A Deep Neural Network for Simultaneous Estimation of b Jet Energy and Resolution

Abstract

We describe a method to obtain point and dispersion estimates for the energies of jets arising from b quarks produced in proton-proton collisions at an energy of $\sqrt{s}=13\text{TeV}$ at the CERN LHC. The algorithm is trained on a large sample of simulated b jets and validated on data recorded by the CMS detector in 2017 corresponding to an integrated luminosity of 41 ${\text{fb}}^{-1}$ . A multivariate regression algorithm based on a deep feed-forward neural network employs jet composition and shape information, and the properties of reconstructed secondary vertices associated with the jet. The results of the algorithm are used to improve the sensitivity of analyses that make use of b jets in the final state, such as the observation of Higgs boson decay to $\text{b}\overline{\text{b}}$ .

Keywords: CMS; Deep learning; Higgs boson; Jet energy; Jet resolution; b jets.

Fig. 1

(upper) The $p_{\mathrm{T}}^{\text{reco}}$ distribution for reconstructed b jets in an MC $\text{t}\overline{\text{t}}$sample. (lower) Distribution of the regression target for the MC $\text{t}\overline{\text{t}}$training sample

Fig. 2

The 25, 40, 50, and 75% quantiles are shown for the b jet energy scale $p_{\mathrm{T}}^{\text{gen}}/p_{\mathrm{T}}^{\text{reco}}$ distribution before (blue dashdot) and after (red solid) applying the regression correction as a function of jet $p_{\mathrm{T}}$ (left), $\eta$ (center), and $\rho$ (right). The $\eta$ and $\rho$ distributions are shown for jets with $p_{\mathrm{T}}$ $\in$ [70, 100] $\text{GeV}$

Fig. 3

Relative jet energy resolution, $\overline{\mathrm{s}}$, as a function of generator-level jet $p_{\mathrm{T}}^{\text{gen}}$ (left), $\eta$ (center), and $\rho$ (right) for b jets from $\text{t}\overline{\text{t}}$ MC events. The average $p_{\mathrm{T}}$ of these b jets is 80 $\text{GeV}$. The $\eta$ and $\rho$ distributions are shown for jets with $p_{\mathrm{T}}$ $\in$ [70, 100] $\text{GeV}$. The blue stars and red squares represent $\overline{\mathrm{s}}$ before and after the DNN correction, respectively. The relative difference $\Delta \overline{\mathrm{s}}/{\overline{\mathrm{s}}}_{\text{baseline}}$ between the $\overline{\mathrm{s}}$ values before and after DNN corrections is shown in the lower panels

Fig. 4

Correlation between jet energy resolution $\mathrm{s}$ and the average jet energy resolution estimator $⟨\widehat{\mathrm{s}}⟩$ for b jets from $\text{t}\overline{\text{t}}$ MC events. The blue circles correspond to the inclusive $p_{\mathrm{T}}$ spectrum, while the blue band represents 20% up and down variations of the fitted $⟨\widehat{\mathrm{s}}⟩$ trend for the inclusive $p_{\mathrm{T}}$ spectrum. The red stars correspond to jets with $p_{\mathrm{T}}$ $\in$ [30, 50] $\text{GeV}$, orange diamonds to $p_{\mathrm{T}}$ $\in$ [50, 70] $\text{GeV}$, and green crosses to $p_{\mathrm{T}}$ $\in$ [110,120] $\text{GeV}$

Fig. 5

Dijet invariant mass distributions for simulated samples of $\text{Z}(\to {\ell }^{+}{\ell }^{-})\text{H}(\to \text{b}\overline{\text{b}})$ events, where two jets and two leptons were selected. Distributions are shown before (dotted blue) and after (solid red) applying the b jet energy corrections. A Bukin function [44] was used to fit the distribution. The fitted mean and width of the core of each distribution are displayed in the figure

Fig. 6

Distribution of the ratio between the transverse momentum of the leading b-tagged jet and that of the dilepton system from the decay of the Z boson. Distributions are shown before (upper) and after (lower) applying the b jet energy corrections. The $\overline{\mathrm{s}}$ values of the core distributions are included in the figures. The black points and histogram show the distributions for data and simulated events, respectively.