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| CMS-PAS-HIG-18-027 | ||
| A deep neural network for simultaneous estimation of b quark energy and resolution | ||
| CMS Collaboration | ||
| September 2019 | ||
| Abstract: We describe a method to obtain point and dispersion estimates for the energy of jets arising from bottom quarks (b jets) in proton-proton (pp) collisions at the CERN LHC. The algorithm is trained using a large simulated sample of b jets produced in pp collisions recorded at an energy of $\sqrt{s}= $ 13 TeV and validated on data recorded by the CMS detector in 2017 with an integrated luminosity of 41 fb$^{-1}$. A multivariate regression estimator employing jet composition and structure information and the properties of the associated reconstructed secondary vertices is implemented using a deep feed-forward neural network. The results of the algorithm are used to improve the experimental sensitivity of analyses that make use of b jets in the final state, such as the recently published observation of the Higgs boson decay to a bottom quark-antiquark pair. | ||
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Links:
CDS record (PDF) ;
CADI line (restricted) ;
These preliminary results are superseded in this paper, CSBS 4 (2020) 10. The superseded preliminary plots can be found here. |
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| Figures | |
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Figure 1:
(left) The $ {p_\text {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. |
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Figure 1-a:
The $ {p_\text {T}}^{\text {reco}}$ distribution for reconstructed b jets in an MC ${\mathrm{t} \mathrm{\bar{t}}}$ sample. |
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Figure 1-b:
Distribution of the regression target for the MC ${\mathrm{t} \mathrm{\bar{t}}}$ training sample. |
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Figure 2:
25, 40, 50, and 75% quantiles are shown for b jet energy scale $ {p_\text {T}}^{\text {gen}}/ {p_\text {T}}^{\text {reco}}$ distribution before (blue) and after (red) applying the regression correction as a function of jet ${p_{\mathrm {T}}}$ (left), $\eta $ (center), and $\rho $ (right). |
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Figure 2-a:
25, 40, 50, and 75% quantiles are shown for b jet energy scale $ {p_\text {T}}^{\text {gen}}/ {p_\text {T}}^{\text {reco}}$ distribution before (blue) and after (red) applying the regression correction as a function of jet ${p_{\mathrm {T}}}$. |
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Figure 2-b:
25, 40, 50, and 75% quantiles are shown for b jet energy scale $ {p_\text {T}}^{\text {gen}}/ {p_\text {T}}^{\text {reco}}$ distribution before (blue) and after (red) applying the regression correction as a function of jet $\eta $. |
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Figure 2-c:
25, 40, 50, and 75% quantiles are shown for b jet energy scale $ {p_\text {T}}^{\text {gen}}/ {p_\text {T}}^{\text {reco}}$ distribution before (blue) and after (red) applying the regression correction as a function of jet $\rho $. |
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Figure 3:
Relative jet energy resolution, $\bar{\sigma}$, as a function of generator-level jet $ {p_\text {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 $\bar{\sigma}$ before and after the DNN correction, respectively. The relative difference between the $\bar{\sigma}$ values before and after DNN corrections are shown in the lower panels. |
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Figure 3-a:
Relative jet energy resolution, $\bar{\sigma}$, as a function of generator-level $ {p_\text {T}}^{\text {gen}}$ 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 $\bar{\sigma}$ before and after the DNN correction, respectively. The relative difference between the $\bar{\sigma}$ values before and after DNN corrections are shown in the lower panel. |
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Figure 3-b:
Relative jet energy resolution, $\bar{\sigma}$, as a function of generator-level $\eta $ 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 $\bar{\sigma}$ before and after the DNN correction, respectively. The relative difference between the $\bar{\sigma}$ values before and after DNN corrections are shown in the lower panel. |
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Figure 3-c:
Relative jet energy resolution, $\bar{\sigma}$, as a function of generator-level $\rho $ 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 $\bar{\sigma}$ before and after the DNN correction, respectively. The relative difference between the $\bar{\sigma}$ values before and after DNN corrections are shown in the lower panel. |
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Figure 4:
Correlation between jet resolution $\sigma $ and the mean jet energy resolution estimator $\hat{\sigma}$ values for b jets from ${\mathrm{t} \mathrm{\bar{t}}}$ MC events. Blue circles correspond to the inclusive ${p_{\mathrm {T}}}$ spectrum, while the blue band represents 20% up and down variations of the $\hat{\sigma}$ value. 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. |
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Figure 5:
Dijet invariant mass distributions for simulated samples of ${\mathrm{Z} (\to \ell ^+\ell ^-)\mathrm{H} (\to \mathrm{b} \mathrm{\bar{b}})}$ events, where two jets and two leptons were selected. Jets compatible with hadronization of b quarks were required to have ${p_{\mathrm {T}}} > $ 20 GeV and $ {| \eta |} < $ 2.4, leptons were required to have ${p_{\mathrm {T}}} > $ 20 GeV, and Z boson candidates constructed from lepton pairs were required to have ${p_{\mathrm {T}}} > $ 150 GeV. Distributions are shown before (dotted blue) and after (red line) applying the b jet energy corrections. A Bukin function [42] is used to fit the distribution. The fitted mean and width of the core of the distribution are displayed on the figure. |
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Figure 6:
Distribution of the ratio between the transverse momentum of the leading jet compatible with the hadronization of a b quark and that of the dilepton system from the Z boson decay. Distributions are shown before (left) and after (right) applying the b jet energy corrections. The mean and $\bar{\sigma}$ of the core of the distribution are displayed on the figures. The black points and histogram show the distributions for data and simulated events, respectively. |
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Figure 6-a:
Distribution of the ratio between the transverse momentum of the leading jet compatible with the hadronization of a b quark and that of the dilepton system from the Z boson decay. Distributions are shown before applying the b jet energy corrections. The mean and $\bar{\sigma}$ of the core of the distribution are displayed on the figure. The black points and histogram show the distributions for data and simulated events, respectively. |
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Figure 6-b:
Distribution of the ratio between the transverse momentum of the leading jet compatible with the hadronization of a b quark and that of the dilepton system from the Z boson decay. Distributions are shown after applying the b jet energy corrections. The mean and $\bar{\sigma}$ of the core of the distribution are displayed on the figure. The black points and histogram show the distributions for data and simulated events, respectively. |
| Tables | |
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Table 1:
Relative differences between the $\bar{\sigma}$ values obtained before and after applying the DNN energy correction for b jets produced in the different physics processes indicated. |
| Summary |
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We have described an algorithm that makes it possible to obtain point and dispersion estimates of the energy of jets arising from bottom quarks in proton-proton (pp) collisions at the LHC. We trained a deep feed-forward neural network, with inputs based on jet composition information and on properties of the associated reconstructed secondary vertices for a sample of simulated b jets arising from the decays of top quark-antiquark pairs. The neural network simultaneously finds a robust centroid estimator of the energy of a b jet, based on the Huber loss function, and estimators of the 25 and 75% quantiles. The algorithm leverages the information contained in a large training dataset consisting of nearly 100 million simulated b jets, and improves the b jet energy resolution by roughly 13% compared to baseline corrections. The improvement is also observed in samples of b jets coming from simulated Higgs boson decays. 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 based 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, defined as half the difference between the 75 and 25% quantiles of the target distribution, is further shown to predict the actual resolution of b jets with an accuracy better than 20% over a ${p_{\mathrm{T}}}$ range greater than an order of magnitude. The results of the algorithm described here are applied by the CMS Collaboration in several physics analyses targeting final states containing b jets, including the recently announced observation of the Higgs boson decay to a pair of b quarks [13]. |
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