Observables used in the neural network

The previously mentioned measurements of top-quark charge relied on using theb-jet charge as the proxy. Nevertheless, the hadronically-decayingWboson also carries extra charge information and its charge of±1 is three times larger in magnitude than that of thebquark. Previous measurements have not exploited this option, presumably because the correct matching of light-quark jets to the corresponding hadronically-decayingW-boson is challenging. However, for boosted top-quark decays, the decay

(5)The jet momentum vector is sometimes replaced with a unit vector in the momentum direction. Given the normalisation term in the denominator, both such definitions are equivalent.

8. Prospect of charge asymmetry measurement in boosted all-hadronictt¯events

products are highly-collimated and can be clustered within a single large-Rjet. The identification of tracks from individual quarks contained within the large-Rjet is attempted using anti-k_t track jets with R =0.2, ghost-matched with the large-Rjet. Since top quark has three decay products, in an ideal case, it is expected that there should be three track jets within the large-Rjet, one of which isb-tagged.

Therefore the charges of the leading-p_Tb-tagged track jet and two leading-p_T non-b-tagged track jets are considered as inputs for the NN.

The choice of using three track jets, out of which one is b-tagged, is motivated by Fig. 8.1, showing the true origin of the track jets based on the matching with partonic decay products of the top (anti-)quark. Theb-tagged track jet in approximately 90 % of the cases originates from ab-quark, and most of the background jets are mistagged charm jets. The two highest-p_Tnon-b-tagged track jets are most frequently matched to non-b-quarks from the top (anti-)quark decay, with the sub-leading non-b-jet not being matched to any of the decay products in approximately 22 %. Including more track jets as inputs is discouraged based on Fig.8.1d, which shows that in more than 60 % of cases, the 3^rd-leading-p_Tnon-b-tagged track jet is not matched to any of the decay products of a top (anti-)quark.

¯b ¯c ¯s ¯d ¯u ? u d s c b Leading track jet matched parton 0.05 Subleading track jet matched parton 0.05 3^rd-leadingpTtrack jet matched parton 0.1

Fig. 8.1: The classification of the origin ofb-tagged track jet (a), the leading (b), 2^nd-leading (c) and 3^rd-leading (d) non-b-tagged track jet matched to a candidate large-Rjet. The classification is based on matching a decay product from hadronically decaying top (anti-)quark with the track jet based on

∆R(parton,track jet) <0.2. The middle column in the plots, labelled as "?", marks track jets which were not matched to any of the decay products.

The JVC discriminant shows that exploiting information from displaced vertices of aB-hadron decay can provide additional discrimination power. The charges of secondary and tertiary vertices reconstructed by JetFitter forb-tagged track jets and relevant auxiliary variables are thus also considered for inclusion as NN inputs. The charge of the vertices reconstructed by the SV inclusive vertex-finding

8.3. Top-quark charge discrimination using neural networks

algorithm described in Sec.4.4.5is also considered. The aim is to examine whether there is additional information not extracted by JetFitter observables, that can be exploited for further discrimination of the charge of theB-hadrons initiating theb-tagged track-jets contained within the large-Rjet candidates.

The JVC discriminant itself is not used as an input for the NN, primarily because it was optimised on an inclusive sample oftt¯events. Such a sample typically does not contain sufficient amount of generated evens for outlier regions of phase space, such as the high-p_T region examined in the all-hadronic channel. It is argued here, that adding some of the input observables directly into the NN trained in this study is more preferable, than nesting the JVC NN output as an input into another NN.

Table 8.4: List of observables of the track-jets matched to a large-Rjet, which are considered as the NN input observables.

Variable(s) Description

b-tagged track jet variables Q^b Charge of theb-tagged track jet

p_T^b p_Tof theb-tagged track jet

N_trk^b Track multiplicity of theb-tagged track jet Q^SV Charge of the SV vertex of theb-tagged track jet N_trk^SV Track multiplicity of the SV vertex

L^SV_3D Distance of the SV vertex from primary vertex

∆L^SV_3D Uncertainty on the distance

Q^JFS Charge of the JetFitter secondary vertex

N_trk^JFS Track multiplicity of the JetFitter secondary vertex

L^JFS_3D Distance of the JetFitter secondary vertex from primary vertex

∆L^JFS_3D Uncertainty on the distance

Q^JFT Charge of the JetFitter tertiary vertex

N_trk^JFT Track multiplicity of the JetFitter tertiary vertex

L^JFT_3D Distance of the JetFitter tertiary vertex from primary vertex

∆L^JFT_3D Uncertainty on the distance

Non-b-tagged track jet variables

Q¹,Q² Charge of the leading and sub-leading non-b-tagged track jet p_T¹,p²_T p_Tof the leading and sub-leading non-b-tagged track jet

N_trk¹ ,N_trk² Track multiplicity of the leading and sub-leading non-b-tagged track jet Binary-decision variables

d¹ Whether the large-Rjet has at least one non-b-tagged track jet d² Whether the large-Rjet has at least two non-b-tagged track jets d^JFS Whether JetFitter secondary vertex is reconstructed

d^JFT Whether JetFitter tertiary vertex is reconstructed d^SV Whether SV vertex is reconstructed

The full list of observables investigated for the NN is listed in Table8.4. Since not all of the observables are always defined, the binary-decision variablesd¹,d², d^JFS,d^JFTandd^SV are added, which have a value of zero if the respective object is undefined, or one, if it is defined. The fraction

8. Prospect of charge asymmetry measurement in boosted all-hadronictt¯events

of large-Rjets in the sample, where the variables are defined, is listed in Table8.5. For undefined objects, the respective variables such asp_T, track multiplicity or vertex position are set to zero. The corresponding charges are also set to zero, thus giving no discrimination for the class of the considered large-Rjet. This is an alternative, simplified approach, where it is possible to train a single NN with inputs that are not always defined, in contrast to the approach employed for the JVC, where for each combination of defined variables, a separate NN was trained.

For the charge observables, the method of how the charges of the tracks should be weighted, and the value of κmust be chosen. The definitions of jet charge which are considered, are defined in Eq.8.1and8.3. The figure of merit in the optimisation is the separation power of the charge variables.

The κvalue is optimised separately for the individual charge observables. It is found that the two charge definitions give very similar separation for equalκvalues, yielding no preference of one over the other. As such, the definition in Eq.8.3is chosen. The optimised values ofκfrom a scan in the range ofκ = 0.1 up to 1.0 are shown in Table8.6. In all cases a maximum in the scanned interval was found, corresponding to separation power quoted in the table. For illustration, theQ^bandQ¹jet charge variables using the respective optimisedκvalues are shown in Fig.8.2. All of the distributions of the NN input variables are shown in App.D.1.

−1.0 −0.5 0.0 0.5 1.0 Q^b 10000

20000 30000 40000 50000 60000 70000 80000 90000

Events Large-R Jet (top)

Large-R Jet (anti-top)

(a)

−1.0 −0.5 0.0 0.5 1.0 Q¹ 10000

20000 30000 40000 50000 60000 70000 80000

Events Large-R Jet (top)

Large-R Jet (anti-top)

(b)

Fig. 8.2: Distribution of theQ^b(a) andQ¹(b) track jet charges for large-Rjets originating from top quark (red line) and top anti-quark (blue line). The spikes at values±1 correspond to track jets, where all tracks have the same charge. Most frequently, these track jets consist of two tracks, which is the minimum track multiplicity requirement.

Table 8.5: Fraction of large-Rjets for which respective features are defined, denoted by the binary-decision variables listed in the table.

Feature d¹ d² d^JFS d^JFT d^SV [%] of cases defined 95 59 95 54 95

Except for the charge observables in Table8.6, the other variables areauxiliaryin the sense that they do not have discrimination power itself, but may provide additional information to the NN through correlations. Of particular interest are observables which have different correlations for each of the two classes of large-Rjets, because such observables bring additional discrimination power that the NN can exploit. The correlations and anti-correlations of track multiplicities with charge are an example of this property, as shown in Fig.8.4and8.5, motivating why the track multiplicity variables are included

8.3. Top-quark charge discrimination using neural networks

Table 8.6: Optimised values ofκparameter for the charge definition of the individual charge observables.

The separation powerSfor the optimal value ofκis also shown, based on the definition in Sec.7.3.1.

Variable Q^b Q¹ Q² Q^SV Q^JFS Q^JFT

κ 0.6 0.4 0.4 0.4 0.5 0.5

S[%] 8.8 15.2 9.2 9.6 5.1 1.4

as the NN inputs. The distances of vertices from primary vertex and corresponding fitted distance errors are tested as NN input observables since they could be expected to provide some metric of the quality of the reconstructed vertex. Similarly the p_T of the individual jets are tested as NN inputs under the assumption that the kinematic information may be relevant since the tracking performance is expected to deteriorate with highp_T. Whether these assumptions transfer into a better discrimination of the trained NN is not clear, therefore a test needs to be designed to assess the gain of inclusion of these observables in the NN. The approach used in this study is to train multiple NN setups with different choices of input observables, and compare the performance of these networks. First, the NN architecture and training is discussed in the following section, and subsequently the NN setups are compared in Sec.8.3.4.