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\Title{Heavy-Flavor Results at CMS}

\bigskip\bigskip

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

\begin{raggedright}  

{\it Roberto Covarelli for the CMS collaboration\index{Covarelli, R.}\\
Department of Physics and Astronomy\\
University of Rochester\\
I-14327 Rochester, UNITED STATES}
\bigskip\bigskip
\end{raggedright}

The CMS experiment \cite{CMS_final} at the LHC is a multi-purpose
detector.
Due to its versatility, especially of the trigger
system, and to the excellent muon transverse-momentum ($p_T$) resolution, 
several heavy-flavor physics results have been
obtained, using proton-proton data recorded in 2010--11 at a
center-of-mass energy of 7 TeV.

\section{Quarkonia}

From the theoretical point of view, the prompt charmonium cross section
is a clean probe of Non Relativistic QCD approaches.
Recently, $J/\psi$ and $\psi \mathrm{(2S)}$ cross-sections have been
computed at Next-to-Leading Order (NLO) in these models, using the
long-distance matrix elements as determined in Tevatron data.
In the same model, predictions for the ratio of $\chi_c$ over $J/\psi$
production rate, and the analogous for $\chi_{c2}$ over $\chi_{c1}$, 
have been obtained.
At relatively high $p_T$, a significant fraction of the $J/\psi$ and
$\psi \mathrm{(2S)}$ comes from  
$b$-hadron decays and, if it is separated experimentally from the
prompt component, provides a direct test of the 
Fixed-Order Next-to-Leading-Log (FONLL) prediction for 
the $b \rightarrow \psi$
production cross section. 

The differential cross sections can be expressed as: 
\begin{equation} 
\frac{d^2\sigma}{dp_{T}dy}(Q{\bar Q}) \cdot \mbox{B}(Q{\bar Q}\rightarrow 
\mu^{+}\mu^{+}) = \frac{N_{\mbox{rec}}(Q{\bar Q})}{\int{\cal L}dt\cdot\langle A 
\cdot \varepsilon \rangle \Delta p_T \Delta y}
\end{equation} 
where $N_{\mbox{rec}}(Q{\bar Q})$ is the $Q{\bar Q}$ yield in a given 
$p_{T}$-$y$ bin,  
$\int{\cal L}dt$ is the integrated luminosity, $\langle A 
\cdot \varepsilon \rangle$ is the average value in the bin of the geometrical 
acceptance, determined using Monte Carlo (MC) simulations, times the reconstruction 
efficiency of the di-muon, and $\Delta p_{T} \Delta y$ is the size
of the bin. Multiplication by $1-f_B$
($f_B$) yields the prompt (non-prompt) component of the 
total inclusive cross section.
Muon trigger and reconstruction efficiencies are determined in CMS
from the data
using the ``tag-and-probe'' method~\cite{bib-muonreco}, which uses
independent $J/\psi$ samples
to provide a sample of muons unbiased with respect to the
selection under investigation.

The measurement of the $J/\psi$ and $\psi \mathrm{(2S)}$ differential cross 
sections~\cite{psip} uses a data sample corresponding to an integrated 
luminosity of
37~pb$^{-1}$. Using a fit to the invariant mass and decay length
distributions, production cross sections
have been measured separately for prompt and non-prompt charmonium
states, as a function of the transverse
momentum in several rapidity ranges (Fig.~\ref{fig:charm}, left).
The ratio of the differential production cross sections of
the two states, where many systematic uncertainties (e.g. from luminosity and 
muon efficiency)
cancel, is also determined. The branching
fraction of the inclusive $B \rightarrow \psi(\mathrm{2S}) X$
decay is extracted from the ratio of the non-prompt cross
sections to be
$(3.08 \pm 0.12\,(\mathrm{stat.+syst.}) \pm 0.13\,(\mathrm{theor.}) \pm 0.42 \,(\mathcal{B}_\mathrm{PDG})) \times 10^{-3}
$.

The $p_T$-differential measurement of the relative prompt production rate 
of $\chi_{c2}$ and 
$\chi_{c1}$  is based on a sample of 4.6 fb$^{-1}$ of data~\cite{chic}. 
The two states are reconstructed in their radiative decays 
$ \chi_c \rightarrow J/\psi + \gamma$, with the photon converting 
into an $e^+e^-$ pair in the tracker barrel region. A very good signal purity
is obtained with this method, as well as a resolution of about 6 MeV/$c^2$,
that allows a clear separation of the two states. Results for the 
cross-section ratio are shown in Fig.~\ref{fig:charm}, right.

\begin{figure}[htpb!]
\centering 
{ 
\includegraphics[width=6.9cm]{XS_all_p_sg_psi2s_teor_paper.pdf} 
\includegraphics[width=6.5cm]{chic_ratio.pdf}
} 
\caption{Left: Measured differential cross section for prompt $\psi \mathrm{(2S)}$ production 
as a function of $p_T$ for different rapidity bins.
The blue histograms indicate the theoretical predictions from NRQCD calculations. Right: Measured $\chi_{c2}$ over $\chi_{c1}$ cross section ratio as a function of $J/\psi$ $p_T$.}
\label{fig:charm}
\end{figure}

\section{$b$-baryons}

Precise measurements of the $\Lambda_b$ and ${\bar \Lambda}_b$ cross-sections,
as well as searches for new $b$-baryon states have been performed at CMS, 
using data samples of 1.9-5.3 fb$^{-1}$.

$\Lambda_b$ baryons are reconstructed through their 
decays to $J/\psi \Lambda \rightarrow \mu^+ \mu^- p \pi^-$~\cite{lambdab}. 
A good resolution
is obtained with a mass-constrained vertex fit to the 4-particle candidates,
while the request of a large significance of $J/\psi$ and $\Lambda$ vertex 
displacement rejects background from prompt tracks.
Efficiencies are determined from ``tag-and-probe'' and MC simulation. 
A slight excess of the total measured cross section with respect to MC@NLO 
predictions is found, consistent with CMS measurements of other $b$-hadron
species. However, unlike other $b$-hadrons, the $p_T$ spectrum falls more
rapidly than NLO QCD predictions, and this is attributed to a difference in 
the hadronization mechanism. The particle over anti-particle cross-section 
ratio is found to be compatible with 1 at all $p_T$ values.

Among the neutral ``cascade'' $b$-baryons ($\Xi_b^0$), only the $J^P = \frac{1}{2}^+$ state had been previously observed; however color hyperfine splitting
predicts the mass of the $J^P = \frac{3}{2}^+$ state to be large enough
for a $\Xi_b^{0*} \rightarrow \Xi_b^- \pi^+$ decay. Therefore the state is searched
in this channel~\cite{ernestion}, profiting of the presence of three weakly decaying particles
in the chain ($\Xi_b^-$, $\Xi^-$, $\Lambda^0$) which allows reconstruction of
three detached vertices to reject background from prompt tracks. 
The result is an observation with a significance corresponding to 6.9
standard deviations. The measured mass of the new resonance is
$5945.0 \pm 0.7\, \mathrm{(stat.)} \pm 0.3\, \mathrm{(syst.)} \pm 2.7\, \mathrm{(PDG)}$ MeV/$c^2$, in agreement with theoretical predictions (Fig.~\ref{fig:xib}).

\begin{figure}[htpb!]
\centering 
{ 
\includegraphics[width=6.9cm]{xib0_Zoom.pdf} 
} 
\caption{$Q =M(J/\psi \Xi^- \pi^+) - M(J/\psi \Xi^-) - M(\pi^+)$ distribution in the $0 < Q < 50$  MeV/$c^2$ range, along with the result of the signal-plus-background fit (blue solid curve);
    the background term is also shown (red dashed curve).}
\label{fig:xib}
\end{figure}

\section{Rare decays}

In CMS searches for $B^0_s$, $B^0$ and $D^0 \rightarrow \mu^+ \mu^-$ decays
have been performed. These decays are predicted to be rare in the Standard 
Model (SM) and, especially in the $B$ sector, a significant enhancement over 
the SM branching ratios ($\mathcal{B}_{\mathrm{SM}} \sim 10^{-10}-10^{-9}$) 
is predicted
in most supersymmetric theories. An observation of a non-SM value of the
branching fraction would therefore represent an indirect evidence for new
physics.

For the $B^0_s$ and $B^0$ analysis~\cite{bsubs}, the dataset corresponds to 
an integrated luminosity of 5.0 fb$^{-1}$.
The analysis is performed separately in two channels, at low 
and high muon pseudo-rapidity, and then combined for the final result. 
A ``normalization'' sample of events with $B^+ \rightarrow J/\psi K^+$ decays 
is used 
to remove uncertainties related to the $b{\bar b}$ production cross section 
and the integrated luminosity and reduce uncertainties on efficiencies, which 
are determined from MC. Selection is based on several types of variables,
including high $p_T$, vertex displacement and dimuon isolation, and has 
been optimized to mitigate the effects of high pileup. A ``blind'' analysis approach is applied.  

An event-counting experiment is performed in dimuon mass regions around the 
$B^0_s$ and $B^0$ masses. 
MC simulations are used to estimate backgrounds due to other rare 
$B$ decays and 
combinatorial backgrounds are evaluated from the data in dimuon invariant mass 
sidebands. The observed number of events is consistent with background plus 
SM signals.
The resulting upper limits on the branching fractions are  
${\cal B}(B^0_s \rightarrow \mu^+ \mu^-) < 7.7\times10^{-9}$ and ${\cal B}(B^0 \rightarrow \mu^+ \mu^-) < 1.8\times10^{-9}$
at 95\% CL.

Similar techniques are exploited in the search for $D^0 \rightarrow \mu^+ \mu^-$~\cite{dzero}, but the data sample used corresponds to 90 pb$^{-1}$ only, due to 
the trigger limitations in selecting the normalization sample $D^0 \rightarrow K^- \mu^+ \nu_{\mu}$. The resulting upper limit is  
${\cal B}(D^0 \rightarrow \mu^+ \mu^-) < 5.4\times10^{-7}$
at 95\% CL.

\begin{thebibliography}{99}

%%
%%  bibliographic items can be constructed using the LaTeX format in SPIRES:
%%    see    http://www.slac.stanford.edu/spires/hep/latex.html
%%  SPIRES will also supply the CITATION line information; please include it.
%%

\bibitem{CMS_final}
The CMS Collaboration, S.~Chatrchyan {\it et al.},
% \emph{The CMS Experiment at the CERN LHC},
JINST {\bf 3}, S08004 (2008).

\bibitem{bib-muonreco}
The CMS Collaboration,
% \emph{Performance of muon identification in pp collisions at $\sqrt s$=7 TeV},
CMS-PAS MUO-10-004 (2011).

\bibitem{psip}
The CMS Collaboration, S.~Chatrchyan {\it et al.},
% \emph{$J/\psi$ and $\psi(\mathrm{2S})$ production in pp collisions at $\sqrt{s}$ = 7 TeV},
JHEP {\bf 1202}, 011 (2012).

\bibitem{chic}
The CMS Collaboration,
% \emph{Measurement of $\sigma(\chi_{c2}) / \sigma(\chi_{c1})$ at $\sqrt{s}$ = 7 TeV},
CMS-PAS BPH-11-010 (2012).

\bibitem{lambdab}
The CMS Collaboration, S.~Chatrchyan {\it et al.},
% \emph{Measurement of the $\Lambda_b$ cross section and the ${\bar \Lambda}_b$ to $\Lambda_b$ ratio with $J/\psi \Lambda$ decays in pp collisions at $\sqrt{s}$ = 7 TeV},
Phys. Lett. {\bf B714}, 136 (2012).

\bibitem{ernestion}
The CMS Collaboration, S.~Chatrchyan {\it et al.},
% \emph{Observation of a new $\Xi_b$ baryon},
Phys. Rev. Lett. 108, 252002 (2012).

\bibitem{bsubs}
The CMS Collaboration, S.~Chatrchyan {\it et al.},
% \emph{Search for $B^0_s \rightarrow \mu^+ \mu^-$ and $B^0 \rightarrow \mu^+ \mu^-$ decays},
JHEP {\bf 1204}, 033 (2012).

\bibitem{dzero}
The CMS Collaboration,
% \emph{Search for the FCNC decay $D^0 \rightarrow \mu^+ \mu^-$ in CMS at 7 TeV },
CMS-PAS BPH-11-017 (2012).


\end{thebibliography}


 
\end{document}

