## 3 The Data
For a mathematical definition of quantities such as the DCCA or \(IP\) see, e.g., Ref. [43]. More details are given in the text. Figure 4: Characterization of the signal and background and definition of several variables to discriminate between them. For the \(\mu\mu\) background, the usual candidates are formed by muons from different \(B\) mesons that are incorrectly matched together. Figure 4 also explains the characterization of background events. We used the same type of Pythia processes to generate \(b\bar{b}\) events, but there is no redecay at all this time, taking the event as it was originally fully simulated. We selected the charged pions and muons appearing in the event, grouped them, and applied the same cuts indicated in Table 1. For some of the cuts, we needed to generate a fake \(B\) meson decay vertex, which we used as the point in space minimizing the sum of distances to all the daughter particles. In order to train the classifiers, we selected a list of variables (features) that was similar to those used to select the signal and background samples. These features are coherent between different types of classifiers to make the comparison fair. Note that some of the features chosen depend on the decay channel that was chosen. For instance, the \(B\to 4\pi\) decay has four particles in the final state, which means the \(IP\) of two more particles is included compared to, e.g., \(B\to\pi^{+}\pi^{-}\). As explained below, different sub-selections of features were also tried to provide as complete a picture as possible. The full list of features that were used can be found in Table A1. An additional aspect we have accounted for is the detector resolution. Our simulation provides the \"true\" value of features, but real-life detectors have some inherent inaccuracies due to their resolutions, as discussed in the introduction, so what they measure differs from this; for instance, the resolution damages the discrimination power of some of the features we work with. While, in principle, this would be only be a problem when trying to find a realistic performance of the classifiers, our goal here is only to compare their performance. In any case, to use a dataset that is as close as possible to that used by LHCb analysts, we conducted a Gaussian smear of the variables that are most affected by resolution effects. These are the momenta of the particles, the DOCAs and \(IPs\). To determine the associated resolutions, we based ourselves in References [44; 45]. Apart from the features introduced above, for the \(B\to\mu^{+}\mu^{-}\) case we added an additional variable, the isolation, which is known to provide excellent signal-background discrimination in analyses of this kind [14]. The isolation exploits the fact that the usual \(B\to\mu^{+}\mu^{-}\) decays have nothing \"around\" other than the muons, while the background contains additional objects produced in \(b-\)hadron decays (see Figure 4). To quantify this isolation, we calculated it as the minimum DOCA between our selected muons and every other charged particle in the event. These other particles were selected by applying the cuts in Table 3. Defined in this way, the isolation peaks at lower values for background and has larger peaks for the signal. The simulated data consist of around 3000 samples of both signal and background events, generated as explained above. A normal LHC analysis may face difficulties in finding enough signal or background events to train a classifier, for instance, due to the very small selection efficiencies that require the simulation of an unreasonable amount of events. Additionally, analysts often face the choice between computing \"low\"- or \"high\"-level features. The former are those that were directly measured by the detector (for instance, the position or momentum or charged tracks), while the latter are combinations of those that are known to behave differently for the signal and backgrounds (such as the DOCA or \(IP\), introduced above).