[a,1]Viacheslav Matiunin 11footnotetext: On behalf of the LHCb Collaboration.

# Studies of b-hadrons at LHCb

###### Abstract

A large data set collected at the LHCb experiment in proton-proton collisions
during Runs 1 and 2 of the Large Hadron Collider has opened a unique
possibility to study heavy beauty hadron states and to broaden knowledge of
their spectroscopy and production. Recent results on searches for new excited
$\mathrm{b}$-hadron states, and studies of $\mathrm{b}$-hadron production, are
reviewed. In particular, the observation of new excited
${\Omega^{-}_{\mathrm{b}}}$ states, the observation of two new narrow
${{\Lambda}_{\mathrm{b}}(6146)^{0}}$ and ${{\Lambda}_{\mathrm{b}}(6152)^{0}}$
states, the observation of new ${{\Lambda}_{\mathrm{b}}^{**0}}$ state
consistent with the ${{\Lambda}_{\mathrm{b}}(2\mathrm{S})^{0}}$ prediction, a
precise measurement of the mass and width of
${{\Lambda}_{\mathrm{b}}(5912)^{0}}$ and ${{\Lambda}_{\mathrm{b}}(5920)^{0}}$
states, and a measurement of the ${{\mathrm{B}}_{\mathrm{c}}^{-}}$ meson
production fraction and
${{\mathrm{B}}_{\mathrm{c}}^{-}}-{{\mathrm{B}}_{\mathrm{c}}^{+}}$ production
asymmetry in 7 and 13  TeV of proton-proton collisions are presented.

##  1 Introduction

Over the last few years numerous outstanding results have been obtained within
the analyses of $\mathrm{b}$-hadrons. Among those there are observation of
pentaquark and tetraquark resonances, observation of series of excited heavy
baryons and many others. Still, many of the conventional states remain
unobserved, parameters of some of the known hadron states are poorly measured
and on top of that there are a number of the states which do not fit into the
conventional quarkonium spectrum. Hence study of $\mathrm{b}$-hadrons
spectroscopy is of particular interest in the modern high energy physics.

The results described below are based on the data samples collected by the
LHCb experiment in proton-proton ($\mathrm{p}\mathrm{p}$) collision at the
Large Hadron Collider (LHC) with centre-of-mass energies $\sqrt{\rm s}=7$ and
$8\,\text{\,Te\kern-1.00006ptV}$ corresponding to a total integrated
luminosity of $3\,\text{\,fb}^{-1}$ (LHC Run 1) and with centre-of-mass energy
$\sqrt{\rm s}=13\,\text{\,Te\kern-1.00006ptV}$ corresponding to a total
integrated luminosity of $6\,\text{\,fb}^{-1}$ (LHC Run 2).

##  2 Observation of excited ${\Omega^{-}_{\mathrm{b}}}$ states

Recently, the new five narrow excited ${\Omega^{0}_{\mathrm{c}}}$ baryons has
been observed [1]. Some of the theoretical models describing
${\Omega^{0}_{\mathrm{c}}}$ peaks also predict ${\Omega^{-}_{\mathrm{b}}}$
states decaying to ${\Xi^{0}_{\mathrm{b}}}{{\mathrm{K}}^{-}}$ final state.
Therefore, it is of great interest to search for the analogous excited states
with the LHCb experiment data. The ${\Xi^{0}_{\mathrm{b}}}{{\mathrm{K}}^{-}}$
mass spectrum is studied to search for narrow resonances close to the
kinematic threshold [2]. The analysis is done using $\mathrm{p}\mathrm{p}$
collision data samples corresponding to an integrated luminosity of
$9.0~{}\text{\,fb}^{-1}$ (LHC Run 1 and 2). The ${\Xi^{0}_{\mathrm{b}}}$
baryons are reconstructed using ${\Xi^{+}_{\mathrm{c}}}{{\uppi}^{-}}$ decay
mode, where ${\Xi^{+}_{\mathrm{c}}}$ baryons are reconstructed with the
$\mathrm{p}{{\mathrm{K}}^{-}}{{\uppi}^{+}}$ final state. The distributions of
right-sign combination mass difference
$\mathrm{M}({\Xi^{0}_{\mathrm{b}}}{{\mathrm{K}}^{-}})-\mathrm{M}({\Xi^{0}_{\mathrm{b}}})$
and wrong-sign combination mass difference
$\mathrm{M}({\Xi^{0}_{\mathrm{b}}}{{\mathrm{K}}^{+}})-\mathrm{M}({\Xi^{0}_{\mathrm{b}}})$
are shown in Fig. 1 (a) and (b), respectively. Four narrow peaks are seen in
right-sign distribution. Simultaneous fit to wrong-sign and right-sign spectra
with common background shape is performed. The peak parameters obtained from
the fit results together with the significance of the peaks are shown in Table
1. The mass and width of the new resonances are consistent with expectations
for excited ${\Omega^{-}_{\mathrm{b}}}$ states.

(a)(b)

Figure 1: The distributions of (a) right-sign $\mathrm{M}({\Xi^{0}_{\mathrm{b}}}{{\mathrm{K}}^{-}})-\mathrm{M}({\Xi^{0}_{\mathrm{b}}})$ and (b) wrong-sign $\mathrm{M}({\Xi^{0}_{\mathrm{b}}}{{\mathrm{K}}^{+}})-\mathrm{M}({\Xi^{0}_{\mathrm{b}}})$ mass differences. Different components employed in the fit are indicated in the legend.  Table 1: The masses, 90% (95%) confidence level upper limits on the natural widths and global (local) significance for the four peaks. The uncertainties are statistical, systematic, and due to the world-average value of the ${\Xi^{0}_{\mathrm{b}}}$ mass (for the masses). For the ${\Omega_{\mathrm{b}}(6350)^{-}}$ peak, the central value of the width is also indicated. | Mass [MeV] | Width [MeV] | Significance [$\sigma$]
---|---|---|---
${\Omega_{\mathrm{b}}(6316)^{-}}$ | $6315.64\pm 0.31\pm 0.07\pm 0.50$ | $<2.8~{}(4.2)$ | 2.1 (3.6)
${\Omega_{\mathrm{b}}(6330)^{-}}$ | $6330.30\pm 0.28\pm 0.07\pm 0.50$ | $<3.1~{}(4.7)$ | 2.6 (3.7)
${\Omega_{\mathrm{b}}(6340)^{-}}$ | $6339.71\pm 0.26\pm 0.05\pm 0.50$ | $<1.5~{}(1.8)$ | 6.7 (7.2)
${\Omega_{\mathrm{b}}(6350)^{-}}$ | $6349.88\pm 0.35\pm 0.05\pm 0.50$ | $<2.8~{}(3.2)$ | 6.2 (7.0)
|  | $~{}~{}\,\,1.4\,^{+\,1.0}_{-\,0.8}\pm 0.1$ |

##  3 Excited ${\Lambda_{\mathrm{b}}^{0}}$ baryons

Beyond the lightest beauty baryon, ${\Lambda_{\mathrm{b}}^{0}}$ baryon, a rich
spectrum of radially and orbitally excited states is expected at higher
masses. The excited states has been searched in the
${{\Lambda_{\mathrm{b}}^{0}}{{\uppi}^{+}}{{\uppi}^{-}}}$ spectrum by the LHCb
experiment with the discovery of two narrow states [3]. Therefore, it is both
interesting and promising to study the
${{\Lambda_{\mathrm{b}}^{0}}{{\uppi}^{+}}{{\uppi}^{-}}}$ spectrum with the
full statistics collected by the LHCb experiment. The
${{\Lambda_{\mathrm{b}}^{0}}{{\uppi}^{+}}{{\uppi}^{-}}}$ mass spectrum is
studied by the LHCb experiment using the full LHC Run 1 and 2 data sample of
$\mathrm{p}\mathrm{p}$ collisions, corresponding to an integrated luminosity
of 9 $\text{\,fb}^{-1}$ [4, 5]. The ${\Lambda_{\mathrm{b}}^{0}}$ baryon is
reconstructed using two decay modes
${{\Lambda_{\mathrm{c}}^{+}}{{\uppi}^{-}}}$ and
${{{\mathrm{J}\mskip-3.0mu/\mskip-2.0mu\uppsi\mskip
2.0mu}}\mathrm{p}{{\mathrm{K}}^{-}}}$. The study is performed in three
${{\Lambda_{\mathrm{b}}^{0}}{{\uppi}^{+}}{{\uppi}^{-}}}$ mass intervals:
high-, middle- and low-mass.

(a)

Candidates / $3\,\text{\,Me\kern-0.70004ptV}$

$\mathrm{M}({{\Lambda_{\mathrm{b}}^{0}}{{\uppi}^{+}}{{\uppi}^{-}}})\quad\quad[\text{\,Ge\kern-0.70004ptV}]$(b)

Candidates / $0.4\,\text{\,Me\kern-0.70004ptV}$

$\mathrm{M}({{\Lambda_{\mathrm{b}}^{0}}{\uppi}{\uppi}})\quad\quad\quad[\text{\,Ge\kern-0.70004ptV}]$(c)

Candidates / $0.4\,\text{\,Me\kern-0.70004ptV}$

$\mathrm{M}({{\Lambda_{\mathrm{b}}^{0}}{\uppi}{\uppi}})\quad\quad\quad[\text{\,Ge\kern-0.70004ptV}]$

Figure 2: (a) Mass distributions of
${{\Lambda_{\mathrm{b}}^{0}}{{\uppi}^{+}}{{\uppi}^{-}}}$ combination for the
three regions in ${{\Lambda_{\mathrm{b}}^{0}}{{\uppi}^{\pm}}}$ mass: (top)
${\Sigma_{\mathrm{b}}^{\mp}}$, (middle) ${\Sigma_{\mathrm{b}}^{*\mp}}$ and
(bottom) nonresonant region. Mass spectra of (top)
${{\Lambda_{\mathrm{b}}^{0}}{{\uppi}^{+}}{{\uppi}^{-}}}$, (middle)
${{\Lambda_{\mathrm{b}}^{0}}{{\uppi}^{+}}{{\uppi}^{+}}}$ and (bottom)
${{\Lambda_{\mathrm{b}}^{0}}{{\uppi}^{+}}{{\uppi}^{+}}}$ combinations for the
(b) ${\Lambda_{\mathrm{b}}^{0}}\to{{\Lambda_{\mathrm{c}}^{+}}{{\uppi}^{-}}}$
and (c)
${\Lambda_{\mathrm{b}}^{0}}\to{{{\mathrm{J}\mskip-3.0mu/\mskip-2.0mu\uppsi\mskip
2.0mu}}\mathrm{p}{{\mathrm{K}}^{-}}}$ sample. Different components employed in
the fit are indicated in the legend.

In the high ${{\Lambda_{\mathrm{b}}^{0}}{{\uppi}^{+}}{{\uppi}^{-}}}$ mass
interval a new peaking structure at approximately
$6.15\,\text{\,Ge\kern-1.00006ptV}$ is observed [4]. The peak is above
${\Sigma_{\mathrm{b}}^{(*)\mp}\pi^{\pm}}$ threshold, hence, spectrum is
investigated in three non-overlapping
${{\Lambda_{\mathrm{b}}^{0}}{{\uppi}^{\pm}}}$ mass regions: two resonant
${\Sigma_{\mathrm{b}}^{\mp}}$ and ${\Sigma_{\mathrm{b}}^{*\mp}}$ regions and
nonresonant one. Simultaneous fit to the three
${{\Lambda_{\mathrm{b}}^{0}}{{\uppi}^{+}}{{\uppi}^{-}}}$ mass distributions is
performed. The two-peak hypothesis is favoured with respect to the single-peak
hypothesis with more than $7\,\sigma$ statistical significance. The
${{\Lambda_{\mathrm{b}}^{0}}{{\uppi}^{+}}{{\uppi}^{-}}}$ mass distributions
are shown in Fig. 2 (a). Mass and width of the two peaks are

$\displaystyle\mathrm{M}_{{{\Lambda}_{\mathrm{b}}(6146)^{0}}}=6146.17\pm
0.33\pm 0.22\pm
0.16\text{\,Me\kern-1.00006ptV},\quad\Gamma_{{{\Lambda}_{\mathrm{b}}(6146)^{0}}}=2.9\pm
1.3\pm 0.3\text{\,Me\kern-1.00006ptV},$ (1)
$\displaystyle\mathrm{M}_{{{\Lambda}_{\mathrm{b}}(6152)^{0}}}=6152.51\pm
0.26\pm 0.22\pm
0.16\text{\,Me\kern-1.00006ptV},\quad\Gamma_{{{\Lambda}_{\mathrm{b}}(6152)^{0}}}=2.1\pm
0.8\pm 0.3\text{\,Me\kern-1.00006ptV},$ (2)

here and throughout the Section the first uncertainty is statistical, the
second one is systematic and third one is due to the uncertainty in the
nominal ${\Lambda_{\mathrm{b}}^{0}}$ baryon mass. The measured masses are
consistent with predictions for ${\Lambda}_{\mathrm{b}}(\rm 1D)^{0}$ doublet
with $\mathrm{J}^{\mathrm{P}}=\frac{3}{2}^{+}$ and $\frac{5}{2}^{+}$ [6, 7].

(a)

Candidates / $0.4\,\text{\,Me\kern-0.70004ptV}$

$\mathrm{M}({{\Lambda_{\mathrm{b}}^{0}}{\uppi}{\uppi}})\;\;\,\quad\quad\quad[\text{\,Ge\kern-0.70004ptV}]$(b)

Candidates / $0.4\,\text{\,Me\kern-0.70004ptV}$

$\mathrm{M}({{\Lambda_{\mathrm{b}}^{0}}{\uppi}{\uppi}})\;\;\,\quad\quad\quad[\text{\,Ge\kern-0.70004ptV}]$

Figure 3: Mass spectra of (top)
${{\Lambda_{\mathrm{b}}^{0}}{{\uppi}^{+}}{{\uppi}^{-}}}$, (middle)
${{\Lambda_{\mathrm{b}}^{0}}{{\uppi}^{+}}{{\uppi}^{+}}}$ and (bottom)
${{\Lambda_{\mathrm{b}}^{0}}{{\uppi}^{+}}{{\uppi}^{+}}}$ combinations for the
(a) ${\Lambda_{\mathrm{b}}^{0}}\to{{\Lambda_{\mathrm{c}}^{+}}{{\uppi}^{-}}}$
and (b)
${\Lambda_{\mathrm{b}}^{0}}\to{{{\mathrm{J}\mskip-3.0mu/\mskip-2.0mu\uppsi\mskip
2.0mu}}\mathrm{p}{{\mathrm{K}}^{-}}}$ sample. Different components employed in
the fit are indicated in the legend.

In the intermediate ${{\Lambda_{\mathrm{b}}^{0}}{{\uppi}^{+}}{{\uppi}^{-}}}$
mass interval a new baryon state is observed [5]. The simultaneous fit to the
six mass distributions where ${\Lambda_{\mathrm{b}}^{0}}$ baryon is
reconstructed via two different decay modes and in each case for one right-
sign ${{\Lambda_{\mathrm{b}}^{0}}{{\uppi}^{+}}{{\uppi}^{-}}}$ and two wrong-
sign ${{\Lambda_{\mathrm{b}}^{0}}{{\uppi}^{\pm}}{{\uppi}^{\pm}}}$ spectra is
performed. The ${{\Lambda_{\mathrm{b}}^{0}}{{\uppi}^{+}}{{\uppi}^{-}}}$ mass
distributions are shown in Fig. 2 (b) and (c). Mass and width of the new peak
are

$\displaystyle\mathrm{M}_{{{\Lambda}_{\mathrm{b}}^{**0}}}=6072.3\pm 2.9\pm
0.6\pm
0.2\text{\,Me\kern-1.00006ptV},\quad\Gamma_{{{\Lambda}_{\mathrm{b}}^{**0}}}=72\pm
11\pm 2\text{\,Me\kern-1.00006ptV}.$ (3)

The observed peak is consistent with broad excess reported by the CMS
experiment [8]. The measured mass and width are in agreement with expectations
for the ${\Lambda}_{\mathrm{b}}(2\mathrm{S})^{0}$ state. The contributions
from ${\Sigma_{\mathrm{b}}^{(*)\pm}}$ resonances are also studied and the
nonresonant component is found to give a dominant contribution.

In the low ${{\Lambda_{\mathrm{b}}^{0}}{{\uppi}^{+}}{{\uppi}^{-}}}$ mass
interval the two states observed earlier [3] are confirmed. The simultaneous
fit to the six mass distributions where ${\Lambda_{\mathrm{b}}^{0}}$ baryon is
reconstructed via two different decay modes and in each case for one right-
sign ${{\Lambda_{\mathrm{b}}^{0}}{{\uppi}^{+}}{{\uppi}^{-}}}$ and two wrong-
sign ${{\Lambda_{\mathrm{b}}^{0}}{{\uppi}^{\pm}}{{\uppi}^{\pm}}}$ spectra is
performed. The mass spectra are shown in Fig. 3. The mass and width of the
states are measured to be

$\displaystyle\mathrm{M}_{{{\Lambda}_{\mathrm{b}}(5912)^{0}}}$
$\displaystyle=5912.21\pm 0.03\pm 0.01\pm
0.21\text{\,Me\kern-1.00006ptV},\quad\Gamma_{{{\Lambda}_{\mathrm{b}}(5912)^{0}}}<0.25\,(0.28)\text{\,Me\kern-1.00006ptV},$
(4) $\displaystyle\mathrm{M}_{{{\Lambda}_{\mathrm{b}}(5920)^{0}}}$
$\displaystyle=5920.11\pm 0.02\pm 0.01\pm
0.21\text{\,Me\kern-1.00006ptV},\quad\Gamma_{{{\Lambda}_{\mathrm{b}}(5920)^{0}}}<0.19\,(0.20)\text{\,Me\kern-1.00006ptV}.$
(5)

For the natural widths the upper limits at $90\%~{}(95\%)$ confidence level is
specified. The parameters are measured with about four times higher precision
with respect to those reported in Ref. [3].

##  4 Measurement of the ${{\mathrm{B}}_{\mathrm{c}}^{-}}$ meson production
fraction and asymmetry in $\mathrm{p}\mathrm{p}$ collisions at 7 and 13  TeV

The $\mathrm{b}$-hadrons cross-sections as functions of transverse momentum
($p_{\mathrm{T}}$) and pseudorapidity ($\eta$) are predicted using non-
relativistic quantum chromodynamics along with fragmentation functions. The
corresponding literature is systematically reviewed in the Ref. [9]. The
measurement of the ${{\mathrm{B}}_{\mathrm{c}}^{-}}$ production fraction would
allow to further probe quantum chromodynamics.

(a)(b)

Figure 4: Ratio of production fractions as a function of (a) $p_{\mathrm{T}}$
and (b) $\eta$ of ${\mathrm{B}}$ mesons for the 7  TeV data sample. The
statistical uncertainties are shown with smaller error bars, whereas larger
bars include both statistical and systematic uncertainties.

The production fraction ratio
$\dfrac{\mathrm{f}_{\mathrm{c}}}{\mathrm{f}_{\mathrm{u}}+\mathrm{f}_{\mathrm{d}}}$
and the ${{\mathrm{B}}_{\mathrm{c}}^{-}}-{{\mathrm{B}}_{\mathrm{c}}^{+}}$
production asymmetry are measured by the LHCb experiment [10]. The analysis is
done using data samples of 7 and 13  TeV $\mathrm{p}\mathrm{p}$ collisions
corresponding to an integrated luminosity of $1.0$ and
$1.6~{}\text{\,fb}^{-1}$, respectively. The ${\mathrm{B}}$ mesons in the
analysis are reconstructed using the
${{{\mathrm{B}}_{\mathrm{c}}^{-}}\to{{\mathrm{J}\mskip-3.0mu/\mskip-2.0mu\uppsi\mskip
2.0mu}}{\upmu^{-}}{{\overline{}\upnu}_{{\upmu}}}}$,
${{\mathrm{B}^{0}}\to{\mathrm{D}^{+}}\mathrm{X}{\upmu^{-}}{{\overline{}\upnu}_{{\upmu}}}}$
and
${{{\mathrm{B}}^{-}}\to{\mathrm{D}^{0}}\mathrm{X}{\upmu^{-}}{{\overline{}\upnu}_{{\upmu}}}}$
decay modes. The $\mathrm{X}$ symbol is used here and throughout to refer to
any additional undetected particles. The production fractions are obtained as
a function of $p_{\mathrm{T}}$ and $\eta$ of the ${\mathrm{B}}$ mesons. The
measured production fraction for the 7  TeV data sample is shown in Fig. 4 (a)
and (b). There is a small dependence on the transverse momentum, but no
dependence on $\eta$ is observed. The ratio of production fractions averaged
over $p_{\mathrm{T}}$ and $\eta$ of the ${\mathrm{B}}$ mesons are measured to
be

$\displaystyle\dfrac{\mathrm{f}_{\mathrm{c}}}{\mathrm{f}_{\mathrm{u}}+\mathrm{f}_{\mathrm{d}}}$
$\displaystyle=(3.63\pm 0.08\pm 0.12\pm 0.86)\times
10^{-3}\rm\;\,for\;\,7~{}\text{\,Te\kern-1.00006ptV},$ (6)
$\displaystyle\dfrac{\mathrm{f}_{\mathrm{c}}}{\mathrm{f}_{\mathrm{u}}+\mathrm{f}_{\mathrm{d}}}$
$\displaystyle=(3.78\pm 0.04\pm 0.15\pm 0.89)\times
10^{-3}\rm\;\,for\;\,13~{}\text{\,Te\kern-1.00006ptV},$ (7)

where the first uncertainty is statistical, the second one is systematic and
third one is due to the spread of theoretical predictions of the
${{{\mathrm{B}}_{\mathrm{c}}^{-}}\to{{\mathrm{J}\mskip-3.0mu/\mskip-2.0mu\uppsi\mskip
2.0mu}}{\upmu^{-}}{{\overline{}\upnu}_{{\upmu}}}}$ branching fraction
available in literature (see references in Ref. [10]). Recently the HPQCD
collaboration provided the first lattice prediction of the
${{{\mathrm{B}}_{\mathrm{c}}^{-}}\to{{\mathrm{J}\mskip-3.0mu/\mskip-2.0mu\uppsi\mskip
2.0mu}}{\upmu^{-}}{{\overline{}\upnu}_{{\upmu}}}}$ decay width, which has an
uncertainty of only 10% [11].

The ${{\mathrm{B}}_{\mathrm{c}}^{-}}-{{\mathrm{B}}_{\mathrm{c}}^{+}}$
production asymmetry is measured in different intervals of $p_{\mathrm{T}}$
and $\eta$ of the ${\mathrm{B}}$ mesons, no significant asymmetry is observed.
The ${{\mathrm{B}}_{\mathrm{c}}^{-}}$ meson production asymmetries, averaged
over $p_{\mathrm{T}}$ and $\eta$, are measured to be $(-2.5\pm 2.1\pm 0.5)\%$
and $(-0.5\pm 1.1\pm 0.4)\%$ for the 7 and 13  TeV data samples, respectively.

##  5 Conclusion

A significant contribution to the knowledge of beauty hadron spectroscopy is
provided by the LHCb experiment. In particular, the new excited
${\Omega^{-}_{\mathrm{b}}}$ and ${\Lambda_{\mathrm{b}}^{0}}$ states are
observed, mass and width of newly observed states are measured. The production
fraction of ${{\mathrm{B}}_{\mathrm{c}}^{-}}$ meson with respect to
${{\mathrm{B}}^{+}}$ and ${\mathrm{B}^{0}}$ mesons and
${{\mathrm{B}}_{\mathrm{c}}^{-}}-{{\mathrm{B}}_{\mathrm{c}}^{+}}$ production
asymmetry are measured in $\mathrm{p}\mathrm{p}$ collisions at centre-of mass
energies of 7 and 13  TeV.

##  6 Acknowledgements

This work is supported by the Russian Foundation for Basic Research under
grant № 20-32-90166. The author would like to express his gratitude to the
Olga Igonkina Foundation for supporting this talk. Also, the author would like
to express special thanks to the ICHEP’2020 organizers for the great virtual
conference.

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