{$p_{\rm T}$}>4\mathrm{\,Ge\kern-1.00006ptV}$, and of varying the
boundaries of the three bins of the companion pion $p_{\rm T}$.

Possible biases in the fits are investigated with ensembles of
pseudoexperiments. No significant bias is found for most of the parameters,
but shifts in the means and widths of the $B_{J}(5840)^{0}$ and
$B_{J}(5960)^{0}$ states of up to 30% of the statistical uncertainty are found
and corrected for. Systematic uncertainties corresponding to the size of the
bias seen in the ensembles are assigned to all parameters.

Further systematic uncertainties are evaluated for the fixed fit parameters.
The spins of the higher mass states are changed from zero to two, the Blatt-
Weisskopf effective radius is varied from its nominal value of
$4\mathrm{\,Ge\kern-1.00006ptV}^{-1}$ to $2$ and
$6\mathrm{\,Ge\kern-1.00006ptV}^{-1}$, and the $B^{*}-B$ mass difference is
varied within its uncertainty [2]. The effects on the other parameters of the
fit, when the $B_{J}(5840)^{0}$ and $B_{J}(5960)^{0}$ states are assumed to
have natural spin-parity and hence contribute two peaks to the spectrum, are
assigned as systematic uncertainties; the effects on the parameters of the
$B_{J}(5840)^{0}$ and $B_{J}(5960)^{0}$ states themselves when changing this
assumption are presented in Table 3. Finally, the fits are repeated allowing
for an additional state with a peak around $Q\sim
800\mathrm{\,Me\kern-1.00006ptV}$. The additional state is not statistically
significant, but the changes in the fitted parameters are assigned as
systematic uncertainties. The systematic uncertainties due to the momentum
scale calibration are found to be negligible.

In addition, various cross-checks are performed to ensure fit stability and
reliability. The stability of the data fits is studied by splitting the sample
by the year of data taking, magnet polarity, and the charge of the companion
pion. The resulting independent samples are fitted using the same
configuration as the nominal fit, and the results within each split are found
to be consistent.

##  7 Interpretation and conclusions

The analysis of the invariant mass spectra of $B^{+}\pi^{-}$ and
$B^{0}\pi^{+}$ combinations reconstructed with the LHCb detector reported in
this paper provides measurements of the properties of a number of $B^{**}$
resonant states. The interpretation of the results is now given in two parts:
firstly for the narrow $B^{**}$ signals, and subsequently for the broad,
higher mass $B^{**}$ signals.

The narrow states are identified with the previously observed
$B_{1}(5721)^{0}$ and $B_{2}^{*}(5747)^{0}$ states, and their
$B_{1}(5721)^{+}$ and $B_{2}^{*}(5747)^{+}$ isospin counterparts. The peak
positions in the $Q$-value distributions reported in Sec. 5 can be converted
into absolute masses using the known $B$ and $\pi$ meson masses and the
$B^{*}-B$ mass difference [2], leading to

$\begin{array}[]{rccccccccccc}\displaystyle
m_{B_{1}(5721)^{0}}&=&5727.7\phantom{1}&\pm&0.7\phantom{1}&\pm&1.4\phantom{1}&\pm&0.17&\pm&0.4&\mathrm{\,Me\kern-1.00006ptV}\,,\\\
\displaystyle
m_{B_{2}^{*}(5747)^{0}}&=&5739.44&\pm&0.37&\pm&0.33&\pm&0.17&&&\mathrm{\,Me\kern-1.00006ptV}\,,\\\
\displaystyle
m_{B_{1}(5721)^{+}}&=&5725.1\phantom{1}&\pm&1.8\phantom{1}&\pm&3.1\phantom{1}&\pm&0.17&\pm&0.4&\mathrm{\,Me\kern-1.00006ptV}\,,\\\
\displaystyle
m_{B_{2}^{*}(5747)^{+}}&=&5737.20&\pm&0.72&\pm&0.40&\pm&0.17&&&\mathrm{\,Me\kern-1.00006ptV}\,,\\\
\displaystyle\Gamma_{B_{1}(5721)^{0}}&=&\phantom{1}\phantom{1}30.1\phantom{1}&\pm&1.5\phantom{1}&\pm&3.5\phantom{1}&&&&&\mathrm{\,Me\kern-1.00006ptV}\,,\\\
\displaystyle\Gamma_{B_{2}^{*}(5747)^{0}}&=&\phantom{1}\phantom{1}24.5\phantom{1}&\pm&1.0\phantom{1}&\pm&1.5\phantom{1}&&&&&\mathrm{\,Me\kern-1.00006ptV}\,,\\\
\displaystyle\Gamma_{B_{1}(5721)^{+}}&=&\phantom{1}\phantom{1}29.1\phantom{1}&\pm&3.6\phantom{1}&\pm&4.3\phantom{1}&&&&&\mathrm{\,Me\kern-1.00006ptV}\,,\\\
\displaystyle\Gamma_{B_{2}^{*}(5747)^{+}}&=&\phantom{1}\phantom{1}23.6\phantom{1}&\pm&2.0\phantom{1}&\pm&2.1\phantom{1}&&&&&\mathrm{\,Me\kern-1.00006ptV}\,.\end{array}$

The listed uncertainties are, from left to right: the statistical uncertainty,
the experimental systematic uncertainty, and, where applicable, the
uncertainty on the $B$ meson mass and the uncertainty on the $B^{*}-B$ mass
difference. Note that $B_{1}(5721)^{0,+}$ and $B_{2}^{*}(5747)^{0,+}$
notations are maintained here for consistency with the previous literature,
even though the values of the masses no longer agree with these labels within
uncertainty. The results reported above are the most precise determinations of
these quantities to date.

The relative branching fractions for the $B_{2}^{*}(5747)^{0,+}$ decays are
measured to be

$\begin{array}[]{rcccccc}\displaystyle\frac{{\cal
B}\left(B_{2}^{*}(5747)^{0}\rightarrow B^{*+}\pi^{-}\right)}{{\cal
B}\left(B_{2}^{*}(5747)^{0}\rightarrow
B^{+}\pi^{-}\right)}&=&0.71&\pm&0.14&\pm&0.30\,,\\\ \\\
\displaystyle\frac{{\cal B}\left(B_{2}^{*}(5747)^{+}\rightarrow
B^{*0}\pi^{+}\right)}{{\cal B}\left(B_{2}^{*}(5747)^{+}\rightarrow
B^{0}\pi^{+}\right)}&=&1.0\phantom{1}&\pm&0.5\phantom{1}&\pm&0.8\phantom{1}\,,\end{array}$

where the uncertainties are statistical and systematic, respectively. The
significances of the $B_{2}^{*}(5747)^{0,+}\rightarrow B^{*}\pi$ decays are
evaluated using a likelihood ratio test. Values of $6.5\sigma$ and $1.8\sigma$
are obtained for $B^{*+}\pi^{-}$ and $B^{*0}\pi^{+}$, respectively, when only
the statistical uncertainty is considered. The inclusion of systematic
uncertainties reduces the significance for the $B^{*+}\pi^{-}$ case to
$3.7\sigma$. This result therefore corresponds to the first evidence for the
$B_{2}^{*}(5747)^{0}\rightarrow B^{*+}\pi^{-}$ decay. The relative branching
fractions for the $B_{2}^{*}(5747)^{0,+}$ decays are in agreement with
theoretical predictions [47, 48, 49, 50, 10].

Structures at higher mass are clearly observed in the $Q$-value distributions.
To investigate the significance of the high mass states, large samples of
pseudoexperiments are generated and fitted with different configurations. To
cover the dominant systematic uncertainty on the yield of these states which
arises due to lack of knowledge of the shape of the AP component, the
pseudoexperiments are generated with the AP shape that minimises the
significance. A first ensemble is generated without any high mass states
included. Each pseudoexperiment in this ensemble is fitted twice, once with
the same model as used for generation and once with an additional high mass
resonance included. The distribution of the difference of $\chi^{2}$ values
between the two fits is extrapolated to obtain the $p$-value corresponding to
the probability to find a $\chi^{2}$ difference as large or larger than that
obtained from the corresponding fits to data. This procedure gives
significances of $9.6\sigma$ for the $B^{+}\pi^{-}$ case and $4.8\sigma$ for
the $B^{0}\pi^{+}$ case.

A second ensemble of pseudoexperiments is generated with a configuration that
corresponds to the best fit to the data with a single high mass resonance. The
pseudoexperiments in this ensemble are fitted both with the model used for
generation and with a second high mass resonance included. The significances
of the second peaks, again obtained from the difference in $\chi^{2}$ values,
are found to be $7.5\sigma$ and $4.6\sigma$ for the $B^{+}\pi^{-}$ and
$B^{0}\pi^{+}$ cases, respectively. Since isospin symmetry is expected to hold
for these states, this shows that under the hypothesis that the high mass
structures are due to resonances, two new pairs of particles are observed.

Masses and widths of the $B_{J}(5840)^{0,+}$ and $B_{J}(5960)^{0,+}$ states
are obtained with different fit models, as discussed in Sec. 4, and the
corresponding results are shown in Table 6. The properties of the
$B_{J}(5960)^{0,+}$ states are consistent with and more precise than those
obtained by the CDF collaboration when assuming decay to $B\pi$ [16]. If the
$B_{J}(5840)^{0,+}$ and $B_{J}(5960)^{0,+}$ states are considered under the
quark model hypothesis, their properties are consistent with those expected
for the $B(2{\rm S})$ and $B^{*}(2{\rm S})$ radially excited states.

Table 6:  Parameters of the $B_{J}(5840)^{0,+}$ and $B_{J}(5960)^{0,+}$ states obtained with different fit models. The empirical fit uses two, and the quark model fits three, RBW shapes to model the broad resonances. The listed uncertainties are, from left to right: the statistical uncertainty, the experimental systematic uncertainty, and, where applicable, the uncertainty on the $B$ meson mass and the uncertainty on the $B^{*}-B$ mass difference. Note that any state not explicitly labelled as “natural” is considered to have unnatural spin-parity (and not to be $0^{+}$); the reported mass can be converted into the corresponding result under the $0^{+}$ spin-parity assumption by subtracting the $B^{*}-B$ mass difference. Units of $\mathrm{\,Me\kern-1.00006ptV}$ are implied. | Empirical model
---|---
$m_{B_{J}(5840)^{0}}$ | 5862.9 | $\pm$ |  15.0 | $\pm$ |  16.7 | $\pm$ | 0.2 |  |
$\Gamma_{B_{J}(5840)^{0}}$ |  1127.4 | $\pm$ | 16.7 | $\pm$ | 34.2 |  |  |  |
$m_{B_{J}(5960)^{0}}$ | 5969.2 | $\pm$ |  12.9 | $\pm$ |  15.1 | $\pm$ | 0.2 |  |
$\Gamma_{B_{J}(5960)^{0}}$ |  1182.3 | $\pm$ |  17.7 | $\pm$ |  19.4 |  |  |  |
$m_{B_{J}(5840)^{+}}$ | 5850.3 | $\pm$ | 12.7 | $\pm$ | 13.7 | $\pm$ | 0.2 |  |
$\Gamma_{B_{J}(5840)^{+}}$ |  1224.4 | $\pm$ | 23.9 | $\pm$ | 79.8 |  |  |  |
$m_{B_{J}(5960)^{+}}$ | 5964.9 | $\pm$ |  14.1 | $\pm$ |  12.5 | $\pm$ | 0.2 |  |
$\Gamma_{B_{J}(5960)^{+}}$ |  1163.0 | $\pm$ | 14.5 | $\pm$ | 17.2 |  |  |  |
| Quark model, $B_{J}(5840)^{0,+}$ natural
$m_{B_{J}(5840)^{0}}$ | 5889.7 | $\pm$ | 22.2 | $\pm$ |  16.7 | $\pm$ | 0.2 |  |
$\Gamma_{B_{J}(5840)^{0}}$ |  1107.0 | $\pm$ | 19.6 | $\pm$ | 34.2 |  |  |  |
$m_{B_{J}(5960)^{0}}$ | 6015.9 | $\pm$ |  13.7 | $\pm$ |  15.1 | $\pm$ | 0.2 | $\pm$ | 0.4
$\Gamma_{B_{J}(5960)^{0}}$ |  1181.6 | $\pm$ |  19.9 | $\pm$ |  19.4 |  |  |  |
$m_{B_{J}(5840)^{+}}$ | 5874.5 | $\pm$ | 25.7 | $\pm$ | 13.7 | $\pm$ | 0.2 |  |
$\Gamma_{B_{J}(5840)^{+}}$ |  1214.6 | $\pm$ | 26.7 | $\pm$ | 79.8 |  |  |  |
$m_{B_{J}(5960)^{+}}$ | 6010.6 | $\pm$ |  14.0 | $\pm$ |  12.5 | $\pm$ | 0.2 | $\pm$ | 0.4
$\Gamma_{B_{J}(5960)^{+}}$ |  1161.4 | $\pm$ | 14.5 | $\pm$ | 17.2 |  |  |  |
| Quark model, $B_{J}(5960)^{0,+}$ natural
$m_{B_{J}(5840)^{0}}$ | 5907.8 | $\pm$ |  14.7 | $\pm$ |  16.7 | $\pm$ | 0.2 | $\pm$ | 0.4
$\Gamma_{B_{J}(5840)^{0}}$ |  1119.4 | $\pm$ | 17.2 | $\pm$ | 34.2 |  |  |  |
$m_{B_{J}(5960)^{0}}$ | 5993.6 | $\pm$ |  16.4 | $\pm$ |  15.1 | $\pm$ | 0.2 |  |
$\Gamma_{B_{J}(5960)^{0}}$ |  1155.9 | $\pm$ |  16.6 | $\pm$ |  19.4 |  |  |  |
$m_{B_{J}(5840)^{+}}$ | 5889.3 | $\pm$ | 15.0 | $\pm$ | 13.7 | $\pm$ | 0.2 | $\pm$ | 0.4
$\Gamma_{B_{J}(5840)^{+}}$ |  1229.3 | $\pm$ | 26.9 | $\pm$ | 79.8 |  |  |  |
$m_{B_{J}(5960)^{+}}$ | 5966.4 | $\pm$ |  14.5 | $\pm$ |  12.5 | $\pm$ | 0.2 |  |
$\Gamma_{B_{J}(5960)^{+}}$ |  1160.8 | $\pm$ | 14.0 | $\pm$ | 17.2 |  |  |  |

In summary, the $B^{+}\pi^{-}$ and $B^{0}\pi^{+}$ invariant mass distributions
obtained from LHC $pp$ collision data recorded at centre-of-mass energies of 7
and 8 $\mathrm{\,Te\kern-1.00006ptV}$, corresponding to an integrated
luminosity of $3.0\mbox{\,fb}^{-1}$, have been investigated in order to study
excited $B$ mesons. Precise measurements of the masses and widths of the
$B_{1}(5721)^{0,+}$ and $B_{2}^{*}(5747)^{0,+}$ states are reported. Evidence
is found for the $B_{2}^{*}(5747)^{0}\rightarrow B^{*+}\pi^{-}$ decay. Clear
enhancements over background are observed in the mass range
$5850$–$6000\mathrm{\,Me\kern-1.00006ptV}$ in both $B^{+}\pi^{-}$ and
$B^{0}\pi^{+}$ combinations. Fits to the data, accounting for the apparent
enhanced production of the high mass states in the high transverse momentum
region, allow the parameters of these states, labelled $B_{J}(5840)^{0,+}$ and
$B_{J}(5960)^{0,+}$, to be determined under different hypotheses for their
quantum numbers.

## Acknowledgements

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 (France); BMBF, DFG, HGF and MPG (Germany); INFN (Italy);
FOM and NWO (The Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania);
MinES and FANO (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU
(Ukraine); STFC (United Kingdom); NSF (USA). 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 indebted
to the communities behind the multiple open source software packages on which
we depend. We are also thankful for the computing resources and the access to
software R&D tools provided by Yandex LLC (Russia). Individual groups or
members have received support from EPLANET, Marie Skłodowska-Curie Actions and
ERC (European Union), Conseil général de Haute-Savoie, Labex ENIGMASS and
OCEVU, Région Auvergne (France), RFBR (Russia), XuntaGal and GENCAT (Spain),
Royal Society and Royal Commission for the Exhibition of 1851 (United
Kingdom).

##  Appendix A Covariance matrices

Tables 7 and 8 each show both statistical and systematic correlations between
the main parameters of interest in the $B^{+}\pi^{-}$ and $B^{0}\pi^{+}$ fits,
respectively. In each Table, the masses and widths of the two broad states are
seen to be heavily correlated with each other because they overlap, while the
parameters of the narrow states are correlated because of the overlap between
the $B_{1}(5721)^{0,+}$ state and the $B_{2}^{*}(5747)^{0,+}$ feed-down.

Table 7:  Statistical (top) and systematic (bottom) covariance matrices of the
nominal $B^{+}\pi^{-}$ fit, where $\mu$ and $\Gamma$ stand for the mean and
width respectively. The parameters related to the AP and WS shapes and the
signal yields are suppressed for brevity. Units of
$\mathrm{\,Me\kern-1.00006ptV}$ for $\mu$ and $\Gamma$ are implied.

| $B_{1}(5721)^{0}$ | $B_{2}^{*}(5747)^{0}$ | $B_{J}(5840)^{0}$ | $B_{J}(5960)^{0}$
---|---|---|---|---
| $\mu$ | $\Gamma$ | BF ratio | $\mu$ | $\Gamma$ | $\mu$ | $\Gamma$ | $\mu$ | $\Gamma$
$B_{1}(5721)^{0}$ $\mu$ | $\phantom{-}0.5$ |  |  |  |  |  |  |  |
$B_{1}(5721)^{0}$ $\Gamma$ | $\phantom{-}0.8$ | $\phantom{-}2.3$ |  |  |  |  |  |  |
$B_{2}^{*}(5747)^{0}$ BF ratio | $-0.1$ | $-0.1$ | $\phantom{-}0.0$ |  |  |  |  |  |
$B_{2}^{*}(5747)^{0}$ $\mu$ | $\phantom{-}0.1$ | $\phantom{-}0.1$ | $\phantom{-}0.0$ | $\phantom{-}0.1$ |  |  |  |  |
$B_{2}^{*}(5747)^{0}$ $\Gamma$ | $-0.2$ | $-0.4$ | $\phantom{-}0.0$ | $\phantom{-}0.0$ | $\phantom{-}1.0$ |  |  |  |
$B_{J}(5840)^{0}$ $\mu$ | $\phantom{-}0.0$ | $-0.4$ | $\phantom{-}0.0$ | $\phantom{-}0.0$ | $\phantom{-}0.0$ | $\phantom{-}24.5$ |  |  |
$B_{J}(5840)^{0}$ $\Gamma$ | $-0.1$ | $\phantom{-}2.0$ | $\phantom{-}0.0$ | $-0.4$ | $-1.2$ | $\phantom{-}23.1$ | 278.9 |  |
$B_{J}(5960)^{0}$ $\mu$ | $\phantom{-}0.0$ | $\phantom{-}0.1$ | $\phantom{-}0.0$ | $\phantom{-}0.0$ | $\phantom{-}0.0$ | $\phantom{-}\phantom{1}7.4$ | $\phantom{-}21.2$ | $\phantom{-}\phantom{1}8.3$ |
$B_{J}(5960)^{0}$ $\Gamma$ | $\phantom{-}0.1$ | $\phantom{-}0.6$ | $\phantom{-}0.0$ | $\phantom{-}0.1$ | $\phantom{-}0.9$ | $-21.4$ | $-41.2$ | $-10.2$ | $\phantom{1}59.4$
$B_{1}(5721)^{0}$ $\mu$ | $\phantom{-}1.9$ |  |  |  |  |  |  |  |
$B_{1}(5721)^{0}$ $\Gamma$ | $\phantom{-}1.0$ | 12.2 |  |  |  |  |  |  |
$B_{2}^{*}(5747)^{0}$ BF ratio | $-0.1$ | $-0.1$ | $\phantom{-}0.1$ |  |  |  |  |  |
$B_{2}^{*}(5747)^{0}$ $\mu$ | $\phantom{-}0.1$ | $\phantom{-}0.1$ | $\phantom{-}0.0$ | $\phantom{-}0.1$ |  |  |  |  |
$B_{2}^{*}(5747)^{0}$ $\Gamma$ | $-0.2$ | $-0.3$ | $\phantom{-}0.0$ | $\phantom{-}0.0$ | $\phantom{-}2.2$ |  |  |  |
$B_{J}(5840)^{0}$ $\mu$ | $\phantom{-}0.1$ | $\phantom{-}0.1$ | $\phantom{-}0.0$ | $\phantom{-}0.0$ | $\phantom{-}0.0$ | $\phantom{-}44.6$ |  |  |
$B_{J}(5840)^{0}$ $\Gamma$ | $-0.2$ | $-0.4$ | $\phantom{-}0.0$ | $\phantom{-}0.0$ | $\phantom{-}0.1$ | $\phantom{-}\phantom{1}0.0$ | 1172 |  |
$B_{J}(5960)^{0}$ $\mu$ | $\phantom{-}0.0$ | $\phantom{-}0.0$ | $\phantom{-}0.0$ | $\phantom{-}0.0$ | $\phantom{-}0.0$ | $\phantom{-}\phantom{1}0.0$ | $\phantom{-}0.0$ | $\phantom{-}26.0$ |
$B_{J}(5960)^{0}$ $\Gamma$ | $\phantom{-}0.2$ | $\phantom{-}0.3$ | $\phantom{-}0.0$ | $\phantom{-}0.0$ | $\phantom{-}0.0$ | $\phantom{-}\phantom{1}0.0$ | $-0.1$ | $\phantom{-}\phantom{1}0.0$ | $\phantom{1}88.6$

Table 8:  Statistical (top) and systematic (bottom) covariance matrices of the
nominal $B^{0}\pi^{+}$ fit, where $\mu$ and $\Gamma$ stand for the mean and
width respectively. The parameters related to the AP and WS shapes and the
signal yields are suppressed for brevity. Units of
$\mathrm{\,Me\kern-1.00006ptV}$ for $\mu$ and $\Gamma$ are implied.

| $B_{1}(5721)^{+}$ | $B_{2}^{*}(5747)^{+}$ | $B_{J}(5840)^{+}$ | $B_{J}(5960)^{+}$
---|---|---|---|---
| $\mu$ | $\Gamma$ | BF ratio | $\mu$ | $\Gamma$ | $\mu$ | $\Gamma$ | $\mu$ | $\Gamma$
$B_{1}(5721)^{+}$ $\mu$ | $\phantom{-}3.3$ |  |  |  |  |  |  |  |
$B_{1}(5721)^{+}$ $\Gamma$ | $\phantom{-}5.0$ | 12.7 |  |  |  |  |  |  |
$B_{2}^{*}(5747)^{+}$ BF ratio | $-0.9$ | $-1.5$ | $\phantom{-}0.3$ |  |  |  |  |  |
$B_{2}^{*}(5747)^{+}$ $\mu$ | $\phantom{-}0.4$ | $\phantom{-}0.4$ | $-0.1$ | $\phantom{-}0.5$ |  |  |  |  |
$B_{2}^{*}(5747)^{+}$ $\Gamma$ | $-0.8$ | $-1.9$ | $\phantom{-}0.2$ | $\phantom{-}0.1$ | $\phantom{-}4.0$ |  |  |  |
$B_{J}(5840)^{+}$ $\mu$ | $\phantom{-}0.5$ | $-3.2$ | $-0.1$ | $\phantom{-}1.6$ | $\phantom{-}8.8$ | 161.3 |  |  |
$B_{J}(5840)^{+}$ $\Gamma$ | $\phantom{-}2.2$ | $\phantom{-}9.4$ | $-0.7$ | $-0.9$ | $-7.6$ | $-42.5$ | $\phantom{-}571.2$ |  |
$B_{J}(5960)^{+}$ $\mu$ | $\phantom{-}0.1$ | $\phantom{-}0.0$ | $\phantom{-}0.0$ | $\phantom{-}0.2$ | $\phantom{-}1.0$ | $\phantom{-}20.7$ | $\phantom{1}-7.8$ | $\phantom{-}16.6$ |
$B_{J}(5960)^{+}$ $\Gamma$ | $-0.3$ | $\phantom{-}1.0$ | $\phantom{-}0.0$ | $-0.4$ | $-2.0$ | $-95.8$ | $-107.4$ | $-22.4$ | 210.2
$B_{1}(5721)^{+}$ $\mu$ | $\phantom{-}9.6$ |  |  |  |  |  |  |  |
$B_{1}(5721)^{+}$ $\Gamma$ | $\phantom{-}3.7$ | 18.3 |  |  |  |  |  |  |
$B_{2}^{*}(5747)^{+}$ BF ratio | $-0.8$ | $-1.1$ | $\phantom{-}0.6$ |  |  |  |  |  |
$B_{2}^{*}(5747)^{+}$ $\mu$ | $\phantom{-}0.2$ | $\phantom{-}0.3$ | $-0.1$ | $\phantom{-}0.2$ |  |  |  |  |
$B_{2}^{*}(5747)^{+}$ $\Gamma$ | $-0.8$ | $-1.2$ | $\phantom{-}0.2$ | $-0.1$ | $\phantom{-}4.3$ |  |  |  |
$B_{J}(5840)^{+}$ $\mu$ | $-0.2$ | $-0.3$ | $\phantom{-}0.0$ | $\phantom{-}0.0$ | $\phantom{-}0.1$ | 187.7 |  |  |
$B_{J}(5840)^{+}$ $\Gamma$ | $\phantom{-}3.0$ | $\phantom{-}4.3$ | $-0.9$ | $\phantom{-}0.2$ | $-1.0$ | $-0.3$ | 6371 |  |
$B_{J}(5960)^{+}$ $\mu$ | $\phantom{-}0.0$ | $\phantom{-}0.0$ | $\phantom{-}0.0$ | $\phantom{-}0.0$ | $\phantom{-}0.0$ | $\phantom{-}0.0$ | $\phantom{-}0.0$ | $\phantom{-}\phantom{1}6.4$ |
$B_{J}(5960)^{+}$ $\Gamma$ | $\phantom{-}0.0$ | $\phantom{-}0.0$ | $\phantom{-}0.0$ | $\phantom{-}0.0$ | $\phantom{-}0.0$ | $-0.1$ | $\phantom{-}0.0$ | $\phantom{-}\phantom{1}0.0$ | 295.2

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LHCb collaboration

R. Aaij41, B. Adeva37, M. Adinolfi46, A. Affolder52, Z. Ajaltouni5, S. Akar6,
J. Albrecht9, F. Alessio38, M. Alexander51, S. Ali41, G. Alkhazov30, P.
Alvarez Cartelle53, A.A. Alves Jr25,38, S. Amato2, S. Amerio22, Y. Amhis7, L.
An3, L. Anderlini17,g, J. Anderson40, R. Andreassen57, M. Andreotti16,f, J.E.
Andrews58, R.B. Appleby54, O. Aquines Gutierrez10, F. Archilli38, A.
Artamonov35, M. Artuso59, E. Aslanides6, G. Auriemma25,n, M. Baalouch5, S.
Bachmann11, J.J. Back48, A. Badalov36, C. Baesso60, W. Baldini16, R.J.
Barlow54, C. Barschel38, S. Barsuk7, W. Barter38, V. Batozskaya28, V.
Battista39, A. Bay39, L. Beaucourt4, J. Beddow51, F. Bedeschi23, I. Bediaga1,
S. Belogurov31, I. Belyaev31, E. Ben-Haim8, G. Bencivenni18, S. Benson38, J.
Benton46, A. Berezhnoy32, R. Bernet40, A. Bertolin22, M.-O. Bettler47, M. van
Beuzekom41, A. Bien11, S. Bifani45, T. Bird54, A. Bizzeti17,i, T. Blake48, F.
Blanc39, J. Blouw10, S. Blusk59, V. Bocci25, A. Bondar34, N. Bondar30,38, W.
Bonivento15, S. Borghi54, A. Borgia59, M. Borsato7, T.J.V. Bowcock52, E.
Bowen40, C. Bozzi16, D. Brett54, M. Britsch10, T. Britton59, J. Brodzicka54,
N.H. Brook46, A. Bursche40, J. Buytaert38, S. Cadeddu15, R. Calabrese16,f, M.
Calvi20,k, M. Calvo Gomez36,p, P. Campana18, D. Campora Perez38, L.
Capriotti54, A. Carbone14,d, G. Carboni24,l, R. Cardinale19,38,j, A.
Cardini15, P. Carniti20, L. Carson50, K. Carvalho Akiba2,38, R. Casanova
Mohr36, G. Casse52, L. Cassina20,k, L. Castillo Garcia38, M. Cattaneo38, Ch.
Cauet9, G. Cavallero19, R. Cenci23,t, M. Charles8, Ph. Charpentier38, M.
Chefdeville4, S. Chen54, S.-F. Cheung55, N. Chiapolini40, M. Chrzaszcz40,26,
X. Cid Vidal38, G. Ciezarek41, P.E.L. Clarke50, M. Clemencic38, H.V. Cliff47,
J. Closier38, V. Coco38, J. Cogan6, E. Cogneras5, V. Cogoni15,e, L.
Cojocariu29, G. Collazuol22, P. Collins38, A. Comerma-Montells11, A.
Contu15,38, A. Cook46, M. Coombes46, S. Coquereau8, G. Corti38, M. Corvo16,f,
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O. Deschamps5, F. Dettori38, B. Dey40, A. Di Canto38, A Di Domenico25, F. Di
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Farinelli41, N. Farley45, S. Farry52, R. Fay52, D. Ferguson50, V. Fernandez
Albor37, F. Ferreira Rodrigues1, M. Ferro-Luzzi38, S. Filippov33, M.
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Gao3, J. García Pardiñas37, J. Garofoli59, J. Garra Tico47, L. Garrido36, D.
Gascon36, C. Gaspar38, U. Gastaldi16, R. Gauld55, L. Gavardi9, G. Gazzoni5, A.
Geraci21,v, E. Gersabeck11, M. Gersabeck54, T. Gershon48, Ph. Ghez4, A.
Gianelle22, S. Gianì39, V. Gibson47, L. Giubega29, V.V. Gligorov38, C.
Göbel60, D. Golubkov31, A. Golutvin53,31,38, A. Gomes1,a, C. Gotti20,k, M.
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T. Gys38, C. Hadjivasiliou59, G. Haefeli39, C. Haen38, S.C. Haines47, S.
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Herwijnen38, M. Heß63, A. Hicheur2, D. Hill55, M. Hoballah5, C. Hombach54, W.
Hulsbergen41, T. Humair53, N. Hussain55, D. Hutchcroft52, D. Hynds51, M.
Idzik27, P. Ilten56, R. Jacobsson38, A. Jaeger11, J. Jalocha55, E. Jans41, A.
Jawahery58, F. Jing3, M. John55, D. Johnson38, C.R. Jones47, C. Joram38, B.
Jost38, N. Jurik59, S. Kandybei43, W. Kanso6, M. Karacson38, T.M. Karbach38,
S. Karodia51, M. Kelsey59, I.R. Kenyon45, M. Kenzie38, T. Ketel42, B.
Khanji20,38,k, C. Khurewathanakul39, S. Klaver54, K. Klimaszewski28, O.
Kochebina7, M. Kolpin11, I. Komarov39, R.F. Koopman42, P. Koppenburg41,38, M.
Korolev32, L. Kravchuk33, K. Kreplin11, M. Kreps48, G. Krocker11, P.
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K. Kurek28, T. Kvaratskheliya31, V.N. La Thi39, D. Lacarrere38, G. Lafferty54,
A. Lai15, D. Lambert50, R.W. Lambert42, G. Lanfranchi18, C. Langenbruch48, B.
Langhans38, T. Latham48, C. Lazzeroni45, R. Le Gac6, J. van Leerdam41, J.-P.
Lees4, R. Lefèvre5, A. Leflat32, J. Lefrançois7, O. Leroy6, T. Lesiak26, B.
Leverington11, Y. Li7, T. Likhomanenko64, M. Liles52, R. Lindner38, C. Linn38,
F. Lionetto40, B. Liu15, S. Lohn38, I. Longstaff51, J.H. Lopes2, P. Lowdon40,
D. Lucchesi22,r, H. Luo50, A. Lupato22, E. Luppi16,f, O. Lupton55, F.
Machefert7, I.V. Machikhiliyan31, F. Maciuc29, O. Maev30, S. Malde55, A.
Malinin64, G. Manca15,e, G. Mancinelli6, P Manning59, A. Mapelli38, J.
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F. Martinez Vidal66, D. Martins Tostes2, A. Massafferri1, R. Matev38, Z.
Mathe38, C. Matteuzzi20, A Mauri40, B. Maurin39, A. Mazurov45, M. McCann53, J.
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M. Meissner11, M. Merk41, D.A. Milanes62, M.-N. Minard4, N. Moggi14, J. Molina
Rodriguez60, S. Monteil5, M. Morandin22, P. Morawski27, A. Mordà6, M.J.
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I. Nasteva2, M. Needham50, N. Neri21, S. Neubert11, N. Neufeld38, M. Neuner11,
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Goicochea2, A. Otto38, P. Owen53, A. Oyanguren66, B.K. Pal59, A. Palano13,c,
F. Palombo21,u, M. Palutan18, J. Panman38, A. Papanestis49, M. Pappagallo51,
L.L. Pappalardo16,f, C. Parkes54, C.J. Parkinson9,45, G. Passaleva17, G.D.
Patel52, M. Patel53, C. Patrignani19,j, A. Pearce54,49, A. Pellegrino41, G.
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E. Pesen68, K. Petridis46, A. Petrolini19,j, E. Picatoste Olloqui36, B.
Pietrzyk4, T. Pilař48, D. Pinci25, A. Pistone19, S. Playfer50, M. Plo
Casasus37, F. Polci8, A. Poluektov48,34, I. Polyakov31, E. Polycarpo2, A.
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Rakotomiaramanana39, M. Rama23, M.S. Rangel2, I. Raniuk43, N. Rauschmayr38, G.
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1Centro Brasileiro de Pesquisas Físicas (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, Université Savoie Mont-Blanc, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
7LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Université Pierre et Marie Curie, Université Paris Diderot,
CNRS/IN2P3, Paris, France
9Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
10Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
11Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
12School of Physics, University College Dublin, Dublin, Ireland
13Sezione INFN di Bari, Bari, Italy
14Sezione INFN di Bologna, Bologna, Italy
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 Milano, Milano, Italy
22Sezione INFN di Padova, Padova, Italy
23Sezione INFN di Pisa, Pisa, Italy
24Sezione INFN di Roma Tor Vergata, Roma, Italy
25Sezione INFN di Roma La Sapienza, Roma, Italy
26Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
27AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
28National Center for Nuclear Research (NCBJ), Warsaw, Poland
29Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
30Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
31Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
32Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
33Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN),
Moscow, Russia
34Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State
University, Novosibirsk, Russia
35Institute for High Energy Physics (IHEP), Protvino, Russia
36Universitat de Barcelona, Barcelona, Spain
37Universidad de Santiago de Compostela, Santiago de Compostela, Spain
38European Organization for Nuclear Research (CERN), Geneva, Switzerland
39Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
40Physik-Institut, Universität Zürich, Zürich, Switzerland
41Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
42Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, The Netherlands
43NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
44Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
45University of Birmingham, Birmingham, United Kingdom
46H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
47Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
48Department of Physics, University of Warwick, Coventry, United Kingdom
49STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
50School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
51School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
52Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
53Imperial College London, London, United Kingdom
54School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
55Department of Physics, University of Oxford, Oxford, United Kingdom
56Massachusetts Institute of Technology, Cambridge, MA, United States
57University of Cincinnati, Cincinnati, OH, United States
58University of Maryland, College Park, MD, United States
59Syracuse University, Syracuse, NY, United States
60Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
61Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
62Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
63Institut für Physik, Universität Rostock, Rostock, Germany, associated to 11
64National Research Centre Kurchatov Institute, Moscow, Russia, associated to
31
65Yandex School of Data Analysis, Moscow, Russia, associated to 31
66Instituto de Fisica Corpuscular (IFIC), Universitat de Valencia-CSIC,
Valencia, Spain, associated to 36
67Van Swinderen Institute, University of Groningen, Groningen, The
Netherlands, associated to 41
68Celal Bayar University, Manisa, Turkey, associated to 38

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
cUniversità di Bari, Bari, Italy
dUniversità di Bologna, Bologna, Italy
eUniversità di Cagliari, Cagliari, Italy
fUniversità di Ferrara, Ferrara, Italy
gUniversità di Firenze, Firenze, Italy
hUniversità di Urbino, Urbino, Italy
iUniversità di Modena e Reggio Emilia, Modena, Italy
jUniversità di Genova, Genova, Italy
kUniversità di Milano Bicocca, Milano, Italy
lUniversità di Roma Tor Vergata, Roma, Italy
mUniversità di Roma La Sapienza, Roma, Italy
nUniversità della Basilicata, Potenza, Italy
oAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
pLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
qHanoi University of Science, Hanoi, Viet Nam
rUniversità di Padova, Padova, Italy
sUniversità di Pisa, Pisa, Italy
tScuola Normale Superiore, Pisa, Italy
uUniversità degli Studi di Milano, Milano, Italy
vPolitecnico di Milano, Milano, Italy