subm

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

 CERN-PH-EP-2015-277 LHCb-PAPER-2015-047

Evidence for the strangeness-changing weak decay ${{\mathchar
28932\relax}^{-}_{b}}\rightarrow{{\mathchar 28931\relax}^{0}_{b}}{{\pi}^{-}}$

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

Using a $pp$ collision data sample corresponding to an integrated luminosity
of 3.0 fb-1, collected by the LHCb detector, we present the first search for
the strangeness-changing weak decay ${{\mathchar
28932\relax}^{-}_{b}}\rightarrow{{\mathchar 28931\relax}^{0}_{b}}{{\pi}^{-}}$.
No $b$ hadron decay of this type has been seen before. A signal for this
decay, corresponding to a significance of 3.2 standard deviations, is
reported. The relative rate is measured to be

$\displaystyle\frac{f_{{{\mathchar 28932\relax}^{-}_{b}}}}{f_{{{\mathchar
28931\relax}^{0}_{b}}}}{\cal{B}}({{\mathchar
28932\relax}^{-}_{b}}\rightarrow{{\mathchar
28931\relax}^{0}_{b}}{{\pi}^{-}})=(5.7\pm 1.8^{+0.8}_{-0.9})\times 10^{-4},$

where $f_{{{\mathchar 28932\relax}^{-}_{b}}}$ and $f_{{{\mathchar
28931\relax}^{0}_{b}}}$ are the $b\rightarrow{{\mathchar
28932\relax}^{-}_{b}}$ and $b\rightarrow{{\mathchar 28931\relax}^{0}_{b}}$
fragmentation fractions, and ${\cal{B}}({{\mathchar
28932\relax}^{-}_{b}}\rightarrow{{\mathchar 28931\relax}^{0}_{b}}{{\pi}^{-}})$
is the branching fraction. Assuming $f_{{{\mathchar
28932\relax}^{-}_{b}}}/f_{{{\mathchar 28931\relax}^{0}_{b}}}$ is bounded
between 0.1 and 0.3, the branching fraction ${\cal{B}}({{\mathchar
28932\relax}^{-}_{b}}\rightarrow{{\mathchar 28931\relax}^{0}_{b}}{{\pi}^{-}})$
would lie in the range from $(0.57\pm 0.21)\%$ to $(0.19\pm 0.07)\%$.

Published in Phys. Rev. Lett.

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

Measurements of the lifetimes of beauty baryons provide an important test of
Heavy Quark Effective Theory (HQET) [1, 2, 3, 4, 5, 6, 7, 8] in which it is
predicted that the decay width is dominated by the weak decay of the heavy $b$
quark. Large samples of $b$ baryons have been collected by LHCb, enabling
precise measurements of their masses and lifetimes [9, 10, 11, 12], which are
generally in good agreement with HQET predictions. Recently, it has been noted
[13, 14, 15, 16] that for the ${{\mathchar 28932\relax}^{-}_{b}}$ and
${{\mathchar 28932\relax}^{0}_{b}}$ baryons, the weak decay of the $s$ quark
could contribute about 1% to the total decay width. It has also been argued
[13] that if the light diquark system has $J^{P}=0^{+}$ and exhibits the
diquark correlations suggested in Refs. [17, 18], this could enhance the
contribution from the weak decay of the $s$ quark in the ${{\mathchar
28932\relax}^{-}_{b}}$ (${{\mathchar 28932\relax}^{0}_{b}}$) baryon to a level
that ranges from 2% to 8% (1% to 4%). Such a large rate would affect the
comparison between HQET predictions and measurements of the ${{\mathchar
28932\relax}^{-}_{b}}$ and ${{\mathchar 28932\relax}^{0}_{b}}$ lifetimes.

These ideas can be tested by studying the decay ${{\mathchar
28932\relax}^{-}_{b}}\rightarrow{{\mathchar 28931\relax}^{0}_{b}}{{\pi}^{-}}$,
in which the $s$ quark in the ${{\mathchar 28932\relax}^{-}_{b}}~{}(bds)$
undergoes a $s\rightarrow u\bar{u}d$ weak transition to a ${{\mathchar
28931\relax}^{0}_{b}}$ ($bud$) baryon and a ${{\pi}^{-}}$ meson. A measurement
of the rate of this process would provide valuable experimental input on the
size of the aforementioned contributions to the ${{\mathchar
28932\relax}^{-}_{b}}$ decay width, as well as on the $J^{P}=0^{+}$ diquark
potential.

We present a search for the decay ${{\mathchar
28932\relax}^{-}_{b}}\rightarrow{{\mathchar 28931\relax}^{0}_{b}}{{\pi}^{-}}$,
where the ${{\mathchar 28931\relax}^{0}_{b}}$ baryon is reconstructed through
its decay to ${{\mathchar 28931\relax}^{+}_{c}}{{\pi}^{-}}$, with ${{\mathchar
28931\relax}^{+}_{c}}\rightarrow p{{K}^{-}}{{\pi}^{+}}$. The signal yield is
normalized with respect to the total number of ${{\mathchar
28931\relax}^{0}_{b}}$ decays reconstructed in the same final state. Charge
conjugate processes are implied throughout. The quantity that is measured is

$\displaystyle r_{s}\equiv\frac{f_{{{\mathchar
28932\relax}^{-}_{b}}}}{f_{{{\mathchar
28931\relax}^{0}_{b}}}}{\cal{B}}({{\mathchar
28932\relax}^{-}_{b}}\rightarrow{{\mathchar
28931\relax}^{0}_{b}}{{\pi}^{-}})=\frac{N({{\mathchar
28932\relax}^{-}_{b}}\rightarrow{{\mathchar
28931\relax}^{0}_{b}}{{\pi}^{-}})}{N({{\mathchar
28931\relax}^{0}_{b}})}\epsilon_{\rm rel}$ (1)

where $f_{{{\mathchar 28932\relax}^{-}_{b}}}$ and $f_{{{\mathchar
28931\relax}^{0}_{b}}}$ are the $b\rightarrow{{\mathchar
28932\relax}^{-}_{b}}$ and $b\rightarrow{{\mathchar 28931\relax}^{0}_{b}}$
fragmentation fractions, $N({{\mathchar
28932\relax}^{-}_{b}}\rightarrow{{\mathchar 28931\relax}^{0}_{b}}{{\pi}^{-}})$
and $N({{\mathchar 28931\relax}^{0}_{b}})$ are the signal yields and
$\epsilon_{\rm rel}$ is the relative efficiency between the normalization and
signal modes. The signal for the ${{\mathchar
28932\relax}^{-}_{b}}\rightarrow{{\mathchar 28931\relax}^{0}_{b}}{{\pi}^{-}}$
decay is a narrow peak at $38.8\pm
0.5$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ [12] in the spectrum of the
mass difference, $\delta m\equiv M({{\mathchar
28931\relax}^{0}_{b}}{{\pi}^{-}})-M({{\mathchar
28931\relax}^{0}_{b}})-m_{\pi}$, where $M({{\mathchar
28931\relax}^{0}_{b}}{{\pi}^{-}})$ and $M({{\mathchar 28931\relax}^{0}_{b}})$
are the invariant masses of the respective candidates, and $m_{\pi}$ is the
${{\pi}^{-}}$ mass [19].

The measurement uses proton-proton ($pp$) collision data samples collected by
the LHCb experiment, corresponding to an integrated luminosity of
3.0$\mbox{\,fb}^{-1}$, of which 1.0$\mbox{\,fb}^{-1}$ was recorded at a
center-of-mass energy of 7$\mathrm{\,Te\kern-1.00006ptV}$ and
2.0$\mbox{\,fb}^{-1}$ at 8$\mathrm{\,Te\kern-1.00006ptV}$.

The LHCb detector [20] 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 relative uncertainty of
about 0.5% from 2$-$100 ${\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and an impact
parameter resolution of 20${\,\upmu\rm m}$ for particles with large transverse
momentum ($p_{\rm T}$). The polarity of the dipole magnet is reversed
periodically throughout data-taking to reduce asymmetries in the detection of
charged particles. Ring-imaging Cherenkov detectors [21] are used to
distinguish different types of charged hadrons. Photon, electron and hadron
candidates are identified using a calorimeter system, which is followed by
detectors to identify muons [22].

The trigger [23] consists of a hardware stage, based on information from the
calorimeter and muon systems, and a software stage, which applies a full event
reconstruction [23, 24]. The software trigger requires a two-, three- or four-
track secondary vertex that is significantly displaced from the primary $pp$
interaction vertices (PVs) and whose tracks have a large scalar $p_{\rm T}$
sum. At least one track should have $\mbox{$p_{\rm
T}$}>1.7{\mathrm{\,Ge\kern-1.00006ptV\\!/}c}$ and be inconsistent with coming
from any of the PVs. The signal candidates are also required to pass a
multivariate software trigger selection algorithm [24].

Proton-proton collisions are simulated using Pythia [25] with a specific LHCb
configuration [26]. Decays of hadronic particles are described by EvtGen [27],
in which final-state radiation is generated using Photos [28]. The interaction
of the generated particles with the detector, and its response, are
implemented using the Geant4 toolkit [29, *Agostinelli:2002hh] as described in
Ref. [31].

Candidate ${{\mathchar 28931\relax}^{0}_{b}}$ decays are formed by combining
${{\mathchar 28931\relax}^{+}_{c}}\rightarrow p{{K}^{-}}{{\pi}^{+}}$ and
${{\pi}^{-}}$ candidates in a kinematic fit [32]. The selection criteria are
identical to those used in Ref. [12], except that no requirement is made on
the particle identification (PID) information for the ${{\pi}^{-}}$ candidate.
For each combination of a ${{\mathchar 28931\relax}^{0}_{b}}$ candidate and a
PV in the event, the quantity $\chi^{2}_{\rm IP}$ is computed, defined to be
the difference in $\chi^{2}$ of the PV fit when the ${{\mathchar
28931\relax}^{0}_{b}}$ particle is included or excluded from the fit. The
${{\mathchar 28931\relax}^{0}_{b}}$ candidate is assigned to the PV with the
smallest $\chi^{2}_{\rm IP}$.

Right-sign (RS) ${{\mathchar 28932\relax}^{-}_{b}}\rightarrow{{\mathchar
28931\relax}^{0}_{b}}{{\pi}^{-}}$ candidates are obtained by combining a
${{\mathchar 28931\relax}^{0}_{b}}$ candidate with mass in the range
5560–5680${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ with a ${{\pi}^{-}}$
candidate, and wrong-sign (WS) candidates are likewise formed from
${{\mathchar 28931\relax}^{0}_{b}}{{\pi}^{+}}$ combinations. The pions are
required to have $\mbox{$p_{\rm
T}$}>100$${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$, and to have PID information
consistent with a ${{\pi}^{\pm}}$ meson. Because these pions are generally
consistent with emanating from the PV, the PID requirement helps to suppress
background from other particle types. A second kinematic fit is used to
compute $\delta m$; it exploits both vertex and invariant mass constraints,
requiring for the latter that the invariant masses of the
$p{{K}^{-}}{{\pi}^{+}}$ and ${{\mathchar 28931\relax}^{+}_{c}}{{\pi}^{-}}$
systems are equal to the known ${{\mathchar 28931\relax}^{+}_{c}}$ and
${{\mathchar 28931\relax}^{0}_{b}}$ masses.

Three boosted decision tree (BDT) multivariate discriminants [33, 34] are used
to suppress background, one for the normalization mode (BDT1), and two for the
signal mode (BDT2 and BDT3). BDT1 is used specifically to suppress the
combinatorial background contribution in the ${{\mathchar
28931\relax}^{0}_{b}}$ normalization mode. Five input variables are used: the
$\chi^{2}$ of the ${{\mathchar 28931\relax}^{0}_{b}}$ kinematic fit; the
$\chi^{2}_{\rm IP}$ of the ${{\mathchar 28931\relax}^{0}_{b}}$, ${{\mathchar
28931\relax}^{+}_{c}}$ and ${{\pi}^{-}}$ candidates; and the $\chi^{2}_{\rm
VS}$ of the ${{\mathchar 28931\relax}^{0}_{b}}$ candidate. Here,
$\chi^{2}_{\rm VS}$ is the difference between the $\chi^{2}$ of the PV fit
with and without the ${{\mathchar 28931\relax}^{0}_{b}}$ daughter particles
included in the fit. A large $\chi^{2}_{\rm VS}$ indicates that the
${{\mathchar 28931\relax}^{0}_{b}}$ decay vertex is well separated from its
associated PV. Simulated ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{\mathchar 28931\relax}^{+}_{c}}{{\pi}^{-}}$
decays are used to model the signal distributions of the BDT1 input variables,
and candidates with $M({{\mathchar
28931\relax}^{+}_{c}}{{\pi}^{-}})>5700{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$
are used to model the corresponding background spectra. A loose selection on
the BDT1 output is applied, which provides an efficiency of $(98.6\pm 0.5)\%$,
while reducing the background by a factor of four.

Figure 1: Invariant mass spectrum for selected ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{\mathchar 28931\relax}^{+}_{c}}{{\pi}^{-}}$
candidates in data.

The invariant mass spectrum of selected ${{\mathchar
28931\relax}^{+}_{c}}{{\pi}^{-}}$ candidates is displayed in Fig. 1. The yield
is determined from an unbinned extended maximum likelihood fit using the
signal and background shapes as described in Ref. [11]. The fitted number of
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}{{\pi}^{-}}$ decays is $(256.7\pm 0.6)\times 10^{3}$, and
the fraction $N({{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}{{K}^{-}})/N({{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}{{\pi}^{-}})=(5.9\pm 0.2)$%, where the uncertainties are
statistical only. In the mass region
5560–5680${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, the fitted yields of
${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{\mathchar
28931\relax}^{+}_{c}}{{\pi}^{-}}$ and ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{\mathchar 28931\relax}^{+}_{c}}{{K}^{-}}$
decays are 253 300 and 11 700, respectively. Since misidentified ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{\mathchar 28931\relax}^{+}_{c}}{{K}^{-}}$
signal decays also contribute to the ${{\mathchar
28932\relax}^{-}_{b}}\rightarrow{{\mathchar 28931\relax}^{0}_{b}}{{\pi}^{-}}$
signal, they are included in the total normalization mode yield. Thus the
signal yield for the normalization mode is $(265\pm 1)\times 10^{3}$.

The second BDT (BDT2) has the same purpose as BDT1, except that it is applied
to the ${{\mathchar 28931\relax}^{0}_{b}}$ candidates within the ${{\mathchar
28932\relax}^{-}_{b}}\rightarrow{{\mathchar 28931\relax}^{0}_{b}}{{\pi}^{-}}$
sample. This alternate BDT is needed since the lifetime of the ${{\mathchar
28932\relax}^{-}_{b}}$ baryon is about the same as that of the ${{\mathchar
28931\relax}^{0}_{b}}$ baryon, thus leading to larger typical values of
$\chi^{2}_{\rm VS}$ compared to the inclusively produced ${{\mathchar
28931\relax}^{0}_{b}}$ sample. A similar training to that of BDT1 is
performed, except that the signal distributions are taken from simulated
${{\mathchar 28932\relax}^{-}_{b}}\rightarrow{{\mathchar
28931\relax}^{0}_{b}}{{\pi}^{-}}$ decays. A loose selection on the BDT2 output
yields an efficiency of $(99.0\pm 0.5)\%$.

The third BDT (BDT3) is used to distinguish real ${{\mathchar
28932\relax}^{-}_{b}}\rightarrow{{\mathchar 28931\relax}^{0}_{b}}{{\pi}^{-}}$
decays from ${{\mathchar 28931\relax}^{0}_{b}}$ baryons combined with a random
${{\pi}^{-}}$ candidate. Because of the small energy release in the
${{\mathchar 28932\relax}^{-}_{b}}\rightarrow{{\mathchar
28931\relax}^{0}_{b}}{{\pi}^{-}}$ decay, the ${{\mathchar
28931\relax}^{0}_{b}}$ and ${{\pi}^{-}}$ directions are nearly collinear with
that of the ${{\mathchar 28932\relax}^{-}_{b}}$. This makes it difficult to
identify the ${{\mathchar 28931\relax}^{0}_{b}}$ and ${{\pi}^{-}}$ daughters
as particles produced at a secondary vertex. The input variables used in BDT3
are the flight distance and $\chi^{2}_{\rm VS}$ of the ${{\mathchar
28932\relax}^{-}_{b}}$ candidate, the $\chi^{2}_{\rm VS}$ of the ${{\mathchar
28931\relax}^{0}_{b}}$ candidate, and the $\chi^{2}_{\rm IP}$ and $p_{\rm T}$
of the low momentum (slow) ${{\pi}^{-}}$ daughter of the ${{\mathchar
28932\relax}^{-}_{b}}$ candidate. The signal distributions of these variables
are taken from simulated ${{\mathchar
28932\relax}^{-}_{b}}\rightarrow{{\mathchar 28931\relax}^{0}_{b}}{{\pi}^{-}}$
decays, and the background spectra are taken from WS candidates that have
$34<\delta m<44$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. Separate training
and test samples were compared and showed no bias due to overtraining.

A loose selection on the BDT3 output is applied, rejecting about 3% of the
expected signal events. The selected events are divided into two signal-to-
background (S/B) regions according to the BDT3 output: a high S/B region and a
low S/B region. The split between the high and low S/B regions is chosen to
provide optimal expected sensitivity. The expected ratio of yields in the low
S/B to high S/B regions is 1.60, which is fixed in the fit to data.

An event may have more than one ${{\mathchar 28932\relax}^{-}_{b}}$ candidate,
almost always due to a single ${{\mathchar 28931\relax}^{0}_{b}}$ candidate
being combined with more than one ${{\pi}^{-}}$ candidate. The average number
of candidates in events that contain a candidate in the low S/B region is
1.35, and 1.02 in events that contain a candidate in the high S/B region. All
candidates are kept. Potential bias on the signal yield determination due to
this choice was investigated, and none was found.

Four disjoint subsamples of data are used in the fits, split by charge (RS,
WS) and by S/B region (low, high). Including the WS data allows additional
constraints on the shape of the combinatorial background, and also provides a
consistency check that the signal yield in the ${{\mathchar
28931\relax}^{0}_{b}}{{\pi}^{+}}$ mode is consistent with zero. In these four
$\delta m$ spectra we allow for three contributions: a ${{\mathchar
28932\relax}^{-}_{b}}\rightarrow{{\mathchar 28931\relax}^{0}_{b}}{{\pi}^{-}}$
signal, strong decays of ${\mathchar
28934\relax}_{b}^{(*)\pm}\rightarrow{{\mathchar
28931\relax}^{0}_{b}}\pi^{\pm}$ resonances, and combinatorial background. The
low S/B region contains almost all of the ${\mathchar
28934\relax}_{b}^{(*)\pm}\rightarrow{{\mathchar
28931\relax}^{0}_{b}}\pi^{\pm}$ signal decays. The primary reason for
including the low S/B regions is that they contain almost all of the
${\mathchar 28934\relax}_{b}^{(*)\pm}\rightarrow{{\mathchar
28931\relax}^{0}_{b}}\pi^{\pm}$ signal decays. This leads to tighter
constraints on the ${\mathchar 28934\relax}_{b}^{(*)\pm}\rightarrow{{\mathchar
28931\relax}^{0}_{b}}\pi^{\pm}$ mass shapes in the high S/B region, since the
shape parameters are common to the low and high S/B regions. A simultaneous
unbinned extended maximum likelihood fit is performed to the four $\delta m$
spectra, in the range 2–122${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, using
the signal and background shapes discussed below.

The $\delta m$ signal shape is obtained from simulated ${{\mathchar
28932\relax}^{-}_{b}}\rightarrow{{\mathchar 28931\relax}^{0}_{b}}{{\pi}^{-}}$
decays, allowing for different signal shapes in the low and high S/B regions.
Each sample is fit to the sum of two Gaussian functions with a common mean
value. The shapes are slightly different, but the average resolution, given as
the weighted average of the two Gaussian widths, is
1.57${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ in both cases. All signal shape
parameters are fixed in fits to data, including the mean, which is fixed to
$M({{\mathchar 28932\relax}^{-}_{b}})-M({{\mathchar
28931\relax}^{0}_{b}})-m_{{{\pi}^{-}}}=38.8{\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$
[12]. A scale factor of 1.10 is applied to the widths to account for slightly
worse resolution in data than simulation, as determined from a study of the
$\delta m$ resolution in ${{D}^{*+}}\rightarrow{{D}^{0}}{{\pi}^{+}}$ decays
[35]. Variations in this value are considered as a source of systematic
uncertainty.

The contributions from the ${\mathchar 28934\relax}_{b}^{\pm}$ and ${\mathchar
28934\relax}_{b}^{*\pm}$ resonances are each modeled using a relativistic
Breit Wigner shape [36]. Each of them is convolved with a resolution function
obtained from simulated ${\mathchar 28934\relax}_{b}^{(*)-}$ decays, and is
parameterized as the sum of three Gaussian distributions with a common mean.
The average resolution is 1.97${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ for
${\mathchar 28934\relax}_{b}^{-}$ and
2.25${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$ for ${\mathchar
28934\relax}_{b}^{*-}$. The ${\mathchar 28934\relax}^{(*)\pm}$ masses and
natural widths are freely varied in the fit to data, but the Gaussian widths
are fixed and include a scale factor of 1.10, as indicated previously. The
masses and widths of the ${\mathchar 28934\relax}_{b}^{(*)\pm}$ resonances are
being studied in a separate analysis.

The combinatorial background is described by the threshold function

$\displaystyle f_{\rm back}(\delta m)\propto(\delta m)^{A}(1-e^{-\delta
m/C}),$ (2)

where the parameters $A$ and $C$ are freely varied in the fit to data. One set
of parameters is used for the low S/B region, and a separate set for the high
S/B region. For each S/B region, the RS and WS spectra share a common set of
parameters.

The resulting mass fits are shown in Fig. 2.

Figure 2: Fit to the $\delta m$ spectra in data: (top left) RS low S/B, (top
right) WS low S/B, (bottom left) RS high S/B and (bottom right) WS high S/B.

The ${\mathchar 28934\relax}_{b}^{\pm}$ and ${\mathchar
28934\relax}_{b}^{*\pm}$ signals appear prominently, and are constrained by
the data in the low S/B spectra (top pair of plots). The data show an
enhancement at the expected $\delta m$ value for the ${{\mathchar
28932\relax}^{-}_{b}}\rightarrow{{\mathchar 28931\relax}^{0}_{b}}{{\pi}^{-}}$
decay in the RS high S/B region, but no such excess is seen in the
corresponding WS sample. The total fitted signal yields for the RS and WS
samples are $103\pm 33$ and $-7\pm 28$, respectively.

The relative efficiency between the normalization and signal modes can be
expressed as

$\displaystyle\epsilon_{\rm rel}\equiv\frac{\epsilon_{{{\mathchar
28931\relax}^{0}_{b}}}}{\epsilon_{{{\mathchar
28932\relax}^{-}_{b}}}}=\frac{\epsilon_{\rm rel}^{\rm acc}\cdot\epsilon_{\rm
rel}^{\rm rec}\cdot\epsilon_{\rm rel}^{\rm BDT1,2}}{\epsilon_{{{\mathchar
28932\relax}^{-}_{b}}\rm-only}}$ (3)

where $\epsilon_{\rm rel}^{\rm acc}=1.03\pm 0.01$ is the relative efficiency
for all of the stable daughter particles to be within the LHCb acceptance;
$\epsilon_{\rm rel}^{\rm rec}=1.38\pm 0.02$ is the relative efficiency for
reconstruction and selection, including the $\mbox{$p_{\rm
T}$}>100$${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ requirement on the
${{\pi}^{-}}$ meson; $\epsilon_{\rm rel}^{\rm BDT1,2}=1.00\pm 0.01$ is the
relative efficiency of the BDT1 and BDT2 selections; and
$\epsilon_{{{\mathchar 28932\relax}^{-}_{b}}\rm-only}=0.95\pm 0.01$ includes
the BDT3 requirement and the PID selection criteria on the ${{\pi}^{-}}$
candidate. The relative efficiencies are obtained from simulated ${{\mathchar
28932\relax}^{-}_{b}}\rightarrow{{\mathchar 28931\relax}^{0}_{b}}{{\pi}^{-}}$
events and inclusively produced ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{\mathchar 28931\relax}^{+}_{c}}{{\pi}^{-}}$
decays, except for the PID requirements, which are taken from
${{D}^{*+}}\rightarrow{{D}^{0}}{{\pi}^{+}}$ calibration data. The relative
efficiency is therefore $1.47\pm 0.03$.

Several sources of systematic uncertainty affect the signal yield
determination and thus the signal significance. Additional sources of
systematic uncertainty contribute to the determination of $r_{s}$. The
uncertainties are summarized in Table 1. In the default fit, the ${{\mathchar
28932\relax}^{-}_{b}}$ signal peak position is fixed to the nominal value of
$\delta m=38.8$${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, which has an
uncertainty of 0.5${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$. We therefore
refit the data with the peak position shifted by
$\pm$0.5${\mathrm{\,Me\kern-1.00006ptV\\!/}c^{2}}$, obtaining changes of
$-6.4\%$ and $+4.9\%$ in the yield. These values are assigned as a systematic
error. Uncertainty in the signal yield due to the fixed mass resolution scale
factor of 1.10 is investigated by varying it by $\pm$0.05, and we assign the
average change in yield of 3.0% as a systematic error. Variations in the
corresponding scale factor for the ${\mathchar 28934\relax}_{b}^{(*)-}$
resonances were investigated, and were found to have negligible impact on the
${{\mathchar 28932\relax}^{-}_{b}}\rightarrow{{\mathchar
28931\relax}^{0}_{b}}{{\pi}^{-}}$ signal yield. Different choices for the fit
range and the combinatorial background function were investigated, and among
these fit variations, a maximum shift in the signal yield of 12.6% was found.
The full difference is assigned as a systematic uncertainty.

Additional systematic uncertainties that affect $r_{s}$ include the relative
efficiency between the low and high S/B regions, the slow ${{\pi}^{-}}$
detection efficiency, and the yield of ${{\mathchar 28931\relax}^{0}_{b}}$
decays. In comparing the BDT1 distributions for ${{\mathchar
28931\relax}^{0}_{b}}\rightarrow{{\mathchar 28931\relax}^{+}_{c}}{{\pi}^{-}}$
signal in data and simulation, as well as the background distributions for
BDT3 in data and simulation, the relative efficiencies do not vary by more
than 2% for any BDT selection. We therefore assign 2% as a systematic
uncertainty. The ${{\pi}^{-}}$ meson from the ${{\mathchar
28932\relax}^{-}_{b}}$ decay must be reconstructed and have $\mbox{$p_{\rm
T}$}>100{\mathrm{\,Me\kern-1.00006ptV\\!/}c}$. The tracking efficiency
uncertainty is assessed using data-driven techniques [37], and is less than
1.6%. The uncertainty due to the $p_{\rm T}$ requirement is estimated by
interpolating the $p_{\rm T}$ spectrum from
100${\mathrm{\,Me\kern-1.00006ptV\\!/}c}$ to zero in simulated decays, and
assuming that the fraction of signal events in this $p_{\rm T}$ region in data
could differ from the simulated fraction by as much as 25%. This leads to a
model uncertainty of 1.7%. Thus, an uncertainty of 2.3% is assigned to the
detection of the ${{\pi}^{-}}$ from the ${{\mathchar 28932\relax}^{-}_{b}}$
decay.

For the number of ${{\mathchar 28931\relax}^{0}_{b}}$ signal events, we assign
a 1.0% uncertainty, which includes both the statistical component and a
systematic uncertainty due to the signal and background shapes used to fit the
${{\mathchar 28931\relax}^{+}_{c}}{{\pi}^{-}}$ mass spectrum.

Table 1: Relative systematic uncertainties (in percent) on the signal yield determination and on the quantity $\left(f_{{{\mathchar 28932\relax}^{-}_{b}}}/f_{{{\mathchar 28931\relax}^{0}_{b}}}\right){\cal{B}}({{\mathchar 28932\relax}^{-}_{b}}\rightarrow{{\mathchar 28931\relax}^{0}_{b}}{{\pi}^{-}})$, as described in the text. Source | Value (%)
---|---
Mean $\delta m$ | ${}^{+4.9}_{-6.4}$
Signal resolution | 3.0
Combinatorial background shape | 12.6
$\epsilon({\rm High~{}S/B})/\epsilon({\rm Low~{}S/B})$ | 2.0
Slow ${{\pi}^{-}}$ efficiency | 2.3
${{\mathchar 28931\relax}^{0}_{b}}$ normalization mode yield | 1.0
Simulated sample size | 2.1
Total for signal significance | ${}^{+13.9}_{-14.5}$
Total for $r_{s}$ | ${}^{+14.4}_{-15.0}$

To check the robustness of the signal, the data were partitioned into
different subsamples and the fitted yields in each were determined
independently. The subsamples consisted of only 2012 data ($\sim$2/3 of the
data set), only negative magnet polarity data ($\sim$50% of the data sample),
and only ${{\mathchar 28931\relax}^{0}_{b}}{{\pi}^{-}}$ data, not ${{\kern
1.00006pt\overline{\kern-1.00006pt\mathchar
28931\relax}}{}^{0}_{b}}{{\pi}^{+}}$ (expect $\sim$50%). In all three cases
the signal yields are compatible with expectations. Other robustness checks
were also performed, such as placing a stringent PID requirement on the
${{\pi}^{-}}$, fitting only the RS data, and using only raw invariant masses
(without the full kinematic fit). Upward and downward variations are observed,
but in all cases, the fitted yields are consistent with expectations.

The significance of the signal is computed with Wilks’s theorem [38]. The
systematic uncertainty is included by convolving the likelihood function with
a bifurcated Gaussian distribution whose widths are given by the asymmetric
uncertainties in Table 1, which leads to a significance of 3.2$\sigma$. We
thus have evidence for the ${{\mathchar
28932\relax}^{-}_{b}}\rightarrow{{\mathchar 28931\relax}^{0}_{b}}{{\pi}^{-}}$
decay.

With the yields and relative efficiencies presented previously, we find

$\displaystyle\frac{f_{{{\mathchar 28932\relax}^{-}_{b}}}}{f_{{{\mathchar
28931\relax}^{0}_{b}}}}{\cal{B}}({{\mathchar
28932\relax}^{-}_{b}}\rightarrow{{\mathchar
28931\relax}^{0}_{b}}{{\pi}^{-}})=(5.7\pm 1.8\,^{+0.8}_{-0.9})\times 10^{-4},$

where the uncertainties are statistical and systematic, respectively. To
assess what this value implies in terms of ${\cal{B}}({{\mathchar
28932\relax}^{-}_{b}}\rightarrow{{\mathchar
28931\relax}^{0}_{b}}{{\pi}^{-}})$, we consider a plausible range for
$f_{{{\mathchar 28932\relax}^{-}_{b}}}/f_{{{\mathchar 28931\relax}^{0}_{b}}}$
from 0.1–0.3, based on measured production rates of other strange particles
relative to their non-strange counterparts [39, 40, 41, 42, 19]. Assuming
$f_{{{\mathchar 28932\relax}^{-}_{b}}}/f_{{{\mathchar 28931\relax}^{0}_{b}}}$
is bounded between 0.1 and 0.3, the branching fraction ${\cal{B}}({{\mathchar
28932\relax}^{-}_{b}}\rightarrow{{\mathchar 28931\relax}^{0}_{b}}{{\pi}^{-}})$
would be in the range from $(0.57\pm 0.21)\%$ to $(0.19\pm 0.07)\%$.

In summary, we present the first evidence for the ${{\mathchar
28932\relax}^{-}_{b}}\rightarrow{{\mathchar 28931\relax}^{0}_{b}}{{\pi}^{-}}$
decay, which is mediated by the weak transition of the $s$ quark. With the
above assumptions for $f_{{{\mathchar 28932\relax}^{-}_{b}}}/f_{{{\mathchar
28931\relax}^{0}_{b}}}$, the measured value for ${\cal{B}}({{\mathchar
28932\relax}^{-}_{b}}\rightarrow{{\mathchar 28931\relax}^{0}_{b}}{{\pi}^{-}})$
is consistent with the range of 0.19–0.76%, predicted in Ref. [14] assuming
the diquark transitions have roughly the same weak amplitude as in $B$, $D$,
and $K$ meson decays. The results are also consistent with the value of
0.57–0.62%, obtained using either a current algebra or pole model approach,
but are inconsistent with the values of 0.01% and 0.012% using the
factorization approximation or the quark line approach [16]. The measured
value of ${\cal{B}}({{\mathchar 28932\relax}^{-}_{b}}\rightarrow{{\mathchar
28931\relax}^{0}_{b}}{{\pi}^{-}})$ disfavors a large enhancement to the decay
rate of ${{\mathchar 28932\relax}^{-}_{b}}$ baryons from the $s\rightarrow
u\bar{u}d$ transition, which could occur if the short-distance correlations
within the $J^{P}=0^{+}$ diquark system are enhanced, as suggested in Refs.
[13, 17, 18].

## 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 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). We acknowledge the computing resources that
are provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN (Italy),
SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI (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. 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 AvH
Foundation (Germany), EPLANET, Marie Skłodowska-Curie Actions and ERC
(European Union), Conseil Général de Haute-Savoie, Labex ENIGMASS and OCEVU,
Région Auvergne (France), RFBR (Russia), GVA, XuntaGal and GENCAT (Spain), The
Royal Society and Royal Commission for the Exhibition of 1851 (United
Kingdom).

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LHCb collaboration

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Bedeschi23, I. Bediaga1, L.J. Bel41, V. Bellee39, N. Belloli20, I. Belyaev31,
E. Ben-Haim8, G. Bencivenni18, S. Benson38, J. Benton46, A. Berezhnoy32, R.
Bernet40, A. Bertolin22, M.-O. Bettler38, M. van Beuzekom41, A. Bien11, S.
Bifani45, P. Billoir8, T. Bird54, A. Birnkraut9, A. Bizzeti17,h, T. Blake48,
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K. Trabelsi39, M.T. Tran39, M. Tresch40, A. Trisovic38, A. Tsaregorodtsev6, P.
Tsopelas41, N. Tuning41,38, A. Ukleja28, A. Ustyuzhanin65,64, U. Uwer11, C.
Vacca15,e, V. Vagnoni14, G. Valenti14, A. Vallier7, R. Vazquez Gomez18, P.
Vazquez Regueiro37, C. Vázquez Sierra37, S. Vecchi16, J.J. Velthuis46, M.
Veltri17,g, G. Veneziano39, M. Vesterinen11, B. Viaud7, D. Vieira2, M. Vieites
Diaz37, X. Vilasis-Cardona36,o, V. Volkov32, A. Vollhardt40, D. Volyanskyy10,
D. Voong46, A. Vorobyev30, V. Vorobyev34, C. Voß63, J.A. de Vries41, R.
Waldi63, C. Wallace48, R. Wallace12, J. Walsh23, S. Wandernoth11, J. Wang59,
D.R. Ward47, N.K. Watson45, D. Websdale53, A. Weiden40, M. Whitehead48, G.
Wilkinson55,38, M. Wilkinson59, M. Williams38, M.P. Williams45, M. Williams56,
T. Williams45, F.F. Wilson49, J. Wimberley58, J. Wishahi9, W. Wislicki28, M.
Witek26, G. Wormser7, S.A. Wotton47, S. Wright47, K. Wyllie38, Y. Xie61, Z.
Xu39, Z. Yang3, J. Yu61, X. Yuan34, O. Yushchenko35, M. Zangoli14, M.
Zavertyaev10,b, L. Zhang3, Y. Zhang3, A. Zhelezov11, A. Zhokhov31, L. Zhong3,
S. Zucchelli14.

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

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 Urbino, Urbino, Italy
hUniversità di Modena e Reggio Emilia, Modena, Italy
iUniversità di Genova, Genova, Italy
jUniversità di Milano Bicocca, Milano, Italy
kUniversità di Roma Tor Vergata, Roma, Italy
lUniversità di Roma La Sapienza, Roma, Italy
mUniversità della Basilicata, Potenza, Italy
nAGH - University of Science and Technology, Faculty of Computer Science,
Electronics and Telecommunications, Kraków, Poland
oLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
pHanoi University of Science, Hanoi, Viet Nam
qUniversità di Padova, Padova, Italy
rUniversità di Pisa, Pisa, Italy
sScuola Normale Superiore, Pisa, Italy
tUniversità degli Studi di Milano, Milano, Italy
†Deceased