EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-EP-2018-243 LHCb-PAPER-2018-032

Observation of two resonances in the ${{\mathchar
28931\relax}^{0}_{b}}\pi^{\pm}$ systems and precise measurement of ${\mathchar
28934\relax}_{b}^{\pm}$ and ${\mathchar 28934\relax}_{b}^{*\pm}$ properties

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

The first observation of two structures consistent with resonances in the
final states ${{\mathchar 28931\relax}^{0}_{b}}\pi^{-}$ and ${{\mathchar
28931\relax}^{0}_{b}}\pi^{+}$ is reported using samples of $pp$ collision data
collected by the LHCb experiment at $\sqrt{s}=7$ and
$8\mathrm{\,Te\kern-1.00006ptV}$, corresponding to an integrated luminosity of
3$\mbox{\,fb}^{-1}$. The ground states ${\mathchar 28934\relax}_{b}^{\pm}$ and
${\mathchar 28934\relax}_{b}^{*\pm}$ are also confirmed and their masses and
widths are precisely measured.

Submitted to Phys. Rev. Lett.

© 2024 CERN for the benefit of the LHCb collaboration, CC-BY-4.0 licence.

Bottom baryons are composed of a $b$ quark and two lighter quarks
$(bqq^{\prime})$. In the constituent quark model [1, 2], such baryon states
form multiplets according to the symmetries of their flavor, spin, and spatial
wave functions [3]. The ${\mathchar 28931\relax}^{0}_{b}$ baryon is the
lightest of the bottom baryons and forms an isospin ($I$) singlet $(bud)$ with
spin-parity $J^{P}={\frac{1}{2}}^{+}$. Two $I=1$ triplets with
$J^{P}={\frac{1}{2}}^{+}$ (${\mathchar 28934\relax}_{b}$) and
$J^{P}={\frac{3}{2}}^{+}$ (${\mathchar 28934\relax}_{b}^{*}$) are expected,
with the spin of the flavor-symmetric $qq^{\prime}$ diquark
$S_{qq^{\prime}}=1$. Four of those six states, the ${\mathchar
28934\relax}_{b}^{\pm}$ and ${\mathchar 28934\relax}_{b}^{*\pm}$ baryons
($uub$ and $ddb$), have been observed by the CDF collaboration [4, 5] and
reported briefly in a previous LHCb paper [6]. Beyond these ground states,
radially and orbitally excited states are expected at higher masses, but only
a few excited baryons have been observed in the bottom sector [7, 8, 9, 10].
The search for and study of these states will cast light on the internal
mechanisms governing the dynamics of the constituent quarks [11, 12].

In this Letter, we report the observation of structures in both the
${{\mathchar 28931\relax}^{0}_{b}}\pi^{+}$ and ${{\mathchar
28931\relax}^{0}_{b}}\pi^{-}$ mass distributions (charge conjugation is
implied throughout this article) using $pp$ collision data collected by the
LHCb experiment at $\sqrt{s}=7$ and $8\mathrm{\,Te\kern-1.00006ptV}$,
corresponding to an integrated luminosity of 3$\mbox{\,fb}^{-1}$. We refer to
these new states as ${\mathchar 28934\relax}_{b}{(6097)}^{\pm}$ in the rest of
the Letter. We also measure precisely the masses and widths of the ${\mathchar
28934\relax}_{b}^{\pm}$ and ${\mathchar 28934\relax}_{b}^{*\pm}$ ground
states.

The LHCb detector [13, 14] 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 surrounding the $pp$
interaction region [15], a large-area silicon-strip detector located upstream
of a dipole magnet with a bending power of about $4{\mathrm{\,Tm}}$, and three
stations of silicon-strip detectors and straw drift tubes [16] placed
downstream of the magnet. The tracking system provides a measurement of the
momentum, $p$, of charged particles with a relative uncertainty that varies
from 0.5% at low momentum to 1.0% at 200$\mathrm{\,Ge\kern-1.00006ptV}$
(natural units with $c=\hbar=1$ are used throughout this Letter). The momentum
scale is calibrated using samples of ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip
2.0mu}}\rightarrow\mu^{+}\mu^{-}$ and
${{B}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}K^{+}$
decays collected concurrently with the data sample used for this analysis [17,
18]. The relative accuracy of this procedure is estimated to be $3\times
10^{-4}$ using samples of other fully reconstructed ${b}$-hadron,
${{K}^{0}_{\mathrm{\scriptscriptstyle S}}}$, and narrow $\mathchar
28935\relax$ resonance decays. The minimum distance of a track to a primary
vertex (PV), the impact parameter (IP), is measured with a resolution of
$(15+29/p_{\mathrm{T}}){\,\upmu\mathrm{m}}$, where $p_{\mathrm{T}}$ is the
component of the momentum transverse to the beam, in
$\mathrm{\,Ge\kern-1.00006ptV}$. Different types of charged hadrons are
distinguished using information from two ring-imaging Cherenkov detectors
[19]. The online event selection is performed by a trigger [20] which consists
of a hardware stage, based on information from the calorimeter and muon
systems, followed by a software stage, which applies a full event
reconstruction. The software trigger requires a two-, three- or four-track
secondary vertex with significant displacement from all primary $pp$
interaction vertices. A multivariate algorithm [21] is used for the
identification of secondary vertices consistent with the decay of a $b$
hadron. Simulated data samples are produced using the software packages
described in Refs. [22, *Sjostrand:2007gs, 24, 25, 26, 27,
*Agostinelli:2002hh].

Samples of ${\mathchar 28931\relax}^{0}_{b}$ candidates are formed from
${{\mathchar 28931\relax}^{+}_{c}}\pi^{-}$ combinations, where the ${\mathchar
28931\relax}^{+}_{c}$ baryon is reconstructed in the $pK^{-}\pi^{+}$ final
state. All charged particles used to form the $b$-hadron candidates are
required to have particle-identification information consistent with the
appropriate mass hypothesis. Misreconstructed tracks are suppressed by the use
of a neural network trained to discriminate between real and fake particles
[29]. To suppress prompt background, all ${\mathchar 28931\relax}^{0}_{b}$
decay products are required to have significant $\chi^{2}_{\text{IP}}$ with
respect to all PVs in the event, where $\chi^{2}_{\text{IP}}$ is the
difference in $\chi^{2}$ of the vertex fit of a given PV, when a particle is
included or excluded from the fit. The reconstructed ${\mathchar
28931\relax}^{+}_{c}$ vertex is required to have a good fit quality and to be
significantly displaced from all PVs in the event. The reconstructed
${\mathchar 28931\relax}^{+}_{c}$ mass must be within a mass window of $\pm
25$$\mathrm{\,Me\kern-1.00006ptV}$ of its known value [30]. Pion candidates
that have large $\chi^{2}_{\text{IP}}$ with respect to all PVs are combined
with ${\mathchar 28931\relax}^{+}_{c}$ candidates to form ${\mathchar
28931\relax}^{0}_{b}$ candidates, requiring good vertex-fit quality and
separation of the ${\mathchar 28931\relax}^{0}_{b}$ decay point from any PV in
the event. A Boosted Decision Tree (BDT) discriminant [31, 32] is used to
further reduce the background. The BDT exploits nineteen topological
variables, including the $\chi^{2}_{\text{IP}}$ and $p_{\mathrm{T}}$ values of
all the particles in the decay chain, the $\chi^{2}$ values of the ${\mathchar
28931\relax}^{0}_{b}$ and ${\mathchar 28931\relax}^{+}_{c}$ decay vertices,
their flight-distance significance, and the angle between their momentum and
direction of flight, defined by their production and decay vertices. The BDT
is trained using simulated ${\mathchar 28931\relax}^{0}_{b}$ signal decays and
${\mathchar 28931\relax}^{0}_{b}$ candidates in data in the sideband
$5800<m({{\mathchar 28931\relax}^{0}_{b}})<6000\mathrm{\,Me\kern-1.00006ptV}$.
The signal candidates are refitted constraining the mass of the ${\mathchar
28931\relax}^{+}_{c}$ to its known value [30] in order to improve the mass
resolution [33]. The mass distribution of the selected ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{\mathchar 28931\relax}^{+}_{c}}\pi^{-}$,
${{\mathchar 28931\relax}^{+}_{c}}\rightarrow pK^{-}\pi^{+}$ candidates is
shown in Fig. 1. The mass spectrum is fitted with an asymmetric resolution
function for the signal component [34], plus a misreconstructed ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{\mathchar 28931\relax}^{+}_{c}}K^{-}$
component whose yield is fixed relative to that of ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{\mathchar 28931\relax}^{+}_{c}}\pi^{-}$, an
exponential function for the combinatorial background and an empirical
function for partially reconstructed backgrounds as described in Ref. [34].
The resulting ${\mathchar 28931\relax}^{0}_{b}$ signal yield is $234$,$270\pm
900$.

Figure 1: Mass distribution for the selected ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{\mathchar 28931\relax}^{+}_{c}}\pi^{-}$
candidates. The points show experimental data.

The ${\mathchar 28931\relax}^{0}_{b}$ candidates contained in a $\pm
50$$\mathrm{\,Me\kern-1.00006ptV}$ window around the peak maximum are then
combined with a prompt pion, hereafter referred to as $\pi_{s}^{\pm}$, to form
${{\mathchar 28934\relax}_{b}^{\pm}}\rightarrow{{\mathchar
28931\relax}^{0}_{b}}\pi^{\pm}$ combinations (along with
${{\overline{\mathchar 28934\relax}}_{b}^{\mp}}\rightarrow{{\kern
1.00006pt\overline{\kern-1.00006pt\mathchar
28931\relax}}{}^{0}_{b}}\pi^{\mp}$). Initially,
$p_{\mathrm{T}}({\pi_{s}^{\pm}})>200\mathrm{\,Me\kern-1.00006ptV}$ and
${Q\equiv m({{\mathchar 28931\relax}^{0}_{b}}\pi^{\pm})-m({{\mathchar
28931\relax}^{0}_{b}})-m(\pi^{\pm})}<200\mathrm{\,Me\kern-1.00006ptV}$ are
required, where the ${{\mathchar 28931\relax}^{0}_{b}}\pi^{\pm}$ mass is
recomputed constraining the masses of the ${\mathchar 28931\relax}^{+}_{c}$
and ${\mathchar 28931\relax}^{0}_{b}$ baryons to their known values [30]. Then
the search is extended to higher masses up to
$Q=600\mathrm{\,Me\kern-1.00006ptV}$, observing an additional peak in both
${{\mathchar 28931\relax}^{0}_{b}}\pi^{-}$ and ${{\mathchar
28931\relax}^{0}_{b}}\pi^{+}$ spectra. A tighter transverse momentum cut
$p_{\mathrm{T}}(\pi_{s}^{\pm})>1000\mathrm{\,Me\kern-1.00006ptV}$ is applied
to remove the background from prompt pions.

The signal yields and parameters of the ${\mathchar 28934\relax}_{b}^{\pm}$,
${\mathchar 28934\relax}_{b}^{*\pm}$ and ${\mathchar
28934\relax}_{b}{(6097)}^{\pm}$ resonances are determined with extended
unbinned maximum-likelihood fits to the $Q$-value distribution. All signal
components are modeled as relativistic Breit–Wigner functions [35] including
Blatt–Weisskopf form factors [36] with a radius of
$4\mathrm{\,Ge\kern-1.00006ptV}^{-1}$. The orbital angular momentum $l$
between the ${\mathchar 28931\relax}^{0}_{b}$ baryon and $\pi_{s}^{\pm}$
candidate is taken to be 1 in all cases. The relativistic Breit–Wigner
functions are convolved with the detector resolution and corrected for a small
distortion in the shape induced by the $p_{\mathrm{T}}$ requirement on the
$\pi_{s}^{\pm}$ meson. The resolution models are determined from simulation,
in which the three signal resonances are generated at the $Q$ values found in
data. The root-mean-square values of the resolution functions for ${\mathchar
28934\relax}_{b}$, ${\mathchar 28934\relax}_{b}^{*}$, and ${\mathchar
28934\relax}_{b}{(6097)}$ are $0.99$, $1.13$ and
$2.35$$\mathrm{\,Me\kern-1.00006ptV}$, respectively, all below the visible
widths of the mass peaks and consistent with a resolution that scales as
$\sqrt{Q}$. Different empirical parameterizations are used for the two mass
ranges. For $0<Q<200$$\mathrm{\,Me\kern-1.00006ptV}$ the background shape is
described by a smooth threshold function [37, 10, 38], while for
$0<Q<600$$\mathrm{\,Me\kern-1.00006ptV}$ a sigmoid function is used, as in
Refs. [39, 40]. The background shapes are validated by using candidates in the
data sidebands for a wide range of $p_{\mathrm{T}}$ requirements. All of the
masses, widths, and yields are free to vary in the fit, as are the background
parameters; the resolutions of the signal components are fixed to the values
found in simulation. The fit models are validated with pseudoexperiments and
no significant bias is found on any of the free parameters.

The fits to the data sample are shown in Fig. 2 and the resulting parameters
of interest are summarized in Table 1. The fit results are also used to
determine mass differences and isospin splittings (given below). The two new
peaks in ${{\mathchar 28931\relax}^{0}_{b}}\pi^{-}$ and ${{\mathchar
28931\relax}^{0}_{b}}\pi^{+}$ distributions have local statistical
significances of $12.7\sigma$ and $12.6\sigma$, respectively, based on the
differences in log-likelihood between a fit with zero signal and the nominal
fit.

Table 1: Summary of the results of the fits to the $Q\equiv m({{\mathchar 28931\relax}^{0}_{b}}\pi^{\pm})-m({{\mathchar 28931\relax}^{0}_{b}})-m(\pi^{\pm})$ mass spectra. $Q_{0}$ and $\Gamma$ are the mean and the width of the Breit–Wigner function. The quoted uncertainties are statistical only. State |  $Q_{0}$ $[\mathrm{Me\kern-1.00006ptV}]$ |  $\Gamma$ $[\mathrm{Me\kern-1.00006ptV}]$ | Yield
---|---|---|---
${\mathchar 28934\relax}_{b}^{-}$ | $\phantom{0}56.45\pm 0.14$ | $\phantom{0}5.33\pm 0.42$ | $3270\pm 180$
${\mathchar 28934\relax}_{b}^{*-}$ | $\phantom{0}75.54\pm 0.17$ | $10.68\pm 0.60$ | $7460\pm 300$
${\mathchar 28934\relax}_{b}^{+}$ | $\phantom{0}51.36\pm 0.11$ | $\phantom{0}4.83\pm 0.31$ | $3670\pm 160$
${\mathchar 28934\relax}_{b}^{*+}$ | $\phantom{0}71.09\pm 0.14$ | $\phantom{0}9.34\pm 0.47$ | $7350\pm 260$
${\mathchar 28934\relax}_{b}{(6097)}^{-}$ | $338.8\pm 1.7$ | $28.9\pm 4.2$ | $\phantom{0}880\pm 100$
${\mathchar 28934\relax}_{b}{(6097)}^{+}$ | $336.6\pm 1.7$ | $31.0\pm 5.5$ | $\phantom{0}900\pm 110$

Figure 2: Mass distribution for selected ${{{\mathchar
28931\relax}^{0}_{b}}\pi^{\pm}}$ candidates. The points show experimental
data. The left (right) column shows ${{{\mathchar
28931\relax}^{0}_{b}}\pi^{-}}$ (${{{\mathchar 28931\relax}^{0}_{b}}\pi^{+}}$)
combinations. The top row shows the fits to the lower-mass states ${{\mathchar
28934\relax}_{b}^{\pm}}$ and ${{\mathchar 28934\relax}_{b}^{*\pm}}$. The lower
row presents the fits to the new mass peaks with the requirement
$p_{\mathrm{T}}({\pi_{s}^{\pm}})>1000$$\mathrm{\,Me\kern-0.90005ptV}$.

Several sources of systematic uncertainty are considered. The dominant source
of systematic uncertainty on the mass measurements comes from the knowledge of
the momentum scale. This uncertainty is evaluated by adjusting the momentum
scale by the $3\times 10^{-4}$ relative uncertainty from the calibration
procedure [18] and rerunning the mass fit. This procedure is also validated
using a control sample of approximately 3 million
${{D}^{*+}}\rightarrow{{D}^{0}}\pi^{+}$ decays, with ${{D}^{0}}\rightarrow
K^{-}\pi^{+}$. The momentum-scale uncertainties largely cancel in the mass
differences and splittings. A second uncertainty arises from the
parameterization of the background and is estimated by varying the function
used (e.g. polynomial background functions of different order and other
empirical curves). An additional source of uncertainty on the determination of
the natural widths arises from known differences in resolution between data
and simulation. These are expected to agree within $5$%, based on previous
studies [10, 38, 8], and this assumption has been validated with the
${{D}^{*+}}\rightarrow{{D}^{0}}\pi^{+}$ control sample. Systematic
uncertainties on the widths are assessed by varying the width of the
resolution function by $\pm 5$%. Further uncertainties on the masses and
widths arise from the assumed Breit–Wigner parameters. The resonant states are
assumed to decay to ${{\mathchar 28931\relax}^{0}_{b}}\pi^{\pm}$ with angular
momentum $l=1$. For the ${\mathchar 28934\relax}_{b}{(6097)}^{\pm}$ states,
fits assuming $l=0,2,3$ are also performed and the largest changes to the
fitted parameters with respect to the nominal fit are assigned as systematic
uncertainties. The systematic uncertainties are summarised in Table 2; in all
cases they are much smaller than the statistical uncertainties. All numerical
results for the measured masses and widths are presented in Table 3. The mass
values $m$ are obtained using the most precise LHCb combination for the
${\mathchar 28931\relax}^{0}_{b}$ mass, $m({{\mathchar
28931\relax}^{0}_{b}})=5619.62\pm 0.16\pm 0.13$$\mathrm{\,Me\kern-1.00006ptV}$
[41], which dominates by far the current world average [42]. The correlated
uncertainties, mainly deriving from the knowledge of the momentum scale which
is a common source of systematic uncertainty in all LHCb mass measurements,
are propagated as described in Ref. [43]. The isospin splittings of the new
states are consistent with zero, although with large experimental uncertainty.

Table 2: Summary of the systematic uncertainties on the measured masses and
widths. $Q_{0}$ and $\Gamma$ are the mean and the width of the Breit–Wigner
function. All values are in $\mathrm{\,Me\kern-0.90005ptV}$.

|  | ${\mathchar 28934\relax}_{b}^{-}$ |  | ${\mathchar 28934\relax}_{b}^{*-}$ |  | ${\mathchar 28934\relax}_{b}{(6097)}^{-}$
---|---|---|---|---|---|---
Source |  | $Q_{0}$ | $\Gamma$ |  | $Q_{0}$ | $\Gamma$ |  | $Q_{0}$ | $\Gamma$
$p$ scale |  | 0.046 | 0.036 |  | 0.047 | 0.071 |  | 0.130 | 0.013
Resolution |  | 0.001 | 0.038 |  | 0.001 | 0.033 |  | 0.003 | 0.108
Spin assign. |  |  |  |  |  |  |  | 0.370 | 0.462
Radius |  | 0.003 | 0.101 |  | 0.010 | 0.017 |  | 0.080 | 0.081
Background |  | 0.021 | 0.351 |  | 0.033 | 0.315 |  | 0.184 | 0.798
Total |  | 0.051 | 0.369 |  | 0.058 | 0.325 |  | 0.440 | 0.932

|  | ${\mathchar 28934\relax}_{b}^{+}$ |  | ${\mathchar 28934\relax}_{b}^{*+}$ |  | ${\mathchar 28934\relax}_{b}{(6097)}^{+}$
---|---|---|---|---|---|---
Source |  | $Q_{0}$ | $\Gamma$ |  | $Q_{0}$ | $\Gamma$ |  | $Q_{0}$ | $\Gamma$
$p$ scale |  | 0.039 | 0.046 |  | 0.047 | 0.045 |  | 0.128 | 0.090
Resolution |  | 0.001 | 0.040 |  | 0.001 | 0.038 |  | 0.002 | 0.086
Spin assign. |  |  |  |  |  |  |  | 0.113 | 0.342
Radius |  | 0.001 | 0.061 |  | 0.003 | 0.002 |  | 0.001 | 0.031
Background |  | 0.027 | 0.357 |  | 0.026 | 0.256 |  | 0.207 | 0.598
Total |  | 0.047 | 0.367 |  | 0.053 | 0.263 |  | 0.268 | 0.701

In summary, the first observation of two new mass peaks in the ${{\mathchar
28931\relax}^{0}_{b}}\pi^{+}$ and ${{\mathchar 28931\relax}^{0}_{b}}\pi^{-}$
systems is reported. These structures are consistent with single resonances
described by relativistic Breit–Wigner functions. The ground-state ${\mathchar
28934\relax}_{b}^{\pm}$ and ${\mathchar 28934\relax}_{b}^{*\pm}$ baryons are
also confirmed and their masses and widths precisely measured. These values
are in good agreement with those measured by the CDF collaboration [5], with
precision improved by a factor of 5. We also quote the mass differences and
isospin splittings, for which most of the systematic uncertainties cancel.

Table 3: Masses and widths of the ${\mathchar 28934\relax}_{b}{(6097)}^{\pm}$, ${\mathchar 28934\relax}_{b}^{*\pm}$ and ${\mathchar 28934\relax}_{b}^{\pm}$ baryons. Isospin splittings $\Delta({X^{\pm}})=m(X^{+})-m(X^{-})$ and mass differences are also calculated. The first uncertainty is statistical, the second systematic. The systematic uncertainty on $m$ includes the uncertainty from the knowledge of the ${\mathchar 28931\relax}^{0}_{b}$ mass [41]. Quantity | Value $[\mathrm{Me\kern-1.00006ptV}]$
---|---
$m({{\mathchar 28934\relax}_{b}{(6097)}^{-}})$ | 6098.0$\,\pm\;$ | 1.7 $\,\pm\;$ | 0.5
$m({{\mathchar 28934\relax}_{b}{(6097)}^{+}})$ | 6095.8$\,\pm\;$ | 1.7 $\,\pm\;$ | 0.4
$\Gamma({{\mathchar 28934\relax}_{b}{(6097)}^{-}})$ | 28.9$\,\pm\;$ | 4.2 $\,\pm\;$ | 0.9
$\Gamma({{\mathchar 28934\relax}_{b}{(6097)}^{+}})$ | 31.0$\,\pm\;$ | 5.5 $\,\pm\;$ | 0.7
$m({{\mathchar 28934\relax}_{b}^{-}})$ | 5815.64$\,\pm\;$ | 0.14 $\,\pm\;$ | 0.24
$m({{\mathchar 28934\relax}_{b}^{*-}})$ | 5834.73$\,\pm\;$ | 0.17 $\,\pm\;$ | 0.25
$m({{\mathchar 28934\relax}_{b}^{+}})$ | 5810.55$\,\pm\;$ | 0.11 $\,\pm\;$ | 0.23
$m({{\mathchar 28934\relax}_{b}^{*+}})$ | 5830.28$\,\pm\;$ | 0.14 $\,\pm\;$ | 0.24
$\Gamma({{\mathchar 28934\relax}_{b}^{-}})$ | 5.33$\,\pm\;$ | 0.42 $\,\pm\;$ | 0.37
$\Gamma({{\mathchar 28934\relax}_{b}^{*-}})$ | 10.68$\,\pm\;$ | 0.60 $\,\pm\;$ | 0.33
$\Gamma({{\mathchar 28934\relax}_{b}^{+}})$ | 4.83$\,\pm\;$ | 0.31 $\,\pm\;$ | 0.37
$\Gamma({{\mathchar 28934\relax}_{b}^{*+}})$ | 9.34$\,\pm\;$ | 0.47 $\,\pm\;$ | 0.26
$m({{\mathchar 28934\relax}_{b}^{*-}})-m({{\mathchar 28934\relax}_{b}^{-}})$ | 19.09$\,\pm\;$ | 0.22 $\,\pm\;$ | 0.02
$m({{\mathchar 28934\relax}_{b}^{*+}})-m({{\mathchar 28934\relax}_{b}^{+}})$ | 19.73$\,\pm\;$ | 0.18 $\,\pm\;$ | 0.01
$\Delta({{{\mathchar 28934\relax}_{b}{(6097)}^{\pm}}})$ |  $-2.2$$\,\pm\;$ | 2.4 $\,\pm\;$ | 0.3
$\Delta({{{\mathchar 28934\relax}_{b}^{\pm}}})$ |  $-5.09$$\,\pm\;$ | 0.18 $\,\pm\;$ | 0.01
$\Delta({{{\mathchar 28934\relax}_{b}^{*\pm}}})$ |  $-4.45$$\,\pm\;$ | 0.22 $\,\pm\;$ | 0.01

In the heavy-quark limit, five ${{\mathchar 28934\relax}_{b}}(1P)$ states are
expected. Several predictions of their masses have been made [11, 12, 44, 45],
but some or all of these states may be too wide to be accessible
experimentally [44]. Since the expected density of baryon states is high, it
cannot be excluded that the new structures seen are the superpositions of more
than one (near-)degenerate state. Taking into account that the predicted mass
and width depend on the as-yet-unknown spin and parity, the newly observed
structures are compatible with being $1P$ excitations. Other interpretations,
such as molecular states, may also be possible [46].

## Acknowledgements

We thank Jonathan L. Rosner and Marek Karliner for useful discussions on the
interpretation of the theoretical predictions. 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); MOST and NSFC (China); CNRS/IN2P3
(France); BMBF, DFG and MPG (Germany); INFN (Italy); NWO (Netherlands); MNiSW
and NCN (Poland); MEN/IFA (Romania); MSHE (Russia); MinECo (Spain); SNSF and
SER (Switzerland); NASU (Ukraine); STFC (United Kingdom); NSF (USA). We
acknowledge the computing resources that are provided by CERN, IN2P3 (France),
KIT and DESY (Germany), INFN (Italy), SURF (Netherlands), PIC (Spain), GridPP
(United Kingdom), RRCKI and Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH
(Romania), CBPF (Brazil), PL-GRID (Poland) and OSC (USA). We are indebted to
the communities behind the multiple open-source software packages on which we
depend. Individual groups or members have received support from AvH Foundation
(Germany); EPLANET, Marie Skłodowska-Curie Actions and ERC (European Union);
ANR, Labex P2IO and OCEVU, and Région Auvergne-Rhône-Alpes (France); Key
Research Program of Frontier Sciences of CAS, CAS PIFI, and the Thousand
Talents Program (China); RFBR, RSF and Yandex LLC (Russia); GVA, XuntaGal and
GENCAT (Spain); the Royal Society and the Leverhulme Trust (United Kingdom);
Laboratory Directed Research and Development program of LANL (USA).

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LHCb collaboration

R. Aaij27, C. Abellán Beteta44, B. Adeva41, M. Adinolfi48, C.A. Aidala74, Z.
Ajaltouni5, S. Akar59, P. Albicocco18, J. Albrecht10, F. Alessio42, M.
Alexander53, A. Alfonso Albero40, G. Alkhazov33, P. Alvarez Cartelle55, A.A.
Alves Jr41, S. Amato2, S. Amerio23, Y. Amhis7, L. An3, L. Anderlini17, G.
Andreassi43, M. Andreotti16, J.E. Andrews60, R.B. Appleby56, F. Archilli27, P.
d’Argent12, J. Arnau Romeu6, A. Artamonov39, M. Artuso61, K. Arzymatov37, E.
Aslanides6, M. Atzeni44, B. Audurier22, S. Bachmann12, J.J. Back50, S.
Baker55, V. Balagura7,b, W. Baldini16, A. Baranov37, R.J. Barlow56, S.
Barsuk7, W. Barter56, F. Baryshnikov70, V. Batozskaya31, B. Batsukh61, V.
Battista43, A. Bay43, J. Beddow53, F. Bedeschi24, I. Bediaga1, A. Beiter61,
L.J. Bel27, S. Belin22, N. Beliy63, V. Bellee43, N. Belloli20,i, K. Belous39,
I. Belyaev34,42, E. Ben-Haim8, G. Bencivenni18, S. Benson27, S. Beranek9, A.
Berezhnoy35, R. Bernet44, D. Berninghoff12, E. Bertholet8, A. Bertolin23, C.
Betancourt44, F. Betti15,42, M.O. Bettler49, M. van Beuzekom27, Ia.
Bezshyiko44, S. Bhasin48, J. Bhom29, S. Bifani47, P. Billoir8, A. Birnkraut10,
A. Bizzeti17,u, M. Bjørn57, M.P. Blago42, T. Blake50, F. Blanc43, S. Blusk61,
D. Bobulska53, V. Bocci26, O. Boente Garcia41, T. Boettcher58, A. Bondar38,w,
N. Bondar33, S. Borghi56,42, M. Borisyak37, M. Borsato41, F. Bossu7, M.
Boubdir9, T.J.V. Bowcock54, C. Bozzi16,42, S. Braun12, M. Brodski42, J.
Brodzicka29, A. Brossa Gonzalo50, D. Brundu22, E. Buchanan48, A. Buonaura44,
C. Burr56, A. Bursche22, J. Buytaert42, W. Byczynski42, S. Cadeddu22, H.
Cai64, R. Calabrese16,g, R. Calladine47, M. Calvi20,i, M. Calvo Gomez40,m, A.
Camboni40,m, P. Campana18, D.H. Campora Perez42, L. Capriotti15, A.
Carbone15,e, G. Carboni25, R. Cardinale19,h, A. Cardini22, P. Carniti20,i, L.
Carson52, K. Carvalho Akiba2, G. Casse54, L. Cassina20, M. Cattaneo42, G.
Cavallero19,h, R. Cenci24,p, D. Chamont7, M.G. Chapman48, M. Charles8, Ph.
Charpentier42, G. Chatzikonstantinidis47, M. Chefdeville4, V. Chekalina37, C.
Chen3, S. Chen22, S.-G. Chitic42, V. Chobanova41, M. Chrzaszcz42, A.
Chubykin33, P. Ciambrone18, X. Cid Vidal41, G. Ciezarek42, P.E.L. Clarke52, M.
Clemencic42, H.V. Cliff49, J. Closier42, V. Coco42, J.A.B. Coelho7, J. Cogan6,
E. Cogneras5, L. Cojocariu32, P. Collins42, T. Colombo42, A. Comerma-
Montells12, A. Contu22, G. Coombs42, S. Coquereau40, G. Corti42, M. Corvo16,g,
C.M. Costa Sobral50, B. Couturier42, G.A. Cowan52, D.C. Craik58, A.
Crocombe50, M. Cruz Torres1, R. Currie52, C. D’Ambrosio42, F. Da Cunha
Marinho2, C.L. Da Silva75, E. Dall’Occo27, J. Dalseno48, A. Danilina34, A.
Davis3, O. De Aguiar Francisco42, K. De Bruyn42, S. De Capua56, M. De Cian43,
J.M. De Miranda1, L. De Paula2, M. De Serio14,d, P. De Simone18, C.T. Dean53,
D. Decamp4, L. Del Buono8, B. Delaney49, H.-P. Dembinski11, M. Demmer10, A.
Dendek30, D. Derkach37, O. Deschamps5, F. Desse7, F. Dettori54, B. Dey65, A.
Di Canto42, P. Di Nezza18, S. Didenko70, H. Dijkstra42, F. Dordei42, M.
Dorigo42,x, A. Dosil Suárez41, L. Douglas53, A. Dovbnya45, K. Dreimanis54, L.
Dufour27, G. Dujany8, P. Durante42, J.M. Durham75, D. Dutta56, R.
Dzhelyadin39, M. Dziewiecki12, A. Dziurda29, A. Dzyuba33, S. Easo51, U.
Egede55, V. Egorychev34, S. Eidelman38,w, S. Eisenhardt52, U. Eitschberger10,
R. Ekelhof10, L. Eklund53, S. Ely61, A. Ene32, S. Escher9, S. Esen27, T.
Evans59, A. Falabella15, N. Farley47, S. Farry54, D. Fazzini20,42,i, L.
Federici25, P. Fernandez Declara42, A. Fernandez Prieto41, F. Ferrari15, L.
Ferreira Lopes43, F. Ferreira Rodrigues2, M. Ferro-Luzzi42, S. Filippov36,
R.A. Fini14, M. Fiorini16,g, M. Firlej30, C. Fitzpatrick43, T. Fiutowski30, F.
Fleuret7,b, M. Fontana22,42, F. Fontanelli19,h, R. Forty42, V. Franco Lima54,
M. Frank42, C. Frei42, J. Fu21,q, W. Funk42, C. Färber42, M. Féo Pereira
Rivello Carvalho27, E. Gabriel52, A. Gallas Torreira41, D. Galli15,e, S.
Gallorini23, S. Gambetta52, Y. Gan3, M. Gandelman2, P. Gandini21, Y. Gao3,
L.M. Garcia Martin73, B. Garcia Plana41, J. García Pardiñas44, J. Garra
Tico49, L. Garrido40, D. Gascon40, C. Gaspar42, L. Gavardi10, G. Gazzoni5, D.
Gerick12, E. Gersabeck56, M. Gersabeck56, T. Gershon50, D. Gerstel6, Ph.
Ghez4, S. Gianì43, V. Gibson49, O.G. Girard43, L. Giubega32, K. Gizdov52, V.V.
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Greim27, P. Griffith22, L. Grillo56, L. Gruber42, B.R. Gruberg Cazon57, O.
Grünberg67, C. Gu3, E. Gushchin36, Yu. Guz39,42, T. Gys42, C. Göbel62, T.
Hadavizadeh57, C. Hadjivasiliou5, G. Haefeli43, C. Haen42, S.C. Haines49, B.
Hamilton60, X. Han12, T.H. Hancock57, S. Hansmann-Menzemer12, N. Harnew57,
S.T. Harnew48, T. Harrison54, C. Hasse42, M. Hatch42, J. He63, M. Hecker55, K.
Heinicke10, A. Heister10, K. Hennessy54, L. Henry73, E. van Herwijnen42, M.
Heß67, A. Hicheur2, R. Hidalgo Charman56, D. Hill57, M. Hilton56, P.H.
Hopchev43, W. Hu65, W. Huang63, Z.C. Huard59, W. Hulsbergen27, T. Humair55, M.
Hushchyn37, D. Hutchcroft54, D. Hynds27, P. Ibis10, M. Idzik30, P. Ilten47, K.
Ivshin33, R. Jacobsson42, J. Jalocha57, E. Jans27, A. Jawahery60, F. Jiang3,
M. John57, D. Johnson42, C.R. Jones49, C. Joram42, B. Jost42, N. Jurik57, S.
Kandybei45, M. Karacson42, J.M. Kariuki48, S. Karodia53, N. Kazeev37, M.
Kecke12, F. Keizer49, M. Kelsey61, M. Kenzie49, T. Ketel28, E. Khairullin37,
B. Khanji42, C. Khurewathanakul43, K.E. Kim61, T. Kirn9, S. Klaver18, K.
Klimaszewski31, T. Klimkovich11, S. Koliiev46, M. Kolpin12, R. Kopecna12, P.
Koppenburg27, I. Kostiuk27, S. Kotriakhova33, M. Kozeiha5, L. Kravchuk36, M.
Kreps50, F. Kress55, P. Krokovny38,w, W. Krupa30, W. Krzemien31, W.
Kucewicz29,l, M. Kucharczyk29, V. Kudryavtsev38,w, A.K. Kuonen43, T.
Kvaratskheliya34,42, D. Lacarrere42, G. Lafferty56, A. Lai22, D. Lancierini44,
G. Lanfranchi18, C. Langenbruch9, T. Latham50, C. Lazzeroni47, R. Le Gac6, A.
Leflat35, J. Lefrançois7, R. Lefèvre5, F. Lemaitre42, O. Leroy6, T. Lesiak29,
B. Leverington12, P.-R. Li63, T. Li3, Z. Li61, X. Liang61, T. Likhomanenko69,
R. Lindner42, F. Lionetto44, V. Lisovskyi7, X. Liu3, D. Loh50, A. Loi22, I.
Longstaff53, J.H. Lopes2, G.H. Lovell49, D. Lucchesi23,o, M. Lucio Martinez41,
A. Lupato23, E. Luppi16,g, O. Lupton42, A. Lusiani24, X. Lyu63, F. Machefert7,
F. Maciuc32, V. Macko43, P. Mackowiak10, S. Maddrell-Mander48, O. Maev33,42,
K. Maguire56, D. Maisuzenko33, M.W. Majewski30, S. Malde57, B. Malecki29, A.
Malinin69, T. Maltsev38,w, G. Manca22,f, G. Mancinelli6, D. Marangotto21,q, J.
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P. Marino43, J. Marks12, P.J. Marshall54, G. Martellotti26, M. Martin6, M.
Martinelli42, D. Martinez Santos41, F. Martinez Vidal73, A. Massafferri1, M.
Materok9, R. Matev42, A. Mathad50, Z. Mathe42, C. Matteuzzi20, A. Mauri44, E.
Maurice7,b, B. Maurin43, A. Mazurov47, M. McCann55,42, A. McNab56, R.
McNulty13, J.V. Mead54, B. Meadows59, C. Meaux6, F. Meier10, N. Meinert67, D.
Melnychuk31, M. Merk27, A. Merli21,q, E. Michielin23, D.A. Milanes66, E.
Millard50, M.-N. Minard4, L. Minzoni16,g, D.S. Mitzel12, A. Mogini8, J. Molina
Rodriguez1,y, T. Mombächer10, I.A. Monroy66, S. Monteil5, M. Morandin23, G.
Morello18, M.J. Morello24,t, O. Morgunova69, J. Moron30, A.B. Morris6, R.
Mountain61, F. Muheim52, M. Mulder27, C.H. Murphy57, D. Murray56, A. Mödden
10, D. Müller42, J. Müller10, K. Müller44, V. Müller10, P. Naik48, T.
Nakada43, R. Nandakumar51, A. Nandi57, T. Nanut43, I. Nasteva2, M. Needham52,
N. Neri21, S. Neubert12, N. Neufeld42, M. Neuner12, R. Newcombe55, T.D.
Nguyen43, C. Nguyen-Mau43,n, S. Nieswand9, R. Niet10, N. Nikitin35, A.
Nogay69, N.S. Nolte42, D.P. O’Hanlon15, A. Oblakowska-Mucha30, V. Obraztsov39,
S. Ogilvy18, R. Oldeman22,f, C.J.G. Onderwater68, A. Ossowska29, J.M. Otalora
Goicochea2, P. Owen44, A. Oyanguren73, P.R. Pais43, T. Pajero24,t, A.
Palano14, M. Palutan18,42, G. Panshin72, A. Papanestis51, M. Pappagallo52,
L.L. Pappalardo16,g, W. Parker60, C. Parkes56, G. Passaleva17,42, A.
Pastore14, M. Patel55, C. Patrignani15,e, A. Pearce42, A. Pellegrino27, G.
Penso26, M. Pepe Altarelli42, S. Perazzini42, D. Pereima34, P. Perret5, L.
Pescatore43, K. Petridis48, A. Petrolini19,h, A. Petrov69, S. Petrucci52, M.
Petruzzo21,q, B. Pietrzyk4, G. Pietrzyk43, M. Pikies29, M. Pili57, D. Pinci26,
J. Pinzino42, F. Pisani42, A. Piucci12, V. Placinta32, S. Playfer52, J.
Plews47, M. Plo Casasus41, F. Polci8, M. Poli Lener18, A. Poluektov50, N.
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J.H. Rademacker48, M. Rama24, M. Ramos Pernas41, M.S. Rangel2, F.
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M.S. Rudolph61, T. Ruf42, J. Ruiz Vidal73, J.J. Saborido Silva41, N.
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Witek29, G. Wormser7, S.A. Wotton49, K. Wyllie42, D. Xiao65, Y. Xie65, A. Xu3,
M. Xu65, Q. Xu63, Z. Xu3, Z. Xu4, Z. Yang3, Z. Yang60, Y. Yao61, L.E.
Yeomans54, H. Yin65, J. Yu65,aa, X. Yuan61, O. Yushchenko39, K.A. Zarebski47,
M. Zavertyaev11,c, D. Zhang65, L. Zhang3, W.C. Zhang3,z, Y. Zhang7, A.
Zhelezov12, Y. Zheng63, X. Zhu3, V. Zhukov9,35, J.B. Zonneveld52, S.
Zucchelli15.

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
4Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, IN2P3-LAPP, Annecy,
France
5Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-
Ferrand, France
6Aix Marseille Univ, CNRS/IN2P3, CPPM, Marseille, France
7LAL, Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France
8LPNHE, Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3,
Paris, France
9I. Physikalisches Institut, RWTH Aachen University, Aachen, Germany
10Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
11Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
12Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg,
Germany
13School of Physics, University College Dublin, Dublin, Ireland
14INFN Sezione di Bari, Bari, Italy
15INFN Sezione di Bologna, Bologna, Italy
16INFN Sezione di Ferrara, Ferrara, Italy
17INFN Sezione di Firenze, Firenze, Italy
18INFN Laboratori Nazionali di Frascati, Frascati, Italy
19INFN Sezione di Genova, Genova, Italy
20INFN Sezione di Milano-Bicocca, Milano, Italy
21INFN Sezione di Milano, Milano, Italy
22INFN Sezione di Cagliari, Monserrato, Italy
23INFN Sezione di Padova, Padova, Italy
24INFN Sezione di Pisa, Pisa, Italy
25INFN Sezione di Roma Tor Vergata, Roma, Italy
26INFN Sezione di Roma La Sapienza, Roma, Italy
27Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
28Nikhef National Institute for Subatomic Physics and VU University Amsterdam,
Amsterdam, Netherlands
29Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of
Sciences, Kraków, Poland
30AGH - University of Science and Technology, Faculty of Physics and Applied
Computer Science, Kraków, Poland
31National Center for Nuclear Research (NCBJ), Warsaw, Poland
32Horia Hulubei National Institute of Physics and Nuclear Engineering,
Bucharest-Magurele, Romania
33Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
34Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
35Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow,
Russia
36Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS),
Moscow, Russia
37Yandex School of Data Analysis, Moscow, Russia
38Budker Institute of Nuclear Physics (SB RAS), Novosibirsk, Russia
39Institute for High Energy Physics (IHEP), Protvino, Russia
40ICCUB, Universitat de Barcelona, Barcelona, Spain
41Instituto Galego de Física de Altas Enerxías (IGFAE), Universidade de
Santiago de Compostela, Santiago de Compostela, Spain
42European Organization for Nuclear Research (CERN), Geneva, Switzerland
43Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),
Lausanne, Switzerland
44Physik-Institut, Universität Zürich, Zürich, Switzerland
45NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
46Institute for Nuclear Research of the National Academy of Sciences (KINR),
Kyiv, Ukraine
47University of Birmingham, Birmingham, United Kingdom
48H.H. Wills Physics Laboratory, University of Bristol, Bristol, United
Kingdom
49Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
50Department of Physics, University of Warwick, Coventry, United Kingdom
51STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
52School of Physics and Astronomy, University of Edinburgh, Edinburgh, United
Kingdom
53School of Physics and Astronomy, University of Glasgow, Glasgow, United
Kingdom
54Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
55Imperial College London, London, United Kingdom
56School of Physics and Astronomy, University of Manchester, Manchester,
United Kingdom
57Department of Physics, University of Oxford, Oxford, United Kingdom
58Massachusetts Institute of Technology, Cambridge, MA, United States
59University of Cincinnati, Cincinnati, OH, United States
60University of Maryland, College Park, MD, United States
61Syracuse University, Syracuse, NY, United States
62Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de
Janeiro, Brazil, associated to 2
63University of Chinese Academy of Sciences, Beijing, China, associated to 3
64School of Physics and Technology, Wuhan University, Wuhan, China, associated
to 3
65Institute of Particle Physics, Central China Normal University, Wuhan,
Hubei, China, associated to 3
66Departamento de Fisica , Universidad Nacional de Colombia, Bogota, Colombia,
associated to 8
67Institut für Physik, Universität Rostock, Rostock, Germany, associated to 12
68Van Swinderen Institute, University of Groningen, Groningen, Netherlands,
associated to 27
69National Research Centre Kurchatov Institute, Moscow, Russia, associated to
34
70National University of Science and Technology ”MISIS”, Moscow, Russia,
associated to 34
71National Research University Higher School of Economics, Moscow, Russia,
Moscow, Russia
72National Research Tomsk Polytechnic University, Tomsk, Russia, associated to
34
73Instituto de Fisica Corpuscular, Centro Mixto Universidad de Valencia -
CSIC, Valencia, Spain, associated to 40
74University of Michigan, Ann Arbor, United States, associated to 61
75Los Alamos National Laboratory (LANL), Los Alamos, United States, associated
to 61

aUniversidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil
bLaboratoire Leprince-Ringuet, Palaiseau, France
cP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS),
Moscow, Russia
dUniversità di Bari, Bari, Italy
eUniversità di Bologna, Bologna, Italy
fUniversità di Cagliari, Cagliari, Italy
gUniversità di Ferrara, Ferrara, Italy
hUniversità di Genova, Genova, Italy
iUniversità di Milano Bicocca, Milano, Italy
jUniversità di Roma Tor Vergata, Roma, Italy
kUniversità di Roma La Sapienza, Roma, Italy
lAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
mLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
nHanoi University of Science, Hanoi, Vietnam
oUniversità di Padova, Padova, Italy
pUniversità di Pisa, Pisa, Italy
qUniversità degli Studi di Milano, Milano, Italy
rUniversità di Urbino, Urbino, Italy
sUniversità della Basilicata, Potenza, Italy
tScuola Normale Superiore, Pisa, Italy
uUniversità di Modena e Reggio Emilia, Modena, Italy
vMSU - Iligan Institute of Technology (MSU-IIT), Iligan, Philippines
wNovosibirsk State University, Novosibirsk, Russia
xSezione INFN di Trieste, Trieste, Italy
yEscuela Agrícola Panamericana, San Antonio de Oriente, Honduras
zSchool of Physics and Information Technology, Shaanxi Normal University
(SNNU), Xi’an, China
aaPhysics and Micro Electronic College, Hunan University, Changsha City, China
abNational Research University Higher School of Economics, Moscow, Russia
†Deceased