21.2.4. Reconstruction¶

Now after the data acquisition or the simulation we have events which contain the raw detector responses. We need to process this information into something more usable for analysis. At best we want to be able to reconstruct the underlying particles as correctly as possible and get the original four-vectors of particles produced in the interaction.

However, it’s never possible to uniquely identify all the particles in the interaction because for hadronic interactions there are almost always short lived particles that decay before reaching the detector.

In addition there will be signals in the detector which are not what we want: Every detector has an intrinsic noise so some detector channels will fire randomly. In addition there is real background not coming from the event we’re interested in but from other electrons/positrons in the beam randomly interacting with each other or parts of the accelerator structure.

So all we can do is look at the detector response and find a set of most likely particles and then leave it to the analyses to do a proper statistical analysis of the events.

Now the exact same reconstruction is performed on MC data as on real data: We want the exact same algorithms in both cases. However in MC we actually know the correct particles and we can trace which detector response was caused by which particle.

So we run the exact same reconstruction but in addition for MC we also trace the correctness of the reconstruction which we call “MC Truth”.

Clustering¶

One of the first steps in this reconstruction is called clustering where we need to combine the detector responses in each sub detector if they are related.

As a simple example we can look at the PXD: If a particle passes the pixel detector we expect a signal in one of the pixels. But what if the particle passes between pixel boundaries? Or if it flies through the detector at a shallow angle along multiple pixels? We will get multiple pixels caused by the same particle.

So we cluster neighboring pixels, taking the detector intrinsic properties such as noise into account and form groups of pixels. We can then calculate properties of these clusters like size, shape or center. Since our pixel detector has an analog readout and can measure the amount of ionisation per pixel we can use weighted mean calculate the center position. Or we could even use more advanced algorithms depending on the readout characteristics of our detector.

Fig. 21.13 Simple example of 2D clustering with analog signals¶

Now this was an example for the pixel detector but this same principle is also used in the strip detector (in 1D) or in the calorimeter to group neighboring crystals into clusters.

In addition the calorimeter now has different characteristic cluster shapes depending on what particle caused the cluster: hadronic interaction of photons. So the definition of a cluster in the ECL becomes more complicated as the same connected region of crystals might be caused by one or more photons or one hadron. But the principle is the same: Identify all hits caused by a particle and group them into clusters.

Tracking¶

A very important part of our reconstruction is the so-called tracking or track reconstruction. It tries to identify trajectories of particles through the tracking detectors, called tracks. There are mainly two parts of tracking

Track finding: Find patterns (i.e. collections of hits) in the hits or hit clusters in the tracking detectors that look like they could be from a particle flying through the detector.

Fig. 21.14 View of a simulated event in an x-y cross-section of the CDC. The shown CDC hits originate either from charged particles belonging to the event or from beam-induced backgrounds. The principle of track finding is to identify patterns of hits belonging to the same particle, which are then shown in the same color on the right. Hits that remain grey are rejected as background. Hits in the vertex detectors are not shown here, but help with finding tracks in the CDC.¶

Track fitting: Determine the best estimate of the kinematic variables describing the particle trajectories corresponding to each found hit/cluster pattern to obtain the particle position and momentum close to the interaction region as precisely as possible.

Track finding is a very complex process which depends a lot on the detector layout and characteristics and the most complex part of the reconstruction process. It would be impossible to describe it properly here. You can find more details in the Belle II physics book and there is also a paper describing track finding at Belle II

What we can say that track finding and fitting requires a lot of computing time to find all the tracks in our events. As a matter of fact currently our tracking reconstruction takes about twice as long as the simulation of an event.

Question

What are possible reasons for the tracking algorithms to occasionally find apparent tracks that are not associated with real particles, known as fakes?

Hint

Take a good look at the left event display on the left side in Fig. 21.14. This is a relatively clean event and we might get much more hits from beam-induced backgrounds.

Solution

With high numbers of hits from beam-induced backgrounds and resulting high occupancies, the track finding faces a combinatorial challenge: Of the exponential number of possible combinations of hits, it has to find those that correspond to trajectories of real particles. But there’s many wrong combinations of hits that might look like tracks originating from the interaction point and sometimes, they are miss-identified as tracks. These wrong combinations can include both hits from backgrounds or from particles originating from the primary event.

Reconstructed tracks that are caused by an individual beam-background particle are also called fakes. However, they are relatively easy to reject because they don’t originate from the interaction point and have typically high boosts along the beam-axis. But their sheer high number relative to hits from signal tracks is among the things that make tracking at Belle II challenging.

Question

Now assuming reconstruction takes exactly twice as long as simulation and simulation still takes 1 second and we can buy one CPU/hour for $0.025 in a commercial cloud as above.

For the full experiment we will collect $50\ \textrm{ab}^{-1}$. The plan is to have a total trigger cross section of 20 nb (so in addition to the 1.1 nb of $B\bar{B}$ we will also have some fraction of continuum, tau and other events).

How many CPUs do we need to reconstruct all the real data and simulate and reconstruct an equivalent amount of MC in one year? And what will it cost?

Hint

It’s basically the same question as above but we now have a cross section of 20 nb we want to simulate.

And we need to reconstruct both data and MC so we need to simulate once and reconstruct twice.

Solution

Now all together we will have 1 trillion events from the detector. We have to simulate the same amount of events. And reconstruct both.

That leads to 5 trillion seconds of CPU time or 1.4 billion CPU hours and would require 160 thousand CPUs and cost 35 million dollars.

This is of course a very rough estimate: The 1 and 2 seconds assumption for simulation and reconstruction is very very rough. The time also differs slightly for different event types. CPUs or the software might get faster and we will not have this amount of data very quickly. Also the CPU price is sure to change or be negotiable. Nevertheless, Computing cost will always be a major driving factor.

One of the consequences will be that we cannot produce that much MC so for some event types we will only be able have a fraction of the amount of events simulated as we have real data.

Particle Identification¶

Once we have the tracks we can also try to determine the likelihoods for the track belonging to different particle types. For each given track we can then check the sub detectors contributing to particle identification if they saw anything that could be related to this track.

For the CDC we can calculate the total energy loss over the track length and compare this to the expected values for different particle types. For ARICH we know where the track entered the detector and can check this area to see if there are any Cherenkov rings around this position. The same principle applies to TOP, ECL or KLM: we know where the track entered the detectors and can check for any related information from these sub detectors.

These detectors then calculate likelihoods for the signal caused by different particle types which we attach to the track information for later use by analysts.

Organization of Reconstruction¶

As mentioned above the reconstruction can take a long time and be very expensive, especially if we have a lot of data. It also depends on a lot of expert knowledge:

the conditions during data taking need to be taken into account: beam energies and positions, detector status, … .
the conversion from raw detector signal to energy needs to be properly calibrated.
the position of the tracking detector sensors needs to be well known and corrected in software (a process called alignment).

As for the simulation this is something which we centrally organize in Belle II. So, not very surprising, the Data Production group takes charge and coordinates with the detector experts the reconstruction of our data.

Data formats¶

When an $e^+e^-$ collision happens, the resulting products will leave signal in the Belle II subdetectors that are acquired, matched in time as each subsystem have a different delay and response time (event building), and saved to disk in a packed, binary format. Several steps have to be performed in order to produce a physics result of these hardly-intelligible raw data. These steps are unpacking, calibration, reconstruction and finally analysis. Each of these steps reads and writes different objects, and produces files in different formats.

Note

All the Belle II data files are root files, where the relevant objects are stored in the branches of a tree. When we say “different formats”, we refer simply to the different branches contained in those trees.

Let’s start from the data objects we save. There are four groups of them: raw, low-level, reconstruction-level and analysis-level.

raw objects: Raw objects are the output of the single subsystems: digitized PMT signals from the TOP, digitized ADC signals form the CDC, and so on. Without any further processing, these objects cannot be used.
low-level objects: Low-level objects come from the very first step of the data processing, the unpacking. The RAW signals are turned into more abstract and understandable objects: the CDC ACD signals are converted to CDChits, the TOP PMT signals are turned into TOPDigits, and so on. The low-level objects are fundamental to understand the detector performance, but they cannot yet be directly used to perform an analysis.
reconstruction-level objects: The last step is called reconstruction, and consists in running algorithm on the collection of digits to produce analysis-friendly quantities. The output of the reconstruction is are high-level variables like ECL clusters, resulting from running cluster algorithms on the ECLDigits, tracks resulting from running the tracking algorithms over the collections of CDC, SVD and PXD hits, PID likelihood resulting from the analysis of the TOP signals. In the process of reconstruction the calibrations are applied, correcting for the fluctuations in the detector response.
analysis-level objects: These high-level objects are finally read by the analysis software, and turned into analysis-level objects: charged particles, photons, missing energies and all the quantities used to present a physics result.

In Belle II there are four different data formats, reflecting which data objects are stored in a file:

RAW: This is the most basic format. It contains the un-processed, un-calibrated output of the detector. Analysis cannot be run on these data, but they serve as base for the production of the subsequent data format.
cDST (calibration Data Summary Table): This format contains the same objects as the RAW (so a full reconstruction could be performed starting from it), plus the results of the tracking, which is the most demanding part of the reconstruction. The scope of this format is to perform low-level detector studies and calculate calibration constants.
mDST (mini Data Summary Table): This is the basic data-analysis format. It contains only the high level information that can be directly used to perform a physics analysis. However, it is not the suggested format to perform analysis.
uDST (user Data Summary Table): This is the main format for data analysis. It’s the result of the analysis skim procedure, that selects from the mDST only the few events that can be useful for a certain type of analysis (events with a well reconstructed J/psi per example). Skimming is described in more detail in the next section. The content of this format is the same as the mDST, with the addition of the reconstructed particles used in the skimming selection (if you look at the $J/\psi$ skim, you will also find a list of $J/\psi$ already reconstructed for you in the file).

Note

If you are simply running an analysis, you will mostly use uDST, if you are also involved in performance studies you will probably use cDST as well and if your core activity will be hardware operations, you will be mostly dealing with the RAW and cDST formats.

Key points

The “reconstruction” is the process where we process the raw detector signal into high level objects like particle trajectories, ECL clusters and PID likelihoods.
Clustering is the process of finding connected regions of detector signal that most likely originated from the same particle
Tracking is the process of reconstructing the trajectories of particles flying through the tracking detectors and infer position and momentum as precisely as possible.
Reconstruction takes quite some time and is handled centrally by the Data Production Group
We have different data formats what contain different subsets of information. Analysis usually runs on udst.

Stuck? We can help!

If you get stuck or have any questions to the online book material, the #starterkit-workshop channel in our chat is full of nice people who will provide fast help.

Refer to Collaborative Tools. for other places to get help if you have specific or detailed questions about your own analysis.

Improving things!

If you know how to do it, we recommend you to report bugs and other requests with JIRA. Make sure to use the documentation-training component of the Belle II Software project.

If you just want to give very quick feedback, use the last box “Quick feedback”.

Please make sure to be as precise as possible to make it easier for us to fix things! So for example:

typos (where?)
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etc.

If you are familiar with git and want to create your first pull request for the software, take a look at How to contribute. We’d be happy to have you on the team!

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Author(s) of this lesson

Umberto Tamponi, Martin Ritter, Oskar Hartbrich, Michael Eliachevitch, Sam Cunliffe