21.2.1. Introduction¶
Almost regardless of the quantity you are going to measure in your analysis, you will have to face some basic problems:
select events you want to study (the signal) over similar events that mimic them (the background, more about this later),
estimate efficiency of your selection,
(possibly) estimate the intrinsic resolution of the quantities you will measure,
and finally you will want to count how many signal events you observe,
or measure other quantities like an invariant mass (i.e. the position of a peak)
or a polarization from an angular distribution.
Cuts and signal selection¶
The most basic way to select a signal is to apply what, in jargon, are called “cuts”. A cut is nothing but selection, usually binary, over one quantity that has some separation power between signal and background. Of course multiples cuts can be applied in sequence, leading to quite effective background reductions. Before deciding on the selection criteria however, one must define the variable that will be used to count of many signal events are left. A good variable has a very peaking distribution for signal, and a smooth, uniform distribution for the background.
Example
In many b-physics analyses you will make candidate B mesons from combinations of tracks and calorimeter clusters. You will work through an example of this in a later lesson, but for now, consider the energy of your candidate B in the centre-of-momentum system.
Question
What is the the energy of a B meson produced in the decay of an \(\Upsilon(4S)\) in the rest frame of the \(\Upsilon\)?
Solution
Half of its rest mass: \(\sim 5.3\ \textrm{GeV}\)
The difference between half of the energy in the centre-of-momentum and the total energy of the B candidate is called \(\Delta E\). An early cut you might make is to require that this quantity is close to zero.
That is, you would accept B meson candidates which satisfy: \(-150\ \textrm{MeV} < \Delta E < 150\ \textrm{MeV}\) and reject those which don’t.
Backgrounds, backgrounds, backgrounds¶
An interesting event for most B physics analyses is one where the \(e^+e^-\) produced an \(\Upsilon(4S)\), which subsequently decay into a \(B\bar{B}\) meson pair. However this is not the most probable result in an \(e^+e^-\) collision.
Question
What is the most likely final state for an \(e^+e^-\) collision at \(\sqrt{s}=10\) GeV? What is its cross section? Also look up the cross section for hadronic events and for \(B\bar B\) hadronic events.
Hint
You should be able to find this information on confluence.
Another hint
Probably you are looking for this page.
Solution
At around 125 nb, the most probably process is \(e^+e^-\to e^+e^-\). The cross section for hadronic events is around 5.8 nb, the cross section for \(B\bar B\) hadronic events is around 1.1 nb. Note that the measured cross sections depend on the selection criteria that were being applied to the events.
We call anything that is not “what you want to analyse”: background. But this is a bit of a sloppy definition. In fact, you will encounter roughly four things in a Belle II analysis that people call “background”. It depends a bit on how one counts.
Warning
We will always specify in these lessons. But in your working life (in meetings etc), you might hear the word “background” and you will need to infer from the context precisely what is being discussed.
The example we’ve just discussed (such as \(e^+e^- \to e^+e^-\)) are background events or background processes. These are relatively easy to reject and can be done in the trigger or by rather simple cuts. More on this later on in this lesson. You don’t need to worry too much about these if you are doing B physics. But these background processes can be important for low-multiplicity analyses.
The second kind of background arises from physics processes that mimic your signal.
Example
If you want to analyse \(B\to K^{(*)}\ell^+\ell^-\) decays then you would be concerned with the (much higher branching fraction) \(B\to J/\psi K^{(*)}\) process where the \(J/\psi\) subsequently decays to a pair of leptons.
Most people would call this a “physics background”.
You would also get backgrounds of this second kind where there was some particle mis-identification or mis-reconstruction.
The third kind of background arises from the non-resonant \(e^+e^- \to q\bar{q}\) hadronic events. As you saw in the exercises before, \(B\bar B\) is only part of the hadronic cross section. You will also get hadronisation of light quarks (\(uds\)), and the charm quark (which is a background to B physics, for example, but obviously the signal for charm physics measurements). These hadronic events produce many tracks (around 10 or 11) per event. You are therefore, just by probability, likely to find some combination of genuine tracks and clusters that mimic your signal but aren’t from a \(B\) decay. We call this continuum background.
This background can be suppressed to a certain extent, although many analyses leave some part of this background in the data sample as it is relatively straightforward to model and cutting too strictly on continuum suppression variables will hurt signal efficiency at some stage. You will have a lesson about continuum suppression and examples of modelling later in these tutorials.
The fourth thing people will refer to as “background” is something rather different. Beam-induced background are tracks and clusters that are not produced from the primary \(e^+e^-\) collision, but from other interactions in the beam itself. These are more prevalent in Belle II compared to Belle (and previous experiments) since the beams are significantly more focused at SuperKEKB. Beam background tracks and clusters are rather easy to reject at the final stages of an analysis the presence of such tracks and clusters is usually tolerable (you can just ignore them). They are, however, relevant during reconstruction and in the high-level trigger.
It might be obvious but let us state an obvious thing: even events that are really from your signal can contain these background clusters and tracks. You do not need to reject the whole event just because of some beam background.
Tip
You should discuss the backgrounds that you are expecting to encounter in your analysis with your supervisor. This is a very important and useful conversation.
Key points
There are four(ish) important kinds of “background”.
Trigger background and background processes.
Physics background (more of a problem when you get into your analysis).
Continuum background (from \(uds\) and maybe \(c\)).
Beam-induced background.
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?)
missing bits of information (what?)
bugs (what did you do? what goes wrong?)
too hard exercises (which one?)
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!
Quick feedback!
Author(s) of this lesson
Umberto Tamponi, Martin Ritter, Oskar Hartbrich, Michael Eliachevitch, Sam Cunliffe