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\Title{Search for New Physics with rare decays of\\ $B^0$, $B^+$  and $B^0_s$ mesons at LHCb}

\bigskip\bigskip


\begin{raggedright}  

{\it Johannes Albrecht\index{Albrecht, J.}\\
CERN, Geneva, Switzerland\\
on behalf of the LHCb collaboration}
\bigskip\bigskip
\end{raggedright}

\section{Introduction}

The rare processes $b \rightarrow s \ell^+ \ell^-$ and $b\rightarrow
s \gamma$ are flavour changing neutral currents that are forbidden at
tree level in the Standard Model (SM). They can proceed via
higher order electroweak ($Z^0, \gamma$) penguin or box diagrams. In
extensions to the SM, new virtual particles can enter at loop level,
leading to significant deviations form the SM predictions.
These deviations may be the enhancement (or suppression) of branching
fractions, where a good example, the search for the very
rare decays $B^0_{(s)}\rightarrow \mu^+ \mu^-$ is presented here\footnote{In
   this proceedings, the inclusion of charge conjugate states are
   implicit.}.
They might also be observable in the modification of angular
distributions, e.g.~in $B^0 \rightarrow K^*\mu^+ \mu^-$, or in the
modification of $CP$ or Isospin asymmetries such as those observable in
the radiative decays $B^0\rightarrow K^* \gamma$ and $B_s^0\rightarrow
\phi \gamma$. The last presented probe for extensions to the SM is the
search for Majorana neutrinos in same sign decays of $B^+ \rightarrow
h^- \mu^+ \mu^+$, where $h^-$ represents a $K^-$ or $\pi^-$. 
These rare decay processes provide a complementary approach to direct
searches at the general purpose detectors and can provide sensitivity
to new particles with masses up to higher scales than directly accessible.

\vskip 0.2cm

At the time of the conference Physics at LHC 2011 (PLHC), June 2011, a
published LHCb measurement 
of the search for the very rare decays $B^0_{(s)}\rightarrow \mu^+
\mu^-$ using 37\,pb$^{-1}$ existed~\cite{bsmm2010}. 
The angular analysis of $B^0\rightarrow K^* \mu^+\mu^-$ as well as the
radiative decay measurements were in preparation for the EPS
conference in July 2011. 
In the meantime, these three measurements have been performed using
about 300\,pb$^{-1}$ of data. Hence, this proceedings describes the existing
measurements~\cite{bsmm2011,kstmm,rad} rather than an outdated status
at the time of PLHC. The Majorana neutrino search was presented for
the first time at PLHC.


\subsection{The LHCb Detector and data taking in 2010 and 2011}

The LHCb detector is described in detail elsewhere~\cite{lhcb}. The 
published searches for $B^0_{(s)}\rightarrow \mu^+ \mu^-$ decays and for 
Majorana neutrinos were performed on a dataset corresponding to
an integrated luminosity of about 37\,pb$^{-1}$, collected in 2010 
at $\sqrt{s}$~=~7\,TeV. 
%
The main results described in sections~\ref{sec:bsmm}, \ref{sec:kstmm}
and \ref{sec:rad} are based on a dataset corresponding to an
integrated luminosity of about 300\,pb$^{-1}$, collected in the first
half of 2011.
% 
This luminosity was delivered by the LHC at instantaneous
luminosities of $3-3.5 \times 10^{32}\,$cm$^{-2}$s$^{-1}$, 50\% above the
design luminosity of LHCb. At this instantaneous luminosity, LHCb
collected more than 1fb$^{-1}$ of integrated luminosity in 2011. 


\section{Search for the very rare decays $B^0_{(s)}\rightarrow \mu^+ \mu^-$}
\label{sec:bsmm}

The SM prediction for the Branching Ratios ($BR$) of the decays $B^0_{(s)}
\to \mu^+ \mu^-$ have been computed~\cite{Buras2010} to be $BR(B^0_s
\to \mu^+ \mu^-) = (3.2 \pm 0.2) \times 10^{-9}$ and  $BR(B^0 \to
\mu^+ \mu^-) = (0.10 \pm 0.01) \times 10^{-9}$.
However, many extensions of the SM predict large enhancements to
these BR. Before the LHC measurements of these BR, the most
restrictive limits about a factor 13 above the SM prediction, measured
by the CDF and D0 experiments.
The measurements presented here use about 300\,pb$^{-1}$ of
data. Assuming the SM branching ratio, about 3.4 (0.32)
$B^0_{s}\rightarrow \mu^+ \mu^-$ ($B^0\rightarrow \mu^+
\mu^-$) events are expected to be reconstructed and selected in the
analyzed sample.
 
\vskip 0.2cm

The first step of the analysis is a simple selection, which removes
the dominant part of the background and keeps about 60\% of the
reconstructed signal events. 
Then, each event is given a probability to be signal or background in a
two-dimensional probability space defined by the dimuon invariant mass
and a multivariate discriminant likelihood. This likelihood combines 
kinematic and topological variables of the $B^0_{(s)}$ decay using a
Boosted Decision Tree (BDT). The BDT is defined and trained on
simulated events for both signal and background. The signal BDT shape
is then calibrated using decays of the type $B^0_{(s)} \rightarrow h^+
h^{'-}$, where $h^\pm$ represents a $K^\pm$ or $\pi^\pm$. These
decays have an identical topology as the signal. The invariant mass
resolution is calibrated with an interpolation of $J/\psi$, $\psi(2S)$
and $\Upsilon(1S)$, $\Upsilon(2S)$ and $\Upsilon(3S)$ decays to two muons. The background shapes
are calibrated simultaneously in the mass and the BDT using the
invariant mass sidebands. This procedure ensures that even though the BDT
is defined using simulated events, the result will not be biased by
discrepancies between data and simulation. 

The number of expected signal events is evaluated by normalizing with
channels of known branching ratio. Three independent channels are
used: $B^+\rightarrow J/\psi K^+$, $B^0_s\rightarrow J/\psi \phi$ and
$B^0 \rightarrow  K^+ \pi^-$. The first two decays have similar
trigger and muon identification efficiency to the signal but a
different number of particles in the final state, while the third
channel has the same two-body topology but is selected with a
hadronic trigger. The event selection for these
channels is specifically designed to be as close as possible to the
signal selection. The ratios of reconstruction and selection
efficiencies are estimated from the simulation, while the ratios of
trigger efficiencies on selected events are determined from data. 
The compatibility of the observed distribution of events with a given
branching fraction hypothesis is computed using the CLs method~\cite{cls}. 

The measured upper limit for the branching ratio is
BR($B^0_{s}\rightarrow \mu^+ \mu^-$)$< 1.3  \ (1.6) \times 10^{-8}$ at
90\,\% (95\,\%) confidence level (CL),  
while in the case of the $B^0$, the measured upper 
limit is BR($B^0\rightarrow \mu^+ \mu^-$)$< 4.2 \ (5.1) \times
10^{-9}$ at 90\,\% (95\,\%) CL. 
A combination with the LHCb observations on the 2010 dataset results 
in BR($B^0_{s}\rightarrow \mu^+ \mu^-$)$<1.2 \ (1.5) \times 10^{-8}$
at 90\,\% (95\,\%) CL. The 95\% CL limit on BR($B^0_{s}\rightarrow
\mu^+ \mu^-$) is less than a factor 5 from the SM prediction.

\section{Angular analysis of the decay $B^0\rightarrow K^* \mu^+ \mu^-$}
\label{sec:kstmm}
The rare decay $B^0\rightarrow K^* \mu^+ \mu^-$ is a $b \rightarrow s$
flavour changing neutral current decay which is in the SM mediated by
electroweak box and penguin diagrams. It can be a highly sensitive
probe for new right handed currents and new scalar and pseudoscalar
couplings. These NP contributions can be probed by fits to the angular
distributions of the $B^0$ daughter particles. The most prominent
observable is the forward-backward asymmetry of the muon system
($A_{FB}$). $A_{FB}$ varies with the invariant mass-squared of the
dimuon pair ($q^2$) and in the SM changes sign at a well defined
point, where the leading hadronic uncertainties cancel. In many NP
models the shape of $A_{FB}$ as a function of $q^2$ can be dramatically
altered. 

The present analysis uses 309\,pb$^{-1}$ of data collected by the LHCb
experiment during 2011 to measure $A_{FB}$, the fraction of
longitudinal polarisation 
of the $K^{∗0}$, $F_L$, and the differential branching fraction,
$dB/dq^2$, as a function of the dimuon invariant mass squared, $q^2$.    
There is good agreement between recent Standard Model predictions and
the LHCb measurement of $A_{FB}$, $F_L$ and $dB/dq^2$ in the six $q^2$
bins. In a $1 < q^2 < 6$\,GeV$^2$ bin, LHCb measures $A_{FB} = −0.10
\pm 0.14 \pm 0.05$, to be compared with theoretical predictions of
$A_{FB} = −0.04 \pm0.03$. The experimental uncertainties are presently
statistically dominated, and will improve with a larger data set. Such
a data set would also enable LHCb to explore a wide range of new
observables.

\section{Radiative decays in LHCb}
\label{sec:rad}

The precise measurement of the branching ratios, asymmetries or
angular distributions of radiative decays are promising modes to test
for New Physics. LHCb has measured the ratio of branching ratios of
the radiative decays $B^0\rightarrow K^* \gamma$ and $B_s^0\rightarrow
\phi \gamma$ using 340\,pb$^{-1}$ of data recorded in 2011~\cite{rad}.
The obtained value for the ratio is
$1.52\pm0.14(stat)\pm0.10(syst)\pm0.12(fs/fd)$. Using the HFAG value
for BR($B^0\rightarrow K^* \gamma$), BR($B_s^0\rightarrow \phi \gamma$)
has been found to be $(2.8 \pm 0.5) \times 10^{-5}$. 

\section{Search for Majorana Neutrinos}

LHCb has performed a search for heavy Majorana neutrinos in the same
sign decays $B^+ \rightarrow K^- \mu^+ \mu^+$ and $B^+ \rightarrow
\pi^- \mu^+ \mu^+$~\cite{mn}. These decays are forbidden in the SM but allowed
in models with a Majorana neutrino. No signal is observed in either
channel and limits of BR($B^+ \rightarrow K^- \mu^+ \mu^+$) $<
5.4 \times 10^{-8}$ and BR($B^+ \rightarrow \pi^-
\mu^+ \mu^+$) $< 5.8 \times 10^{-8}$ are set at the 95\% confidence
level. These improve the previous best limits by factors of 40 and 30
respectively. 

\section{Conclusion}

The worlds tightest limit on the branching fraction of the decay
$B^0_{s}\rightarrow \mu^+ \mu^-$ is presented, using about
300\,pb$^{-1}$ of data collected by the LHCb experiment. This limit is
less than a factor 5 above the SM prediction. 
The first LHCb measurement of the forward-backward asymmetry
of the muons from $B^0\rightarrow K^* \mu^+ \mu^-$ decays is the
most precise measurement of this quantity, in agreement with the SM
prediction. A first measurement of the ratio of the branching fraction
of $B^0\rightarrow K^* \gamma$ and $B_s^0\rightarrow \phi \gamma$ is
performed, opening the field to measure $CP$ asymmetries in
radiative decays in LHCb. 







\begin{thebibliography}{99}

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\bibitem{bsmm2010} The LHCb Collaboration, Phys. Lett. B 699 (2011) 330-340, arXiv:1103.2465
\bibitem{bsmm2011} The LHCb Collaboration, LHCb-CONF-2011-037 (2011)
\bibitem{kstmm} The LHCb Collaboration, LHCb-CONF-2011-038 (2011)
\bibitem{rad} The LHCb Collaboration, LHCb-CONF-2011-055 (2011)
\bibitem{lhcb} The LHCb Collaboration, {\em JINST} {\bf 3} (2008) S08005
\bibitem{Buras2010} A.J.~Buras, arXiv:1012.1447;
  E.~Gamiz {\it et al}, Phys. Rev. D \textbf{80} (2009) 014503. 
\bibitem{cls} A.L. Read, J. Phys. G 28 (2002) 2693; T. Junk, N.I.M. A 434 (1999) 435.
\bibitem{mn} The LHCb Collaboration, CERN-PH-EP-2011-156 (2011), arXiv:1110.0730
\end{thebibliography}

 
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