This chapter provides a comparison between different sets of input variables used for the training of the classification BDT. Version v2 of the classification BDT is used as reference for the following studies. Such version was trained with 17 input variables, including both the likelihood discriminant and two variables related to the reconstruction BDT (see Sec- tion 7.2.2). This version is compared with other two: v3, which adds ten variables associated to the reconstruction of jets with larger radius, and v4, which includes another set of ten kinematic variables on top of the previous ten.
The usage of jets with a larger radius is motivated by the fact that, at high masses, the decay products of the charged Higgs boson are expected to be very boosted, i.e. to have a large momentum. This is due to the large difference between the mass of the H+and the masses of the top and bottom quarks, which is converted in kinetic energy. Consequently, the particles produced by the decay of the two quarks can be quite collimated and jets with large radius have a good chance of including the full final state of each of the decays. The reconstruction of the large-radius jets is performed with the anti-ktalgorithm (see Section 4.5.1), with a radius
set to r = 1.0. However, the algorithm is not applied to the topo-clusters of the calorimeters, but on the small-radius jets, which are used for further re-clustering [160, 161]. The benefit of performing the re-clustering on the small-radius jets is that their calibration is inherited by the re-clustered jets and no additional systematic uncertainties are needed. In order to minimise contaminations from pile-up, the re-clustered jets are required to include at least two small-radius jets and to have a mass larger than 50 GeV. Furthermore, small-radius jets are subtracted from each re-clustered jet if their pT is lower than 5% of its total transverse momentum. Lastly, all large-radius jets are required to have an |η| ≤ 2. Large-radius jets with a mass larger than 100 GeV and a transverse momentum larger than 300 GeV are defined "top-tagged".
The variables used for the training of version v3 include: • the number of re-clustered jets in the event;
• the number of top-tagged re-clustered jets in the event; • the invariant mass and pT of the leading re-clustered jet;
Additional studies on the BDT input variables
• the invariant mass and pT of the leading top-tagged re-clustered jet; • the number of small-radius jets contained in the leading re-clustered jet;
• the number of b-tagged small-radius jets contained in the leading re-clustered jet; • the invariant mass of the system made of the leading re-clustered jet and the leading
b-jet (not included in the re-clustered jet);
• the invariant mass of the system made of the leading re-clustered jet and the leading light-jet (not included in the re-clustered jet);
The input variables used for the training of version v4 include the set above and the following: • ∆RMax(pT)
bb : the angular distance between the two b-jets with the maximum pT; • MjjMin(∆R): the invariant mass of the closest jets;
• pjet3
T : the transverse momentum of the third jet (ordered from the highest to the lowest
pT); • Hall
4 : the fourth Fox-Wolfram moment calculated using all leptons and jets in the event; • MMax(pT)
bj : the invariant mass of the system made of the jet and b-jet with the maximum pT;
• MbjMin(∆R): the invariant mass of the system made of the closest jet and b-jet; • Hall
T : the sum of the transverse momentum of all jets, leptons and neutrinos in the event;
• MMax(pT)
jj : the invariant mass of the system made of the jets with the maximum pT; • ∆RMin(∆R)lj : the angular distance between the lepton and its closest jet;
• ∆ηMax(∆η)jj : the maximum difference in pseudorapidity between jets;
The three versions were trained (and tested) inclusively in the ≥5j≥3b region, using 300 trees, with a maximum depth of 5. The performances of the three classification BDTs are compared in Figure D.1 (a) and Figure D.1 (b). The addition of the re-clustered jet variables has almost no impact on the separation power of the BDT, while some change is observed for version v4. The relative improvement is however smaller than 5% in both cases. The small change in performance is most probably due to the limited number of training events. This is particularly true for the variables related to the re-clustered jets. In fact, given the requirements on the mass and pT of the large-radius jets, the percentage of background events including one or more re-clustered jet is very low (∼ 8%). Furthermore, the reconstruction BDT is already capable of performing a "re-clustering" and it has the advantage of being able to exploit the full kinematics of the small-radius jets, instead of their angular separation only.
(a) AUCs.
(b) Relative improvement.
Figure D.1: Performance of the classification BDTs. Sub-figure (a) presents the AUC values obtained with versions v2, v3 and v4 of the BDT, while sub-figure (b) shows the relative improvement provided by version v3 and v4 with respect to v2. The AUCs are computed comparing the BDT distribution of the signal with the one produced by the full set of SM backgrounds, in the ≥5j≥3b region.