EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2014-279 LHCb-PAPER-2014-061 January 8, 2015

Observation of two new ${{\mathchar 28932\relax}^{-}_{b}}$ baryon resonances

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

Two structures are observed close to the kinematic threshold in the
${{\mathchar 28932\relax}^{0}_{b}}{{\pi}^{-}}$ mass spectrum in a sample of
proton-proton collision data, corresponding to an integrated luminosity of
3.0$\mbox{\,fb}^{-1}$, recorded by the LHCb experiment. In the quark model,
two baryonic resonances with quark content $bds$ are expected in this mass
region: the spin-parity $J^{P}=\frac{1}{2}^{+}$ and $J^{P}=\frac{3}{2}^{+}$
states, denoted ${{\mathchar 28932\relax}^{\prime-}_{b}}$ and ${{\mathchar
28932\relax}^{*-}_{b}}$. Interpreting the structures as these resonances, we
measure the mass differences and the width of the heavier state to be

$\displaystyle m({{\mathchar 28932\relax}^{\prime-}_{b}})-m({{\mathchar
28932\relax}^{0}_{b}})-m(\pi^{-})$ $\displaystyle=$ $\displaystyle 3.653\pm
0.018\pm 0.006{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}},$ $\displaystyle
m({{\mathchar 28932\relax}^{*-}_{b}})-m({{\mathchar
28932\relax}^{0}_{b}})-m(\pi^{-})$ $\displaystyle=$ $\displaystyle 23.96\pm
0.12\pm 0.06{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}},$
$\displaystyle\Gamma({{\mathchar 28932\relax}^{*-}_{b}})$ $\displaystyle=$
$\displaystyle 1.65\pm 0.31\pm 0.10\mathrm{\,Me\kern-1.00006ptV},$

where the first and second uncertainties are statistical and systematic,
respectively. The width of the lighter state is consistent with zero, and we
place an upper limit of $\Gamma({{\mathchar
28932\relax}^{\prime-}_{b}})<0.08$$\mathrm{\,Me\kern-1.00006ptV}$ at 95%
confidence level. Relative production rates of these states are also reported.

Submitted to Phys. Rev. Lett.

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

In the constituent quark model [1, 2], baryonic states form multiplets
according to the symmetry of their flavor, spin, and spatial wavefunctions.
The ${\mathchar 28932\relax}_{b}$ states form isodoublets composed of a
${\mathchar 28932\relax}^{0}_{b}$ ($bsu$) and a ${\mathchar
28932\relax}^{-}_{b}$ ($bsd$) state. Three such ${{\mathchar
28932\relax}_{b}}$ isodoublets that are neither orbitally nor radially excited
are expected to exist, and can be categorized by the spin $j$ of the $su$ or
$sd$ diquark and the spin-parity $J^{P}$ of the baryon: one with $j=0$ and
$J^{P}=\frac{1}{2}^{+}$, one with $j=1$ and $J^{P}=\frac{1}{2}^{+}$, and one
with $j=1$ and $J^{P}=\frac{3}{2}^{+}$. This follows the same pattern as the
well-known ${\mathchar 28932\relax}_{c}$ states [3], and we therefore refer to
these three isodoublets as the ${\mathchar 28932\relax}_{b}$, the ${\mathchar
28932\relax}^{\prime}_{b}$, and the ${\mathchar 28932\relax}^{*}_{b}$. The
spin-antisymmetric $J^{P}=\frac{1}{2}^{+}$ state, observed by multiple
experiments [4, 5, 6, 7, 8, 9, 10, 11], is the lightest and therefore decays
through the weak interaction. The others should decay predominantly strongly
through a $P$-wave pion transition (${{\mathchar
28932\relax}^{(\prime,*)}_{b}}\rightarrow{{\mathchar 28932\relax}_{b}}\pi$) if
their masses are above the kinematic threshold for such a decay; otherwise
they should decay electromagnetically (${{\mathchar
28932\relax}^{(\prime,*)}_{b}}\rightarrow{{\mathchar
28932\relax}_{b}}\gamma$). Observing such electromagnetic decays at hadron
colliders is challenging due to large photon multiplicities and worse energy
resolution for low energy photons compared to charged particles.

There are numerous predictions for the mass spectrum of these low-lying states
[12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23]. The consensus is that the
isospin-averaged value of the mass difference $m({{\mathchar
28932\relax}^{*}_{b}})-m({{\mathchar 28932\relax}_{b}})$ is above threshold
for strong decay but that the isospin-averaged difference $m({{\mathchar
28932\relax}^{\prime}_{b}})-m({{\mathchar 28932\relax}_{b}})$ is near the
kinematic threshold. However, it is expected that the mass difference
$m({{\mathchar 28932\relax}^{\prime-}_{b}})-m({{\mathchar
28932\relax}^{0}_{b}})$ is larger than $m({{\mathchar 28932\relax}^{\prime
0}_{b}})-m({{\mathchar 28932\relax}^{-}_{b}})$ due to the relatively large
isospin splitting between the charged and neutral ${\mathchar
28932\relax}_{b}$ states. For the ground state, the measured isospin splitting
of $m({{\mathchar 28932\relax}^{-}_{b}})-m({{\mathchar
28932\relax}^{0}_{b}})=5.92\pm 0.64$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$
[24] is in good agreement with the predicted value of $6.24\pm
0.21$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ [13]. While the equivalent
isospin splitting for the ${\mathchar 28932\relax}^{\prime}_{b}$ and
${\mathchar 28932\relax}^{*}_{b}$ states is likely to be smaller due to
differences in the hyperfine mass corrections, the mass difference
$m({{\mathchar 28932\relax}^{\prime-}_{b}})-m({{\mathchar
28932\relax}^{0}_{b}})$ could well be
5–10${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ larger than $m({{\mathchar
28932\relax}^{\prime 0}_{b}})-m({{\mathchar 28932\relax}^{-}_{b}})$. It is
therefore plausible that the decay ${{\mathchar
28932\relax}^{\prime-}_{b}}\rightarrow{{\mathchar
28932\relax}^{0}_{b}}{{\pi}^{-}}$ is kinematically allowed, while ${{\mathchar
28932\relax}^{\prime 0}_{b}}\rightarrow{{\mathchar
28932\relax}^{-}_{b}}{{\pi}^{+}}$ is not. This is consistent with the recent
CMS observation [25] of a single peak in the ${{\mathchar
28932\relax}^{-}_{b}}\pi^{+}$ mass spectrum, interpreted as the ${{\mathchar
28932\relax}^{*0}_{b}}$ resonance. We note that ${{\mathchar
28932\relax}^{\prime 0}_{b}}\rightarrow{{\mathchar
28932\relax}^{0}_{b}}{{\pi}^{0}}$ may also be allowed even if ${{\mathchar
28932\relax}^{\prime 0}_{b}}\rightarrow{{\mathchar
28932\relax}^{-}_{b}}{{\pi}^{+}}$ is not.

In this Letter we present the results of a study of the ${{\mathchar
28932\relax}^{0}_{b}}{{\pi}^{-}}$ mass spectrum using $pp$ collision data
recorded by the LHCb experiment, corresponding to an integrated luminosity of
3.0$\mbox{\,fb}^{-1}$. One third of the data were collected at a center-of-
mass energy of 7$\mathrm{\,Te\kern-1.00006ptV}$ and the remainder at
8$\mathrm{\,Te\kern-1.00006ptV}$. We observe two highly significant
structures, which are interpreted as the ${\mathchar
28932\relax}^{\prime-}_{b}$ and ${\mathchar 28932\relax}^{*-}_{b}$ baryons.
The properties of these new states are reported. Charge-conjugate processes
are implicitly included.

The LHCb detector [26] 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, which provides a momentum measurement with precision of about 0.5%
from 2$-$100 ${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and impact parameter
resolution of approximately 20${\,\upmu\rm m}$ for particles with large
transverse momentum ($p_{\rm T}$). Ring-imaging Cherenkov detectors [27] are
used to distinguish charged hadrons. Photon, electron and hadron candidates
are identified using a calorimeter system, which is followed by detectors to
identify muons [28].

The trigger [29] consists of a hardware stage, based on information from the
calorimeter and muon systems, followed by a software stage. The software
trigger requires a two-, three- or four-track secondary vertex which is
significantly displaced from all primary $pp$ vertices (PVs) and for which the
scalar $p_{\rm T}$ sum of the charged particles is large. At least one
particle should have $\mbox{$p_{\rm
T}$}>1.7{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and be inconsistent with coming
from any of the PVs. A multivariate algorithm [30] is used to identify
secondary vertices consistent with the decay of a $b$ hadron.

In the simulation, $pp$ collisions are generated using Pythia [31,
*Sjostrand:2007gs] with a specific LHCb configuration [33]. Decays of hadrons
are described by EvtGen [34], in which final-state radiation is generated
using Photos [35]. The interaction of the generated particles with the
detector, and its response, are implemented using the Geant4 toolkit [36,
*Agostinelli:2002hh] as described in Ref. [38].

Signal candidates are reconstructed in the final state ${{\mathchar
28932\relax}^{0}_{b}}{\pi_{\mathrm{s}}^{-}}$, where ${{\mathchar
28932\relax}^{0}_{b}}\rightarrow{{\mathchar 28932\relax}^{+}_{c}}{{\pi}^{-}}$
and ${{\mathchar 28932\relax}^{+}_{c}}\rightarrow{p}{{K}^{-}}{{\pi}^{+}}$. The
first pion is denoted $\pi_{\mathrm{s}}^{-}$ to distinguish it from the
others. The ${\mathchar 28932\relax}^{0}_{b}$ decay mode is the same as that
studied in [9], and the selection used for this analysis is heavily inspired
by it and by other LHCb studies with baryons or low-momentum pions in the
final state (e.g. [39, 40]). At each stage of the decay chain, the particles
are required to meet at a common vertex with good fit quality. In the case of
the ${{\mathchar 28932\relax}^{0}_{b}}{\pi_{\mathrm{s}}^{-}}$ candidate, this
vertex is constrained to be consistent with one of the PVs in the event. Track
quality requirements are applied, along with momentum and transverse momentum
requirements, to reduce combinatorial background. Particle identification
criteria are applied to the final-state tracks to suppress background from
misidentified particles. To remove cross feed from other charm hadrons,
${{\mathchar 28932\relax}^{+}_{c}}$ candidates are rejected if they are
consistent with ${{D}^{+}}\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}}$,
${{D}^{+}_{s}}\rightarrow{{K}^{+}}{{K}^{-}}{{\pi}^{+}}$,
${{D}^{+}}\rightarrow{{\pi}^{+}}{{K}^{-}}{{\pi}^{+}}$, or
${{D}^{*+}}\rightarrow{{D}^{0}}({{K}^{+}}{{K}^{-}}){{\pi}^{+}}$ decays. To
reduce background formed from tracks originating at the PV, the decay vertices
of ${\mathchar 28932\relax}^{+}_{c}$ and ${\mathchar 28932\relax}^{0}_{b}$
candidates are required to be significantly displaced from all PVs.

The ${\mathchar 28932\relax}^{+}_{c}$ candidates are required to have an
invariant mass within 20${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ of the
known mass [3], corresponding to approximately $\pm 3\sigma_{{{\mathchar
28932\relax}^{+}_{c}}}$ where $\sigma_{{{\mathchar 28932\relax}^{+}_{c}}}$ is
the mass resolution. Candidate ${\mathchar 28932\relax}^{0}_{b}$ decays are
required to satisfy $5765<m_{\mathrm{cand}}({{\mathchar
28932\relax}^{0}_{b}})-m_{\mathrm{cand}}({{\mathchar
28932\relax}^{+}_{c}})+m_{{{\mathchar
28932\relax}^{+}_{c}}}<5825$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, where
$m_{\mathrm{cand}}$ and $m_{{{\mathchar 28932\relax}^{+}_{c}}}$ refer to the
candidate and world-average masses, corresponding to approximately $\pm
2\sigma_{{{\mathchar 28932\relax}^{0}_{b}}}$. In addition, the following
kinematic requirements are imposed: $\mbox{$p_{\rm T}$}({{\mathchar
28932\relax}^{+}_{c}})>1$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$,
$\mbox{$p_{\rm T}$}({{\mathchar
28932\relax}^{0}_{b}})>2$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$,
$\mbox{$p_{\rm T}$}({{\mathchar
28932\relax}^{0}_{b}}{\pi_{\mathrm{s}}^{-}})>2.5$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$,
and $\mbox{$p_{\rm
T}$}({\pi_{\mathrm{s}}^{-}})>0.15$${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$.
Defining $\delta m\equiv m_{\mathrm{cand}}({{\mathchar
28932\relax}^{0}_{b}}{\pi_{\mathrm{s}}^{-}})-m_{\mathrm{cand}}({{\mathchar
28932\relax}^{0}_{b}})-m_{{{\pi}^{-}}}$, the region of consideration is
$\delta m<45$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. There are on average
1.15 candidates retained in this region per event. Such multiple candidates
are due almost entirely to cases where the same ${\mathchar
28932\relax}^{0}_{b}$ candidate is combined with different
$\pi_{\mathrm{s}}^{-}$ candidates from the same PV. All ${{\mathchar
28932\relax}^{0}_{b}}\pi_{s}^{-}$ candidates are kept.

The $m_{\mathrm{cand}}({{\mathchar 28932\relax}^{0}_{b}})$ projection of the
${{\mathchar 28932\relax}^{0}_{b}}{\pi_{\mathrm{s}}^{-}}$ candidates passing
the full selection apart from the $m_{\mathrm{cand}}({{\mathchar
28932\relax}^{0}_{b}})$ requirement, but including the $\delta m$ requirement,
is shown in Fig. 1. Control samples, notably wrong-sign combinations
${{\mathchar 28932\relax}^{0}_{b}}{{\pi}^{+}}$, are also used to study
backgrounds. The $\delta m$ spectra for the signal and the wrong-sign sample
are shown in Fig. 2. Two peaks are clearly visible, a narrow one at $\delta
m\approx 3.7$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and a broader one at
$\delta m\approx 24$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. No structure
is observed in the wrong-sign sample, nor in studies of the ${\mathchar
28932\relax}^{0}_{b}$ mass sidebands.

Figure 1:  Distribution of $m_{\mathrm{cand}}({{\mathchar
28932\relax}^{0}_{b}})$ for ${{\mathchar
28932\relax}^{0}_{b}}{\pi_{\mathrm{s}}^{-}}$ candidates passing the full
selection apart from the $m_{\mathrm{cand}}({{\mathchar
28932\relax}^{0}_{b}})$ requirement. Inset: The subset of candidates that lie
in the $\delta m$ signal regions of $3.0<\delta
m<4.2$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and $21<\delta
m<27$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$.  Figure 2:  Distribution of
the mass difference, $\delta m$, for ${{\mathchar
28932\relax}^{0}_{b}}{\pi_{\mathrm{s}}^{-}}$ candidates in data. The points
with error bars show right-sign candidates in the ${\mathchar
28932\relax}^{0}_{b}$ mass signal region, and the hatched histogram shows
wrong-sign candidates with the same selection. The curve shows the nominal fit
to the right-sign candidates. Inset: detail of the region
$2.0$–$5.5$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$.

Accurate determination of the masses, widths, and signal yields of these two
states requires knowledge of the signal shapes, and in particular, the mass
resolution of the two peaks. These are obtained from large samples of
simulated decays with $\delta m$ values of
3.69${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and
23.69${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, corresponding to the two
peaks. The natural widths, $\Gamma$, are set to negligible values so that the
width measured in simulation is due entirely to the mass resolution. The
resolution function is parameterized as the sum of three Gaussian
distributions with independent mean values. Separate sets of parameters are
determined for the two peaks. An indication of the scale of the resolution is
given by the weighted averages of the three Gaussian widths, which are
0.21${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and
0.54${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ for the lower- and higher-mass
peaks. In the nominal fits to data, the parameters of the three Gaussian
distributions are kept fixed to the values obtained from simulation, given in
the Supplementary Material [41]. Small corrections, obtained from simulation,
are applied to the masses to account for offsets in the resolution functions.
The combinatorial background is modeled by a threshold function of the form

$f(\delta m)=\left(1-e^{-\delta m/C}\right)\,(\delta m)^{A},$

where $A$ and $C$ are freely varying parameters determined in the fit to the
data.

The masses, widths and yields of the two peaks are determined from an unbinned
maximum likelihood fit to the $\delta m$ spectrum. In an initial fit, each
peak is described using a $P$-wave relativistic Breit-Wigner (RBW) line shape
[42] with a Blatt-Weisskopf barrier factor [43], convolved with the resolution
function obtained from simulation. The fitted width of the lower-mass peak is
found to be consistent with zero and consequently its width is set to zero in
the nominal fit, shown in Fig. 2. The fitted yields in the lower- and higher-
mass peaks are $121\pm 12$ and $237\pm 24$ events, with statistical
significances in excess of 10$\sigma$. The nonzero value of the natural width
of the higher-mass peak is also highly significant: the change in likelihood
when the width is fixed to zero corresponds to a $p$-value of $4\times
10^{-14}$ using Wilks’s theorem [44].

An upper limit on the natural width of the lower-mass peak is set using
ensembles of pseudoexperiments with the same parameters as in data, but with
natural widths ranging from 0.01 to 0.12$\mathrm{\,Me\kern-1.00006ptV}$. The
upper limit is taken to be the value of $\Gamma$ for which a width equal to or
greater than that obtained in data is observed in 95% of the
pseudoexperiments. The resulting upper limit is $\Gamma({{\mathchar
28932\relax}^{\prime-}_{b}})<0.08$$\mathrm{\,Me\kern-1.00006ptV}$ at 95%
confidence level (CL).

A number of cross checks are performed to ensure the robustness of the
measured masses and natural widths of these states and to assess systematic
uncertainties. These include changing the assumed angular momentum (spin 0, 2)
and radial parameter (1–5$\mathrm{\,Ge\kern-1.00006ptV}$ -1) of the RBW and
barrier factor; inflating the widths of the resolution functions by a fixed
factor of $1.1$, the value found in a large
${{D}^{*+}}\rightarrow{{D}^{0}}\pi$ data sample [45]; inflating the widths of
the resolution functions by a common factor floated in the fit (with $1.03\pm
0.11$ obtained); using a symmetric resolution function; using a non-
relativistic BW for the higher-mass peak; using a different background
function; varying the fit range; checking the effect of finite sample size and
of the variation of mass resolution with particle mass; keeping only one
candidate in each event; imposing additional trigger requirements; separating
the data by charge and LHCb magnet polarity; and fitting the wrong-sign
sample. Where appropriate, systematic uncertainties are assigned based on the
differences between the nominal results and those obtained in these tests. The
calibration of the momentum scale [11, 46] is validated by measuring
$m({{D}^{*+}})-m({{D}^{0}})$ in a large sample of ${{D}^{*+}}$,
${{D}^{0}}\rightarrow{{K}^{-}}{{K}^{+}}$ decays [45]. The mass difference
agrees with a recent BaBar measurement[47, *Lees:2013zna] within
6${\mathrm{\,ke\kern-1.00006ptV\\!/}c^{2}}$, corresponding to $1.3\sigma$ when
including the mass scale uncertainty for that decay. The uncertainties are
summarized in Table †. Taking these into account, we obtain

$\displaystyle\delta m({{\mathchar 28932\relax}^{\prime-}_{b}})$
$\displaystyle=$ $\displaystyle 3.653\pm 0.018\pm
0.006{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}},$ $\displaystyle\delta
m({{\mathchar 28932\relax}^{*-}_{b}})$ $\displaystyle=$ $\displaystyle
23.96\pm 0.12\pm 0.06{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}},$
$\displaystyle\Gamma({{\mathchar 28932\relax}^{*-}_{b}})$ $\displaystyle=$
$\displaystyle 1.65\pm 0.31\pm 0.10\mathrm{\,Me\kern-1.00006ptV},$
$\displaystyle\Gamma({{\mathchar 28932\relax}^{\prime-}_{b}})$
$\displaystyle<$ $\displaystyle
0.08\,\mathrm{\,Me\kern-1.00006ptV}~{}{\mbox{\rm at~{}95\%~{}CL}}.$

Combining these with the measurement of $m({{\mathchar
28932\relax}^{0}_{b}})=5791.80\pm
0.50$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ obtained previously at LHCb
[9], the masses of these states are found to be

$\displaystyle m({{\mathchar 28932\relax}^{\prime-}_{b}})$ $\displaystyle=$
$\displaystyle 5935.02\pm 0.02\pm 0.01\pm
0.50{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}},$ $\displaystyle m({{\mathchar
28932\relax}^{*-}_{b}})$ $\displaystyle=$ $\displaystyle 5955.33\pm 0.12\pm
0.06\pm 0.50{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}},$

where the uncertainties are statistical, systematic, and due to the
$m({{\mathchar 28932\relax}^{0}_{b}})$ measurement, respectively.

Table 1:  Systematic uncertainties, in units of
${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ (masses) and
$\mathrm{\,Me\kern-1.00006ptV}$ (width). The statistical uncertainties are
also shown for comparison.

Source | $\delta m({{\mathchar 28932\relax}^{\prime}_{b}})$ | $\delta m({{\mathchar 28932\relax}^{*}_{b}})$ | $\Gamma({{\mathchar 28932\relax}^{*}_{b}})$
---|---|---|---
Simulated sample size | 0.002 | 0.005 |
Multiple candidates | 0.004 | 0.048 | 0.055
Resolution model | 0.002 | 0.003 | 0.070
Background description | 0.001 | 0.003 | 0.019
Momentum scale | 0.003 | 0.014 | 0.003
RBW spin and radial parameter | 0.000 | 0.023 | 0.028
Sum in quadrature | 0.006 | 0.055 | 0.095
Statistical uncertainty | 0.018 | 0.119 |

Helicity angle [49] distributions may be used to distinguish between spin
hypotheses for resonances. We consider the decay sequence ${{\mathchar
28932\relax}^{(\prime,*)\,-}_{b}}\rightarrow{{\mathchar
28932\relax}^{0}_{b}}{{\pi}^{-}}$, ${{\mathchar
28932\relax}^{0}_{b}}\rightarrow{{\mathchar 28932\relax}^{+}_{c}}{{\pi}^{-}}$,
where the ${\mathchar 28932\relax}^{(\prime,*)\,-}_{b}$ has spin $J$ and the
${\mathchar 28932\relax}^{0}_{b}$, ${\mathchar 28932\relax}^{+}_{c}$, and
${\pi}^{-}$ have spin-parity $\frac{1}{2}^{+}$, $\frac{1}{2}^{+}$, and
$0^{-}$, respectively, which is analogous to the scenario considered in Ref.
[50]. Defining $\theta_{h}$ as the angle between the three-momentum of the
${\mathchar 28932\relax}^{0}_{b}$ in the ${\mathchar
28932\relax}^{(\prime,*)\,-}_{b}$ rest frame and the three-momentum of the
${\mathchar 28932\relax}^{+}_{c}$ in the ${\mathchar 28932\relax}^{0}_{b}$
rest frame, the $\cos\theta_{h}$ distribution is a polynomial of order
$(2J-1)$. For $J=\frac{1}{2}$ this would yield a flat distribution, and hence
a nonuniform distribution would imply $J>\frac{1}{2}$. The converse does not
follow, however: a higher-spin resonance that is unpolarized will lead to a
flat distribution. For each of the two peaks, the background-subtracted,
efficiency-corrected $\cos\theta_{h}$ distributions are studied. Both are
found to be consistent with flat distributions. When fitted with a function of
the form $f(\cos\theta_{h})=\left[a+3(1-a)\cos^{2}\theta_{h}\right]/2$, the
fitted values of $a$ are $0.89\pm 0.11$ and $0.88\pm 0.11$, and the quality of
the fits does not improve significantly. Thus, the available data are
consistent with the quark model expectations that the lower-mass peak
corresponds to a $J=\frac{1}{2}$ state and the higher one to a $J=\frac{3}{2}$
state (if unpolarized or weakly polarized), but other values of $J$ are not
excluded.

We measure the production rates of the two signals relative to that of the
${\mathchar 28932\relax}^{0}_{b}$ state, selected inclusively and passing the
same ${\mathchar 28932\relax}^{0}_{b}$ selection criteria as the signal
sample. To remain within the bandwidth restrictions of the offline data
reduction process, 10% of the candidates in the normalization mode are
randomly selected and retained for use in this analysis. To ensure that the
efficiencies are well understood, we use only the subset of events in which
one or more of the ${\mathchar 28932\relax}^{0}_{b}$ decay products is
consistent with activating the hardware trigger in the calorimeter.

For this subsample of events, the fitted yields are $93\pm 10$ for the lower-
mass ${{\mathchar 28932\relax}^{0}_{b}}{\pi_{\mathrm{s}}^{-}}$ state, $166\pm
20$ for the higher-mass ${{\mathchar
28932\relax}^{0}_{b}}{\pi_{\mathrm{s}}^{-}}$ state, and $162\pm 15$ for the
${\mathchar 28932\relax}^{0}_{b}$ normalization sample. The efficiency ratios
are determined with simulated decays, applying the same trigger,
reconstruction, and selection procedures that are used for the data.
Systematic uncertainties (and, where appropriate, corrections) are assigned
for those sources that do not cancel in the efficiency ratios. These
uncertainties include the modeling of the ${\mathchar 28932\relax}_{b}$
momentum spectra, the $\pi_{\mathrm{s}}^{-}$ reconstruction efficiency [51],
the fit method, and the efficiency of those selection criteria that are
applied to the ${{\mathchar 28932\relax}^{0}_{b}}{\pi_{\mathrm{s}}^{-}}$
candidates but not to the ${\mathchar 28932\relax}^{0}_{b}$ normalization
mode. Combining the 7$\mathrm{\,Te\kern-1.00006ptV}$ and
8$\mathrm{\,Te\kern-1.00006ptV}$ data samples, the results obtained are

$\displaystyle\frac{\sigma(pp\rightarrow{{\mathchar
28932\relax}^{\prime-}_{b}}X)\mathcal{B}({{\mathchar
28932\relax}^{\prime-}_{b}}\rightarrow{{\mathchar
28932\relax}^{0}_{b}}{{\pi}^{-}})}{\sigma(pp\rightarrow{{\mathchar
28932\relax}^{0}_{b}}X)}$ $\displaystyle=$ $\displaystyle 0.118\pm 0.017\pm
0.007,$ $\displaystyle\frac{\sigma(pp\rightarrow{{\mathchar
28932\relax}^{*-}_{b}}X)\mathcal{B}({{\mathchar
28932\relax}^{*-}_{b}}\rightarrow{{\mathchar
28932\relax}^{0}_{b}}{{\pi}^{-}})}{\sigma(pp\rightarrow{{\mathchar
28932\relax}^{0}_{b}}X)}$ $\displaystyle=$ $\displaystyle 0.207\pm 0.032\pm
0.015,$ $\displaystyle\frac{\sigma(pp\rightarrow{{\mathchar
28932\relax}^{*-}_{b}}X)\mathcal{B}({{\mathchar
28932\relax}^{*-}_{b}}\rightarrow{{\mathchar
28932\relax}^{0}_{b}}{{\pi}^{-}})}{\sigma(pp\rightarrow{{\mathchar
28932\relax}^{\prime-}_{b}}X)\mathcal{B}({{\mathchar
28932\relax}^{\prime-}_{b}}\rightarrow{{\mathchar
28932\relax}^{0}_{b}}{{\pi}^{-}})}$ $\displaystyle=$ $\displaystyle 1.74\pm
0.30\pm 0.12,$

where the first and second uncertainties are statistical and systematic,
respectively, $\sigma$ denotes a cross-section measured within the LHCb
acceptance and extrapolated to the full kinematic range with Pythia,
$\mathcal{B}$ represents a branching fraction, and $X$ refers to the rest of
the event. Given that isospin partner modes ${{\mathchar 28932\relax}^{\prime
0}_{b}}\rightarrow{{\mathchar 28932\relax}^{0}_{b}}{{\pi}^{0}}$ and
${{\mathchar 28932\relax}^{*0}_{b}}\rightarrow{{\mathchar
28932\relax}^{0}_{b}}{{\pi}^{0}}$ are also expected, these results imply that
a large fraction of ${\mathchar 28932\relax}^{0}_{b}$ baryons in the forward
region are produced in the decays of ${\mathchar 28932\relax}_{b}$ resonances.

As a further check, the ${{\mathchar
28932\relax}^{0}_{b}}{\pi_{\mathrm{s}}^{-}}$ mass spectrum is studied with
additional ${\mathchar 28932\relax}^{0}_{b}$ decay modes. Significant peaks
are seen with the mode ${{\mathchar
28932\relax}^{0}_{b}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}({p}{{K}^{-}}{{\pi}^{+}}){{K}^{-}}{{\pi}^{+}}{{\pi}^{-}}$
for both ${\mathchar 28932\relax}^{\prime-}_{b}$ $(6.4\sigma)$ and ${\mathchar
28932\relax}^{*-}_{b}$ $(4.7\sigma)$. The peaks are also seen with reduced
significance in other ${\mathchar 28932\relax}^{0}_{b}$ final states:
$4\sigma$ for ${\mathchar 28932\relax}^{\prime-}_{b}$ and $2\sigma$ for
${\mathchar 28932\relax}^{*-}_{b}$ in ${{\mathchar
28932\relax}^{0}_{b}}\rightarrow{{D}^{0}}({{K}^{-}}{{\pi}^{+}})p{{K}^{-}}$;
and $3\sigma$ for ${\mathchar 28932\relax}^{\prime-}_{b}$ and $3\sigma$ for
${\mathchar 28932\relax}^{*-}_{b}$ in ${{\mathchar
28932\relax}^{0}_{b}}\rightarrow{{D}^{+}}({{K}^{-}}{{\pi}^{+}}{{\pi}^{+}})p{{K}^{-}}{{\pi}^{-}}$.
The modes ${{\mathchar 28932\relax}^{0}_{b}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}({p}{{K}^{-}}{{\pi}^{+}}){{K}^{-}}{{\pi}^{+}}{{\pi}^{-}}$
and ${{\mathchar
28932\relax}^{0}_{b}}\rightarrow{{D}^{+}}({{K}^{-}}{{\pi}^{+}}{{\pi}^{+}})p{{K}^{-}}{{\pi}^{-}}$
have not been observed before, and are being studied in separate analyses.

With a specific configuration of other excited ${\mathchar 28932\relax}_{b}$
states, it is possible to produce a narrow peak in the ${{\mathchar
28932\relax}^{0}_{b}}{{\pi}^{-}}$ mass spectrum that is not due to a
${\mathchar 28932\relax}^{\prime-}_{b}$ resonance. This can arise from the
decay chain ${{\mathchar 28932\relax}^{**-}_{b}}\rightarrow{{\mathchar
28932\relax}^{\prime 0}_{b}}{{\pi}^{-}},~{}{{\mathchar 28932\relax}^{\prime
0}_{b}}\rightarrow{{\mathchar 28932\relax}^{0}_{b}}{{\pi}^{0}}$, where the
${\mathchar 28932\relax}^{**-}_{b}$ is the $L=1$, $J^{P}=\frac{1}{2}^{-}$
state analogous to the ${{\mathchar 28932\relax}_{c}}(2790)$. If both decays
are close to threshold, the particles produced will be kinematically
correlated such that combining the ${\mathchar 28932\relax}^{0}_{b}$ daughter
with the ${\pi}^{-}$ from the ${\mathchar 28932\relax}^{**-}_{b}$ would
produce a structure in the $m({{\mathchar 28932\relax}^{0}_{b}}{{\pi}^{-}})$
spectrum. In general such a structure would be broader than that seen in Fig.
2 and would be accompanied by a similar peak in the wrong-sign ${{\mathchar
28932\relax}^{0}_{b}}{{\pi}^{+}}$ spectrum from the isospin-partner decay,
${{\mathchar 28932\relax}^{**0}_{b}}\rightarrow{{\mathchar
28932\relax}^{\prime-}_{b}}{{\pi}^{+}},~{}{{\mathchar
28932\relax}^{\prime-}_{b}}\rightarrow{{\mathchar
28932\relax}^{0}_{b}}{{\pi}^{-}}$. However, if a number of conditions are
fulfilled, including the ${\mathchar 28932\relax}^{**-}_{b}$ and ${\mathchar
28932\relax}^{\prime 0}_{b}$ states being $279.0\pm 0.5$ and $135.8\pm
0.5$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ heavier than the ${\mathchar
28932\relax}^{0}_{b}$ ground state, respectively, it is possible to circumvent
these constraints. This would also require that the production rate of the
$L=1$ state be comparable to that of the $L=0$, $J^{P}=\frac{3}{2}^{+}$ state.
Although this scenario is contrived, it cannot be excluded at present.

In conclusion, two structures are observed with high significance in the
${{\mathchar 28932\relax}^{0}_{b}}{{\pi}^{-}}$ mass spectrum with mass
differences above threshold of $\delta m=3.653\pm 0.018\pm
0.006$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ and $23.96\pm 0.12\pm
0.06$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. These values are in general
agreement with quark model expectations for the $J^{P}=\frac{1}{2}^{+}$
${\mathchar 28932\relax}^{\prime-}_{b}$ and $J^{P}=\frac{3}{2}^{+}$
${\mathchar 28932\relax}^{*-}_{b}$ states. Their natural widths are measured
to be $\Gamma({{\mathchar
28932\relax}^{\prime-}_{b}})<0.08$$\mathrm{\,Me\kern-1.00006ptV}$ at 95% CL
and $\Gamma({{\mathchar 28932\relax}^{*-}_{b}})=1.65\pm 0.31\pm
0.10$$\mathrm{\,Me\kern-1.00006ptV}$. The observed angular distributions in
the decays of these states are consistent with the spins expected in the quark
model, but other $J$ values are not excluded. The relative production rates
are also measured.

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).

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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 Cartelle37, 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. Barter47, V. Batozskaya28, V.
Battista39, A. Bay39, L. Beaucourt4, J. Beddow51, F. Bedeschi23, I. Bediaga1,
S. Belogurov31, K. Belous35, 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, P.M. Bjørnstad54, 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, L. Carson50, K. Carvalho
Akiba2,38, RCM Casanova Mohr36, G. Casse52, L. Cassina20,k, L. Castillo
Garcia38, M. Cattaneo38, Ch. Cauet9, 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, L. Cojocariu29, G. Collazuol22, P. Collins38, A. Comerma-
Montells11, A. Contu15,38, A. Cook46, M. Coombes46, S. Coquereau8, G. Corti38,
M. Corvo16,f, I. Counts56, B. Couturier38, G.A. Cowan50, D.C. Craik48, A.C.
Crocombe48, M. Cruz Torres60, S. Cunliffe53, R. Currie53, C. D’Ambrosio38, J.
Dalseno46, P. David8, P.N.Y. David41, A. Davis57, K. De Bruyn41, S. De
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A Di Domenico25, H. Dijkstra38, S. Donleavy52, F. Dordei11, M. Dorigo39, A.
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Sedes37, R. Santacesaria25, C. Santamarina Rios37, E. Santovetti24,l, A.
Sarti18,m, C. Satriano25,n, A. Satta24, D.M. Saunders46, D. Savrina31,32, M.
Schiller38, H. Schindler38, M. Schlupp9, M. Schmelling10, B. Schmidt38, O.
Schneider39, A. Schopper38, M.-H. Schune7, R. Schwemmer38, B. Sciascia18, A.
Sciubba25,m, A. Semennikov31, I. Sepp53, N. Serra40, J. Serrano6, L.
Sestini22, P. Seyfert11, M. Shapkin35, I. Shapoval16,43,f, Y. Shcheglov30, T.
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Smith52, E. Smith55,49, E. Smith53, J. Smith47, M. Smith54, H. Snoek41, M.D.
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2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil 3Center
for High Energy Physics, Tsinghua University, Beijing, China 4LAPP, Université
de Savoie, 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 65Instituto de Fisica Corpuscular (IFIC), Universitat
de Valencia-CSIC, Valencia, Spain, associated to 36 66Van Swinderen Institute,
University of Groningen, Groningen, The Netherlands, associated to 41 67Celal
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