text:
\section{Introduction}
\label{sec:intro}
\newcommand{\AtlasCoordFootnote}{
ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP)
in the center of the detector and the \(z\)-axis along the beam pipe.
The \(x\)-axis points from the IP to the center of the LHC ring,
and the \(y\)-axis points upwards.
Cylindrical coordinates \((r,\phi)\) are used in the transverse plane,
\(\phi\) being the azimuthal angle around the \(z\)-axis.
The pseudorapidity is defined in terms of the polar angle \(\theta\) as \(\eta = -\ln \tan(\theta/2)\).
Angular distance is measured in units of \(\Delta R \equiv \sqrt{(\Delta\eta)^{2} + (\Delta\phi)^{2}}\).}

The primary physics aim of the heavy-ion programme at the Large Hadron Collider (LHC) is to produce
and study the quark--gluon plasma (QGP), the high-temperature state of quantum-chromodynamic (QCD) matter
in which quarks and gluons are no longer confined within protons and neutrons (for a recent review, see
Ref.~\cite{Busza:2018rrf}).
Measurements of jets arising from hard-scattered partons produced in the early stages of
heavy-ion collisions provide information about the short-distance-scale
interactions of high-energy partons with the QGP.  The overall rate of jets in central Pb+Pb collisions at a given transverse momentum,
\pt, is found to be significantly lower than expectations based on
\pp\ collisions, up to a \pt of approximately 1~\TeV~\cite{Aaboud:2018twu,Acharya:2019jyg,CMS:2021vui}.
The showering partons which give rise to jets
undergo medium-induced gluon radiation and
elastic scattering off the QGP constituents; both processes
broaden the angular distribution of the energy from the parton shower~\cite{ATLAS:2019pid}.
This leads
to the measurement of lower-energy jets  than in \pp\ collisions as some of the parton's energy is moved
outside of the jet cone.

The interactions between high-energy partons
and the QGP are expected to depend on the parton's QCD colour charge and
mass. Thus,
jets originating from \bquarks, \bjets,
(for a recent review, see Ref.~\cite{Dong:2019byy})
are of particular interest because the quark mass is large
compared to light quarks. Additionally, the QCD colour charge is controlled;
this contrasts with inclusive jets, which
mostly originate from  a mixture of light quarks and gluons.
The \bjets\ produced in hadronic collisions  consist  of jets in which the \bquark\
is directly produced in the hard scattering (e.g.\ $gg \to b\bar{b}$)
and jets in which a hard-scattered gluon splits into a $b\bar{b}$ pair ($g \to b\bar{b}$) as part of the
showering process.

Inclusive jets and \bjets\ are expected to be sensitive to
different effects in the QGP.
Medium-induced gluon radiation is expected to be
suppressed for heavy quarks by the dead-cone effect~\cite{Dokshitzer:2001zm}.
As the velocity of the \bquark\ increases
the importance of the dead-cone effect decreases.
Calculations for \mbox{Pb+Pb}\ collisions
show that the dead-cone effect reduces the suppression of \mbox{$B$-mesons}\
up to transverse momenta of approximately 50~\GeV~\cite{Zigic:2018ovr}.
This does not simply translate to a specific jet \pt\ range because
\bquarks\ in jets from gluon splitting tend to have lower momentum
than those directly from hard scattering at the same jet \pt.
Differences in the interactions between the QGP and the
developing parton shower between \bjets\ and inclusive jets
could  also arise from
differences in how quarks and gluons interact with the QGP~\cite{Spousta:2015fca}.
Measurements of heavy-quark jets in
heavy-ion collisions are also expected to be sensitive to
the mixture of radiative and collisional energy loss in the
QGP~\cite{Wicks:2005gt, Ke:2018tsh, Dai:2018mhw}.
Due to these  different effects, which are expected to lead to
differences between \bjets\ and inclusive jets in \mbox{Pb+Pb}\ collisions,
it is important to compare the \bjet\ and inclusive-jet suppression
in \mbox{Pb+Pb}\ collisions over as wide a kinematic range as possible.

Prior measurements have investigated the effects of energy loss for heavy quarks.
Many measurements are based on electrons or muons from the
semileptonic decay of charm and bottom
hadrons~\cite{Adare:2006nq,Adare:2015hla,ALICE:2020sjb,ATLAS:2021xtw,STAR:2021uzu}.
Other measurements have partially~\cite{ATLAS:2018hqe,CMS:2012bms,CMS:2016mah,CMS:2018bwt}
or fully~\cite{CMS:2017qjw,CMS:2017uoy,STAR:2018zdy} reconstructed the heavy-flavour hadrons.
One limitation of these measurements is  that they do not
provide direct information about the total jet energy.
This is important because the fragmentation functions of \bjets\ are
very different from those of inclusive jets~\cite{ParticleDataGroup:2020ssz};  thus, it is
not possible to directly compare
the suppression of \bquarks\ with that of light quarks and gluons
without full jet measurements.
CMS has measured
the suppression of \bjets\ in \mbox{Pb+Pb}\ collisions at 2.76~\TeV\ and found it to be consistent
with that of inclusive jets over the jet transverse
momentum, \mbox{$p_{\mathrm{T}}^{\mathrm{jet}}$}, range of 70--250~\GeV~\cite{Chatrchyan:2013exa},
although the uncertainties are large.

Jets are clustered with the \antikt\ algorithm~\cite{Cacciari:2008gp} using radius parameters
\mbox{$R= 0.2$}\ (in both \mbox{Pb+Pb}\ and \pp\ collisions) and \mbox{$R = 0.4$}\ (only in \pp\ collisions).
At generator level, a jet is considered as a \bjet if a \mbox{$b$-hadron}\
with $\pt > 5$~\GeV\ is found within an angular distance\footnote{ATLAS uses a right-handed
coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector, and the $z$-axis along the beam pipe.
The $x$-axis points from the IP to the centre of the LHC ring, and the $y$-axis points upward.
Cylindrical coordinates $(r,\phi)$ are used in the transverse plane, $\phi$ being the azimuthal angle around the $z$-axis.
The pseudorapidity is defined in terms of the polar angle $\theta$ as $\eta=-\ln\tan(\theta/2)$.
The rapidity is defined as $y = 0.5\ln[(E + p_z)/(E-p_z)]$ where $E$ and $p_z$ are the energy and $z$-component of the momentum along the beam direction, respectively.
Transverse momentum and transverse energy are defined as $\pt = p \sin\theta$ and $\ET = E \sin\theta$, respectively.
The angular distance between two objects with relative differences $\Delta \eta$ in pseudorapidity and $\Delta \phi$ in azimuth is given by $\Delta R = \sqrt{(\Delta \eta )^2 + (\Delta \phi)^2}$.}
of $\Delta R = 0.3$ from the jet axis.
The \bjets\ are identified statistically from a sample
of jets containing muons.
The muons from
\mbox{$b$-hadron}\ decays
are distinguished from muons arising from charm- and light-hadron decays by the difference between
their transverse momenta, \mbox{$p_{{\mathrm{T}}}^{\mu}$},
relative to the {jet}+$\mu$\ axis. The {jet}+$\mu$\ axis is defined in the transverse plane by
\begin{equation}
\vec{u}_\textrm{T}^{\textrm{jet}+\mu} = \frac{\vec p_\textrm{T}^{\mu}+\vec p_\textrm{T}^{\mathrm{jet}}}{\left|\vec p_\textrm{T}^{\mu}+\vec p_\textrm{T}^{\mathrm{jet}}\right|}
\label{eq:jetmuaxis}
\end{equation}
(where the vector notation indicates the vector quantity is meant instead of the magnitude of the vector), and the transverse momentum of the muon relative to the jet axis,
\mbox{$p_\mathrm{T}^\mathrm{rel}$}, is defined as
\begin{equation}
\mbox{$p_\mathrm{T}^\mathrm{rel}$}\ = \left| \vec p_\mathrm{T}^{\mu} \times \vec{u}_\textrm{T}^{\textrm{jet}+\mu} \right| .
\label{eq:ptrel}
\end{equation}
This method was used previously by ATLAS for \pp\ collisions at 7~\TeV\ and
the results were compared with those based on the reconstruction of secondary vertices~\cite{ATLAS:2011ac}.
Only  \mbox{$R= 0.2$}\ jets are used in \mbox{Pb+Pb}\ collisions because they have better
angular resolution and have a smaller contribution from accidental jet--muon overlaps
in \mbox{Pb+Pb}\ collisions; both of these features improve the performance of the \mbox{$p_\mathrm{T}^\mathrm{rel}$}\ method.

This paper reports measurements of inclusive jet and \bjet cross-sections in \pp collisions and
the per-event yield for inclusive jets and \bjets\ in \mbox{Pb+Pb}\ collisions at 5.02~\TeV.
In both collision  systems, the spectra are corrected to the generator level
(just before the \mbox{$b$-hadron}\ decays for \bjets).
For \mbox{$R= 0.2$}\ jets the nuclear modification factor, \mbox{$R_{\mathrm{AA}}$}, is calculated for \bjets\ as
\begin{equation*}
\mbox{$R_{\mathrm{AA}}$}^{\bjet} \equiv \left. \left.\frac{1}{N_\textrm{evt}} \frac{\textrm{d}^2 N_\textrm{AA}^{\bjet}}{\textrm{d}\pt\textrm{d}y}\right|_\textrm{cent} \middle/ \langle T_{\textrm{AA}}\rangle
\frac{\textrm{d}^{2}\sigma_{\pp}^{\bjet}}{\textrm{d}\pt \textrm{d}y} \right.
\label{eq:RAAb}
\end{equation*}
where $\textrm{d}^2 N_\textrm{AA}^{\bjet}/\textrm{d}\pt\textrm{d}y$ is the yield of \bjets\
in \mbox{Pb+Pb}\ collisions for the centrality,
\pt, and rapidity range of interest;
$\textrm{d}^{2}\sigma_{\pp}^{\bjet}/\textrm{d}\pt \textrm{d}y$
is the \bjet\ cross-section in \pp\ collisions;  $\langle T_{\textrm{AA}}\rangle$
is the nuclear thickness function~\cite{Miller:2007ri}; and
$N_\textrm{evt}$ is the number of  minimum-bias (MB) \mbox{Pb+Pb}\
events for the centrality selection under consideration.
Analogously, the nuclear modification factor for inclusive jets is defined as
\begin{equation*}
\mbox{$R_{\mathrm{AA}}$}^{\mathrm{inclusive \: jet}} \equiv \left. \left. \frac{1}{N_\textrm{evt}}
\frac{\textrm{d}^2 N_\textrm{AA}^{\mathrm{inclusive \: jet}}}{\textrm{d}\pt\textrm{d}y}\right|_\textrm{cent}
\middle/ \langle T_{\textrm{AA}}\rangle
\frac{\textrm{d}^{2}\sigma_{\pp}^{\mathrm{inclusive \: jet}}}{\textrm{d}\pt \textrm{d}y} \right.
\label{eq:RAAinc}
\end{equation*}
where the yield and cross-section are for inclusive jets and the other quantities
remain the same.

The measurements are performed in Pb+Pb collisions at $\sqrt{s_{_\textrm{NN}}}=5.02$~\TeV\ collected during 2018,
with an integrated luminosity of 1.4~$\textrm{nb}^{-1}$ for the \bjet sample and 1.7~$\textrm{nb}^{-1}$
for the inclusive jet sample,
and in \pp collisions at $\sqrt{s}=5.02$~\TeV\ collected during 2017,
with an integrated luminosity of 260~\mbox{${\mathrm{pb}^{-1}}$}.
The measurements are presented for jets with $80<\pt<290$~\GeV\ and $|y|<2.1$.

The paper is structured as follows. Section~\ref{sec:detector} describes the ATLAS detector, and
Section~\ref{sec:selection} discusses the selection procedure applied to the data.
The data analysis is presented in Section~\ref{sec:analysis}
and the systematic uncertainties are presented in Section~\ref{sec:systematics}.
The results and a summary are presented in Sections~\ref{sec:result} and~\ref{sec:summary}.

\section{ATLAS detector}
\label{sec:detector}

The ATLAS detector~\cite{PERF-2007-01} at the LHC covers nearly the entire solid angle around the collision point.
It consists of an inner tracking detector surrounded by a thin superconducting solenoid, electromagnetic and hadronic calorimeters,
and a muon spectrometer incorporating three large superconducting toroidal magnets.

The inner-detector system (ID) is immersed in a \SI{2}{\tesla} axial magnetic field
and provides charged-particle tracking in the range \(|\eta| < 2.5\).
The high-granularity silicon pixel detector covers the vertex region,
and is composed of four layers including
the insertable B-layer~\cite{ATLAS-TDR-19,PIX-2018-001}.
It is followed by the silicon microstrip tracker, which usually provides four two-dimensional measurement points per track.
These silicon detectors are complemented by the transition radiation tracker (TRT),
which enables radially extended track reconstruction up to \(|\eta| = 2.0\).

The calorimeter system covers the pseudorapidity range \(|\eta| < 4.9\).
Within the region \(|\eta|< 3.2\), electromagnetic calorimetry is provided by barrel and
endcap high-granularity lead/liquid-argon (LAr) electromagnetic calorimeters,
with an additional thin LAr presampler covering \(|\eta| < 1.8\)
to correct for energy loss in material upstream of the calorimeters.
The hadronic calorimeters have three sampling layers longitudinal in
shower depth in \(|\eta| < 1.7\) and four sampling layers in \(1.5 < |\eta| < 3.2\),
with a slight overlap in \(\eta\).
The solid angle coverage is completed with forward copper/LAr and tungsten/LAr calorimeter modules (FCal)
optimised for electromagnetic and hadronic measurements respectively.

The muon spectrometer (MS) comprises separate trigger and
high-precision tracking chambers measuring the deflection of muons in a magnetic field generated by the superconducting air-core toroids.
The field integral of the toroids ranges between \num{2.0} and \SI{6.0}{\tesla\metre}
across most of the detector.
A set of precision chambers covers the region \(|\eta| < 2.7\) with three layers of monitored drift tubes,
complemented by cathode strip chambers in the forward region, where the background is highest.
The muon trigger system covers the range \(|\eta| < 2.4\) with resistive plate chambers in the barrel, and thin gap chambers in the endcap regions.

The zero-degree calorimeters (ZDCs) are located symmetrically at $z = \pm 140$~m and cover $|\eta| > 8.3$ during the \mbox{Pb+Pb}\ data-taking period.
The ZDCs use tungsten plates as absorbers and quartz rods sandwiched between the tungsten plates as the active medium.
In Pb+Pb collisions the ZDCs primarily measure spectator neutrons,
which are neutrons that do not interact hadronically when the incident nuclei collide.
A ZDC coincidence trigger is implemented by requiring the pulse height from each
ZDC to be above a threshold set to accept the energy of a single neutron.

A two-level trigger system is used to select interesting events~\cite{ATLAS:2020esi}.
The first-level trigger is implemented in hardware and uses a subset of detector information,
including ZDC coincidences in \mbox{Pb+Pb}\ collisions,
to reduce the event rate to a design value of at most 100~kHz.
This is followed by a software-based high-level trigger which reduces the event rate to several kHz.
An extensive software suite~\cite{ATL-SOFT-PUB-2021-001} is used in the reconstruction and analysis of real
and simulated data, in detector operations, and in the trigger and data acquisition systems of the experiment.

\section{Data selection and Monte Carlo samples}
\label{sec:selection}

All events are required to have at least one reconstructed
vertex, to have been collected during stable beam conditions,
and to satisfy detector and data-quality requirements~\cite{ATLAS:2019fst}.

These events were selected by two sets of triggers: single-jet triggers,
and muon--jet triggers requiring a muon spatially matched to a jet at the
trigger level~\cite{ATLAS:2021piz}. In both \mbox{Pb+Pb}\ and \pp\ collisions,
the muon--jet triggers require a muon with $\pt>$~4~\GeV\
matched to an \mbox{$R = 0.4$}\ jet with various \pt\ thresholds. The spatial matching
of the jet to the muon is made within a cone of size
$\Delta R =0.5$ around the jet axis; this matching is fully efficient.
All events are in a kinematic range where the jet trigger is fully efficient.

The overlap area of two colliding nuclei in Pb+Pb collisions is characterized by the total transverse energy
deposited in the FCal~\cite{HION-2016-06}. This analysis uses three centrality
intervals which are defined according to
successive percentiles of the $\sum E_\textrm{T}^\textrm{FCal}$ distribution obtained in MB
collisions.
The centrality regions used in this analysis, going from the most central
(largest $\sum E_\textrm{T}^\textrm{FCal}$) collisons to the peripheral (lowest $\sum E_\textrm{T}^\textrm{FCal}$)
collisions are 0--20\%, 20--50\%, and 50--80\%.
The values of  $\langle\mbox{$T_{\mathrm{AA}}$}\rangle$
and the number of binary nucleon--nucleon collisions, $\langle N_\textrm{coll}\rangle$, for
each centrality interval are evaluated by a
Monte Carlo (MC) Glauber model analysis~\cite{Loizides:2014vua,Miller:2007ri} of the $\sum E_\textrm{T}^\textrm{FCal}$ distribution,
and are shown in Table~\ref{tab:TAANcoll}.

\begin{table}[htbp]
\centering
\caption{The $\langle\mbox{$T_{\mathrm{AA}}$}\rangle$ and $\langle N_\textrm{coll}\rangle$ values and uncertainties in each centrality bin. These are the results from the Glauber modelling of the summed transverse energy in the forward calorimeters, $\sum E_\textrm{T}^\textrm{FCal}$.}
\vspace{0.2cm}
\begin{tabular}{ccc}
\toprule
Centrality [\%] &  $\langle\mbox{$T_{\mathrm{AA}}$}\rangle$ $[\textrm{mb}^{-1}]$ & $\langle N_\textrm{coll}\rangle$ \\
\midrule
~~0--20         & 18.84$\pm$0.18~~     & 1319$\pm$90~~ \\
20--50       & 5.41$\pm$0.15       & 378$\pm$23\\
50--80       & 0.69$\pm$0.05       & 48$\pm$4\\
\bottomrule
\end{tabular}
\label{tab:TAANcoll}
\end{table}

A small fraction of the triggered \mbox{Pb+Pb}\ events $(< 0.5\%)$ contain multiple collisions, known as `pile-up'.
The expected
anti-correlation between $\sum E_\textrm{T}^\textrm{FCal}$
and the number of neutrons detected in the ZDCs is used to reject these pile-up events.
The pile-up contribution is not rejected in \pp\ collisions.

This analysis uses several MC samples to evaluate the performance of the detector
and the analysis procedure, and to correct the measured distributions for detector effects.
All MC samples were produced with the full ATLAS detector simulation based on the
$\GEANT4$ toolkit~\cite{Agostinelli:2002hh,Aad:2010ah}.
Dijet samples were generated with \pythiaeight~\cite{Sjostrand:2014zea}, using the parameter values of the
A14 tune~\cite{TheATLAScollaboration:2014rfk} with the \textsc{NNPDF23lo} set of parton
distribution functions (PDFs)~\cite{Ball:2012cx}.
These were generated both with no additional requirements and with the
requirement of a muon with $\pt >$~3~\GeV\
at the generator level (such as from heavy-flavour hadron decays).
The \EVTGEN  package~\cite{Lange:2001uf} was used to fully simulate \mbox{$b$-hadron}\ decays.

In \pp\ collisions,
pile-up from additional interactions in the same bunch crossing was generated by \pythiaeight,
using the parameter values of the A3 tune~\cite{ATLAS:2016puo}  with the \textsc{NNPDF23lo} PDFs;
the distribution of the number of extra collisions was matched to that of data.
In \mbox{Pb+Pb}\ collisions the simulated events were overlaid with events from a dedicated sample of \mbox{Pb+Pb}\ data events.
This sample was recorded with a combination of MB triggers and total energy triggers to
increase the number of events from central collisions. This `data overlay' sample was reweighted on an event-by-event
basis to obtain the same centrality distribution as in the jet-triggered data sample.

For muon reconstruction studies, prompt $(\pp\rightarrow J/\psi\rightarrow \mu\mu)$ and
non-prompt $(\pp\rightarrow bb\rightarrow J/\psi\rightarrow \mu\mu)$ samples of $J/\psi$
events
were produced with \pythiaeight\ and corrected for electromagnetic radiation with \textsc{Photos}~\cite{BARBERIO1994291}.
The A14 tune and CTEQ6L1 PDFs~\cite{Pumplin:2002vw} were used.
Generator-level \pp\ {\textsc{Herwig++}}~\cite{Bahr:2008pv} events,
using the UEEE5 tune~\cite{Gieseke:2012ft} and the
CTEQ6L1 PDFs~\cite{Pumplin:2002vw}, are used to study systematic uncertainties.

\section{Analysis}
\label{sec:analysis}

\subsection{Jet reconstruction}

All jets are reconstructed using  procedures which
follow those used by ATLAS for previous jet measurements in \mbox{Pb+Pb}\ collisions~\cite{Aaboud:2018twu,ATLAS:2021ktw}.
Jets are reconstructed using
the \antikt\ algorithm~\cite{Cacciari:2008gp} implemented in the FastJet software package~\cite{Cacciari:2011ma}. In both \pp\ and \mbox{Pb+Pb}\ collisions, jets with
$R=0.2$ and \mbox{$R = 0.4$}\ are formed by
clustering calorimetric towers of spatial size $\Delta\eta \times\Delta\phi=0.1\times\pi/32$. The energies in the towers are obtained
by summing the energies of calorimeter cells at the electromagnetic energy scale~\cite{PERF-2011-03} within the tower boundaries.
In \mbox{Pb+Pb}\ collisions, a background
subtraction procedure is applied to estimate, within each event, the underlying event (UE) average transverse energy density,
$\rho(\eta,\phi)$, where the $\phi$ dependence is due to global azimuthal correlations in the particle production from
hydrodynamic flow~\cite{HION-2016-06}. The modulation accounts for the contribution to the UE of the second-, third-, and fourth-order azimuthal anisotropy harmonics
characterized by values of flow coefficients $v_n^\mathrm{UE}$~\cite{HION-2016-06}.
Additionally, the
UE is also corrected for $\eta$- and $\phi$-dependent non-uniformities of the detector response
by correction factors derived in MB \mbox{Pb+Pb}\ data.
In \pp\ collisions, the same background subtraction procedure is applied without the $\phi$-dependent
modulation and without the correction for $\eta$- and $\phi$-dependent non-uniformities
to remove the pile-up contribution to the jet.

An iterative procedure is used to remove the impact of jets on the estimated $\rho$ and $v_n^\mathrm{UE}$
values.  The first estimate of the average transverse energy density of the UE, $\rho(\eta)$, is evaluated in 0.1 intervals of $\eta$, excluding towers
within $\Delta R =0.4$ of `seed' jets. In the first subtraction step, the seeds are defined to be an union of $R = 0.2$ jets and $R=0.4$ track-jets. Track-jets are
reconstructed by applying the \antikt\ algorithm with $R = 0.4$ to charged particles with $\pT > 4$~\GeV. The $R=0.2$ jets must pass a requirement on the
minimum value of the tower $E_{\mathrm{T}}$  and on a ratio of maximum tower  $E_{\mathrm{T}}$ to
average tower  $E_{\mathrm{T}}$,
while the track-jets are required to have $\pT > 7$~\GeV. The background is then subtracted from each tower
constituent and the jet kinematics are recalculated. After the first iteration, the $\rho$ and $v_n$ values are updated by excluding from the UE determination
the regions within $\Delta{R} = 0.4$ of both the track-jets and the newly reconstructed $R=0.2$ jets with $\pt > 25$~\GeV\ (8~\GeV) in \mbox{Pb+Pb}\ (\pp) collisions. The updated
$\rho$ and $v_n^\mathrm{UE}$ values are used to update the jet kinematic properties in the second iteration.

Jet $\eta$- and $\pT$-dependent correction factors derived in simulations are applied to the measured jet
energy to correct for the calorimeter energy response~\cite{ATLAS:2014hvo}. An additional correction based on in situ studies of jets recoiling
against photons, \Zboson\ bosons, and jets in other regions of the calorimeter is applied~\cite{HION-2018-06}. This calibration is followed by a
cross-calibration which relates the jet energy scale of jets reconstructed by the procedure outlined in this section to the jet energy scale
in 13~\TeV\ \pp\ collisions~\cite{ATLAS:2015twa}.

Jets are defined at the truth level in the MC sample before detector simulation by applying the \antikt\
algorithm with the appropriate $R$ value
to stable particles with a proper lifetime greater than 30~ps, but excluding muons and neutrinos, which do not
leave significant energy deposits in the calorimeter.
The \mbox{$\Delta R$}\ between the truth jet and reconstructed jet is required to be $\mbox{$\Delta R$} < 0.15$ (0.30) for \mbox{$R= 0.2$}\ (\mbox{$R = 0.4$}) jets.
The  corrections for muons and neutrinos from semileptonic decays are discussed below.

\subsection{Muon reconstruction}
Muon candidates in both \mbox{Pb+Pb}\ and \pp\ collisions
are formed by combining charged-particle tracks reconstructed
in the ID and the MS that pass the `tight' selection requirements detailed in Ref.~\cite{ATLAS:2016lqx},
except the requirement on the number of TRT hits.

Muons are selected with $\mbox{$p_{{\mathrm{T}}}^{\mu}$}  > 4$~\GeV\ and $|\eta^{\mu}|<2.4$ requirements.
If the muon is required in the  trigger,
the data is corrected to account for the muon trigger inefficiency, and the reconstructed muon must be within
$\Delta R =0.01$ of the trigger muon object.
The muon selection is the same in both \pp\ collisions and \mbox{Pb+Pb}\ collisions.
Muons and jets are judged to be associated if $\mbox{$\Delta R$}(\textrm{jet},\mu)$ is less than the jet
radius, $R$. If more
than one muon passes this selection, the muon with the largest momentum is used.

The muon trigger efficiency with respect to reconstructed muons
is estimated from \pp data by using the tag-and-probe method~\cite{Aad:2020uyd,ATLAS:2021xtw}
in bins of \mbox{$p_{{\mathrm{T}}}^{\mu}$}\ and $\eta^{\mu}$. A small centrality dependence of the muon trigger efficiency was observed in Pb+Pb data;
this is corrected by an extra factor, which is the
Pb+Pb to \pp data-driven efficiency ratio, applied to Pb+Pb data as a function of the centrality.
In \pp collisions, the trigger efficiency plateaus at 78\% for $\mbox{$p_{{\mathrm{T}}}^{\mu}$} > 6$~\GeV\
and $|\eta^{\mu}|<1.05$, and at 90\% for $\mbox{$p_{{\mathrm{T}}}^{\mu}$} > 9$~\GeV\ and $|\eta^{\mu}|>1.05$.
In \mbox{Pb+Pb}\ collisions,
the efficiency is lower than in \pp\ collisions by 9\% in the most central collisions;
the efficiency in peripheral \mbox{Pb+Pb}\ collisions is the same as in \pp\ collisions.

The muon reconstruction efficiency is estimated from simulated prompt and non-prompt $J/\psi\rightarrow\mu\mu$ events using the tag-and-probe method~\cite{ATLAS:2016lqx,ATLAS:2021xtw},
in fine bins of \mbox{$p_{{\mathrm{T}}}^{\mu}$}\ and $\eta^{\mu}$. Mis-modelling of the reconstruction performance in simulation, quantified by the ratio of measured
efficiencies in \pp data and the simulation, is accounted for by applying a multiplicative
correction which changes the efficiency by less than 5\%.
For $\mbox{$p_{{\mathrm{T}}}^{\mu}$} > 10$~\GeV\ in \pp\ collisions, the muon reconstruction efficiency plateaus at 90\% for $|\eta^{\mu}|<1.05$ and at 95\% for $|\eta^{\mu}|>1.05$.
No difference between the muon reconstruction efficiencies in \pp\ and \mbox{Pb+Pb}\ collisions was observed and the same
values were used in both collision systems.

\subsection{\bjet yield reconstruction}
\subsubsection{Templates and fitting}

At the generator level, the jet flavour is defined by matching jets to hadrons with $\pt > 5$~\GeV.
The jet is considered a \bjet\ if a \mbox{$b$-hadron}\ is found within $\Delta R =0.3$ of the jet axis;
otherwise, if a \textit{c}-hadron\ is found within the same distance the jet is labelled as a \textit{c}-jet.
All other jets are considered to be \textit{light}-jets.

Since the muons in the momentum range of interest generally
do not stop in the calorimeter, their momentum is not included in
the calorimetric jet \pt.  In order to better characterize the jets, the {jet}+$\mu$\ scale
is defined as
the \pt of the sum of the muon and jet four-vectors.
The \mbox{$p_\mathrm{T}^\mathrm{rel}$}\ distributions in the data and MC samples are constructed for selections in
this {jet}+$\mu$\ object at the reconstruction level, \mbox{$p_{\mathrm{T, reco}}^{\textrm{jet}+\mu}$}.
In order to form a {jet}+$\mu$\ pair, jets are required to have a
minimum calorimetric \mbox{$p_{\mathrm{T, reco}}^\textrm{jet}$}\ of 40~\GeV\ (58~\GeV)
in \pp\ (\mbox{Pb+Pb}) collisions.

In semileptonic \mbox{$b$-hadron}\ decays, the \pt of the lepton relative
to the {jet}+$\mu$-axis (see Eqs.~(\ref{eq:jetmuaxis}) and~(\ref{eq:ptrel})),
\mbox{$p_\mathrm{T}^\mathrm{rel}$}, is used to distinguish between $b$-, $c$-, and \textit{light}-jets~\cite{ATLAS:2011ac}.
Due to the large mass of \mbox{$b$-hadrons}\ relative to hadrons containing charm or light quarks,
their decay products are more energetic.
Consequently, muons originating from \mbox{$b$-hadron}\ decays have a harder \mbox{$p_\mathrm{T}^\mathrm{rel}$}\
spectrum than muons in \textit{c}-jets\ and \textit{light}-jets.

The templates distributions of \mbox{$p_\mathrm{T}^\mathrm{rel}$}\
for $b$- and \textit{c}-jets\  are extracted from the muon-filtered MC samples.
The \mbox{$b$-hadron}\ mixture is taken from Tevatron measurements~\cite{Amhis:2014hma},
which are consistent with
those from the LHCb Collaboration~\cite{LHCb:2019fns}.
The \textit{c}-hadron\ mixture is taken from default \pythiaeight\ simulation.
The \textit{light}-jet\ template is obtained from track-jet pairs in the data inclusive-jet sample
as in Refs.~\cite{CMS:2011xhf,ATLAS:2011ac} (in the same centrality class as the {jet}+$\mu$\ pair for \mbox{Pb+Pb}\ collisions).
The tracks are selected with the standard selection,
with no additional requirements on the distance of closest approach to the vertex.
The \pt\ spectra of the tracks
are reweighted to reproduce the muon \pt spectrum from \textit{light}-jets\ from the inclusive dijet MC sample.

In \pp\ collisions, these three templates are inputs to a template fit of the
data \mbox{$p_\mathrm{T}^\mathrm{rel}$}\ spectrum
to obtain the fractions of $b$-, $c$-, and \textit{light}-jets.
A binned maximum-likelihood fit is
performed using the RooFit framework~\cite{Verkerke:2003ir}.
The model for the fit is
defined as a normalized sum of three templates:
\textit{light}-jets\ (\mbox{$F_{\mathrm{l},i}$}(\mbox{$p_\mathrm{T}^\mathrm{rel}$})), \textit{c}-jets\ (\mbox{$F_{\mathrm{c},i}$}(\mbox{$p_\mathrm{T}^\mathrm{rel}$})), and \bjets (\mbox{$F_{\mathrm{b},i}$}(\mbox{$p_\mathrm{T}^\mathrm{rel}$})). The \pp fit model,
$M^{\pp}$, is structured as
\begin{equation*}
M^{\pp}_{i}\!\left(\mbox{$p_\mathrm{T}^\mathrm{rel}$}\right) = \mbox{$f_{\mathrm{b},i}$} \mbox{$F_{\mathrm{b},i}$}\!\left(\mbox{$p_\mathrm{T}^\mathrm{rel}$}\right) +
\left(1-\mbox{$f_{\mathrm{b},i}$}\right)\left[ \mbox{$f_{\mathrm{c},i}$} \mbox{$F_{\mathrm{c},i}$}\!\left(\mbox{$p_\mathrm{T}^\mathrm{rel}$}\right) +
\left(1-\mbox{$f_{\mathrm{c},i}$}\right)\mbox{$F_{\mathrm{l},i}$}\!\left(\mbox{$p_\mathrm{T}^\mathrm{rel}$}\right) \right]
\label{eq:ppmodel}
\end{equation*}
where \mbox{$f_{\mathrm{b},i}$}\ is the fraction of \bjets\ in the total sample,
\mbox{$f_{\mathrm{c},i}$}\ is the fraction of \textit{c}-jets\ in the non-\bjet\ sample, and the index $i$ denotes the \pt bin.
The fit model has two free parameters, \mbox{$f_{\mathrm{b},i}$}\ and \mbox{$f_{\mathrm{c},i}$}\ for each \mbox{$p_{\mathrm{T, reco}}^{\textrm{jet}+\mu}$}\ bin.

In \mbox{Pb+Pb}\ collisions the model has an additional term
which accounts for combinatoric muon--jet pairs.
These are muon--jet pairs which pass the $\Delta R$ matching requirements, but the
muon and jet  do not come from the same hard scattering.
These are the most common in central \mbox{Pb+Pb}\ collisions, where the multiplicity
of jets and muons is the highest.  In \pp\ collisions, this
effect is negligibly small.  For the combinatoric pairs, both the shape, \mbox{$F_{\mathrm{mix},i}$},
and the amplitude, \mbox{$f_{\mathrm{mix},i}$}, are determined by event mixing in the \mbox{Pb+Pb}\ data.
This procedure uses a muon from one event and a jet from another event;
all the analysis selections are applied, including the requirement on the $\Delta R$ separation between the muon
and jet.
Events which are mixed together  are required to have $\sum E_\textrm{T}^\textrm{FCal}$ values that agree within 0.05~\TeV\
and vertex $z$-positions that agree within 10~mm.
The nominal data sample and mixed-event sample are found to agree
well in the large $\Delta R$ region where there is no correlated signal.
The \mbox{Pb+Pb}\ model, $M^\textrm{Pb+Pb}$, is structured as
\begin{equation*}
M^\textrm{Pb+Pb}_{i}\!\left(\mbox{$p_\mathrm{T}^\mathrm{rel}$}\right) =
\left(1-\mbox{$f_{\mathrm{mix},i}$}\right)\times M^{\pp}_{i}\!\left(\mbox{$p_\mathrm{T}^\mathrm{rel}$}\right) + \mbox{$f_{\mathrm{mix},i}$}\times \mbox{$F_{\mathrm{mix},i}$}\!\left(\mbox{$p_\mathrm{T}^\mathrm{rel}$}\right).
\label{eq:pbpbmodel}
\end{equation*}
The background fraction is largest in central collisions and is always less than 1.5\%.

The data \mbox{$p_\mathrm{T}^\mathrm{rel}$}\ distributions are resampled 500 times and the mean and width of the range of
results are used to set the central value and uncertainties in the fit.
The statistical uncertainty of the templates is taken to be part of the statistical uncertainty
of the yield. Example fits for \pp and  \mbox{Pb+Pb}\ collisions are shown in Figures~\ref{fig:fitslow} and~\ref{fig:fitshigh},
for low and high \mbox{$p_{\mathrm{T, reco}}^{\textrm{jet}+\mu}$}\ respectively.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.4\textwidth]{fig_01a.pdf}
\includegraphics[width=0.4\textwidth]{fig_01b.pdf}
\includegraphics[width=0.4\textwidth]{fig_01c.pdf}
\includegraphics[width=0.4\textwidth]{fig_01d.pdf}
\caption{The \mbox{$p_\mathrm{T}^\mathrm{rel}$}\ distributions in \pp collisions (top left) and 50--80\% (top right), 20--50\% (bottom left),
and 0--20\% (bottom right) centrality \mbox{Pb+Pb}\ collisions.
The data are shown for
the range $80.7 < \mbox{$p_{\mathrm{T, reco}}^{\textrm{jet}+\mu}$} < 95.0$~\GeV. The stacked histograms
show the fit results.
Middle and bottom panels of each plot show the pulls and data-to-fit ratios, respectively.
The error bars in the ratio plots show the statistical uncertainties of the data and MC
samples.}
\label{fig:fitslow}
\end{figure}

\begin{figure}[htbp]
\centering
\includegraphics[width=0.4\textwidth]{fig_02a.pdf}
\includegraphics[width=0.4\textwidth]{fig_02b.pdf}
\includegraphics[width=0.4\textwidth]{fig_02c.pdf}
\includegraphics[width=0.4\textwidth]{fig_02d.pdf}
\caption{The \mbox{$p_\mathrm{T}^\mathrm{rel}$}\ distributions in \pp collisions (top left) and 50--80\% (top right), 20--50\% (bottom left),
and 0--20\% (bottom right) centrality \mbox{Pb+Pb}\ collisions.
The data are shown for
the range $113.4 < \mbox{$p_{\mathrm{T, reco}}^{\textrm{jet}+\mu}$} < 142.3$~\GeV. The stacked histograms
show the fit results.
Middle and bottom panels of each plot show the pulls and data-to-fit ratios, respectively.
The error bars in the ratio plots show the statistical uncertainties of the data and
MC samples.}
\label{fig:fitshigh}
\end{figure}

The raw \bjet\ \pt\ spectrum
is constructed in each \mbox{Pb+Pb}\ centrality bin and in \pp\ collisions by taking
each \mbox{$f_{\mathrm{b},i}$}\ value and multiplying it by the number of jets in \mbox{\textit{i}-th}\ bin in the total \mbox{$p_{\mathrm{T, reco}}^{\textrm{jet}+\mu}$}\ spectrum.
\subsubsection{Comparing muon momentum distributions in the data and simulations}

The \bjet\ fragmentation function in \mbox{Pb+Pb}\ collisions has not been
measured. Significant
modification to the \mbox{$b$-hadron}\ longitudinal momentum due to jet quenching could bias the \bjet\ template.
In order to ensure that the simulations reproduce the data sufficiently well, a check of
the longitudinal momentum distribution of the muon with respect to the {jet}+$\mu$\ axis
is performed.  The fitting results as a function of centrality and \mbox{$p_{\mathrm{T, reco}}^{\textrm{jet}+\mu}$}\ from the
previous subsection are used to weight the
{jet}+$\mu$\ pairs from the MC samples (used for the charm and bottom templates) and those used in
constructing the data-driven \textit{light}-jet\ template to have the same
flavour fractions as the data.  Muons which have a
transverse distance to the primary vertex, $d_0$, greater than 0.25~mm are selected;
this requirement further enhances the heavy-flavour fractions relative to the light jets.
For these {jet}+$\mu$\ pairs,  the distribution of
\begin{equation*}
\mbox{$z$} \equiv \mbox{$p_{{\mathrm{T}}}^{\mu}$} \cos\!\left(\theta\right) / \mbox{$p_{\mathrm{T, reco}}^{\textrm{jet}+\mu}$}\ ,
\end{equation*}
where $\theta$ is the angle between the muon and the {jet}+$\mu$\ axis,  is constructed.
This combined distribution from the pairs in the charm-, bottom-, and \textit{light}-jet\ templates is compared with the
data distribution for the same quantity.  Since the \textit{light}-jet\ template is data-driven, it should
agree between the data and the template, and thus
the comparison between data and simulations is sensitive to
the degree to which the MC modelling of the charm and bottom templates
agrees with the data.
These distributions are shown in Figure~\ref{fig:longmuon} for \pp\ and
0--20\% centrality \mbox{Pb+Pb}\ collisions.  The data and the simulations
(including the data-driven \textit{light}-jet\ template)
agree in both \pp\ and \mbox{Pb+Pb}\ collisions.
Thus, within the current uncertainties, the longitudinal momentum fraction
of the muon is unmodified in \mbox{Pb+Pb}\ collisions  and  the \mbox{$p_\mathrm{T}^\mathrm{rel}$}\ distributions are
largely sensitive to the \mbox{$b$-hadron}\ decay kinematics.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.49\textwidth]{fig_03a.pdf}
\includegraphics[width=0.49\textwidth]{fig_03b.pdf}\\
\includegraphics[width=0.49\textwidth]{fig_03c.pdf}
\includegraphics[width=0.49\textwidth]{fig_03d.pdf}
\caption{The \mbox{$z$}\ distributions for data and simulations (including the data-driven
\textit{light}-jet\ template) for \pp\ collisions (top row) and 0--20\% centrality \mbox{Pb+Pb}\ collisions
(bottom row) for two \mbox{$p_{\mathrm{T, reco}}^{\textrm{jet}+\mu}$}\ selections.  In each figure the top panel shows the distributions
themselves and the bottom panel shows the ratio of data to simulations.
The error bars in the ratio plots show the statistical uncertainties on the data and MC samples.}
\label{fig:longmuon}
\end{figure}
\subsection{Corrections to the raw spectra}
The raw jet spectra are constructed from all the measured jets for the inclusive jets and from
the muon--jet pairs, scaled by the \mbox{$f_{\mathrm{b},i}$}\ values, for the \bjets.
The raw spectra are unfolded to account for bin migrations due to the finite jet energy resolution,
and any reconstruction
inefficiency for the jets (and muon and neutrino energies in the \bjet\ sample).
Both the \bjet\ and inclusive jet \pt\ spectra are unfolded using the one-dimensional (1D) Bayesian
unfolding~\cite{DAgostini:1994fjx} from the \textsc{RooUnfold} software package~\cite{Adye:2011gm}.
The \bjet\ response matrices are built from the muon-filtered MC samples
using truth-level \bjets\ (including the muon and
neutrino momenta)
that are matched to reconstructed jets in simulations
and have $|y_\textrm{truth}^{\bjet}|<2.1$.
The inclusive jet response matrices are built from the dijet MC samples using all
truth jets and not including any muon or neutrino momenta.

The response matrices are generated separately for \pp collisions and for each
centrality interval in \mbox{Pb+Pb}\ collisions.
To better represent the data, the response matrices are reweighted
along the truth-\mbox{$p_{\mathrm{T}}^{\mathrm{jet}}$}\ axis by the reconstruction-level data to simulation ratio.
The number of iterations in the unfolding was chosen such that the result is stable
when changing the number of iterations while minimizing the amplification of statistical uncertainties. Four
iterations are used in all cases presented here.
The reconstructed \mbox{$p_{\mathrm{T, reco}}^{\textrm{jet}+\mu}$}\ values are required to be larger than 72~\GeV\ in \mbox{Pb+Pb}\
collisions and 64~\GeV\ in \pp collisions for both \mbox{$R= 0.2$}\ and \mbox{$R = 0.4$}\ jets. The inclusive-jet
minimum
reconstructed \pt is required to be larger than 72~\GeV\ for both \mbox{Pb+Pb}\ and \pp\ collisions.
Reconstructed jets below these thresholds that
match to truth-\pt values in the measurement region are
corrected via the unfolding procedure.
Fully unfolded results are presented starting from 80~\GeV\ for both categories of jets.

As described in Section~\ref{sec:selection}, the main MC sample used in the \bjet\ analysis required
the truth-muon \pt to be larger than 3~\GeV.
The missing part of the cross-section from \bjets\ with  muons below this threshold
is addressed through an acceptance correction based
on the \pythiaeight\ dijet MC samples
which is applied after unfolding. The size of the correction is
approximately 22\% (25\%)  at 80~\GeV\ and 19\% (23\%) at 250~\GeV\ for \mbox{$R= 0.2$}\ (\mbox{$R = 0.4$}) jets.

\subsection{Observables}

The \bjet\ cross-section in \pp collisions  is defined as
\begin{equation}
\frac{\textrm{d}^{2}\sigma_{\bjet}}{\textrm{d}\pt \textrm{d}y} = \frac{1}{L_\textrm{int}\mathcal{B}}\frac{N^\textrm{Unfol.}_\textrm{\bjet}}{\Delta\pt\Delta y }\ ,
\label{eq:Xsecpp}
\end{equation}
where $L_\textrm{int}$ is the integrated luminosity and $\mathcal{B}$ is the branching ratio which includes
direct $(b\rightarrow\mu)$ and
cascade $(b\rightarrow c\rightarrow\mu)$ semileptonic decays.  The
value of $\mathcal{B}$ is
$(20.6\pm0.6)$\%~\cite{ParticleDataGroup:2020ssz}. The quantity $N^\textrm{Unfol.}_\textrm{\bjet}$ is the
\bjet\ yield after the unfolding and acceptance correction described above,
and $\Delta\pt$ and $\Delta y$ are the widths of the \pt and $y$ bins.
Following the same approach, the per-event yield of \bjets\ measured in \mbox{Pb+Pb}\
collisions is calculated as
\begin{equation}
\left. \frac{1}{N_\textrm{evt}}\frac{\textrm{d}^{2}N_\textrm{\bjet}}{\textrm{d}\pt \textrm{d}y}\right|_\textrm{cent} = \left.\frac{1}{N_\textrm{evt}\mathcal{B}}\frac{N^\textrm{Unfol.}_\textrm{\bjet}}{\Delta\pt\Delta y}\right|_\textrm{cent},
\label{eq:PeYHI}
\end{equation}
where $N_\textrm{evt}$ is the number of MB events in the centrality class `cent'.
The inclusive jet cross-section and per-event yields are
defined in the same way as in Eq.~(\ref{eq:Xsecpp}) and Eq.~(\ref{eq:PeYHI}) but without the $\mathcal{B}$ factor.

\section{Systematic uncertainties}
\label{sec:systematics}

The systematic uncertainties of the jet cross-sections and per-event yields
common to both the inclusive jet and the \bjet\ measurements arise from the jet
energy scale and resolution,
the unfolding procedure, luminosity (\pp\ only), and
$\langle \mbox{$T_{\mathrm{AA}}$} \rangle$ determination (\mbox{Pb+Pb}\ only).
There are additional contributions to the \bjet\ measurements from the modelling of the \mbox{$p_\mathrm{T}^\mathrm{rel}$}\ distributions,
the fitting procedure, the branching ratio of \mbox{$b$-hadrons}\ to
muons, and the muon performance.
The uncertainties are discussed in detail below.

The systematic uncertainty of the jet energy scale (JES) has five parts. First,
there is a centrality-independent baseline component that is determined from in situ
studies of the calorimeter response for jets reconstructed with the procedure used in 13~\TeV\ \pp\ collisions~\cite{PERF-2011-03,Aaboud:2017jcu},
including an additional term for \bjet\ energy scale~\cite{PERF-2011-03}.
The second is a centrality-independent component which
accounts for the relative energy scale difference between the jet reconstruction procedure
used in this paper and that in 13~\TeV\ \pp\ collisions~\cite{ATLAS:2015twa}. Potential inaccuracies in the MC  description
of the relative abundances of jets initiated by quarks and gluons and of the calorimetric response to quark and gluon jets
are accounted for by a third, JES flavour,
component; this component is estimated independently
for the inclusive-jet and \bjet energy scale by varying the quark and gluon fractions from
their \pythiaeight\ values to those extracted from {\textsc{Herwig++}}.
The fourth, centrality-dependent, component (in \mbox{Pb+Pb}\ collisions only) accounts for a different structure~\cite{ATLAS:2018bvp}, and
possibly a different detector response, for jets in \mbox{Pb+Pb}\ collisions that is not modelled by the simulations.
It is evaluated by the method used
for 2015 and 2011 data~\cite{ATLAS:2015twa} that compares the calorimetric
jet \pt\ and the sum of the transverse momentum of charged particles
within the jet in data and MC samples. The size of the centrality-dependent uncertainty in the JES reaches 1.2\% in the most central collisions; it is smaller
for more peripheral collisions.
The systematic uncertainties from
the JES discussed above are derived for $R=0.4$ jets and applied to both \mbox{$R = 0.4$}\ and \mbox{$R= 0.2$}\
jets.
An additional component applies only to \mbox{$R= 0.2$}\ jets and
accounts for a potential uncertainty difference between  $R = 0.4$ and $R = 0.2$ jets.
The uncertainty is assessed by comparing the ratio of \mbox{$R= 0.2$}\ jet \pt\ to \mbox{$R = 0.4$}\ jet \pt\ in data and simulations.

The uncertainty due to the jet energy resolution (JER) is evaluated by repeating the unfolding procedure with modified response matrices, where an additional contribution is added to the resolution of the reconstructed \pT\ using a Gaussian smearing procedure.
The smearing factor is evaluated using an in situ technique in 13~\TeV\ \pp\ data that involves studies of dijet
\pT\ balance~\cite{Aad:2012ag,Aaboud:2019ibw}.
Additionally, an uncertainty is included to account for differences between the tower-based jet reconstruction and the jet reconstruction used in
analyses of 13~\TeV\ \pp\ data, as well as differences in calibration procedures.
Similarly to the JES, an additional uncertainty in the JER accounting for differences between $R = 0.2$  and $R = 0.4$ jets is added.
The resulting uncertainty from the JER is symmetrized.

Muon-related uncertainties are associated with the trigger and reconstruction efficiency measurement.
The systematic uncertainties are estimated by varying the tag-and-probe method
as described in Refs.~\cite{ATLAS:2016lqx,Aad:2020uyd}.
Additionally, the statistical uncertainty of the factor used to correct the centrality dependence of
the trigger efficiency
in Pb+Pb collisions and the  difference between the data-driven reconstruction efficiencies
in \mbox{Pb+Pb}\ and \pp\ collisions
are taken as muon systematic uncertainties that apply only to \mbox{Pb+Pb}\ collisions.

The uncertainties in modelling the \mbox{$p_\mathrm{T}^\mathrm{rel}$}\ distributions come from several sources, which are common to \pp and \mbox{Pb+Pb}\ collisions.
For the fraction of \mbox{$b$-hadrons}\ which
arise from gluon splitting, the analysis uses that from \pythiaeight\ simulation as the central value. In \pp collisions,
the gluon-splitting fraction
is reweighted to the value obtained from the {\textsc{Herwig++}}\ sample~\cite{ATLAS:2021agf}.
In \mbox{Pb+Pb}\ collisions,
there is no information about the modification of the gluon-splitting contribution to
\bjets.  Additionally, the fragmentation functions of \bjets\ in \mbox{Pb+Pb}\ collisions have not
been measured.
In order to cover both of these effects, the gluon-splitting fraction is conservatively varied between zero and 100\%.
For the \textit{c}-jets, the gluon-splitting uncertainty is estimated by varying the
\pythiaeight\ value of the gluon-splitting fraction
by a factor of two, based on measurements in Ref.~\cite{CMS:2019jis}.
The fraction of muons which arise from \mbox{$b$-hadron}\ decays which include
an intermediate \mbox{$D$-meson}\ is varied in accord with Ref.~\cite{ParticleDataGroup:2020ssz}.
The fractions of the various \mbox{$b$-hadron}\ species are varied according to the world average values in Ref.~\cite{Amhis:2014hma}.
The modelling of the muon momentum in the \mbox{$b$-hadron}\ rest frame is crucial for the \mbox{$p_\mathrm{T}^\mathrm{rel}$}\ method.
The modelling in \pythiaeight\ is used for the central values.
The \pythiaeight\ distributions were compared
with the measurement from DELPHI~\cite{Abdallah:2005cx}
and the difference between \pythiaeight\ and the DELPHI measurement is used as a
systematic uncertainty.
The uncertainty in the \textit{light}-jet\
template is evaluated by using muons with a distance of closest
approach to the collision vertex smaller than 0.01~mm,
to minimize the contribution from heavy-flavour jets, and remaking the templates.
In \mbox{$R= 0.2$}\ jets in \pp  collisions, the dominant components of modelling uncertainties
stem from the \textit{light}-jet\ template and the fraction of \mbox{$b$-hadrons};
for \mbox{$R = 0.4$}\ jets, the \textit{light}-jet\ template uncertainty dominates.
For \mbox{Pb+Pb}\ collisions, the dominant modelling uncertainties
stem from the \textit{light}-jet\ template and gluon-splitting components.

The uncertainty in the unfolding procedure is determined in all cases by
constructing response matrices
from the MC distributions without the reweighting factors that are used to match
the MC distributions to those in data. The uncertainty due to using a particular
MC model in unfolding \bjets\ is addressed by reweighting
the 2D \mbox{$p_{\mathrm{T}}^{\mathrm{jet}}$}$-$\mbox{$p_{{\mathrm{T}}}^{\mu}$}\ distribution in \pythiaeight\ to that observed in {\textsc{Herwig++}}.
The inclusive jet analysis has an uncertainty associated with
the non-closure of the unfolding procedure when the MC sample is divided
and one portion is used in place of the data and the other portion
used to generate a response matrix;
in the \bjet\ analysis the closure was found to be consistent with
unity within the statistical uncertainties and no uncertainty is added.

Uncertainties from the finite size of the MC samples
are combined with the data statistical uncertainties.
A systematic uncertainty associated with the template
fit procedure is addressed by allowing the templates to
deform in \mbox{Pb+Pb}\ collisions by
convolving the nominal template with a Gaussian function
where the width parameter is free.
Deformations of the templates account for mismodelling due to the large UE,
such as via the jet position resolution, muon momentum resolution, or other effects.
A similar uncertainty was applied in Ref.~\cite{ATLAS:2021xtw}.
The small non-closure of the fitting procedure, when the \mbox{$f_{\mathrm{b},i}$}\
extraction is tested in simulations,
is also included in the
systematic uncertainties.

For each uncertainty component discussed above, the entire analysis procedure
is repeated with the variation under consideration and the resulting changes
are added in quadrature to form the total systematic uncertainty of the measurement.
A summary of the systematic uncertainties for the
\mbox{$R = 0.4$}\ and \mbox{$R= 0.2$}\ \bjet cross-sections is shown in Figure~\ref{fig:sysXsec}.
For the \mbox{$R = 0.4$}\ jets, the largest contribution is the modelling component, while for
\mbox{$R= 0.2$}\ jets, the jet and modelling components have
similar magnitudes.

The integrated luminosity determined for 2017 \pp data was calibrated using data from dedicated
beam-separation scans, also known as van der Meer scans~\cite{ATLAS:2016fhk}.
Sources of systematic uncertainty similar to those examined in the 2012 \pp
luminosity calibration~\cite{ATLAS:2016fhk}
were studied in order to assess the systematic uncertainties for the 2017 data.
The combination of these systematic uncertainties results in a relative uncertainty of 1.6\%.
The uncertainty of the mean nuclear thickness function arises from geometric modelling uncertainties (nucleon--nucleon inelastic cross-section,
Woods--Saxon parameterization of the nucleon distribution) and the uncertainty in the fraction of selected inelastic Pb+Pb collisions.
The values of these uncertainties are taken from Ref.~\cite{Aaboud:2018twu}.
The  branching ratio for \mbox{$b$-hadrons}\ into muons is $(20.6 \pm 0.6)\%$ and is
taken from Ref.~\cite{ParticleDataGroup:2020ssz}.

The uncertainties which are common to \pp\ and \mbox{Pb+Pb}\ collisions are treated as correlated when
determining the uncertainty in the \mbox{$R_{\mathrm{AA}}$}\ value, with the
exception of gluon splitting, where the uncertainties
account for possible production and fragmentation mechanism differences
between \pp and \mbox{Pb+Pb}\
collisions, and the unfolding.
Similarly, the uncertainties which are common to inclusive jets
and \bjets\ cancel out when ratios of cross-sections or \mbox{$R_{\mathrm{AA}}$}\ values are taken;
the remaining uncertainties are the JES flavour component,
the \bjet-specific JES uncertainty, and the unfolding.
A summary of the systematic uncertainties for inclusive jet and \bjet \mbox{$R_{\mathrm{AA}}$}\
is shown in Figure~\ref{fig:sysRAA}.
The uncertainties in the $\mbox{$R_{\mathrm{AA}}$}^{\bjet}/\mbox{$R_{\mathrm{AA}}$}^\textrm{inclusive jet}$ ratio
are shown in Figure~\ref{fig:sysRAA_ratio}; the uncertainties in the
gluon-splitting contribution and deformation of the templates in \mbox{Pb+Pb}\ collisions dominate in
most cases.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.45\textwidth]{fig_04a.pdf}
\includegraphics[width=0.45\textwidth]{fig_04b.pdf}\\
\includegraphics[width=0.45\textwidth]{fig_04c.pdf}
\includegraphics[width=0.45\textwidth]{fig_04d.pdf}\\
\caption{The relative systematic uncertainties for several categories,
as a function of $b$-jet \pt\ for
(top) the \pp cross-section for \mbox{$R = 0.4$}\ (left) and \mbox{$R= 0.2$}\ (right) jets, and
(bottom) the Pb+Pb per-event-yield in peripheral (left) and central (right) collisions
for \mbox{$R= 0.2$}\ jets.}
\label{fig:sysXsec}
\end{figure}

\begin{figure}[htbp]
\centering
\includegraphics[width=0.45\textwidth]{fig_05a.pdf}
\includegraphics[width=0.45\textwidth]{fig_05b.pdf}\\
\includegraphics[width=0.45\textwidth]{fig_05c.pdf}
\includegraphics[width=0.45\textwidth]{fig_05d.pdf}\\
\includegraphics[width=0.45\textwidth]{fig_05e.pdf}
\includegraphics[width=0.45\textwidth]{fig_05f.pdf}
\caption{Relative size of systematic uncertainties for several categories,
as a function of jet \pt\ for
\bjet \mbox{$R_{\mathrm{AA}}$}\ (left column) and  inclusive jet \mbox{$R_{\mathrm{AA}}$}\ (right column),
in  peripheral (top row),
semi-central (middle row) and  central (bottom row) \mbox{Pb+Pb}\ collisions.}
\label{fig:sysRAA}
\end{figure}

\begin{figure}[htbp]
\centering
\includegraphics[width=0.55\textwidth]{fig_06a.pdf}\\
\includegraphics[width=0.55\textwidth]{fig_06b.pdf}\\
\includegraphics[width=0.55\textwidth]{fig_06c.pdf}
\caption{Relative size of systematic uncertainties of the ratio
$\mbox{$R_{\mathrm{AA}}$}^{\bjet}/\mbox{$R_{\mathrm{AA}}$}^\textrm{inclusive jet}$
shown for the most relevant components,
as a function of jet \pt\ for
50--80\% (top),
20--50\% (middle), and 0--20\% (bottom) centrality \mbox{Pb+Pb}\ collisions.}
\label{fig:sysRAA_ratio}
\end{figure}

\FloatBarrier
\section{Results}
\label{sec:result}

\subsection{Cross-section in \pp\ collisions}

Figure~\ref{fig:Xsec5pp_theory}  shows the \textit{b}-jet cross-section
as a function of \textit{b}-jet \pt in \pp collisions at 5.02 \TeV\ for \mbox{$R= 0.2$}\ and \mbox{$R = 0.4$}\ jets with $|y|<2.1$.
Additionally, \bjet\ cross-sections for both \mbox{$R= 0.2$}\ and \mbox{$R = 0.4$}\ jets are
compared with theory and generator calculations.
The data is in good agreement with the calculations by Li and Vitev~\cite{Li:2018xuv}
for both \mbox{$R = 0.4$}\ and \mbox{$R= 0.2$}\ jets. This calculation is based on
semi-inclusive jet functions where the cross-section is expressed in terms of
the parton distribution functions, the hard kernel and the jet functions.
The jet functions have terms in $\ln(R)$, which are resummed.
The $\SHERPA\,2.2.4$ calculations~\cite{Dai:2018mhw} for \mbox{$R= 0.2$}\ jets underestimate
the measured \bjet\ cross-sections by an amount which increases with \pt.
A calculation~\cite{Ke:2018jem,Ke:2018tsh} which is based
on \pythiaeight\ where the PDFs and $\alpha_{s}(\textrm{M}_{Z})$ is set with $\mathrm{pSet} = 8$~\cite{Sjostrand:2014zea}
is approximately consistent with
the upper edge of the uncertainty band of the \mbox{$R= 0.2$}\ jet yields.
The \pythiaeight\ calculation using the \textsc{NNPDF23lo} PDF~\cite{Ball:2012cx} and the A14 tune~\cite{TheATLAScollaboration:2014rfk}
is 20--30\% higher than data for both \mbox{$R = 0.4$}\ and \mbox{$R= 0.2$}\ jets.
The {\textsc{Herwig++}}\ calculations~\cite{Bellm:2015jjp}
using the \textsc{NNPDF30nlo} PDF  underestimate
the measured cross-sections at both jet radii.
There is no uncertainty estimate for the generator calculations, and the sensitivity of the
results to the choice of parameter values has not been investigated.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.49\textwidth]{fig_07a.pdf}
\includegraphics[width=0.49\textwidth]{fig_07b.pdf}
\caption{(left) Differential cross-section for \bjet\ production
for \mbox{$R= 0.2$}\ and \mbox{$R = 0.4$}\ jets with $|y|<2.1$
as a function of \pt\
in 5.02~\TeV\ \pp data.
(right) Ratio of the predictions to the measured \textit{b}-jet cross-section in \pp collisions at 5.02~\TeV\
for \mbox{$R = 0.4$}\ (top) and \mbox{$R= 0.2$}\ (bottom) jets.
The \mbox{$R = 0.4$}\ jets are compared with calculations from Ref.~\cite{Li:2018xuv} and \mbox{$R= 0.2$}\ jets are compared with calculations from Refs.~\cite{Li:2018xuv,Ke:2018jem,Ke:2018tsh,Dai:2018mhw}.
Both cross-sections are compared with \pythiaeight\ and {\textsc{Herwig++}}\ calculations.
The bands around unity represent the total uncertainty of the data.
The text provides additional discussion.}
\label{fig:Xsec5pp_theory}
\end{figure}

Figure~\ref{fig:Xsecpp_inclusive} shows
a comparison of the \bjet\ and inclusive jet cross-sections for \mbox{$R= 0.2$}\ jets
and their ratio.
The figure also shows the same ratio from the \pythiaeight\ MC
sample; it agrees with the data.
The cross-section ratio measured at 7~\TeV\ for \mbox{$R = 0.5$}\ jets with $|y|<0.5$
by the CMS Collaboration~\cite{Chatrchyan:2012dk}
is also shown; the jet radii in this measurement are larger than in
the present analysis but the results are qualitatively similar.
No significant \pt\ dependence of the \bjet\ to inclusive jet cross-section
ratio is observed.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.49\textwidth]{fig_08a.pdf}
\includegraphics[width=0.49\textwidth]{fig_08b.pdf}
\caption{(left) Cross-section of \mbox{$R= 0.2$}\ \bjet and inclusive jet production in \pp collisions at 5.02~\TeV,
and (right) the \bjet to inclusive jet cross-section ratio, together
with \pythiaeight\ simulation and measurements
from the CMS Collaboration at 7~\TeV\ for \mbox{$R = 0.5$}\ jets~\cite{Chatrchyan:2012dk}.
For the current measurement,
the boxes represent the systematic uncertainties and the error bars represent the statistical uncertainties.
For the CMS data the bars represent the total uncertainty.}
\label{fig:Xsecpp_inclusive}
\end{figure}

\subsection{Per-event yields and \mbox{$R_{\mathrm{AA}}$}\ in \mbox{Pb+Pb}\ collisions}

The inclusive jet and \bjet\ per-event yields in \mbox{Pb+Pb}\ collisions scaled by $\langle\mbox{$T_{\mathrm{AA}}$}\rangle$
are shown in Figure~\ref{fig:Xsec_PEY_syst} for the three centrality classes used
in this analysis overlaid with the values of the \pp\ cross-sections.
Figure~\ref{fig:RAA_light_b_comp} shows a direct comparison of the inclusive jet and \bjet\ \mbox{$R_{\mathrm{AA}}$}\
for each centrality class.
The \mbox{$R_{\mathrm{AA}}$}\ values for both types of jets decrease going from peripheral to central collisions.
Both are consistent with unity in peripheral collisions.  In central and semi-central collisions
the \mbox{$R_{\mathrm{AA}}$}\ central values for inclusive jets are lower than those for \bjets.
A difference between the slopes of the inclusive jet and \bjet\ differential cross-sections
could cause the \mbox{$R_{\mathrm{AA}}$}\ values to differ between the two categories of jets;
however, the ratio of the \bjet\ to inclusive jet cross-section, shown in Figure~\ref{fig:Xsecpp_inclusive},
does not vary with \pt.

\begin{figure}[!h]
\centering
\includegraphics[width=0.49\textwidth]{fig_09a.pdf}
\includegraphics[width=0.49\textwidth]{fig_09b.pdf}
\caption{
Per-event yields scaled by $\langle\mbox{$T_{\mathrm{AA}}$}\rangle$ in \mbox{Pb+Pb}\ collisions
for three centrality classes for \mbox{$R= 0.2$}\  \bjets (left) and  inclusive jets (right).
The boxes show the systematic uncertainties and the bars represent the statistical uncertainties.
The different centrality classes are offset by the factors shown on the plot for clarity.
The values of the \pp\ cross-sections are shown by the black lines; they are offset by the factors
shown on the plot.
The size of the \mbox{$T_{\mathrm{AA}}$}\ uncertainties are noted in the legend.}
\label{fig:Xsec_PEY_syst}
\end{figure}
The \mbox{$R_{\mathrm{AA}}$}\ values for both inclusive jets and \bjets\  are
compared with two theory calculations.
The first calculation is the LIDO model~\cite{Ke:2018jem,Ke:2018tsh,Ke:2020nsm},
which includes both energy loss and diffusion of heavy quarks.
The dead-cone effect for \bjets\
is included and the medium is implemented via (2+1)D
viscous hydrodynamics with averaged initial conditions.
The parameter which controls the coupling between the jet and the medium, $\mu_\textrm{min}$,
is varied between  $1.3\pi T$ and $1.8 \pi T$, where $T$ is the temperature of the QGP
in the model, in the calculation shown here.
The choice of  $\mu_\textrm{min}$ values is motivated by comparisons with other
jet measurements.
These parameters have been shown~\cite{Ke:2020nsm} to provide
a reasonable description of measurements of the \mbox{$R_{\mathrm{AA}}$}\
values of $B$- and $D$-mesons~\cite{Sirunyan:2017oug,CMS:2017qjw}.
The calculation by Dai et al.\
in Ref.~\cite{Dai:2018mhw} is based on a Langevin transport model
describing the evolution of \bquarks\ and their collisional energy loss and a
higher-twist description of radiative energy loss for both heavy and light partons.
This model also includes the dead-cone effect for
\bjets\ and also uses a (2+1)D viscous hydrodynamic medium with averaged initial conditions.
The medium parameter, $q_0$, is set to be 1.2~$\GeV^2/$fm.
The LIDO model shows good agreement with the data for both inclusive jet and \bjet\ \mbox{$R_{\mathrm{AA}}$},
although with the inclusive jets on the low side and the \bjet\ case on the high side,
for all three centralities considering model and data uncertainties.
The calculation in Ref.~\cite{Dai:2018mhw} is below the measured \mbox{$R_{\mathrm{AA}}$}\
in central and semi-central collisions for both \bjets\ and inclusive jets.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.65\textwidth]{fig_10.pdf}
\caption{\bjet\  (filled points) \mbox{$R_{\mathrm{AA}}$}\
for three centrality classes compared with the inclusive jet
\mbox{$R_{\mathrm{AA}}$}\ (open points) at 5.02~\TeV.
Both \mbox{$R_{\mathrm{AA}}$}\ measurements
are compared with theory calculations~\cite{Ke:2018jem,Ke:2018tsh,Dai:2018mhw}.
The boxes represent the systematic uncertainties and the error bars
represent the statistical uncertainties.
For the LIDO calculation, the width of the band shows the variation of the $\mu_\textrm{min}$
parameter from $1.3\pi T$ (lower edge) to $1.8\pi T$ (upper edge).
The boxes at unity represent the scale uncertainties from $\langle\mbox{$T_{\mathrm{AA}}$}\rangle$ and
the luminosity determination.}
\label{fig:RAA_light_b_comp}
\end{figure}
In order to assess any difference between the \bjet\ and inclusive jet
\mbox{$R_{\mathrm{AA}}$}, the ratio $\mbox{$R_{\mathrm{AA}}$}^{\bjet} / \mbox{$R_{\mathrm{AA}}$}^\textrm{inclusive jet}$ is presented in
Figure~\ref{fig:RAA_light_b_comp_ratio}
for each centrality class.
This provides a
more precise comparison of the \mbox{$R_{\mathrm{AA}}$}\ values than in Figure~\ref{fig:RAA_light_b_comp}.
The results suggest that in central collisions the suppression of \bjets\ is less than
that of inclusive jets, with an overall significance of approximately $1.7\sigma$.
The calculation by Dai et al.~\cite{Dai:2018mhw} agrees well with the ratio in all centrality classes,
while LIDO model calculations tend to overestimate the double ratio at low \pt,
especially in central collisions, but agree well with the data at higher \pt.
In the LIDO model, the difference between the inclusive jet and \bjet\ \mbox{$R_{\mathrm{AA}}$}\ values
is not expected to be entirely a result of the large mass of the \bquark,
and qualitatively similar differences are seen between the two \mbox{$R_{\mathrm{AA}}$}\ values in that model
with and without the inclusion of the dead-cone effect~\cite{Ke:2020nsm}.

Differences in the internal structure of the \bjets, such as those that come from gluon-splitting processes,
are also expected to be important in determining the \bjet\ \mbox{$R_{\mathrm{AA}}$}\ value.
Based on the \pythiaeight\ MC samples,
the fractions of jets in which gluons participate in the
hard scattering in the inclusive jet and \bjet\ samples have
opposite trends with \pt.  The fraction increases from 23\% to 45\% over the range of 80 to 250~\GeV\
for the \bjets\  and decreases from 61\% to 47\% over the same range for the inclusive
jets.

These measurements highlight
the importance of measuring the fragmentation functions of \bjets\  in heavy-ion collisions.
These results are compatible with previous results from
CMS~\cite{Chatrchyan:2013exa} (although both the collision energy and
jet radius are different) but have better precision.

\begin{figure}[htbp]
\centering
\includegraphics[width=0.65\textwidth]{fig_11.pdf}
\caption{Ratio of \bjet\ \mbox{$R_{\mathrm{AA}}$}\ to the inclusive jet \mbox{$R_{\mathrm{AA}}$}\ for each centrality class.
Ratios are compared with theory calculations~\cite{Ke:2018jem,Ke:2018tsh,Dai:2018mhw}.
The boxes represent the systematic uncertainties and the error bars
represent the statistical uncertainties.
For the LIDO calculation, the width of the band shows the variation of the $\mu_\textrm{min}$
parameter from $1.3\pi T$ (upper edge) to $1.8\pi T$ (lower edge).}
\label{fig:RAA_light_b_comp_ratio}
\end{figure}

\FloatBarrier

\section{Summary}
\label{sec:summary}

This paper reports cross-sections for \bjets\ and inclusive jets in \mbox{Pb+Pb}\ and \pp\ collisions,
both at $\sqrt{s_{_\textrm{NN}}}=5.02$~\TeV, and recorded by the ATLAS detector at the LHC.
The measurement uses three datasets:
1.4~\mbox{${\mathrm{nb}^{-1}}$}\ and 1.7~\mbox{${\mathrm{nb}^{-1}}$}\ of \mbox{Pb+Pb}\ collisions collected in 2018 for \mbox{$R= 0.2$}\ \bjets and inclusive jets respectively,
and 260~\mbox{${\mathrm{pb}^{-1}}$}\ of \pp\ collisions collected in 2017 for \mbox{$R= 0.2$}\ and \mbox{$R = 0.4$}\ \bjets\ and \mbox{$R= 0.2$}\ inclusive jets.
The \bjet\ cross-section in \pp\ collisions is compared with a theoretical calculation
and Monte Carlo generator predictions.
The \bjet\ and inclusive jet per-event yields for \mbox{$R= 0.2$}\ jets
and the corresponding nuclear modification factor, \mbox{$R_{\mathrm{AA}}$}, are also reported for
\mbox{Pb+Pb}\ collisions at the same per-nucleon collision energy.
The \mbox{$R_{\mathrm{AA}}$}\ values are found to decrease with increasing collision centrality
for both \bjets\ and inclusive jets.
In order to more directly compare the suppression of \bjets\ and inclusive jets,
the ratio of the \mbox{$R_{\mathrm{AA}}$}\ values is presented. The central values of this ratio
suggest that the \mbox{$R_{\mathrm{AA}}$}\ for \bjets\ is larger than that for inclusive jets
in central \mbox{Pb+Pb}\ collisions.
Thus within this model, the differences may arise from the inclusive jet mixture of quarks and gluons,
where gluons lose more energy, and the $b$-quark mass effect may be subdominant at these \pt values.
However, the current systematic uncertainties do not permit a more definitive statement.
This highlights the need for more precise measurements of this quantity, mainly the necessity to measure the fragmentation functions of \bjets\ in heavy-ion collisions.
The measurements are compared with theoretical calculations and suggest a role for mass and colour-charge effects in partonic energy loss in heavy-ion collisions.

\clearpage

\printbibliography

\clearpage

\end{document}

redpajama_set_name: RedPajamaArXiv


The Bara Bara Band is a folk group based in South London and Bristol, playing a mix of their own songs, traditional British and Appalachian folk songs and tunes.
Ruth and Rupert also play as a duo for smaller venues and folk clubs, with more emphasis on traditional folk songs and tunes.
They also run the monthly folk club TOOTING FOLK, which has become a firm favourite on the London folk scene.


Anyone with a handheld vacuum knows it doesn't replace a bigger one but what a great addition it is to have! No longer will you need to drag a canister vacuum outside to clean your car, but simply use your handheld vacuum to get all the crumbs and dirt out of the tight corners and crevices of your car. It also makes a great tool to clean out your kitchen pantry and cabinets. The small size makes it lightweight and easy to keep out of sight.
Dust Bin Capacity – Because of the size, the handheld vacuum has limited capacity. Make sure to empty it after each use. Not only will it make room for the next time you clean, but it also allows the filters to last longer.
Attachments – Most handheld vacuums will come with basic but useful tools such as the crevice tool and the upholstery brush to clean furniture, car seats and other fabrics. Some of the newer handheld vacuums will even come with a liquid nozzle to clean unexpected spills.
Charging station – Look for one that is small and lets you hang your vacuum from it, making it a great tool for storing inside a cabinet or closet somewhere. You'll need an electrical outlet nearby though, so keep that in mind. A tabletop charging station might work out as well, depending on how much space you have available and where you want to place it.
Run time – Because it isn't meant to replace your normal vacuum, the run time might not be too important to you. Most handhelds have an average run time of 15-40 minutes before having to return to the charging station. Most are made with Lithium-ion batteries, meaning charging it before it's all the way low, won't hurt the battery. Keep in mind the time it takes to charge fully is often around 6-8 hours. So make sure to make it a habit to return it to its charger base after each use.
Weight and dimensions – A major advantage of a handheld vacuum is how lightweight it is. On average they weigh around 3 lbs. making it much lighter than any other kind of vacuum.
Price Range – You can get a decent vacuum for around $30-$150 depending on your budget. If you choose one of the cheaper ones, just keep in mind they might not come with any attachments.


The ANAM initiative, funded by EPSRC, seeks to convert the promise offered by CNTs into commercial reality. This project directly addresses the industrial utilization of CNTs and seeks to close the gap between academic achievement and commercial return.
Carbon Nanotubes (CNTs) are proving one of the most exciting new materials being developed.
With functionalities that have potential applications for many diverse, commercial uses.
Manufacturing CNTs on a large scale remains a challenge, but one that we are working towards.


text:
Russiagate: The Great Unraveling
Daniel Lazare
© Photo: REUTERS/Leah Millis
With no advance warning, the Department of Justice has decided to drop its case against Concord Management and Consulting, one of three Russian companies accused of using Facebook to "sow discord" and manipulate voters into doing the Kremlin's bidding.
It seems that prosecutors had no choice according to the New York Times since defendants were "exploiting the case to gain access to delicate information that Russia could weaponize." Instead of admitting to their old dirty tricks, in other words, they were busy thinking up new ones in order to take advantage of innocent Americans yet again.
Those awful Russians! Doesn't it show that they're all guilty as hell regardless of whether there's a trial or not?
Well no, actually, it doesn't. What it shows, rather, is that the case never made much sense to begin with and now, after years of headlines, the DOJ is finally putting it out of its misery. Questions remain. If prosecutors are so concerned now that the Russian defendants would somehow take advantage of the judicial process and twist it to their advantage, why didn't they think of that in the first place? If they knew the case posed special problems, why did they go for an indictment at all? Why not hit the company with a few additional international sanctions and leave it at that?
After all, a prosecutor has to think about not a lot of things before going to trial, not only whether a case is provable but whether the process will be too expensive, whether it will compromise other investigations, whether the penalty will be too light to warrant all the fuss and bother, and so on. These are questions to ponder before filing charges, not after.
Yet they're questions that Special Prosecutor Robert Mueller's super-high-powered legal team somehow managed to skip. Which leads to another question: why? Why didn't they work through the various problems that a trial might raise? Could it be that after issuing the original charges, they figured that the it wouldn't matter because a trial would never take place?
This is what skeptics have long maintained, this one included. Since the three companies and thirteen individuals named in the original February 2018 indictment were all Russian, it seemed logical to assume that they would remain in situ, beyond the reach of U.S. law. Why fly all the way to Washington just to throw yourself on the mercy of a federal court at a time when anti-Russian passions were shooting through the roof? Who could be so crazy?
No one, it seemed, except for one company that did just that. To universal astonishment, Concord Management and Consulting LLC, one of three indicted corporations owned by Russian businessman Yevgeny Prigozhin, hired the prominent law firm of Reed Smith in May 2018, entered a plea of not guilty, and demanded its day in court.
The Mueller team, according to all available evidence, was stunned. After all, it had all seemed so simple. If a trial was not forthcoming, then an indictment could say whatever prosecutors wanted it to say. They could accuse Prigozhin and his entourage of anything and everything, and as long as they didn't have to lay it out before a judge and jury, no one would care. The press would get its story, Mueller would get his acclaim, and, for the umpteenth time, Russia would be branded the most hellish country on earth. What could go wrong?
But then Concord called Mueller's bluff, and everything went to pot. Since judicial procedure requires something called "discovery," a process by which the defense gets to scrutinize the prosecution's evidence so it can mount an effective rebuttal, Reed Smith partner Eric Dubelier demanded to see what government had.
Prosecutors said no. The material was too "sensitive." If Dubelier saw it, then he might show it to Prigozhin, who would then use it against the U.S. Conceivably, the prosecution could have redacted the evidence by removing proper names and other such material. But no, they wanted Federal Judge Dabney Friedrich to narrow defense access even more. When she refused, they tried to turn tables by demanding sweeping information about Prigozhin and his holdings. When that didn't work, they announced that they had a secret witness who would reveal everything about Prigozhin and his illicit activities that anyone might want to know.
Finally, they threw in the towel, surprising everybody except the few who saw it coming all along. "In light of the defendant's conduct," the prosecution announced, "…its ephemeral presence and immunity to just punishment, the risk of exposure of law enforcement's tools and techniques, and the post-indictment change in the proof available at trial, the balance of equities has shifted. It is no longer in the best interests of justice or the country's national security to continue this prosecution."
Translation: we give up. After years of headlines, revelations, scoops, and other such nonsense, the trial of the decade was off. Explaining how Russia had used Facebook to twist American minds was too much trouble. It was easier to let Prigozhin to continue with his shenanigans while prosecutors attended to more serious matters, such as whether a 62-year-old Connecticut man really threatened to kill House intelligence chairman Adam Schiff.
The emptiness of the entire charade thus stands exposed. Yes, Russians may have pulled a few adolescent tricks on the internet. Yes, Prigozhin may have placed a few inane ads on Facebook. But, contrary to Mueller and his absurd report, Russian intelligence did not steal thousands of DNC emails – WikiLeaks's source was entirely different – while the $44,000 that Prigozhin spent on Facebook ads prior to Election Day 2016 had a minimal impact on the outcome. The whole affair didn't amount to a hill of beans.
Or, to put it another way, the real scandal was the scandal itself, i.e. not what Russiagate revealed about what the Kremlin was up, but what it showed about how intelligence agencies were able to mount a classic disinformation campaign in league with the corporate press. Russiagate had the country in an uproar for years, but now the great unraveling has begun. Hopefully, it will continue until the entire process is laid bare.
Mueller Russiagate United States
They're Not Even Trying to Make Sense Now
Americans Need a Conspiracy Theory They Can All Agree on
U.S. Blacklists Strategic Culture Foundation in Attack on Independent Journalism and Political Dissent
BBC Limits and Related Censorship on Russia Coverage
America in Crisis... Blaming Russia Is Self-Defeating Diversion
Rohrabacher, Mueller, and Assange
Lingering Topics: Ukraine and Russiagate
Putin the Poisoner? More Doubts Over Attempts to Delegitimize Russia's Leader
Bounties? What Bounties?
VIDEO: Welcome to RussiaGate 2.0, Right on Schedule
Daniel Lazare is an American freelance journalist, publicist and blogger.
How Democracies Die
Irony and SolarWinds
A Look Back at Mear One's 'Freedom for Humanity'
Joe Biden and Terrorism

redpajama_set_name: RedPajamaCommonCrawl


text:
U.K. Showbiz
What a shiner! Buff action man Channing Tatum sports a black eye as he bikes around the park in the Big Apple
By Jade Watkins
He plays Rooney Mara's jailed partner in his new film The Bitter Pill.
And it may be that Channing Tatum runs into a spot of trouble in the movie as he was seen sporting a black eye yesterday.
The 32-year-old star was spotted with the purple shiner on his right eye whilst biking around the Big Apple during a break from filming the thriller.
Sporting a shiner: Channing Tatum was seen with a black eye as he went cycling in New York yesterday
He was also seen with a bloody cut on his left forearm.
Whether or not the injuries were obtained onset is unknown.
Regardless, the Magic Mike star wasn't too worried about causing any more wounds, as he was busy texting on his phone whilst pedalling around the Hudson River Parkway.
The actor's famous bulging biceps could also be seen peeking from underneath his green T-shirt, which he teamed with some athletic shorts, special cycling shoes and a backwards cap.
Ouch: A bloody cut could also be seen on his left forearm
Channing is currently filming The Bitter Pill alongside Rooney Mara and Jude Law in The Big Apple.
The Steven Soderbergh directed film is about a woman (Mara) who turns to prescription medication as a way of handling her anxiety concerning her husband's upcoming release from prison.
Catherine Zeta-Jone also stars in the movie and takes on the role of Dr. Erica Siebert,
Eyes front! The Magic Mike star wasn't too worried about causing any more injuries, as he was busy texting on his phone whilst pedalling around the park
The Bitter Pill will be the third collaboration between Catherine and the director after she starred in Traffic and Ocean's Twelve.
It will also be the third for Tatum, who worked with the famous director on his his 2011 action flick Haywire and other upcoming film, Magic Mike.
Tatum stars as veteran stripper Mike 'Magic Mike' Martingano, who teaches a rookie about the profession.
Handsome couple: Channing and his wife Jenna Dewan attended the MTV Movie Awards earlier this month
The film is partially based on Tatum's own experiences as a male dancer 11 years ago at the age of 19 in Tampa, Florida.
Magic Mike works at club Xquisite, which is owned by Dallas, another leather chap wearing lad (played by just married Matthew McConaughey).
It is there that he teaches 'The Kid', played by Alex Pettyfer, the ins and outs of the stripping world.
Stripper pals: Channing is also set to star in Magic Mike alongside fellow buff star Matthew McConaughey
Soderbergh told MTV News of the film: 'It's a fictionalised version of what Channing went through. Channing's sort of playing a version of himself, and Alex is kind of playing a version of Channing.
'They're sort of amalgamations of other people. No one has ever said, 'But that didn't happen,' because it's not really that. It's just the world that I think is really fascinating.'
The movie also stars Matt Bomer, Joe Manganiello, Olivia Munn and Lindsay Lohan.
It hits American cinemas on June 29.
Meanwhile, The Bitter Pill will be released in February next year.
Eye candy: Tatum stars as veteran stripper Mike 'Magic Mike' Martingano, who teaches a rookie about the profession
Channing Tatum sports a black eye as he bikes around New York


Niedawno, w szkole na lekcji języka angielskiego, nauczyciel zadał nam do napisania opowiadanie. Nie mieliśmy określonego tematu, jedynym wymogiem było użycie wcześniej zapisanych zdań. Oczywiście, każde z nich było o czymś zupełnie innym, a opowiadanie musiało mieć sens.
"Fifty million years ago, India collided with Asia." teacher said and all of sudden she stopped talking. She ran out of the class in breakneck speed. Students were surprised. No one knew what had just happened. They were unaware that she's been having diarrhea for a while now. Of course, as soon as she left the class, conversations have began. Only one boy wasn't paying attention on what was happening.
Carlos didn't even bother to listen. He was thinking about something else…Or rather someone else. Sue…the most beautiful girl in his school.
As soon as he decided to do that, he started acting. He was walking toward Sue's desk, when he saw his brother – Juan talking to his dreamed girl. Carlos became very angry about this. He came back to his desk and took out his mobile phone. Unlocked it and searched results in the internet about "how to improve face of somebody who get you riled up". "The amount of information just a click away may be limitless, but the time and energy we have to absorb and evaluate it is not." Carlos agreed with this statement heard somewhere when he realized that he spent half an hour surfing on the internet. He read on some website that pretty girls don't want to be with ugly man, so he thought that massacrated face of his brother will be enough to prevent any relationship between Juan and Sue. Carlos looked around and noticed a big bottle on teacher's desk. He realized that it's what he needs. Glass bottle… This amazing property of being both sold and transparent has given glass many uses throughout the centuries. Carlos didn't know if it was used that way before, but he didn't give it much thought. He stood up and made few quick steps towards his aim. He broke the bottle and took the biggest piece into his hand. Luckily for Carlos, nobody noticed what he'd just done. He came closer to Juan and made him turn face to face with him. "Having a family doesn't exempt me from social responsibilities" said convincingly Carlos.
"But family comes first" replied surprised Juan.
"It shouldn't" answered Carlos and without hesitation raised his hand and wounded Juan's face with the piece of glass. There was sudden silence in the class when the teacher all at once appeared. She saw what happened, called 911 for ambulance and police.
In the police station, Carlos was being questioned, but he wasn't the only one. All of his classmates had to answer lots of questions about his personal life. His two best friends asked if they knew what Carlos had wanted to do, responded just like that: "The new numbers also indicate our original estimate of time of impact was right." Police officers had no idea what to think about it, so they decided to ask for help police psychologist. She discovered that Carlos and his best friends were a part of some sect and that they were mentally unstable for a while now.
Carlos, considering his mental condition, was sentenced to 7 years of imprisonment and special therapy for the rest of his life. His friends were locked in the mental hospital and required treatment for many years. Sue ended as an old single with nine cats. And Juan, thanks to great doctors, fully recovered physically but his mentality couldn't deal with such trauma, so he went to Australia and started living with Aborygens there.
Wiecie, już od dawna nie pisałam żadnego tekstu, który nie byłby recenzją czy felietonem. Takiego, który ma fabułę. Zdążyłam już zapomnieć, jak przyjemnie pisze się taką formę. Sprawiło mi to dużo satysfakcji, więc postanowiłam pisać jedno opowiadanie miesięcznie (po polsku, oczywiście). Piszcie w komentarzach, czy chcecie, żebym publikowała je na blogu i Wasze propozycje tematów do nich.
Dzięki za uwagę i do usłyszenia!


What? Gold in Visual ERP? You betcha.
Have you ever wondered if transactions are being processed properly in Visual? Especially, inventory transactions. There can be so many of these with lots of different people involved. With that volume of transactions there is definitely a possibility for problems. If you want to get a comfort level, have a look for negative inventory. It is like a goldmine because in there are all the different things that are going on incorrectly in your database.
You are not receiving things timely. Did the paperwork get lost? Is the paperwork sitting on the receiver's dock but hasn't been received yet? Or has the paperwork been sent to the office to be processed instead of being done at receiving.
You're shipping an order that hasn't really physically shipped. But you say, I need the paperwork. You may want to consider the picklist instead.
We're shipping the parts in Visual, but we haven't received the work orders in Visual yet. Again, this could be an opportunity for a process improvement. Can the parts be received on the floor as soon as they come off the line? Could they be bar-coded to make it even more efficient?
How about a physical inventory count? The count was entered incorrectly or just plain counted wrong.
Or then there is the fat finger. Or the trigger-happy finger. The latter, is always fun. I remember a case where a user entered 7 into the quantity field on their bar-code system. This was a lot of years ago and response times were not as good as today. So, they clicked on the 7, again and again. On top of that the parts were set to auto-issue. The 7,777,777 for each part on the work order were issued. That was a bit of a mess.
We could even enter the incorrect Part ID on a customer order.
The Work Order Requirement – Unissued Materials Report. This will show you by work order where not enough materials have been issued. Pick a date range to focus your efforts.
Comparative Material Usage Report. Select for All closed work order and pick a date range. I like to modify this report to streamline it a bit. Remove the page breaks, get rid of extra blank lines.
Review your RMA's. What are the reasons for returns? Wrong part shipped?
Inventory Transactions – by filtering on adjustment only. Each time there is an adjustment, you should as why?
So, you might ask, why is this important? Many times, I hear "we just do an adjust in or out to fix. Inventory is then accurate." As an accountant, that makes me cringe. Adjustments don't end up on the cost of the product. Accurate costs are necessary to assess the profitability of parts and customers. It will help guide the company on where to focus the future direction of the business.
So, negative inventory is full of little gems to teach you, or to help you identify places where you need to improve your process and ultimately improve the profitability for the company. Hey, if the company makes more money, they might just pay more. So, it is good for everyone.


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d'Arbois de Jubainville, H.
Revue Celtique
Revue Celtique 9 (1888)
Revue Celtique 9 (1888).
d'Arbois de Jubainville (H.)
Loth (J.)
Ernault (E.)
Dottin (G.)
Revue Celtique, volume 9
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Small but mighty . . .
So as a homeschooling mom I am always looking for ideas to inspire and teach my children. Last year as part of our homeschooling endeavor we watched the movies Food Inc. and Food Matters. They were powerful. We have been interested in nutrition because my boys are both dealing with food allergies and they wanted to understand more about them.
Today I came across this little video which is powerful by an 11 year old homeschool boy who has an amazing message and does it with such eloquence and calm you forget he is 11 years old. I hope you find this as much as I did. It is about our food system and how we can make a difference. It is called Monsanto Corporation Gets Owned by 11 year old boy!
Remember we can make a difference with every purchase we make.
Oh my, I was talking with two friends yesterday (we were working on a plan to save the world-more on that in another post) when I realized that we are going into our 3rd year of homeschooling. I am feeling very grateful so so many things. Words cannot describe just how amazing our lives are and how we have all changed because of our decision to homeschool. Yes, there have been some bumpy spots, I will not lie. In fact there have been times when I wished the bus would stop in front of our home. The good news is that "feeling" passes and we continue, we persevere. Why, because we are committed to this life, this lifestyle and our boys. There really is no one who can love my boys, encourage them and help them grow any more than I do. So we press on with much joy and yes some trepidation.
So stay tuned as we embark on year three (3)! There will be lots of stories and new adventures. I hope you enjoy the ride.
Okay, we don't live in a big city with trains; I am speaking metaphorically. But sometimes you have to stop and regroup. Today was one of those days. The boys are busy with baseball. We are literally at the park every day. I have also been trying to get them their PE during the day as they need time to burn off some steam. On top of that we have school work and other schedules to keep. Today, I could see we hit the wall. I took a deep breath and made an executive, mommy decision - "stop the train!" I let David's coach know we could not make the game tonight, they did not go to their other activities. I fed them dinner early and sent them off to bed with books in hand. It is now 7:30 and they are quietly reading and almost asleep.
Some might think this is an over reaction to a day filled with emotional outbursts. I see it as a day for my boys to just take a night off and rest. They are tired and need the rest. I can see it in their faces and in their behavior. I truly think we as parents need to be careful to not over schedule our guys and give them breathing room. We were doing fine until this week when between the two boys we had 6 games and two practices and no break. I am so glad that God has given me the wisdom to know when enough is enough. The truth is I really am appreciating a night off and with that I have time to update my blogs and do some other activities that have fallen to the sidelines.
It was an emotional day. Tornadoes swept across the country including two in our area. The boys and I watched and waited to see if we should head to the basement. Praise the Lord, we did not have to. Finally, I could get my shower and then we headed out for our day's activities. After a false start, we ended up at my sister's house. We had such a wonderful time of fellowship with her and she seemed to really enjoy the goofiness of my guys. We finally headed back home for a lovely evening. While I was busy creating a yummy dinner, the boys were busy creating a game with their legos and dice. It sounded pretty complicated and they were having a blast. So nice that they can create fun without screen time.
Now I am enjoying a quiet night and reflecting on how great it is to be a homeschooling mom who can change plans on a dime and enjoy each and every moment with my boys. Yes there are times when I feel overwhelmed by the responsibility and yet even in those times, I am amazed at the joy that comes out of even a simple day.
I was sitting here thinking about how different my life is now that I chose to homeschool. As I think about how my days flow and my relationship with my boys, I realized that homeschooling is a lifestyle. We take our time through the day, we have our devotions, we homeschool, we go to the library, we go to the park, we enjoy each other and all the time I am able to build a business. My boys still have time for boy scouts, church youth group, sports activities and play dates. Their only gripe is how sad they feel for all the kids who have to be in school all day and then do homework. They have so little time for play.
I am grateful all the time for our new life and wish we started it sooner. When I find myself regretting ever putting the kids in school, I am reminded how I would not appreciate our life now had I not known what it was like before. When the boys were in school, the stress in our home was unbelievable. Homework was a nightmare. Getting to any after school activity was a daunting task if I wanted to feed my family and get it all done.
Would I go back? I don't plan on it. My hope is to homeschool them through high school. In fact my youngest son, who still is a snuggle bunny, wants to be homeschooled through college. Okay I am a realist, that is not part of my plan, but I love that it is part of his. My point, I am enjoying where I am, being present is the most important part. My boys have a better mom and hence we are a better family.
Shame on me, it has been over a year since I posted. What happened? Well I have no excuse, just got busy and did not make my blog a priority. That is changing today! This year I am focusing on how to not only homeschool my boys, build my business and keep up with my blogs. The truth is it is all related it makes sense to do it all. I hope you enjoy the new look. Come back often to check on me, keep me accountable and add your insights. And if you like what you see, sign up as a follower. I would love to get to know you.
Most of the time I try to be profound and insightful on my blog. Quite honestly I don't know whether I accomplish that. I don't even know if anyone reads my blogs. The truth is that I love to write, strive to improve and want to express myself.
Today I just wanted to share with you a smile. This video is one of the things that makes me smile. In fact anything that Andy Andrews does makes me smile. I hope you enjoy it as much as I have. It maybe something you bookmark and keep handy when you need to have a "discussion" with your children. You may just want to play it for them each morning just to get it out of the way. I hope you enjoy it -- parental sayings by Andy Andrews!
There are times when you just know that you have go with the flow or roll with the punches as they say. Tonight was one of those nights. I had an interview scheduled with Audrey Cupo, a professional organizer from Bucks County, PA. My goal in the interview was to hopefully get a few tips about how to get organized specifically geared toward busy moms. We had all the details taken care of and then came the call. Guess what? No one could hear us, in fact they were in a magical holding space while we were happily doing the call. Only after we completed the call did I find out there were people waiting for us. So we then got back on the line and held the call again. Not a problem, it was our pleasure to do that for the listeners who hung in there.
Many lessons have been learned, and we are clearly not throwing the baby out with the bath water. The one thing that did work was the recording. So if you are interested in the recording of our call here it is: Audrey Cupo.
Also, in case you are looking for a way to get organized and stay organized check out Audrey's site in which she discusses her new program. Imagine being able to have an accountability partner, mentor and trainer all in one package. The best part of the program is that it does not require a lot of time. Further I cannot believe the price. It is great! Here is the information on her coaching program. Keep in mind she only has 40 spots left and spots are filling up fast, so if this is your year to Live an Organized Life check it out.
Thank you again Audrey for a great call. And thank you all for your patience as we worked through this whole process.
I am a homeschooling mom who is a business coach, consultant and trainer who loves helping people reach their goals. My passion is helping people get clients and keep them.


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Жоао Нуно да Силва Кардозо Лукас (; 25. октобар 1979 — 26. мај 2015) био је португалски фудбалер. Играо је на позицији везног играча.

Каријера
Каријеру је почео у Академици, за чији први тим је дебитовао у сезони 1999/00, а касније је играо за Боависту у чијем дресу је за три сезоне одиграо 86 утакмица у Првој лиги Португала.

У јуну 2007. је потписао трогодишњи уговор са Црвеном звездом. Дебитовао је за црвено-беле 4. јула 2007. на пријатељској утакмици против Олимпије из Љубљане. Прву такмичарску утакмицу је одиграо 1. августа 2007. против Левадије у 2. колу квалификација за Лигу шампиона. Са Црвеном звездом није успео да се пласира у Лигу шампиона, јер су црвено-бели након елиминације Левадије испали од Ренџерса. Након тога је преко Гроцлина изборен пласман у групну фазу Купа УЕФА где су противници били Бајерн Минхен, Арис, Болтон и Брага. Лукас је наступио на свих 10 европских утакмица Црвене звезде у овој сезони. Поред тога је одиграо и 13 утакмица у Суперлиги Србије, где је постигао и једини гол у црвено-белом дресу, 12. децембра 2007. у победи 4:0 над чачанским Борцем на Маракани. Последњи пут за Црвену звезду је наступио 19. децембра 2007. године на утакмици против Браге. У црвено-белом дресу је одиграо 23 такмичарске утакмице, а током боравка у београдском клубу са га тренирала тројица тренера, Бошко Ђуровски, Милорад Косановић и Александар Јанковић.

Након тога, Лукашу је установљен проблем са срцем због којег је 17. марта 2008. објавио да завршава своју играчку каријеру. Преминуо је 26. маја 2015. у Порту од последица срчаног удара.

Референце

Спољашње везе

 Жоао Лукас  на foradejogo.net

Рођени 1979.
Умрли 2015.
Португалски фудбалери
Фудбалери Боависте
Фудбалери Црвене звезде
Фудбалери Суперлиге Србије
Везни играчи у фудбалу

redpajama_set_name: RedPajamaWikipedia