CMS-HIG-18-027

CMS-HIG-18-027 ; CERN-EP-2019-261
A deep neural network for simultaneous estimation of b jet energy and resolution
CMS Collaboration
12 December 2019
Computing and Software for Big Science 4 (2020) 10
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 TeV at the CERN LHC. The algorithm is trained on a large simulated sample of b jets and validated on data recorded by the CMS detector in 2017 corresponding to an integrated luminosity of 41 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 $\mathrm{b\bar{b}}$.
Links: e-print arXiv:1912.06046 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: (left) The $ {{p_{\mathrm {T}}} ^\text {reco}}$ distribution for reconstructed b jets in an MC ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample. (right) Distribution of the regression target for the MC ${\mathrm{t} {}\mathrm{\bar{t}}}$ training sample.
png pdf	Figure 1-a: The $ {{p_{\mathrm {T}}} ^\text {reco}}$ distribution for reconstructed b jets in an MC ${\mathrm{t} {}\mathrm{\bar{t}}}$ sample.
png pdf	Figure 1-b: Distribution of the regression target for the MC ${\mathrm{t} {}\mathrm{\bar{t}}}$ training sample.
png pdf	Figure 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).
png pdf	Figure 2-a: 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 ${p_{\mathrm {T}}}$.
png pdf	Figure 2-b: 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 $\eta $.
png pdf	Figure 2-c: 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 $\rho $.
png pdf	Figure 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 ${\mathrm{t} {}\mathrm{\bar{t}}}$ MC events. The average ${p_{\mathrm {T}}}$ of these b jets is 80 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.
png pdf	Figure 3-a: Relative jet energy resolution, ${\overline {\mathrm {s}}}$,
png pdf	Figure 3-b: Relative jet energy resolution, ${\overline {\mathrm {s}}}$,
png pdf	Figure 3-c: Relative jet energy resolution, ${\overline {\mathrm {s}}}$,
png pdf	Figure 4: Correlation between jet energy resolution $\mathrm {s}$ and the average jet energy resolution estimator $< \hat{\mathrm {s}}> $ for b jets from ${\mathrm{t} {}\mathrm{\bar{t}}}$ 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 $< \hat{\mathrm {s}}> $ trend for the inclusive ${p_{\mathrm {T}}}$ spectrum. The red stars correspond to jets with ${p_{\mathrm {T}}}$ $\in $ [30, 50] GeV, orange diamonds to ${p_{\mathrm {T}}}$ $\in $ [50, 70] GeV, and green crosses to ${p_{\mathrm {T}}}$ $\in $ [110,120] GeV.
png pdf	Figure 5: Dijet invariant mass distributions for simulated samples of ${\mathrm{Z} (\to \ell ^+\ell ^-)\mathrm{H} (\to b \mathrm{\bar{b}})}$ 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 [40] was used to fit the distribution. The fitted mean and width of the core of each distribution are displayed in the figure.
png pdf	Figure 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 (left) and after (right) 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.
png pdf	Figure 6-a: 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 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.
png pdf	Figure 6-b: 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 after 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.

Tables
png pdf	Table 1: Relative differences $\Delta {\overline {\mathrm {s}}} / {\overline {\mathrm {s}}} _\text {baseline}$ between the ${\overline {\mathrm {s}}}$ values obtained before and after applying the DNN energy correction for b jets produced in the different physics processes indicated.

Summary

We have described an algorithm that makes it possible to obtain point and dispersion estimates of the energy of jets arising from b quarks in proton-proton collisions. We trained a deep, feed-forward neural network, with inputs based on jet composition and shape information, and on properties of the associated reconstructed secondary vertex for a sample of simulated b jets arising from the decays of top quark-antiquark pairs. The neural network simultaneously finds robust mean, 25 and 75% quantile estimators for the energy of a b jet. The mean estimator is based on the Huber loss function and is used as an energy correction, while the 25 and 75% quantile estimators are used to build a jet-by-jet resolution estimator, defined as half the difference between these quantiles.

The DNN-based algorithm leverages the information contained in a large training data set consisting of nearly 100 million simulated b jets, and improves the resolution of the b jet energy by 12-15% relative to that which is found after baseline corrections. An improvement of about 20% is observed in the resolution of the invariant mass of b jet pairs resulting from the decay of a Higgs boson produced in association with a Z boson. Events containing a dilepton decay of a Z boson produced in association with a b jet are used to validate the performance of the algorithm on proton-proton collision data recorded with the CMS detector. The jet energy resolution improvement observed in data is consistent with that found in simulation. The resolution estimator is further shown to predict the resolution of b jets with an accuracy of 20% over a ${p_{\mathrm{T}}}$ range between 30 and 350 GeV.

The results described here are being used by the CMS Collaboration in several physics analyses targeting final states containing b jets, including the observation of the Higgs boson decay to $\mathrm{b\bar{b}}$ [13].

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