chep06/0040755006534600000170000000000010412237411011707 5ustar cristinauserschep06/chep06.tex0100755006534600000170000005536510412211010013517 0ustar cristinausers\documentclass{CHEP2006}
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\begin{document}
\title{RECONSTRUCTION AND CALIBRATION STRATEGIES FOR THE LHCb RICH DETECTOR}
%\thanks{Revised by Leena Chandran-Wadia, January 12, 2006}}
\author{
%R.~Forty, M.~Patel, CERN, Geneva, Switzerland\\
C.~Lazzeroni\thanks{presenter: cristina@hep.phy.cam.ac.uk}, C.~Jones,
University of Cambridge, Cavendish Laboratory, Cambridge CB3OHE, UK\\
R.~Muresan\thanks{presenter: r.muresan1@physics.ox.ac.uk}, G.~Wilkinson,
University of Oxford, Denys Wilkinson Building, Oxford, OX13RH, UK\\
R.~Forty, M.~Patel, CERN, Geneva, Switzerland
}
\maketitle
%\vspace*{0.5cm}
\begin{abstract}
The LHCb experiment will make high precision studies
of CP violation and
rare phenomena in B hadron decays. Particle
identification in the
momentum range from 2-100~GeV/c is essential for
this physics
programme and will be provided by two Ring Imaging
Cherenkov (RICH)
detectors.
This paper describes the
performance of the
different RICH reconstruction algorithms, evaluated using
Monte Carlo simulations,
and reports on the
strategy for RICH calibration in LHCb.
\end{abstract}
\section{Introduction}
The LHCb physics programme will focus on high precision studies of
CP violation and rare phenomena in B hadron decays.
The ability to distinguish between pions and kaons over a large
range of momenta (2 - 100~GeV/c) is essential.
% for this physics program.
Particle identification (PID) will be provided by
two Ring Imaging Cherenkov (RICH) detectors.
Three types of radiators are used
in the RICH detectors: silica aerogel and $C_4 F_{10}$
to identify particles in the range\\
2-50~GeV/c (RICH1); $CF_4$ for particles up to
$\sim$~100~GeV/c (RICH2)~\cite{RICH1, RICH2}.
These give rise to rings of different radii and varying number
of hits per ring.
The rings are detected by reflecting and focusing the cones
of Cherenkov light onto
arrays of hybrid photon detectors (HPDs).
% and are reconstructed/predicted
%starting from the hit distribution.
The experiment will use several levels of
trigger to reduce
the 10~MHz rate of visible interactions to the 2~kHz
that will be stored.
The final level of the trigger,
which runs in a processor farm, has access to
the information from all
sub-detectors.
The standard offline RICH reconstruction
is efficient~\cite{LHCb2}
%(84\% efficiency for kaons
%and 5\% efficiency for pions if identified as heavy particles)
but is reliant on the availability of good
tracking information.
%would benefit from the removal
%of background from
%rings without
%associated tracks.
In addition,
the algorithm is not fast enough to be used
in the trigger.
%of the order of 100 ms per event which is to be
%compared with the time
%of order 10 ms available to run the entire final level
%trigger.
Alternative RICH reconstruction algorithms, that
complement the standard procedure, are being investigated.
Firstly, algorithms
of greater robustness,
less reliant on the tracking information, are being
developed, using
techniques such as Hough transforms and Metropolis-Hastings Markov chains.
Secondly, simplified algorithms with shorter execution times,
%of order 3 ms,
suitable for use in the trigger are being
evaluated. Finally,
optimal performance requires a calibration procedure
that will enable
the performance of the pattern recognition to be
measured from the
experimental data.
\section{Likelihood method}
An LHCb ring reconstruction algorithm must be able to
find distorted, incomplete rings with variable radius and a
variable number of hits per ring. It must be robust in
the presence of background, capable of processing a large amount of
information ($\sim$ 500 hits in RICH1, $\sim$300 in RICH2) and fast
enough not to exceed the time
limits for the event reconstruction.
In particular, the ring reconstruction is very difficult in RICH1 where
two different radiators are used, giving rise to overlapping rings with
different characteristics. An example event
%that illustrates the
%complexity of the environment
can be seen in Figure~\ref{RICH1}.
\begin{figure}[hb]
\centering
\includegraphics*[width=60mm]{RICH1_24mar.eps}
\caption{Event display with the photodetector planes of RICH1 drawn
side by side. The Cherenkov rings predicted by the likelihood
method are superimposed. A number of hits have not been assigned to a ring.
These come from particles whose tracks have not been reconstructed.}
\label{RICH1}
\end{figure}
The standard offline RICH
reconstruction calculates for each track and
photodetector hit combination a Cherenkov angle,
based on the hit coordinates, the assumed track direction and emission
point and the knowledge of the RICH optics. This calculation
involves solving a quartic equation.
%involves solving
%a quartic equation that describes the RICH optics for
%each hit in the
%RICH detector.
%It then compares the expectation
%on the Cherenkov angle based on
%track information to the observed data~\cite{LHCb2} in order
%to predict the location and the radius of the rings.
%A global likelihood
%minimization is then used, combining
%the information from both RICH detectors along with
%tracking
%information, to determine the best particle
%hypotheses.
%The baseline offline method, likelihood method, uses
%The algorithm uses
%information on the track parameters and knowledge of the RICH
%optics in order to
%predict where the Cherenkov photons will strike the detector plane.
%This is done for each particle hypothesis: pion, kaon, muon etc.
%For each combination of particle hypothesis,
%the prediction is compared with the observed distribution of the photons and a likelihood is
%calculated~\cite{LHCb2}. A global likelihood minimization
%determines the best particle hypotheses.
%One selects the maximum likelihood solution.
As the correct association of hits and tracks
is not apriori known, a pattern recognition is required.
The reconstructed Cherenkov angles are compared with those
expected for a given track particle hypothesis
($\rm e$, $\rm \mu$, $\rm \pi$, $\rm K$ or $\rm p$). A likelihood function
is calculated for the entire RICH system, and this likelihood
maximised to find the best particle hypotheses.
This method has been shown to be
efficient (84\% efficiency for kaons
and 5\% efficiency for pions if identified as heavy particles,
see Figure~\ref{PID})~\cite{LHCb2},
but it is limited by
%both the requirement that the associated track
%has been reconstructed and by
the CPU time required to solve the equation
that describes the optics ($\sim$ 100 ms)\footnote{This and subsequent
CPU times are estimated scaling the present speed to the foreseen
performance of 2007 machines.}. This time should be
compared with the order 10 ms available to run
the entire final level trigger.
\section{Tracking-independent Ring Reconstruction Methods}
Cherenkov rings arising from particles without associated tracks
(``trackless rings'') provide a dangerous correlated background
to the likelihood method.
%A trackless method for ring reconstruction will be of benefit not only
%because will reconstruct the rings that cannot be associated to a particular track, but will also
%allow to eliminate the biases in the reconstructed signal rings with tracks, biases that
%can arise from incertitudes or inefficiencies in tracking,
%the presence of trackless rings and of other sources of noise.
The trackless
ring reconstruction methods presented here, Hough transform and Markov chain,
perform ring finding offline using the information from the
photodetectors alone, and hence provide robustness against
background which does not have associated track information.
A Hough transform~\cite{hough}
reconstructs a given family of shapes from discrete data points,
assuming all the members of the
family can be described by the same kind of equation.
To find the best fitting members of the family of shapes, the data
points are mapped back to the parameter space.
\begin{figure}[htb]
\centering
\includegraphics*[width=60mm]{hough_24mar.eps}
\caption{The Hough transform reconstructed Cherenkov rings in RICH2:
hits in red, Hough
centres in blue, track impact points in pink. The rings for which
the Hough centres are not associated to track impact points would not have
been reconstructed by the
likelihood method.}
\label{hough}
\end{figure}
A Hough transform algorithm has been implemented to find the rings in
RICH2. Here the optical distortions are sufficiently small that the rings can be
found using a circle search.
A circular ring can be described in the data point coordinate space by:
\begin{equation}
f(x,y,x_0, y_0,r)=(x-x_0)^2 +(y-y_0)^2 -r^2=0
\end{equation}
where $x_0$, $y_0$ and $r$, being the centre and radius of the circle,
are the three parameters that describe the parameter space.
To find the mapping between the rings and the space of the
parameters, the parameter space is quantized into a
convenient number of cells. For each cell, $H(x_0,y_0, r)$, in the
parameter space and for each data point, ($x,y$), the value associated to the
content of the cell is increased by one unit if $|f(x, y, x_0,
y_0,r)|