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\begin{document}

\Title {Measurmetns of the B production with the CMS Experiment}


%\bigskip

%+\addtocontents{toc}{{\it D. Reggiano}}
%+\label{ReggianoStart}

\begin{raggedright}
{\it Polina Otiougova on behalf of CMS Collaboration\\
 Physik-Institut der Universit\"at Z\"urich,\\
  Winterthurerstrasse 190, CH-8057 Z\"urich, Switzerland}

%\bigskip\bigskip
\end{raggedright}

\begin{abstract}
We present the measurements of b-quark production in inclusive channels and exclusive decays. The measurements are based on different methods, such as inclusive jet measurements with secondary vertex tagging or selecting a sample of events containing jets and at least one muon. In addition, measurements of $B^{+}$, $B_{0}$ and $B_{s}$ meson production cross sections are presented. Finally, a study of the angular correlations between beauty and anti-beauty hadrons is presented, probing for the first time the small angular separation region.
\end{abstract}

\section{Introduction}

 The presented results were obtained by the CMS Experiment \cite{cms} using the  data accumulated in the year 2010. The obtained data correspond to an integrated luminosity of $40~\mathrm{pb}^{-1}$. Measurements of b-quark production are relevant for the following reasons:  first,  the measurements are performed at a new energy scale,  second, the possibility to compare the data to the MC results, possibility to check the next-to-leading order (NLO) QCD predictions and  third, the obtaining information about the background for  Higgs, SUSY and top physics.


\section{Exclusive B-meson production cross-section}
The CMS collaboration performed the measurement of exclusive productions of $B^{+}$, $B^{0}$, and $B_{s}$ mesons \cite{b_plus,b_zero,b_s} in the following decay modes:  $B^{+} \rightarrow J/\psi(\mu^{+}\mu^{-})K^{+}$; $B^{0}\rightarrow J/\psi K^{0}_{S}$; $B_{s} \rightarrow J/\psi \phi$.
For all three decay channels the analysis strategy is similar.  The $J/\psi$ candidate is selected as two oppositely charged muons with an invariant mass within 150 MeV of the nominal $J/\psi$ mass.
$K_S$ or $\phi$ candidates are reconstructed requiring two oppositely charged tracks which originate from a common vertex with an invariant mass within 10 MeV of the world average $\phi$ mass or within 20 MeV of the world average $K_S$ mass. The $B$ candidates are then selected as a combination of a $\phi$ or a $K_S$ candidate and the $J/\psi$ candidate.
The analysis of the $B^{+}$ decay is done with the data sample which corresponds to an integrated luminosity of $5.8~\mathrm{pb}^{-1}$, while the analysis of $B^{0}$ and $B_{s}$ decay channels correspond to $40~\mathrm{pb}^{-1}$.
The two dimensional unbinned maximum likelihood fits to the invariant masses and the proper decay lengths are performed to extract the exact number of signal and background events. The backgrounds are estimated from the data. The main background contribution comes from prompt- and non-prompt $J/\psi$ decays.
The results of the cross section measurements are presented in Fig.~\ref{1} with comparison to the MC@NLO \cite{Frixione_1,Frixione_2} predictions.

% \begin{figure}[h]
%\includegraphics[width=0.5\textwidth]{fig1.pdf}
%\caption{\label{1}  Summary of B meson cross section measurements. The inner error bars of the data points correspond to the statistical uncertainty, the outer error bars correspond to the quadratic sum of statistical and systematic uncertainties.
%The outermost brackets correspond to the total error, including a luminosity uncertainty. Theory predictions at NLO areo btained using MC@NLO MC generator . }
%\end{figure}


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\begin{figure}[htb]
\begin{center}
\epsfig{file=fig1,height=1.9in}
\caption{Summary of $B$ meson cross section measurements. The inner error bars of the data points correspond to the statistical uncertainty, the outer error bars correspond to the quadratic sum of statistical and systematic uncertainties.
The outermost brackets correspond to the total error, including a luminosity uncertainty. }
\label{1}
\end{center}
\end{figure}
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\section{Inclusive B production cross section with muons}
This analysis \cite{open_b}  is based on the leptonic decays of $B$-hadrons. The data sample used for this analysis corresponds to an integrated luminosity of $85~\mathrm{nb}^{-1}$. The offline selection cuts require a standalone muon with $p_{T}>3~\mathrm{GeV}/c$, a reconstructed primary vertex with more than three tracks, and at least one muon candidate with $p_{T}>6~\mathrm{GeV}/c$ and pseudorapidity $|\eta|<2.1$. Jets are reconstructed using the anti-$k_{T}$ jet algorithm \cite{anti-kt}. To extract the fraction of signal events from all the events passing the selection cuts a fit to the observed $p^{rel}_{T}$ was performed, where  $p^{rel}_{T}=|\vec{p_{\mu}} \times \vec{p_{j}|}/\vec{|p_{j}|}$ and $p_{j}$ is the momentum of the jet and $p_{\mu}$ is the momentum of the muon.
The result of a maximum likelihood fit and the estimation from the simulation templates are shown on Fig.~\ref{2} (right). The result for the cross-section in the given kinematic region is:

\begin{equation}
\sigma(pp \rightarrow b+X \rightarrow \mu + X^{'}) = 1.32 \pm 0.01(\mathrm{stat}) \pm 0.3(\mathrm{syst}) \pm 0.15(\mathrm{lumi}) {\mu}\mathrm{b}.
\end{equation}

The PYTHIA \cite{pythia} MC generator gives a prediction $\sigma_{PYTHIA} = 1.8 ~{\mu}$b, while  the MC@NLO MC generator gives a
$\sigma_{MC@NLO}= 0.84^{+0.36}_{-0.19} (\mathrm{scale}) \pm 0.08(\mathrm{m_{b}}) \pm 0.04(\mathrm{pdf}) ~\mu$b.
The differential cross-section as function of the muon transverse momentum and the comparison with the prediction is shown in
the Fig.\ref{2} (left). The measurement demonstrates reasonable agreement with MC predictions.

%\begin{figure}[h]
%\includegraphics[width=0.7\textwidth]{fig3_combined.pdf}
%\caption{\label{2}  Right: Distribution of the muon $p^{rel}_{t}$ for b (red) and c+light �avor (blue) templates. The black
%              line shows the result of the likelihood ?t, the markers show the data points.  Left:The markers represent data points, the yellow %band indicates  the quadratic sum of statistical and systematic
%uncertainties, not including the luminosity uncertainty. The theoretical prediction from MC@NLO and PYTHIA are
%shown with the blue and red lines respectively.}
%\end{figure}

\begin{figure}[htb]
\begin{center}
\epsfig{file=fig2,height=2.1in}
\caption{ Left: The differential cross-section. The theoretical prediction from MC@NLO and PYTHIA are shown with the lines. The markers represent data points, the  band indicates  the quadratic sum of statistical and systematic uncertainties.
Right: Distribution of the muon $p^{rel}_{T}$ for b  and c+light flavor templates. The black line shows the result of the likelihood fit, the markers show the data points. }
\label{2}
\end{center}
\end{figure}
\section{Inclusive b-jet production cross-section}
This measurement \cite{b-jet}  is performed using approximately $60~\mathrm{nb}^{-1}$ of collected data. The b-jet production is measured in the kinematic range $18$--$300~\mathrm{GeV}/c$ and for rapidities $|y|<2.0$. The jets are reconstructed using the anti-$k_{T}$ algorithm.
The b-jets are tagged using a secondary vertex high-purity tagger (SSVHP \cite{btag}). The secondary
vertex is fit with at least three charged particle tracks. A selection on the reconstructed 3D decay length significance is applied, corresponding to about 0.1$\%$ efficiency to tag light flavor jets and 60$\%$ efficiency to tag b-jets at $p_{T}=100~\mathrm{GeV}/c$.\\
    The differential cross-section of the b-jet production as a function of the b-jet $p_{T}$ compared to the MC@NLO expectations are shown in the Fig.~\ref{3}.  The measurement shows a reasonable agreement with MC@NLO but significant shape differences in $p_{T}$
    and $|y|$.
% \begin{figure}[h]
%\includegraphics[width=0.4\textwidth]{fig4.pdf}
%\caption{\label{3}Differential b-jet cross-section. the yellow band indicates  the quadratic sum of statistical and systematic
%uncertainties, not including the luminosity uncertainty.The theoretical prediction from MC@NLO is
%shown with the red lines.}
%\end{figure}

\begin{figure}[htb]
\begin{center}
\epsfig{file=fig3,height=1.9in}
\caption{Differential b-jet cross-section. The  band indicates  the quadratic sum of statistical and systematic
uncertainties, not including the luminosity uncertainty. The theoretical prediction from MC@NLO is
shown with the lines.}
\label{3}
\end{center}
\end{figure}
\section{$B\bar{B}$ angular correlations}
 In this study \cite{bbbar}  $B\bar{B}$ production was measured as a function of the opening angle between between $B$ hadrons for different event scales.  To perform the analysis, which requires good angular resolution,  a method was introduced based on an iterative inclusive secondary vertex finder that exploits the excellent tracking capabilities of the CMS detector.   The data sample used corresponds to an integrated luminosity of $3.1 \pm 0.3~\mathrm{pb}^{-1}$. The analysis relies on the single-jet trigger in both the hardware-level (L1) and the high-level (HLT) software components of the CMS trigger system \cite{cms}. The visible kinematic range for the measurements is defined at the $B$ hadron level by the requirements  $|\eta(B)|<2.0$  and $p_{T}(B) >15~\mathrm{GeV}/c$ for both $B$ hadrons.  The leading jet used to define the minimum energy scale is required to be within $|\eta(jet)|<3.0$.
 The differential cross section of $B\bar{B}$ pair production is measured as a function of the angular separation variables ($\Delta{R}$ and $\Delta{\phi}$) between two reconstructed B-hadrons for three different energy scales. The measured cross-section as a function of
 $\Delta{R}$  is shown in the Fig.~\ref{4} (left).
It can be noted that  the cross sections at small $\Delta{R}$ values exceed the cross sections observed at large angular separations,where the two B hadrons are emitted in opposite directions.

% \begin{figure}[h]
%\includegraphics[width=0.7\textwidth]{fig5.pdf}
%\caption{\label{4}  Differential cross-section of $B\bar{B}$ pair production as a function of  $\Delta{R}$  (left) and $\Delta{\phi}$  (right). For the data points the inner error bars show statistical uncertainty while the outer ones show the systematic uncertainty.The PYTHIA simulation (shaded) is normalized  to the region $\Delta{R}$ or  $\Delta{\phi}$ as indicated by the shaded normalization regions. }
%\end{figure}

\begin{figure}[htb]
\begin{center}
\epsfig{file=fig4,height=1.9in}
\caption{ Left: Differential cross-section of $B\bar{B}$ pair production as a function of  $\Delta{R}$. The PYTHIA simulation (shaded) is normalized  to the region $\Delta{R}$ as indicated by the shaded normalization regions.  Righ: Ratio between $B\bar{B}$ production cross sections in $\Delta{R}<0.8$ and  $\Delta{R}>2.4$.  The predictions from PYTHIA and MadGraph \cite{madgraph} MC generators are also shown.
For the data points the inner error bars show statistical uncertainty while the outer ones show the systematic uncertainty}
\label{4}
\end{center}
\end{figure}



The measured distributions are compared to the theoretical predictions, based on perturbative QCD calculations.
The higher-order processes, such as gluon radiation which splits into $B\bar{B}$ pairs, are anticipated to have a smaller angular separation between the b quarks.  The measurement of the $B\bar{B}$ cross -section production ratio as a function of leading jet $p_{T}$ is shown in the Fig.\ref{4} (right) and it can be noted that the production ratio increases with the jet  $p_{T}$. At the large values of the jet $p_{T}$ more gluon splitting into $B\bar{B}$ pairs can be expected. This is described by theoretical calculations.

% \begin{figure}[h]
%\includegraphics[width=0.4\textwidth]{fig6.pdf}
%\caption{\label{5} Ratio between BB(bar) production cross sections in $\Delta{R}<0.8$ and  $\Delta{R}>2.4$. The data is averaged over the bins  and are plotted at the mean leading jet $p_{T}$ of the bins. The inner error bars show statistical uncertainty, the outer bars- systematic uncertainty. The predictions from PYTHIA and MadGraph \cite{madgraph} MC generators are also shown.}
%\end{figure}

%  \begin{figure}[htb]
%\begin{center}
%\epsfig{file=fig6,height=1.7in}
%\caption{Ratio between BB(bar) production cross sections in $\Delta{R}<0.8$ and  $\Delta{R}>2.4$. The data is averaged over the bins  and are plotted at the mean leading jet $p_{T}$ of the bins. The inner error bars show statistical uncertainty, the outer bars- systematic uncertainty. The predictions from PYTHIA and MadGraph \cite{madgraph} MC generators are also shown.}
%\label{5}
%\end{center}
%\end{figure}



\begin{thebibliography}{13}
%\begin {footnotesize}
\bibitem{cms}
CMS Collaboartion,
 {\it JINST} 0803, S08004 (2008).

\bibitem{b_plus}
 CMS Collaboration,
 {\it Phys.Rev.Lett.} 106, 112001 (2011).

\bibitem{b_zero}
 CMS Collaboration,
 {\it Phys.Rev.Lett.} 106, 252001 (2011).

\bibitem{b_s}
CMS Collaboartion,
 {\it CMS PAS} BPH-10-013 (2010).

\bibitem{open_b}
 CMS Collaboartion,
 {\it JHEP} 1130, 090 (2011).

 \bibitem{Frixione_1}
 S. ~Frixione, and B. ~R.~ Webber,
 {\it JHEP}  06, 029 (2002)

  \bibitem{Frixione_2}
 S. ~Frixione, P.~Nason and B. ~R.~ Webber,
 {\it JHEP}   08, 007 (2003).

 \bibitem{pythia}
 T. ~Sj\"{o}strand, P. ~Ed\'{e}n, C. ~Friberg, L. ~L\"{o}nnblad, G. ~Miu, S. ~Mrenna, and E. ~Norrbin,
 {\it Computer Phys. Commun.}  135, 238 (2001).

  \bibitem{b-jet}
CMS Collaboartion,
{\it CMS PAS} BPH-10-009 (2010).

\bibitem{anti-kt}
G.~S.~Matteo Cacciari, Gavin P.~Salam,
{\it JHEP} 0804, 063 (2008).

\bibitem{btag}
CMS Collaboration,
 {\it CMS PAS} BTV-10-001 (2010).

 \bibitem{bbbar}
CMS Collaboration,
 {\it JHEP} 1103, 136 (2010).

  \bibitem{madgraph}
J. ~Alwall {\it et al.},
 {\it JHEP}  09, 028 (2007).


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\end{document}
