Measurement of the mass and production rate of $\Xi_b^-$ baryons

TL;DR

This paper reports the first measurement of the production rate and mass of $ ext{Xi}_b^-$ baryons in proton-proton collisions at various energies, using LHCb data, providing precise mass determination and production asymmetries.

Contribution

It presents the first measurement of $ ext{Xi}_b^-$ baryon production rates relative to $ ext{Lambda}_b^0$, and the most precise mass measurement of $ ext{Xi}_b^-$ to date.

Findings

Measured production ratios at different energies.

Determined the $ ext{Xi}_b^-$ mass with high precision.

Reported production asymmetries between baryons and antibaryons.

Abstract

The first measurement of the production rate of $\Xi_b^-$ baryons in $pp$ collisions relative to that of $\Lambda_b^0$ baryons is reported, using data samples collected by the LHCb experiment, and corresponding to integrated luminosities of $1$, $2$ and $1.6$ fb$^{-1}$ at $\sqrt{s}=7,~8$ and $13$ TeV, respectively. In the kinematic region $2 < \eta < 6$ and $p_{\rm T}<20$ GeV/$c$, we measure \begin{align*} \frac{f_{\Xi_b^-}}{f_{\Lambda_b^0}}\frac{{\mathcal{B}}(\Xi_b^-\to J/\psi\Xi^-)}{{\mathcal{B}}(\Lambda_b^0\to J/\psi\Lambda)} &= (10.8\pm0.9\pm0.8)\times10^{-2}~~[\sqrt{s}=7,8~{\rm TeV}],\\ \frac{f_{\Xi_b^-}}{f_{\Lambda_b^0}}\frac{{\mathcal{B}}(\Xi_b^-\to J/\psi\Xi^-)}{{\mathcal{B}}(\Lambda_b^0\to J/\psi\Lambda)} &= (13.1\pm1.1\pm1.0)\times10^{-2}~~[\sqrt{s}=13~{\rm TeV}], \end{align*} where $f_{\Xi_b^-}$ and $f_{\Lambda_b^0}$ are the fragmentation fractions of $b$ quarks into $\Xi_b^-$ and $\Lambda_b^0$ baryons, respectively, ${\mathcal{B}}$ represents branching fractions, and the uncertainties are due to statistical and experimental systematic sources. The values of $f_{\Xi_b^-}/f_{\Lambda_b^0}$ are obtained by invoking SU(3) symmetry in the $\Xi_b^-\to J\psi\Xi^-$ and $\Lambda_b^0\to J/\psi\Lambda$ decays. Production asymmetries between $\Xi_b^-$ and $\bar{\Xi}_b^+$ baryons are also reported. The mass of the $\Xi_b^-$ baryon is also measured relative to that of the $\Lambda_b^0$ baryon, from which it is found that \begin{align*} m(\Xi_b^-) &= 5796.70\pm0.39\pm0.15\pm0.17~{\rm MeV}/c^2, \end{align*} where the last uncertainty is due to the precision on the known $\Lambda_b^0$ mass. This result represents the most precise determination of the $\Xi_b^-$ mass.

Figures

Tables

Table 1. Table 1: Fitted signal yields and peak position of the Λ b 0 subscript superscript Λ 0 𝑏 {{\mathchar 28931\relax}^{0}_{b}} signal peak, as obtained from the fit described in the text. The subscript on the π − superscript 𝜋 {{\pi}^{-}} refers to whether the corresponding track is long or downstream. The uncertainties shown are statistical only.

	$7,\mathrm{\hspace{0.17em}8}$ TeV	13 TeV
$N\left({\Lambda }_b^0\to J/\psi \Lambda \right)$	$\mathrm{\hspace{0.17em}13307}\pm 137$	$\mathrm{\hspace{0.17em}14793}\pm 150$
$N\left({\Xi }_b^{-}\to J/\psi {\Xi }^{-},{\Xi }^{-}\to \Lambda {\pi }_L^{-}\right)$	$203\pm 16$	$258\pm 22$
$N\left({\Xi }_b^{-}\to J/\psi {\Xi }^{-},{\Xi }^{-}\to \Lambda {\pi }_D^{-}\right)$	$266\pm 20$	$357\pm 26$
${\overline{m}}_{{\Lambda }_b^0}$ (MeV/$c^2$)	$5619.52\pm 0.09$	$5619.28\pm 0.09$

Table 2. Table 2: Selection efficiencies as obtained from the simulation of Λ b 0 → J / ψ ​ Λ → subscript superscript Λ 0 𝑏 𝐽 𝜓 Λ {{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{\mathchar 28931\relax} and Ξ b − → J / ψ ​ Ξ − → subscript superscript Ξ 𝑏 𝐽 𝜓 superscript Ξ {{\mathchar 28932\relax}^{-}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{\mathchar 28932\relax}^{-}} , Ξ − → Λ ​ π L − → superscript Ξ Λ subscript superscript 𝜋 L {{\mathchar 28932\relax}^{-}}\rightarrow{\mathchar 28931\relax}\pi^{-}_{\rm L} decays at s = 7 ,  8 𝑠 7 8 \sqrt{s}=7,\,8  TeV and 13  TeV . The efficiencies ( ϵ italic-ϵ \epsilon ) listed are those associated with the detector acceptance (acc), the reconstruction and selection (sel), the trigger (trig), their product, and the relative efficiency.

	7, 8 TeV		13 TeV
Final state	${\Lambda }_b^0\to J/\psi \Lambda$	${\Xi }_b^{-}\to J/\psi {\Xi }^{-}$	${\Lambda }_b^0\to J/\psi \Lambda$	${\Xi }_b^{-}\to J/\psi {\Xi }^{-}$
${ϵ}_{\mathrm{acc}}$ (%)	$18.9\pm 0.1$	$\mathrm{\hspace{0.17em}17.3}\pm 0.1$	$19.8\pm 0.1$	$18.0\pm 0.1$
${ϵ}_{\mathrm{sel}}$ (%)	$\mathrm{\hspace{0.17em}2.86}\pm 0.02$	$0.42\pm 0.01$	$\mathrm{\hspace{0.17em}2.91}\pm 0.01$	$\mathrm{\hspace{0.17em}0.42}\pm 0.01$
${ϵ}_{\mathrm{trig}}$ (%)	$73.2\pm 0.3$	$\mathrm{\hspace{0.17em}75.6}\pm 0.7$	$75.4\pm 0.2$	$77.8\pm 0.5$
$ϵ$ (${10}^{-2}\%$)	$39.5\pm 0.4$	$5.56\pm 0.11$	$43.5\pm 0.3$	$\mathrm{\hspace{0.17em}5.85}\pm 0.06$
${ϵ}_{{\Xi }_b^{-}}/{ϵ}_{{\Lambda }_b^0}$ (%)	$14.1\pm 0.3$		$13.4\pm 0.2$

Table 3. Table 3: Yields of Λ b 0 subscript superscript Λ 0 𝑏 {{\mathchar 28931\relax}^{0}_{b}} and Ξ b − subscript superscript Ξ 𝑏 {{\mathchar 28932\relax}^{-}_{b}} decays, split by the charge of the final state, and their asymmetries, for the combined 7, 8  TeV data samples and the 13  TeV data sample. Uncertainties are statistical only.

	${\Lambda }_b^0\to J/\psi \Lambda$		${\Xi }_b^{-}\to J/\psi {\Xi }^{-}$
	${\Lambda }_b^0$	$\overline{\Lambda }{}_b^0$	${\Xi }_b^{-}$	$\overline{\Xi }{}_b^{+}$
$N_{\sqrt{s}=7,\mathrm{\hspace{0.17em}8}\text{ TeV}}$	$6827\pm 94$	$6480\pm 92$	$236\pm 18$	$230\pm 18$
${\alpha }_{\sqrt{s}=7,\mathrm{\hspace{0.17em}8}\text{ TeV}}$	$\left(2.6\pm 1.0\right)\%$		$\left(1.3\pm 5.4\right)\%$
$N_{\sqrt{s}=13\text{ TeV}}$	$7602\pm 102$	$7182\pm 99$	$304\pm 21$	$326\pm 22$
${\alpha }_{\sqrt{s}=13\text{ TeV}}$	$\left(2.8\pm 1.0\right)\%$		$\left(-3.5\pm 4.8\right)\%$

Table 4. Table 4: Summary of relative systematic uncertainties on the production ratio R 𝑅 R .

Source	Value (%)
${\Lambda }_b^0$, ${\Xi }_b^{-}$ polarization	3.0
Signal and background shape	2.0
${\Xi }_b^{-}$ production spectra	3.0
${\pi }^{-}$ tracking efficiency	4.5
${\Xi }^{-}$ mass resolution & non-resonant $\Lambda {\pi }^{-}$	3.0
${\Xi }^{-}$ selections	1.4
${\Xi }_b^{-}$ lifetime	0.5
Simulated sample sizes	2.0
Total	7.6

Equations

$$\frac{f_{{\text{mathchar}28932}_b^{-}}}{f_{{\text{mathchar}28931}_b^0}}\frac{\mathcal{B}({\text{mathchar}28932}_b^{-}\to J/\psi {\text{mathchar}28932}^{-})}{\mathcal{B}({\text{mathchar}28931}_b^0\to J/\psi \text{mathchar}28931)}$$

$$m({\text{mathchar}28932}_b^{-})$$

$$\frac{\Gamma ({\text{mathchar}28932}_b^{-}\to J/\psi {\text{mathchar}28932}^{-})}{\Gamma ({\text{mathchar}28931}_b^0\to J/\psi \text{mathchar}28931)}=\frac{3}{2}.$$

$$R\equiv \frac{f_{{\text{mathchar}28932}_b^{-}}}{f_{{\text{mathchar}28931}_b^0}}\frac{\mathcal{B}({\text{mathchar}28932}_b^{-}\to J/\psi {\text{mathchar}28932}^{-})}{\mathcal{B}({\text{mathchar}28931}_b^0\to J/\psi \text{mathchar}28931)}=\frac{f_{{\text{mathchar}28932}_b^{-}}}{f_{{\text{mathchar}28931}_b^0}}\frac{\Gamma ({\text{mathchar}28932}_b^{-}\to J/\psi {\text{mathchar}28932}^{-})}{\Gamma ({\text{mathchar}28931}_b^0\to J/\psi \text{mathchar}28931)}\frac{{\tau }_{{\text{mathchar}28932}_b^{-}}}{{\tau }_{{\text{mathchar}28931}_b^0}}$$

$$R=\frac{N({\text{mathchar}28932}_b^{-}\to J/\psi {\text{mathchar}28932}^{-})}{N({\text{mathchar}28931}_b^0\to J/\psi \text{mathchar}28931)}\frac{{ϵ}_{{\text{mathchar}28931}_b^0}}{{ϵ}_{{\text{mathchar}28932}_b^{-}}},$$

$$\delta m$$

$$m({\text{mathchar}28932}_b^{-})$$

$$R$$

$$A_{\mathrm{prod}}({\text{mathchar}28932}_b^{-})-A_{\mathrm{prod}}({\text{mathchar}28931}_b^0)=\alpha ({\text{mathchar}28932}_b^{-})-\alpha ({\text{mathchar}28931}_b^0)-A_{\det }({\pi }^{-}),$$

$$[A_{\mathrm{prod}}({\text{mathchar}28932}_b^{-})-A_{\mathrm{prod}}({\text{mathchar}28931}_b^0)]$$

$$A_{\mathrm{prod}}({\text{mathchar}28932}_b^{-})$$

$$R$$

$$\frac{f_{{\text{mathchar}28932}_b^{-}}}{f_{{\text{mathchar}28931}_b^0}}$$

$$\delta m$$

$$m({\text{mathchar}28932}_b^{-})$$

$$A_{\mathrm{prod}}({\text{mathchar}28932}_b^{-})$$

Full text

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

​​​

CERN-EP-2018-348

LHCb-PAPER-2018-047

Measurement of the mass and production rate of ${{\mathchar 28932\relax}^{-}_{b}}$ baryons

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

The first measurement of the production rate of ${{\mathchar 28932\relax}^{-}_{b}}$ baryons in $pp$ collisions relative to that of ${{\mathchar 28931\relax}^{0}_{b}}$ baryons is reported, using data samples collected by the LHCb experiment, and corresponding to integrated luminosities of 1, 2 and 1.6$\text{\,fb}^{-1}$ at $\sqrt{s}=7,~{}8$ and 13 TeV, respectively. In the kinematic region $2<\eta<6$ and p_{\mathrm{T}}<20$$\text{\,Ge\kern-1.00006ptV\!/}c, we measure

[TABLE]

where $f_{{{\mathchar 28932\relax}^{-}_{b}}}$ and $f_{{{\mathchar 28931\relax}^{0}_{b}}}$ are the fragmentation fractions of $b$ quarks into ${{\mathchar 28932\relax}^{-}_{b}}$ and ${{\mathchar 28931\relax}^{0}_{b}}$ baryons, respectively, ${\mathcal{B}}$ represents branching fractions, and the uncertainties are due to statistical and experimental systematic sources. The values of $f_{{{\mathchar 28932\relax}^{-}_{b}}}/f_{{{\mathchar 28931\relax}^{0}_{b}}}$ are obtained by invoking SU(3) symmetry in the ${{\mathchar 28932\relax}^{-}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{\mathchar 28932\relax}^{-}}$ and ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{\mathchar 28931\relax}$ decays. Production asymmetries between ${{\mathchar 28932\relax}^{-}_{b}}$ and ${{\kern 1.79993pt\overline{\kern-1.79993pt{\mathchar 28932\relax}}}{}_{b}^{+}}$ baryons are also reported.

The mass of the ${{\mathchar 28932\relax}^{-}_{b}}$ baryon is also measured relative to that of the ${{\mathchar 28931\relax}^{0}_{b}}$ baryon, from which it is found that

[TABLE]

where the last uncertainty is due to the precision on the known ${{\mathchar 28931\relax}^{0}_{b}}$ mass. This result represents the most precise determination of the ${{\mathchar 28932\relax}^{-}_{b}}$ mass.

Published in Phys. Rev. D99 052006 (2019)

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

The decays of beauty ($b$) quarks provide a sensitive probe of physics within, and beyond, the Standard Model. Due to the large ${{b}{\overline{b}}}$ production cross-section at the Large Hadron Collider, beauty hadrons of all species are abundantly produced. Measurements of branching fractions in specific decay channels are often needed in order to make quantitative comparisons to theoretical predictions. However, absolute branching fraction measurements at hadron colliders are difficult to perform without external input. Instead, one generally resorts to measuring a particular branching fraction relative to that of a topologically similar decay mode, frequently one that involves either a ${{B}^{0}}$ or a ${{{B}^{-}}}$ meson, whose absolute branching fractions are known from $B$-factory measurements. When ${{B}^{0}_{s}}$ or ${{\mathchar 28931\relax}^{0}_{b}}$ branching fractions are measured relative to those of a ${{B}^{0}}$ decay, knowledge of the ratio of fragmentation fractions, $f_{s}/f_{d}$ for ${{B}^{0}_{s}}$ decays, or $f_{{{\mathchar 28931\relax}^{0}_{b}}}/f_{d}$ for ${{\mathchar 28931\relax}^{0}_{b}}$ decays, is required. Here, $f_{d}$, $f_{s}$ and $f_{{{\mathchar 28931\relax}^{0}_{b}}}$ represents the rates at which a $b$ quark hadronizes into a ${{B}^{0}}$, ${{B}^{0}_{s}}$ or ${{\mathchar 28931\relax}^{0}_{b}}$ hadron, respectively.

Theoretically, the most robust way to measure the $b$-quark fragmentation fractions is to exploit the well tested prediction from heavy quark effective theory [1, 2, 3, 4, 5, 6, 7, 8] that, to first order, all $b$ hadrons containing a single heavy quark have equal semileptonic decay widths. Such analyses have been carried out by the LHCb experiment at $\sqrt{s}=7\text{\,Te\kern-1.00006ptV}$ [9] and 13 TeV [10], where it is found that $\langle f_{s}/f_{d}\rangle\simeq 0.26$ and $\langle f_{{{\mathchar 28931\relax}^{0}_{b}}}/f_{d}\rangle\simeq 0.6$, averaged over the pseudorapidity ($\eta$) and transverse momentum ($p_{\mathrm{T}}$) region $2<\eta<5$ and 3<p_{\mathrm{T}}<25$$\text{\,Ge\kern-1.00006ptV\!/}c. An alternative technique, which relies on factorization and SU(3) flavor symmetry in the ${{B}^{0}_{s}}\rightarrow{{D}^{-}_{s}}{{\pi}^{+}}$ and ${{B}^{0}}\rightarrow{{D}^{-}}{{K}^{+}}$ decays [11], has also been used to measure $f_{s}/f_{d}$, yielding a value consistent with that obtained in semileptonic decays.

With the large samples of $b$ hadrons collected by the LHCb experiment, a number of new decay modes of ${{\mathchar 28932\relax}^{0}_{b}}$, ${{\mathchar 28932\relax}^{-}_{b}}$, and even ${{\mathchar 28938\relax}^{-}_{b}}$ baryons have been searched for, and in many cases have led to first observations [12, 13, 14, 15, 16, 17, 18, 19, 20]. However, when new decay modes of these baryons are observed, absolute branching fractions cannot be determined due to a lack of knowledge of the fragmentation fractions $f_{{{\mathchar 28932\relax}^{0}_{b}}}$, $f_{{{\mathchar 28932\relax}^{-}_{b}}}$ and $f_{{{\mathchar 28938\relax}^{-}_{b}}}$. For example, in one such measurement, evidence of the strangeness-changing weak decay ${{\mathchar 28932\relax}^{-}_{b}}\rightarrow{{\mathchar 28931\relax}^{0}_{b}}{{\pi}^{-}}$ is reported [16], with the result that $(f_{{{\mathchar 28932\relax}^{-}_{b}}}/f_{{{\mathchar 28931\relax}^{0}_{b}}}){\mathcal{B}}({{\mathchar 28932\relax}^{-}_{b}}\rightarrow{{\mathchar 28931\relax}^{0}_{b}}{{\pi}^{-}})=(5.7\pm 1.8^{+0.8}_{-0.9})\times 10^{-4}$. To compute the decay width $\Gamma({{\mathchar 28932\relax}^{-}_{b}}\rightarrow{{\mathchar 28931\relax}^{0}_{b}}{{\pi}^{-}})$ and compare to theoretical predictions requires knowledge of the ratio $f_{{{\mathchar 28932\relax}^{-}_{b}}}/f_{{{\mathchar 28931\relax}^{0}_{b}}}$.

In principle, the same procedure used to measure $f_{s}/f_{d}$ and $f_{{{\mathchar 28931\relax}^{0}_{b}}}/f_{d}$ can be applied to semileptonic ${{\mathchar 28932\relax}^{0}_{b}}\rightarrow{{\mathchar 28932\relax}^{+}_{c}}{\mu^{-}}{{\overline{\nu}}_{\mu}}X$ and ${{\mathchar 28932\relax}^{-}_{b}}\rightarrow{{\mathchar 28932\relax}^{0}_{c}}{\mu^{-}}{{\overline{\nu}}_{\mu}}X$ decays to measure $f_{{{\mathchar 28932\relax}^{0}_{b}}}/f_{d}$ and $f_{{{\mathchar 28932\relax}^{-}_{b}}}/f_{d}$. However, an obstacle to such an analysis is the limited knowledge of absolute branching fractions for the decays of the ${{\mathchar 28932\relax}^{+}_{c}}$ or ${{\mathchar 28932\relax}^{0}_{c}}$ baryon. Recently, the Belle experiment published a first measurement of the absolute branching fractions for three ${{\mathchar 28932\relax}^{0}_{c}}$ decay modes, each with a relative precision of about 40% [21]. No such measurements exist yet for the ${{\mathchar 28932\relax}^{+}_{c}}$ baryon. Precise measurements of branching fractions for both ${{\mathchar 28932\relax}^{+}_{c}}$ and ${{\mathchar 28932\relax}^{0}_{c}}$ decays should be feasible in the Belle II experiment [22].

Production ratio measurements of the hadronic ${{\mathchar 28932\relax}^{0}_{b}}\rightarrow{{\mathchar 28932\relax}^{+}_{c}}{{\pi}^{-}}$ and ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{\mathchar 28931\relax}^{+}_{c}}{{\pi}^{-}}$ decays [14], where both the ${{\mathchar 28932\relax}^{+}_{c}}$ and ${{\mathchar 28931\relax}^{+}_{c}}$ baryons are reconstructed in the $p{{K}^{-}}{{\pi}^{+}}$ final state, have been used to predict $f_{{{\mathchar 28932\relax}^{0}_{b}}}/f_{{{\mathchar 28931\relax}^{0}_{b}}}$. In this case, theoretical estimates of ${\mathcal{B}}({{\mathchar 28932\relax}^{+}_{c}}\rightarrow p{{K}^{-}}{{\pi}^{+}})$ are used, resulting in predictions of $f_{{{\mathchar 28932\relax}^{0}_{b}}}/f_{{{\mathchar 28931\relax}^{0}_{b}}}=0.065\pm 0.020$ [23] and $f_{{{\mathchar 28932\relax}^{0}_{b}}}/f_{{{\mathchar 28931\relax}^{0}_{b}}}=0.054\pm 0.020$ [24].

An alternative approach to either of these two methods is to exploit the decays ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{\mathchar 28931\relax}$ and ${{\mathchar 28932\relax}^{-}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{\mathchar 28932\relax}^{-}}$, where the ${{\mathchar 28932\relax}^{-}}$ baryon is detected in its decay to ${\mathchar 28931\relax}{{\pi}^{-}}$. Charge-conjugate processes are implicitly included. These decay rates are related through SU(3) flavor symmetry, where one finds [25, 26, 27]

[TABLE]

The ratio

[TABLE]

depends on $f_{{{\mathchar 28932\relax}^{-}_{b}}}/f_{{{\mathchar 28931\relax}^{0}_{b}}}$, the partial decay widths, $\Gamma$, and the lifetimes, $\tau$, of the indicated $b$ baryons. Experimentally, $R$ is obtained from the ratio of efficiency-corrected yields

[TABLE]

where $\epsilon$ represents the detection efficiency and $N$ is the yield of the indicated decays.

In this article, we report a first measurement of the ratio $R$ in $pp$ collision data collected by the LHCb experiment, corresponding to integrated luminosities of 1.0$\text{\,fb}^{-1}$ at $\sqrt{s}=7$ TeV, 2.0$\text{\,fb}^{-1}$ at $\sqrt{s}=8$ TeV and 1.6$\text{\,fb}^{-1}$ at $\sqrt{s}=13$ TeV. The measurement of $R$, along with the SU(3) assumption in Eq. 1 and the known ${{\mathchar 28931\relax}^{0}_{b}}$ and ${{\mathchar 28932\relax}^{-}_{b}}$ baryon lifetimes [28], is used to infer the value of $f_{{{\mathchar 28932\relax}^{-}_{b}}}/f_{{{\mathchar 28931\relax}^{0}_{b}}}$. The same data samples are also used to measure the production asymmetry between ${{\mathchar 28932\relax}^{-}_{b}}$ and ${{\kern 1.79993pt\overline{\kern-1.79993pt{\mathchar 28932\relax}}}{}_{b}^{+}}$ baryons, and make the most precise measurement of the ${{\mathchar 28932\relax}^{-}_{b}}$ mass.

The LHCb detector [29, 30] is a single-arm forward spectrometer 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, 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 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$\text{\,Ge\kern-1.00006ptV\!/}c$. The minimum distance of a track to a primary vertex (PV), the impact parameter (IP), is measured with a resolution of $(15+29/p_{\mathrm{T}})\,\upmu\text{m}$, where $p_{\mathrm{T}}$ is expressed in $\text{\,Ge\kern-1.00006ptV\!/}c$. Different types of charged hadrons are distinguished using information from two ring-imaging Cherenkov detectors. Photons, electrons and hadrons are identified by a calorimeter system consisting of scintillating-pad and preshower detectors, an electromagnetic and a hadronic calorimeter. Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers. The online event selection is performed by a trigger 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.

Simulation is required to model the effects of the detector acceptance and the imposed selection requirements. In the simulation, $pp$ collisions are generated using Pythia [31, *Sjostrand:2007gs] with a specific LHCb configuration [33]. Decays of unstable particles 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].

The ${{\mathchar 28932\relax}^{-}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{\mathchar 28932\relax}^{-}}(\rightarrow{\mathchar 28931\relax}{{\pi}^{-}})$ and ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{\mathchar 28931\relax}$ decays both contain a ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ meson and a ${\mathchar 28931\relax}$ baryon in the decay chain, and are kinematically similar. To reduce systematic uncertainties, selection requirements are tailored to exploit the common particles in the final state of the ${{\mathchar 28931\relax}^{0}_{b}}$ and ${{\mathchar 28932\relax}^{-}_{b}}$ decays. At the trigger level, both modes are required to satisfy requirements based solely on the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\rightarrow{\mu^{+}}{\mu^{-}}$ decay. Firstly, the hardware stage must register either a single high-$p_{\mathrm{T}}$ muon or a ${\mu^{+}}{\mu^{-}}$ pair. The software stage [39] then requires a ${\mu^{+}}{\mu^{-}}$ pair whose decay vertex is displaced from all PVs in the event, and that has an invariant mass consistent with the known ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ mass [28].

Selected events may contain more than one PV. Each particle is associated to the PV for which the corresponding value of $\chi^{2}_{\text{IP}}$ is smallest, where $\chi^{2}_{\text{IP}}$ is defined as the difference in the vertex-fit $\chi^{2}$ of a given PV reconstructed with and without the particle under consideration.

In the offline analysis, each muon must have $p_{\mathrm{T}}$ in excess of 550$\text{\,Me\kern-1.00006ptV\!/}c$ and have IP to all PVs in the event that exceeds approximately three times the expected uncertainty. The ${\mu^{+}}{\mu^{-}}$ pair must form a good-quality vertex and have an invariant mass within 40$\text{\,Me\kern-1.00006ptV\!/}c^{2}$ of the known ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ mass, corresponding to about three times the mass resolution.

Reconstructed charged particles are classified into two categories in this analysis. The long category refers to tracks that have reconstructed segments in both the vertex detector and the tracking stations upstream and downstream of the LHCb magnet. The downstream category consists of those tracks that are not reconstructed in the vertex detector, and thus only include information from the tracking detectors just before and after the LHCb magnet. While most of the reconstructed particles from the $pp$ interactions are in the long category, the decay products of long-lived strange particles tend to be mostly reconstructed as downstream tracks. Because of the presence of vertex detector measurements, the trajectories, and hence the IP, of long tracks are measured with better precision than those of downstream tracks.

Candidate ${\mathchar 28931\relax}\rightarrow p{{\pi}^{-}}$ decays are formed by combining downstream $p$ and ${{\pi}^{-}}$ candidates with $p_{\mathrm{T}}$ in excess of 500$\text{\,Me\kern-1.00006ptV\!/}c$ and 100$\text{\,Me\kern-1.00006ptV\!/}c$, respectively. Both tracks are required to be significantly detached from all PVs in the event, and together they must form a good-quality vertex and must satisfy the requirement |M(p{{\pi}^{-}})-m_{{\mathchar 28931\relax}}|<8$$\text{\,Me\kern-1.00006ptV\!/}c^{2}, corresponding to approximately three times the mass resolution. Here and throughout the text, $M$ represents an invariant mass and $m$ represents the known mass of the indicated particle [28].

The ${{\mathchar 28932\relax}^{-}}$ baryon is reconstructed through its decay to ${\mathchar 28931\relax}{{\pi}^{-}}$. Due to the long ${{\mathchar 28932\relax}^{-}}$ and ${\mathchar 28931\relax}$ lifetimes, only ${\mathchar 28931\relax}$ candidates formed from downstream tracks are used, as they contribute about 90% to the ${{\mathchar 28932\relax}^{-}}$ sample in ${{\mathchar 28932\relax}^{-}_{b}}$ decays. To maintain a uniform selection, the same requirement is imposed on ${\mathchar 28931\relax}$ decays in the ${{\mathchar 28931\relax}^{0}_{b}}$ mode. The ${{\pi}^{-}}$ meson from the ${{\mathchar 28932\relax}^{-}}$ decay may be reconstructed as either a long or a downstream track. For the ${{\mathchar 28932\relax}^{-}_{b}}$ mass and production asymmetry measurements, both categories are used. However, for the measurement of $R$, only the long-track sample is used, since the efficiency for detecting the ${{\pi}^{-}}$ meson in the decay ${{\mathchar 28932\relax}^{-}}\rightarrow{\mathchar 28931\relax}{{\pi}^{-}}$ enters directly in Eq. 3, and long-track efficiencies have been precisely calibrated using a tag-and-probe method [40]. No explicit momentum requirement is applied to the ${{\pi}^{-}}$ meson, since it typically has low momentum. When necessary, the notation $\pi^{-}_{\rm L}$ and $\pi^{-}_{\rm D}$ is used to distinguish between long (L) and downstream (D) ${{\pi}^{-}}$ tracks. Tracks in the $\pi^{-}_{\rm L}$ sample are required to be significantly detached from all PVs in the event, corresponding to a requirement that the impact parameter exceeds about four times the corresponding uncertainty; no such requirement is necessary on the $\pi^{-}_{\rm D}$ sample. Exploiting the large ${{\mathchar 28932\relax}^{-}}$ baryon lifetime, ${{\mathchar 28932\relax}^{-}}$ candidates must have $t_{\rm PV}>6$ ps, where $t_{\rm PV}$ is the decay time measured relative to the associated PV. Lastly, ${{\mathchar 28932\relax}^{-}}$ candidates are required to satisfy the mass requirement |M({\mathchar 28931\relax}\pi^{-}_{\rm L,D})-M(p{{\pi}^{-}})+m_{{\mathchar 28931\relax}}-m_{{{\mathchar 28932\relax}^{-}}}|<10$$\text{\,Me\kern-1.00006ptV\!/}c^{2}, corresponding to about three times the mass resolution, and have positive decay time, measured relative to the ${{\mathchar 28932\relax}^{-}_{b}}$ decay vertex.

The ${{\mathchar 28931\relax}^{0}_{b}}$ (${{\mathchar 28932\relax}^{-}_{b}}$) candidates are formed by combining ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ and ${\mathchar 28931\relax}$ (${{\mathchar 28932\relax}^{-}}$) candidates. A vertex fit of good quality is required. To suppress background from prompt ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$ production, the $b$ hadron is required to have a reconstructed decay time larger than 0.2 ps, which is about four times the resolution. Finally, to have a well-defined fiducial region, the ${{\mathchar 28931\relax}^{0}_{b}}$ and ${{\mathchar 28932\relax}^{-}_{b}}$ candidates are required to be within the kinematic region $2<\eta<6$ and p_{\mathrm{T}}<20$$\text{\,Ge\kern-1.00006ptV\!/}c. Multiple candidates in a single event occur in less than 1% of selected events, and all candidates are kept. To improve the mass resolution, an additional kinematic fit is performed on each candidate, employing both vertex and mass constraints on the ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}$, ${\mathchar 28931\relax}$ and ${{\mathchar 28932\relax}^{-}}$ candidates [41]. The resulting mass resolution is about 8$\text{\,Me\kern-1.00006ptV\!/}c^{2}$ for both modes.

The invariant-mass spectra of selected ${{\mathchar 28931\relax}^{0}_{b}}$ and ${{\mathchar 28932\relax}^{-}_{b}}$ candidates are shown in Fig. 1. The data are partitioned into the combined 7, 8 TeV data samples and the 13 TeV data sample, and show the distributions for ${{\mathchar 28931\relax}^{0}_{b}}$ candidates, and ${{\mathchar 28932\relax}^{-}_{b}}$ candidates formed from either long or downstream pions. A simultaneous fit to all six distributions is performed in order to determine the signal yields. Each of the signal shapes is described by the sum of two Crystal Ball (CB) functions [42] with a common peak position and a common width. The tail parameters, which describe the non-Gaussian portion of the signal on either side of the signal peak, are independent for the two CB components. The parameters of the signal shape are determined from large samples of simulated signal decays. The background is described by an exponential function, with the shape parameter left free in the fit to data.

The signal-shape fit parameters are: (i) the peak positions, $\bar{m}$, of the ${{\mathchar 28931\relax}^{0}_{b}}$ mass in the 7, 8 TeV and 13 TeV data, (ii) a single mass difference, $\delta m\equiv\bar{m}_{{{\mathchar 28932\relax}^{-}_{b}}}-\bar{m}_{{{\mathchar 28931\relax}^{0}_{b}}}$, and (iii) a scale factor applied to the simulated width of the CB functions, which allows the mass resolution in data to be slightly different than in simulation. The values of $\bar{m}_{{{\mathchar 28931\relax}^{0}_{b}}}$ are allowed to differ for the 7, 8 TeV data and the 13 TeV data, since the statistical uncertainty on each is about four times smaller than the systematic uncertainty from the momentum scale calibration [43]. However, that same calibration renders the corresponding uncertainty on $\delta m$ negligible.

The fitted signal yields and the values of $\bar{m}_{{{\mathchar 28931\relax}^{0}_{b}}}$ are shown in Table 1. From the fit, it is determined that

[TABLE]

where the uncertainties are statistical only, and we have used $m({{\mathchar 28932\relax}^{-}_{b}})=\delta m+m_{{{\mathchar 28931\relax}^{0}_{b}}}$, with m_{{{\mathchar 28931\relax}^{0}_{b}}}=5619.60\pm 0.17$$\text{\,Me\kern-1.00006ptV\!/}c^{2} [28]. The value of $\delta m$ is corrected by +0.12\pm 0.06$$\text{\,Me\kern-1.00006ptV\!/}c^{2} to account for a bias observed in the obtained value of $\delta m$, as seen in the fit to large samples of simulated signal decays. The uncertainty on this value is due to the size of the simulated samples.

The ratio of efficiencies in Eq. 3 is determined from weighted simulations of the signal decays. The ${{\mathchar 28931\relax}^{0}_{b}}$ simulation is weighted in bins of ($\eta$, $p_{\mathrm{T}}$) of the $b$ baryon to reproduce the 2D distribution observed in the data, after the background contribution is subtracted using the sPlot method [44]. We assume that the ${{\mathchar 28932\relax}^{-}_{b}}$ spectrum is the same as that of the ${{\mathchar 28931\relax}^{0}_{b}}$, and variations are investigated when assessing systematic uncertainties. By studying the distributions of the fraction of the momentum carried by the decay products in each part of the decay chain, it is found that the simulation differs from the corresponding spectra observed in data. The simulation is weighted to match the distributions observed in data for the momentum ratio $p_{{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}}/p_{{{\mathchar 28931\relax}^{0}_{b}}}$ and the momentum asymmetry $(p_{p}-p_{{{\pi}^{-}}})/(p_{p}+p_{{{\pi}^{-}}})$ in the ${\mathchar 28931\relax}$ decay. After this weighting is applied, a large number of other observables are compared, such as decay times, flight distances, $p$, and $p_{\mathrm{T}}$, and good agreement is found between both ${{\mathchar 28931\relax}^{0}_{b}}$ and ${{\mathchar 28932\relax}^{-}_{b}}$ data and simulation. For the ${{\mathchar 28932\relax}^{-}_{b}}$ sample, only the $(\eta,p_{\mathrm{T}})$ and $(p_{p}-p_{{{\pi}^{-}}})/(p_{p}+p_{{{\pi}^{-}}})$ weights are needed to obtain good agreement with the data.

The resulting efficiencies are summarized in Table 2. The efficiencies associated with the detector acceptance, the reconstruction and selection, and the trigger requirements are given, along with the total selection efficiencies. The relative efficiency is approximately 14% for both the 7, 8 TeV and 13 TeV data sets. For the 7, 8 TeV values, the efficiencies represent the weighted average value. This small value is due to the combination of the relatively low momentum and usage of only long tracks for the ${{\pi}^{-}}$ meson in the ${{\mathchar 28932\relax}^{-}}$ decay.

From the signal yields and relative efficiencies, the ratios $R$ are computed to be

[TABLE]

where the uncertainties are statistical only.

The difference between the ${{\mathchar 28932\relax}^{-}_{b}}$ and ${{\mathchar 28931\relax}^{0}_{b}}$ baryon production asymmetries is determined using the relation

[TABLE]

where $\alpha({{\mathchar 28932\relax}^{-}_{b}})$ $[\alpha({{\mathchar 28931\relax}^{0}_{b}})]$ is the raw yield asymmetry between the ${{{\mathchar 28932\relax}^{-}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{\mathchar 28932\relax}^{-}}}$ and ${{{\kern 1.79993pt\overline{\kern-1.79993pt{\mathchar 28932\relax}}}{}_{b}^{+}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{{\kern 1.79993pt\overline{\kern-1.79993pt{\mathchar 28932\relax}}}^{+}}}$ $[{{{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{\mathchar 28931\relax}}$ and ${{{\kern 1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}}{}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{\kern 1.79993pt\overline{\kern-1.79993pt\mathchar 28931\relax}}}]$ decays. In the difference of the raw yield asymmetries, the ${\mathchar 28931\relax}$ detection asymmetry cancels since the kinematical properties are similar. The ${{\pi}^{-}}$ detection asymmetry, $A_{\rm det}({{\pi}^{-}})$, has been measured [45, 46], and, while it is consistent with zero, an asymmetry of up to about 1% in this low momentum region cannot be discounted. In the above expression, it is expected, and assumed, that there is no direct $C\!P$ violation in these decays.

The raw yield asymmetries are obtained by fitting for the signal yields separately for the beauty baryon and antibaryon subsamples. The fit is similar to that which was described previously, except that the CB width scale factors are fixed to the values obtained from the fit to the full sample, since the mass resolution can be assumed to be the same for the $b$ baryons and antibaryons. The fitted signal yields are shown in Table 3, along with the resulting raw asymmetries.

The difference in production asymmetries are readily found to be

[TABLE]

where the uncertainties are due to the signal yields obtained in this analysis.

To obtain $A_{\rm prod}({{\mathchar 28932\relax}^{-}_{b}})$, previous measurements of $A_{\rm prod}({{\mathchar 28931\relax}^{0}_{b}})$ at $\sqrt{s}=7$ and 8 TeV are used [47]. Since the value of $A_{\rm prod}({{\mathchar 28931\relax}^{0}_{b}})$ averaged over the LHCb acceptance is not expected to change significantly with center-of-mass energy [48], and the measured values of $A_{\rm prod}({{\mathchar 28931\relax}^{0}_{b}})$ obtained at $\sqrt{s}=7$ and 8 TeV are compatible [47], they are averaged, taking the systematic uncertainties as fully correlated, to obtain ${A_{\rm prod}({{\mathchar 28931\relax}^{0}_{b}})=(2.4\pm 1.4\pm 0.9)\%}$. An alternate measurement of $A_{\rm prod}({{\mathchar 28931\relax}^{0}_{b}})$ yielded results that are consistent with the above value [49]. The value at 7, 8 TeV is also used for the ${{\mathchar 28932\relax}^{-}_{b}}$ asymmetry measurement at 13 TeV, and a systematic uncertainty, which is discussed below, is assigned. The ${{\mathchar 28932\relax}^{-}_{b}}$ asymmetries are found to be

[TABLE]

In the mass measurement, most sources of systematic uncertainty cancel, since it relies on the mass difference, $\delta m$. The modulus of the correction of 0.12$\text{\,Me\kern-1.00006ptV\!/}c^{2}$ described previously is assigned as a systematic uncertainty. The signal shape uncertainty is quantified by performing an alternate fit using the sum of two Gaussian functions. Apart from a common peak value, all shape parameters are left free in the fit. The difference with respect to the nominal value, 0.06$\text{\,Me\kern-1.00006ptV\!/}c^{2}$, is assigned as a systematic uncertainty. The background shape uncertainty is assessed by using a first-order polynomial in place of the nominal exponential function, and is found to change the result by 0.01$\text{\,Me\kern-1.00006ptV\!/}c^{2}$. The systematic uncertainties due to the momentum scale and energy loss have been evaluated previously [50] and are found to contribute 0.01$\text{\,Me\kern-1.00006ptV\!/}c^{2}$ each. Knowledge of the ${{\mathchar 28932\relax}^{-}}$ mass contributes an uncertainty of 0.07$\text{\,Me\kern-1.00006ptV\!/}c^{2}$. Adding these uncertainties in quadrature, the total systematic uncertainty on $\delta m$ is 0.15$\text{\,Me\kern-1.00006ptV\!/}c^{2}$.

For the measurement of $R$, several sources of uncertainty are considered, which are summarized in Table 4. The efficiency for all decay products to be within the LHCb acceptance is derived from the simulation, and could depend on the polarization of the ${{\mathchar 28931\relax}^{0}_{b}}$ or ${{\mathchar 28932\relax}^{-}_{b}}$ baryon. To investigate this effect, variations in the ${{\mathchar 28931\relax}^{0}_{b}}$ and ${{\mathchar 28932\relax}^{-}_{b}}$ polarization are considered, including full polarization, zero polarization, and using the helicity amplitudes presented in Ref. [51]. All three variations are found to give statistically compatible acceptance corrections. The assigned uncertainty of 3.0% reflects the statistical precision of the test.

The systematic uncertainty due to the signal and background functions is estimated by using alternate choices for each, as described above for the uncertainty on $\delta m$, leading to an uncertainty of 2.0%. The ${{\mathchar 28931\relax}^{0}_{b}}$ and ${{\mathchar 28932\relax}^{-}_{b}}$ simulations are weighted as discussed previously and reproduce well the kinematical distributions of the final-state particles seen in data. However, due to low ${{\mathchar 28932\relax}^{-}_{b}}$ signal yields, variations with respect to the nominal weighting are considered. In particular, a 3% change in the relative efficiency is seen when applying an additional weight to the ${{\mathchar 28932\relax}^{-}_{b}}$ pseudorapidity spectrum that is permissible by the data. A significantly smaller difference is seen when weighting the ${{\mathchar 28932\relax}^{-}_{b}}$ baryon’s $p_{\mathrm{T}}$ spectrum. A 3% uncertainty is therefore assigned to account for potential differences in the $(\eta,p_{\mathrm{T}})$ spectrum of ${{\mathchar 28931\relax}^{0}_{b}}$ and ${{\mathchar 28932\relax}^{-}_{b}}$ baryons.

Uncertainties in the detection efficiency of the ${{\pi}^{-}}$ meson from the ${{\mathchar 28932\relax}^{-}}$ decay enters directly into the result for the ratio $R$. The tracking efficiency in simulation has been calibrated using a tag-and-probe method [40] using ${{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}\rightarrow{\mu^{+}}{\mu^{-}}$ decays, however, the calibration only covers the kinematic region p>5$$\text{\,Ge\kern-1.00006ptV\!/}c and $1.9<\eta<4.9$. Outside this region, no correction to the tracking efficiency in simulation is applied and an uncertainty of 5% is assigned to the tracking efficiency. This value is justified based upon a comparison of the reconstructed momentum spectrum of ${{\pi}^{-}}$ mesons from ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{J\mskip-3.0mu/\mskip-2.0mu\psi\mskip 2.0mu}}{\mathchar 28931\relax}$ decays in data and simulation, where the ${\mathchar 28931\relax}$ baryons are formed from long tracks. These tracks serve as a good proxy for the ${{\pi}^{-}}$ meson from ${{\mathchar 28932\relax}^{-}}$ baryon decay, since they also have low momentum and large impact parameter. Averaging over the tracks within and outside the range covered by the tracking calibration, an uncertainty of 4.5% on the ${{\pi}^{-}}$ tracking efficiency is obtained. As a cross-check, the analysis is repeated using only ${{\pi}^{-}}$ candidates in the range covered by the calibration, and the $R$ values are consistent with the nominal results.

Potential uncertainties due to the ${{\mathchar 28932\relax}^{-}}$ mass requirement may arise from differences in the ${{\mathchar 28932\relax}^{-}}$ mass resolution, or possibly a (Cabibbo-suppressed) nonresonant ${\mathchar 28931\relax}{{\pi}^{-}}$ contribution. To quantify the potential size of such effects, the ${{\mathchar 28932\relax}^{-}_{b}}$ signal yield in the ${{\mathchar 28932\relax}^{-}}$ sideband region, 10<|M({\mathchar 28931\relax}\pi^{-}_{\rm L,D})-M(p{{\pi}^{-}})+m_{{\mathchar 28931\relax}}-m_{{{\mathchar 28932\relax}^{-}}}|<20$$\text{\,Me\kern-1.00006ptV\!/}c^{2} is measured. The yield in that region, which is consistent with zero, is taken as a systematic uncertainty. Other ${{\mathchar 28932\relax}^{-}}$ selections are very loose and are studied by comparing background-subtracted distributions of relevant variables in data with those in simulation. From the observed differences an uncertainty of 1.4% is assigned. The uncertainty on $R$ due to the knowledge of the ${{\mathchar 28932\relax}^{-}_{b}}$ lifetime, $\tau_{{{\mathchar 28932\relax}^{-}_{b}}}=1.571\pm 0.040$ ps [28], is estimated by weighting the simulation to replicate 0.04 ps shorter and longer lifetimes. The effect on $R$ of the ${{\mathchar 28931\relax}^{0}_{b}}$ lifetime uncertainty is negligible. Lastly, the simulated sample sizes contribute 2.0% uncertainty to the relative efficiency.

The uncertainty on the ${{\mathchar 28932\relax}^{-}_{b}}$ production asymmetry receives contributions from the ${{\pi}^{-}}$ detection asymmetry and the measurement of $A_{\rm prod}({{\mathchar 28931\relax}^{0}_{b}})$. The pion detection asymmetry uncertainty is assigned to be 1%, as mentioned previously. Taking the sum in quadrature of the statistical and systematic uncertainties in the value of $A_{\rm prod}({{\mathchar 28931\relax}^{0}_{b}})=(2.4\pm 1.4\pm 0.9)\%$, a 1.7% systematic uncertainty is assigned. Since the average value of $A_{\rm prod}({{\mathchar 28931\relax}^{0}_{b}})$ at $\sqrt{s}=7$ and 8 TeV [47] could differ from that at 13 TeV [48], an additional systematic uncertainty of 1.5% is assigned to the measured value of $A_{\rm prod}({{\mathchar 28932\relax}^{-}_{b}})$ at 13 TeV. The total systematic uncertainty in $A_{\rm prod}({{\mathchar 28932\relax}^{-}_{b}})$ is therefore 1.9% and 2.5% for the 7, 8 TeV and 13 TeV data samples, respectively.

In summary, data samples collected at $\sqrt{s}$ = 7, 8 and 13 TeV have been used to measure the ratio of production rates of ${{\mathchar 28932\relax}^{-}_{b}}$ and ${{\mathchar 28931\relax}^{0}_{b}}$ baryons in the pseudorapidity and $p_{\mathrm{T}}$ region, $2<\eta<6$ and p_{\mathrm{T}}<20$$\text{\,Ge\kern-1.00006ptV\!/}c, to be

[TABLE]

where the uncertainties are statistical and systematic. From the values of $R$, the ratios of fragmentation fractions are determined to be

[TABLE]

The last uncertainty, due to the assumed SU(3) flavor symmetry and taken to be 30%, is an estimate of the typical size of SU(3)-breaking effects between decays related by this symmetry. The LHCb results show no significant dependence on the center-of-mass energy in the 7 to 13 TeV range. These results are consistent with the predictions in Refs. [23, 24], which used production ratio measurements of ${{\mathchar 28932\relax}^{0}_{b}}\rightarrow{{\mathchar 28932\relax}^{+}_{c}}{{\pi}^{-}}$ and ${{\mathchar 28931\relax}^{0}_{b}}\rightarrow{{\mathchar 28931\relax}^{+}_{c}}{{\pi}^{-}}$ decays at 7 and 8 TeV [14] and an estimated value for ${\mathcal{B}}({{\mathchar 28932\relax}^{+}_{c}}\rightarrow p{{K}^{-}}{{\pi}^{+}})$. Assuming that $f_{{{\mathchar 28932\relax}^{0}_{b}}}\approx f_{{{\mathchar 28932\relax}^{-}_{b}}}$, these results indicate that in the forward region, $b$ quarks fragment into ${{\mathchar 28932\relax}_{b}}$ baryons at about 15% of the rate at which they fragment into ${{\mathchar 28931\relax}^{0}_{b}}$ baryons. Previous measurements of $R$ by the CDF [52] and D0 [53] collaborations are about two standard deviations larger than the results reported here, however, those measurements are performed in $p\bar{p}$ collisions at $\sqrt{s}=2$ TeV and in the central rapidity region $|\eta|<2$.

The mass difference, $\delta m$, and the corresponding value of the ${{\mathchar 28932\relax}^{-}_{b}}$ mass, $m({{\mathchar 28932\relax}^{-}_{b}})$, are measured to be

[TABLE]

where the last uncertainty is due to the ${{\mathchar 28931\relax}^{0}_{b}}$ mass. This ${{\mathchar 28932\relax}^{-}_{b}}$ mass measurement includes the data used in Ref. [50], and therefore supersedes those results. This measurement represents the most precise determination of the ${{\mathchar 28932\relax}^{-}_{b}}$ mass, and is consistent with the previous most precise measurement of the mass difference of 178.36\pm 0.46\pm 0.16$$\text{\,Me\kern-1.00006ptV\!/}c^{2} [15].

The ${{\mathchar 28932\relax}^{-}_{b}}$ production asymmetry is also measured for the first time. The values at the lower and higher center-of-mass energies, are

[TABLE]

The asymmetries are consistent with zero at the level of a few percent.

Acknowledgements

We thank M. Voloshin for interesting and helpful discussions on theoretical aspects of this work. 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).