11institutetext: Stanford University 22institutetext: Université Paris-Saclay
33institutetext: CERN

# Potentiality of automatic parameter tuning suite available in ACTS track
reconstruction software framework

Rocky Bala Garg 11<EMAIL_ADDRESS>Corentin Allaire 22
<EMAIL_ADDRESS>Andreas Salzburger 33 Hadrien Grasland 22 Lauren
Tompkins 11 Elyssa Hofgard 11

###### Abstract

Particle tracking is among the most sophisticated and complex part of the full
event reconstruction chain. A number of reconstruction algorithms work in a
sequence to build these trajectories from detector hits. Each of these
algorithms use many configuration parameters that need to be fine-tuned to
properly account for the detector/experimental setup, the available CPU budget
and the desired physics performance. Few examples of such parameters include
the cut values limiting the search space of the algorithm, the approximations
accounting for complex phenomena or the parameters controlling algorithm
performance. The most popular method to tune these parameters is hand-tuning
using brute-force techniques. These techniques can be inefficient and raise
issues for the long-term maintainability of such algorithms. The open-source
track reconstruction software framework known as âA Common Tracking Framework
(ACTS)â offers an alternative solution to these parameter tuning techniques
through the use of automatic parameter optimization algorithms. ACTS come
equipped with an auto-tuning suite that provides necessary setup for
performing optimization of input parameters belonging to track reconstruction
algorithms. The user can choose the tunable parameters in a flexible way and
define a cost/benefit function for optimizing the full reconstruction chain.
The fast execution speed of ACTS allows the user to run several iterations of
optimization within a reasonable time bracket. The performance of these
optimizers has been demonstrated on different track reconstruction algorithms
such as trajectory seed reconstruction and selection, particle vertex
reconstruction and generation of simplified material map, and on different
detector geometries such as Generic Detector and Open Data Detector (ODD). We
aim to bring this approach to all aspects of trajectory reconstruction by
having a more flexible integration of tunable parameters within ACTS.

##  1 Introduction

The reconstruction of trajectories for charged particles is a computationally
demanding yet vital aspect of any high-energy physics experiment. The
computational overload multiplies quadratically with the number of particles
in the detector. Future progress demands dedicated efforts to enhance
algorithmic performance while managing computational overhead. A viable avenue
for such an enhancement involves optimizing algorithmic parameters that span
from particle properties preselection to simplifying detector effects and
limiting search spaces. However, the sheer number of such optimizable
parameters, and their dependence on the specific detector configurations and
experimental circumstances requires a significant amount of work and regular
updates.

This paper puts forth the proposal to utilize the auto-tuning methodologies
for the optimization of parameters within different tracking algorithms. The
effectiveness of these techniques has been demonstrated through the
development of the simplified material models for detectors (known as material
mapping) and the optimization of parameters in track seeding and primary
vertex reconstruction algorithms. These methodologies offer the potential to
identify an optimal parameter set based on the prevailing experimental
conditions, all while minimizing human intervention.

##  2 ACTS and dataset

A Common Tracking Software (ACTS) Ai:2021ghi  is a tracking framework being
developed since 2016 as an international collaboration with the goal of
providing a generic, experiment-independent open-source software framework for
charged particle tracks reconstruction. To facilitate comprehensive research,
ACTS offers two simulated detector geometries: the Generic Detector as shown
in figure 1 is a standard all-silicon LHC-type tracking detector used in the
TrackML Amrouche2023  challenge and the Open Data Detector (ODD)
corentin_allaire_2022_6445359 , an evolved version of Generic Detector
implemented using DD4Hep Frank_2014  that provides the support structure and
the material akin to a real detector. The Generic detector has been used for
the seeding and vertexing optimization studies while ODD has been used for the
material mapping studies in this paper. The adaptability of ACTS to various
detector geometries positions it as an ideal platform for researching and
testing auto-tuning techniques with different algorithmic configurations.

In order to perform the optimization studies, $t\bar{t}$ events generated and
simulated within the ACTS framework are used. These events correspond to the
proton-proton (pp) collisions at a center-of-mass energy $\sqrt{s}=14$ TeV
with an additional pile-up (additional pp interactions within the same bunch-
crossing) of 200, emulating the High Luminosity LHC conditions. The events are
generated using Pythia8 10.21468/SciPostPhysCodeb.8  and only particles with a
transverse momentum p${}_{\textrm{T}}$ $>$ 1 GeV have been considered for
current studies.

Figure 1: Layout of ACTS Generic Detector. The Open Data Detector share
similar layout but have more realistic interaction material.

##  3 Parameter Optimization in ACTS

The automatic parameter optimization techniques featured in this paper have
been integrated into the ACTS library. These techniques are now accessible for
utilization with various detector geometries and tracking algorithms by a
broad community of users.

###  3.1 Optimization Framework

Due to the difficulty of finding the derivatives of the tracking algorithms,
this work explores derivation-free optimization techniques. The objective is
to discover the optimal configuration that yields the best performance. To
achieve this, a scoring function is formulated, drawing from various
performance metrics of the tracking algorithm, such as efficiency and fake
rate. To perform the optimization, the ACTS tracking framework is integrated
with parameter tuning framework as presented in figure 2. The tuning framework
initiates the process by providing a random input parameter configuration to
the tracking framework. Subsequently, the tracking framework assesses its
performance based on this configuration and reports the score back to the
tuning framework. The tuning framework strives to maximize this score, and
consequently, the algorithm’s performance. It employs parameter estimation
techniques to generate another set of parameters, which are then passed to the
tracking algorithm. This iterative process continues for a number of
iterations until a satisfactory score and parameter configuration are
achieved.

Figure 2: Integration of ACTS tracking framework with parameter tuning
framework.

This study explores two distinct optimization frameworks: Oríon
xavier_bouthillier_2022_0_2_6 , an asynchronous framework for black-box
function optimization, and Optuna optuna_2019 , an open source software for
automatic hyperparameter search. Both of these algorithms can be easily
implemented and integrated within ACTS, making it convenient to use them for
the optimization of different algorithms. Within the Oríon framework, a random
search algorithm has been implemented that randomly samples the parameter
configurations from the parameter space and provides an optimal configuration
for a large enough number of trails. Meanwhile, in the Optuna framework, The
Tree-structured Parzen Estimator (TPE) NIPS2011_86e8f7ab  algorithm has been
utilized. TPE is a Bayesian optimization method that determines parameter
configurations based on a probabilistic model.

###  3.2 Implementing optimization in different ACTS algorithms

####  3.2.1 Material Mapping

In a real detector, as particles traverse the detector material, they undergo
deviations from their initial trajectory due to the interactions with matter.
These interactions hold substantial importance in determining the paths of
these particles and needs to be taken into account properly when
reconstructing the trajectory of the particles. To effectively incorporate the
trajectory changes resulting from the material interactions in a virtual
detector, a high degree of precision is essential in determining the quantity
of material at each point within the detector.

Conventional detector simulation frameworks such as Geant4 AGOSTINELLI2003250
excel in accurately simulating detector materials. However, they demand
significant memory resources, and incorporating them into the track
reconstruction process would significantly impede the speed of execution. An
approximation can be achieved by creating a simplified material map, where all
the material is projected onto a predefined set of surfaces within the
detector. Each surface is divided into two-dimensional bins, and the material
within each bin is averaged. The process is visualized in Figure 3(a) that
provides an illustration of the material mapping on one such surface. As a
particle track crosses one of these surfaces, we can identify the specific bin
it intersects and compute the energy loss due to interaction by determining
the material content stored in that bin. The success of this approach depends
significantly on the careful selection of specific surfaces and the choice of
suitable bin sizes for each surface. Opting for coarse bins can result in the
loss of crucial geometric information, leading to biased reconstructions.
Conversely, opting for excessively fine bins will inflate memory consumption.
Therefore, it is essential to optimize these parameters to create an efficient
material map.

We have used automatic optimization algorithm called Oríon to optimize the bin
size of the surfaces used in the material map. The set of surfaces is provided
to the algorithm and the algorithm finds the optimal binning automatically.
For this test, we have used a total of 107 surfaces, that leads to a total of
214 parameters. The algorithm uses a random search approach to find the best
parameters while trying to minimize a score function (defined in equation(1))
which is based on the quality of the map. The $bins$ in the score function
refers to the number of bins in a surface while $variance$ refers to the
variance of all the material projected onto a given bin. The algorithm tries
to minimize the score which in turn minimizes the variance and keeps the
number of bins as small as possible. We were able to achieve optimal results
on 40 CPU cores after one day of running. The resultant material map showed a
good agreement with the map generated by the Geant4 as shown in Figure 3(b).

$Score=\frac{1}{bins}\times\sum_{bin}variance_{bin}\times(1+\sqrt{bins})$ (1)

Figure 3: (a) Projection of the material onto bins (arrows) of different
sizes. (b) Comparison between the material encountered in a Geant4 simulation
vs. the auto-tuned material map in the the open data detector.

####  3.2.2 Track Seeding

Reconstructing particle tracks from the detector hits is a complex challenge
due to the substantial combinatorial nature of the problem when numerous hits
are present in the detector. Therefore, most of the track reconstruction
algorithms start with an initial step called the “Track Seeding”. During this
phase, small tracklets, known as track seeds, are formed using only the
initial few detector layers (usually three or more) and a helicoidal fit is
performed on these tracklets to get a coarse estimate of the corresponding
track parameters. Subsequently, these tracklets serve as the input for the
complete track-finding process.

The track seeding algorithm uses a set of user-defined parameters to select
hits for seed reconstruction and these parameters can differ significantly
depending on the detector geometry and other experimental conditions. Finding
the optimal parameter configuration for a given geometry is critical for
efficient seed reconstruction, as the failure to reconstruct a seed
corresponding to a truth particle can result in the permanent loss of that
particle, significantly affecting tracking performance. On the other hand, too
many seeds per truth particle can slow down the track reconstruction process.

The manual evaluation of these parameters can be a tedious task, so to
streamline this process, we have employed auto-tuning techniques, utilizing
two distinct optimization algorithms: Optuna and Oríon. In this study, we have
focused on optimizing eight seeding parameters while assessing the performance
using three crucial metrics: the efficiency (the fraction of particles
accurately reconstructed as tracks), the fake rate (the fraction of
reconstructed tracks not corresponding to any particle) and the duplicate rate
(the fraction of reconstructed tracks that duplicate previously reconstructed
ones). The first two metrics directly impact the physics performance, while
the third metric impact the speed of reconstruction. A scoring function based
on these metrics was constructed to guide our optimization efforts:

$Score=Efficiency-(FakeRate+\frac{DuplicateRate}{K}+\frac{RunTime}{K})$ (2)

The optimization algorithms try to maximize the score while trying to achieve
a better performing parameter configuration. Remarkably, both Optuna and Oríon
efficiently converged to optimal parameter configurations within one hour of
running. Figure 4 illustrates a comparison of efficiency and duplicate rates
before and after optimization. The results demonstrate a notable enhancement
compared to an un-optimized configuration in both cases.

Figure 4: Comparison of track reconstruction efficiency and duplicate rate
before and after parameter optimization. The track reconstruction efficiency
as a function of transverse momentum and pseudo-rapidity is shown in top-left
and top-right figures while the corresponding distributions for duplicate rate
are shown in two bottom figures. The low statistics in high P${}_{\textrm{T}}$
regions results in large error-bars.

####  3.2.3 Vertexing

In collider experiments, when two beams collide, numerous interactions can
occur simultaneously. The interaction characterized by the highest momentum
exchange is known as the “hard interaction”, while all others are categorized
as the “pile-up interactions”. The collision points where these interactions
occur are denoted as primary and pile-up vertices, respectively. To
differentiate between tracks originating from the primary and pile-up
vertices, the tracks are associated with their corresponding vertices using a
vertex reconstruction algorithm. Within the ACTS framework, we employ an
algorithm known as the Adaptive Multi-Vertex Finder (AMVF) ATL-PHYS-
PUB-2019-015  for this purpose. The AMVF algorithm concurrently fits multiple
tracks to various vertices, assigning different weights to each track-vertex
pairing. Subsequently, it optimally fits all the vertices and assigns each
track to its respective vertex.

Similar to the track seeding algorithm, the performance of the vertexing
algorithm relies on several user-defined parameters that exhibit significant
variation depending on the detector geometry and other experimental
conditions. To enhance the algorithm’s performance, we have employed both
Optuna and Oríon to obtain optimized parameter configurations. For this study,
we have chosen five vertexing parameters for optimization. The following score
function has been constructed based on a number of performance metrics:

$Score=(Eff_{Total}+2Eff_{Cleaned})-(Merged+Split+Fake+Resolution)$ (3)

where $Eff_{Total}$ is the fraction of reconstructed truth vertices,
$Eff_{Cleaned}$ is the fraction of reconstructed truth vertices such that each
reconstructed vertex is associated to only one truth vertex, $Merged$ is the
fraction of reconstructed vertices associated with multiple truth vertices,
$Split$ is the fraction of reconstructed vertices such that multiple vertices
are associated with the same truth vertex, $Fake$ is the fraction of
reconstructed vertices not associated to any truth vertex and $Resolution$ is
reconstructed vertex resolution in $x,y$ and $z$.

Our objective for the vertexing algorithm is to maximize the reconstruction of
clean vertices while maintaining a high overall efficiency. To attain this
objective, our optimization algorithms strive to maximize the score, typically
converging to an optimal configuration within approximately four hours of
runtime. The resulting number of clean and fake vertices is shown as a
function of the pile-up in Figure 5. Notably, substantial improvements in the
number of clean vertices are evident, particularly in high pile-up scenarios,
when compared to the un-optimized configuration. Likewise, a reduction in the
number of fake vertices is also observed.

Figure 5: Comparison of the number of reconstructed vertices as a function of
pile-up. The left plot shows the number of clean vertices while right plot
shows the number of fake vertices.

##  4 Conclusion

Our research demonstrates the effective application of data-driven auto-tuning
algorithms within the realm of track reconstruction. We have successfully
optimized input parameters for various algorithms, including seed
reconstruction, vertex reconstruction, and material mapping. These methods
have been seamlessly integrated into the ACTS framework, making them readily
available for adoption by any experiment utilizing ACTS for their tracking
requirements.

Looking ahead, our ongoing efforts will be directed toward further
generalizing this approach. We aim to extend the scope of automatic parameter
tuning to encompass a broader range of algorithms within the ACTS framework,
simplifying the optimization process for a wider array of tracking tasks.

##  5 Acknowledgments

This project has received funding from the European Unions Horizon 2020
research and innovation programme under grant agreement No 101004761.
This work was supported by the National Science Foundation under Cooperative
Agreement OAC-1836650.

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# Status of the Compressed Baryonic Matter (CBM) Experiment at FAIR††thanks:
Presented at XXIXth International Conference on Ultrarelativistic Nucleus-
Nucleus Collisions (Quark Matter 2022), Krakow, Poland, April 4-10, 2022

Kshitij Agarwal (for the CBM Collaboration)  Physikalisches Institut, Eberhard
Karls Universität Tübingen, Germany

###### Abstract

The CBM experiment at the Facility for Antiproton and Ion Research (FAIR) aims
to explore the QCD phase diagram in the region of high net-baryon densities
using nucleus-nucleus collisions ($\sqrt{s_{NN}}=2.9-4.9$ GeV). CBM will be
utilizing peak interaction rates of up to 10 MHz and an advanced triggerless
data acquisition scheme to provide it with an unique access to rare physics
probes required to accomplish CBM’s physics goals. This contribution will
summarise CBM’s progress in terms of its physics performance simulations and
the status of the comprising detector sub-systems, including their involvement
in FAIR Phase-0 activities.

##  1 Introduction to CBM-FAIR

The Facility for Antiproton and Ion Research (FAIR) [1] is a new particle
accelerator facility currently under construction which aims to examine cosmic
matter in the laboratory. Schwer-Ionen-Synchrotron-100 (SIS-100) is at the
heart of FAIR with heavy-ion beams to be injected from the existing SIS-18
ring accelerator at GSI Helmholtz Centre for Heavy Ion Research in Darmstadt.
The Compressed Baryonic Matter (CBM) experiment [2] is one of the four
scientific pillars of FAIR and will utilise beams from SIS-100 (gold beams
with kinetic energies between 2-11 AGeV; $\sqrt{s_{NN}}=2.9-4.9$ GeV) to study
matter at conditions comparable to astrophysical objects and events [3].
Therefore, CBM’s physics goals are centered to decipher the properties of
Quantum Chromodynamics (QCD) matter at high net-baryon densities and to
understand the equation-of-state of dense nuclear matter, the possible phase
transition from hadronic to partonic phase, and chiral symmetry restoration.
The respective physics observables include sub-threshold strangeness
production, collective flow of emitted particles, excitation function of low-
mass dileptons and charm production amongst many others. A comprehensive
review of CBM’s physics goals and observables are in Ref. [4]. CBM aims to
access these ‘rare probes’ at up to 10 MHz high beam-target interaction rates
by using novel self-triggering, free-streaming and radiation-hard readout
electronics. These features are complemented by inspection of full data stream
in real-time to select and reconstruct events online.

CBM is designed as a fixed-target experiment (depicted in Fig. 1) with an
angular acceptance of $2.5^{\circ}<\theta<25^{\circ}$ and is capable to
measure hadrons and leptons in both their production channels. Located inside
the superconducting dipole magnet are the Micro Vertex Detector (MVD) and the
Silicon Tracking System (STS) tasked to resolve the secondary vertex of short-
lived open-charm mesons and provide momentum determination of charged
particles respectively. Dielectron identification is performed by the Ring
Imaging Cherenkov (RICH) Detector with the UV photon detector planes based on
Multi-Anode Photo Multiplier Tubes. Dimuon identification is done by the Muon
Chamber (MuCh) System containing Gas Electron Multipliers and bakelite
Resistive Plate Chambers sandwiched between hadron absorber plates. One of
CBM’s standout features is the interchangeability of RICH and MuCh, allowing
CBM to systematically measure dileptons in both production channels for the
same detector acceptance. The Transition Radiation Detector (TRD) is also used
for pion suppression, particle tracking, and identification of light nuclei
and fragments via specific energy loss. Charged hadrons detection is performed
by the Time-of-Flight (TOF) wall composed of Multi-Gap Resistive Plate
Chambers (MRPCs) located about 7 m downstream. The Projectile Spectator
Detector (PSD) used to determine the collision centrality and reaction plane
orientation.

Figure 1: CAD view of the CBM (right) and HADES experiment (left). SIS-100
beam will come from left to right of the image (Figure: P. Dahm, GSI
Darmstadt).

##  2 Update on Physics Performance Studies

The particle identification (PID) procedures developed for CBM play a central
role in benchmarking CBM’s physics performance described in subsequent
subsections 2.1-2.3. The Cellular Automaton (CA) method based track finder
reconstructs charged particles’ trajectories in the STS. This, in combination
with the PID information from ToF and TRD, is used to further identify
hadrons, light fragments and hypernuclei under the Kalman Filter Particle
Finder (KFPF) package. This is further complemented by collision centrality
determining methods by using charged particle multiplicities in STS and the
energy of spectator fragments to provide a complete picture of the underlying
collision.

###  2.1 Hadrons and Strangeness

Tools for the multi differential physics analysis have been prepared for doing
a comprehensive analysis of strange hadrons and hypernuclei (see Fig. 2).
Further optimisation of reconstruction yields of $K_{s}^{0}$, $\Lambda$ and
$\Xi^{-}$ have been done by using Machine Learning (ML) techniques to
successfully demonstrate high signal purity and efficient rejection of the
combinatorial background by $>40\%$ for same efficiency (see Fig. 2).
Additionally, CBM’s capabilities to reconstruct proton’s transverse momentum
spectrum within $5\%$ systematic error for different underlying EoSs in the
Three-fluid Hydrodynamics-based Event Simulator (THESEUS) have been shown.

Figure 2: (a) Reconstructed invariant mass distribution of double $\Lambda$
hypernuclei - ${}^{6}_{\Lambda\Lambda}He$ (Figure: I. Vassiliev, GSI
Darmstadt). (b) Comparison of $\Lambda$ invariant mass distributions for
particle selection criteria based on KFPF in blue and XGBoost Machine Learning
Model in red (Figure: S. Khan, EKU Tübingen).

###  2.2 Correlation, Flow and Fluctuation

Multi-differential analysis of the $v_{1}$ flow harmonic for $K_{s}^{0}$,
$\Lambda$ and $\Xi^{-}$ hyperons have been performed as a function of rapidity
and transverse momentum for different centrality classes. This flow analyses
is further complemented with feasibility studies using multiparticle azimuthal
correlations. This analyses is challenging due to CBM’s fixed-target geometry
and energy range (non uniform acceptance and low multiplicities), but
feasibility in terms of symmetric cumulants (SC($m,n$)) was successfully shown
(see Fig. 3). Feasibility studies to conduct measurements of proton-proton and
pion-pion correlations via femtoscopic measurements have also been performed.
Further femtoscopic analysis with higher statistics and realistic cuts is
ongoing for precise reconstruction of source properties.

###  2.3 Dileptons

Performance studies, in terms of reconstruction of freezeout cocktail have
been done for dileptons (in both production channels $e^{+}e^{-}$ and
$\mu^{+}\mu^{-}$) with realistic detector geometries, material budget, and
response over the entire SIS-100 energy range. This has allowed to access the
underlying thermal signal and reconstruct clear peaks for the low mass vector
mesons ($\sigma_{M}(\omega)=14$ MeV/c2) with a pair detection probability of
$\approx 10\%$. A particular emphasis has also been placed on using sub-
threshold charmonium measurements to study cold nuclear matter effects p+A
collisions and to study pQCD inspired models at low energies (see Fig. 3).

Figure 3: (a) Variation of symmetric cumulants (SC(3,2) and SC(4,2)) with
centrality and their comparison with ALICE measurements (A. Bilandzic, TU
München). (b) Reconstructed $J/\psi$ invariant mass spectra with
($\sigma_{M}(J/\psi)=35$ MeV/c2) at $\sqrt{s_{NN}}=7.6$ GeV p+Au collision
(Figure: S. Chatterjee, Bose Institute Kolkata).

##  3 Detector Updates and FAIR Phase-0

Almost all CBM detector sub-systems have completed their R&D phases, with
their Technical Design Reports available in Ref. [5]. MVD has shown production
readiness for the pre-production sensor version. The engineering and
production readiness of various STS components was reviewed for pre-production
to start in late-2022. MuCh has built and tested real size GEM and RPC
chambers, and have conceptually reviewed their mechanical aspects. RICH has
accomplished its “first of series test” for their electronics and is
constructing a full-size photo-camera demonstrator. TRD has submitted the
proposal for their inner high-rate inner modules with novel 2D readout pads.
TOF has undertaken an extensive campaign to determine their rate limits and
mitigation efforts towards observed aging are ongoing. Technical designs of
the target mechanism, beam pipe and beam monitors have been developed.
Evaluation of the impact on the project of sanctions imposed on Russia,
especially regarding the superconducting dipole magnet, the PSD and the CBM’s
timeline is presently ongoing.

Different aspects of CBM have been and are continued to be thoroughly tested
in FAIR’s precursor programme - FAIR Phase 0. The 2021 campaign of
mCBM$@$SIS-18 at GSI [6] has successfully demonstrated the triggerless-
streaming readout and data transport of CBM with a setup composed of prototype
components of all CBM’s detector sub-systems with the readout chain interfaced
with the Common Readout Interface (CRI) boards (see Fig. 4). Moreover,
detailed high-rate tests have been performed for radiation tolerance
validation of various sub-system’s components. Other FAIR Phase-0 activities
include: (i) the successful implementation of CBM’s KFPF package in STAR’s
express analysis chain and endcap Time-of-Flight (eTOF) comprising 36 CBM-TOF
modules for BES-II campaign [7, 8]; (ii) HADES-RICH upgrade with 428 MAPMTs
from CBM-RICH [9].

Figure 4: (a) mCBM setup for the 2021 campaign (Figure: C. Sturm, GSI
Darmstadt). (b) Time synchronicity between all sub-systems for O+Ni collisions
at 2.0 AGeV at about 1 MHz collision rate (Figure: A. Weber, JLU Giessen).

##  4 Conclusion and Outlook

CBM, with its foreseen capabilities can map out the high-density region of the
QCD phase diagram by studying conditions similar to the core of neutron stars
and can help usher a new era of multi-messenger physics. This is substantiated
by the recent physics performance studies focusing on the rare probes required
to achieve this goal. All detector sub-subsystems are progressing well towards
the strategic objective to be ready for series production. The active
participation in FAIR Phase-0 has contributed substantially to CBM’s
understanding of the underlying sub-systems. mCBM after verifying CBM’s
readout concept is currently undertaking benchmark runs targeting $\Lambda$
baryon reconstruction in Au+Au collisions at 1.24 AGeV and Ni+Ni collisions at
1.93 AGeV.

##  5 Acknowledgements and Funding

The CBM experiment is being developed by a collaboration consisting more than
400 persons from 47 institutions and 11 countries. CBM is supported by
national funding agencies of CBM member institutions. The author acknowledges
the support from the German Federal Ministry of Education and Research
(Project-ID 05P19VTFC1) and the Helmholtz Graduate School for Hadron and Ion
Research (HGS-HIRe).

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