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CMS-TAU-16-003 ; CERN-EP-2018-229

Performance of reconstruction and identification of $\tau$ leptons decaying to hadrons and $\nu_{\tau}$ in pp collisions at $ \sqrt{s} = $ 13 TeV

CMS Collaboration

8 September 2018

JINST 13 (2018) P10005

Abstract: The algorithm developed by the CMS Collaboration to reconstruct and identify $\tau$ leptons produced in proton-proton collisions at $\sqrt{s}= $ 7 and 8 TeV, via their decays to hadrons and a neutrino, has been significantly improved. The changes include a revised reconstruction of $\pi^{0}$ candidates, and improvements in multivariate discriminants to separate $\tau$ leptons from jets and electrons. The algorithm is extended to reconstruct $\tau$ leptons in highly Lorentz-boosted pair production, and in the high-level trigger. The performance of the algorithm is studied using proton-proton collisions recorded during 2016 at $\sqrt{s} = $ 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The performance is evaluated in terms of the efficiency for a genuine $\tau$ lepton to pass the identification criteria and of the probabilities for jets, electrons, and muons to be misidentified as $\tau$ leptons. The results are found to be very close to those expected from Monte Carlo simulation.

Links: e-print arXiv:1809.02816 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ;

Figures
png pdf	Figure 1: Distance in $\eta $ (left) and in $\phi $ (right) between the $ {{\tau} _\mathrm {h}} $ and $ {\mathrm {e}}/ {\gamma} $ candidates for $ {{\tau} _\mathrm {h}} $ decay products, as a function of the $ {p_{\mathrm {T}}} $ of the $ {\mathrm {e}}/ {\gamma} $ candidate, in simulated $ {{\tau} _\mathrm {h}} $ decays. The points show the 95% envelope for a given bin, and the solid red lines represent the fitted functions $f$ and $g$ given in Eq. 3.
png pdf	Figure 1-a: Distance in $\eta $ between the $ {{\tau} _\mathrm {h}} $ and $ {\mathrm {e}}/ {\gamma} $ candidates for $ {{\tau} _\mathrm {h}} $ decay products, as a function of the $ {p_{\mathrm {T}}} $ of the $ {\mathrm {e}}/ {\gamma} $ candidate, in simulated $ {{\tau} _\mathrm {h}} $ decays. The points show the 95% envelope for a given bin, and the solid red lines represent the fitted functions $f$ and $g$ given in Eq. 3.
png pdf	Figure 1-b: Distance in $\phi $ between the $ {{\tau} _\mathrm {h}} $ and $ {\mathrm {e}}/ {\gamma} $ candidates for $ {{\tau} _\mathrm {h}} $ decay products, as a function of the $ {p_{\mathrm {T}}} $ of the $ {\mathrm {e}}/ {\gamma} $ candidate, in simulated $ {{\tau} _\mathrm {h}} $ decays. The points show the 95% envelope for a given bin, and the solid red lines represent the fitted functions $f$ and $g$ given in Eq. 3.
png pdf	Figure 2: Misidentification probabilities as a function of the $ {{\tau} _\mathrm {h}} $ identification efficiencies, evaluated for $ {\mathrm {H}} \to {\tau} {\tau}$ (left) and $ {\mathrm {Z}}^{'}(2 TeV) \to {\tau} {\tau}$ (right), and for QCD multijet MC events. Four configurations of the reconstruction and isolation method are compared. The three points on each curve correspond, from left to right, to the tight, medium, and loose WPs. The solid curves are obtained by imposing cutoffs on $I_{{{\tau} _\mathrm {h}}}$ that decrease linearly from small to large efficiency.
png pdf	Figure 2-a: Misidentification probabilities as a function of the $ {{\tau} _\mathrm {h}} $ identification efficiencies, evaluated for $ {\mathrm {H}} \to {\tau} {\tau}$, and for QCD multijet MC events. Four configurations of the reconstruction and isolation method are compared. The three points on each curve correspond, from left to right, to the tight, medium, and loose WPs. The solid curves are obtained by imposing cutoffs on $I_{{{\tau} _\mathrm {h}}}$ that decrease linearly from small to large efficiency.
png pdf	Figure 2-b: Misidentification probabilities as a function of the $ {{\tau} _\mathrm {h}} $ identification efficiencies, evaluated for $ {\mathrm {Z}}^{'}(2 TeV) \to {\tau} {\tau}$, and for QCD multijet MC events. Four configurations of the reconstruction and isolation method are compared. The three points on each curve correspond, from left to right, to the tight, medium, and loose WPs. The solid curves are obtained by imposing cutoffs on $I_{{{\tau} _\mathrm {h}}}$ that decrease linearly from small to large efficiency.
png pdf	Figure 3: Misidentification probabilities for $ {{\tau} _\mathrm {h}} $ as a function of their identification efficiency, evaluated using $ {\mathrm {H}} \to {\tau} {\tau}$ (left), $ {\mathrm {Z}}^{'}(2 TeV) \to {\tau} {\tau}$ (right), and QCD multijet MC events. The MVA-based discriminants trained on their corresponding MC events are compared to each other, as well as to the isolation-sum discriminants. The points correspond to different working points of the discriminants. The three points for the isolation-sum discriminants from left to right correspond to the tight, medium, and loose WPs. Similarly, the six points of the MVA-based discriminants define the WP as very-very tight, very tight, tight, medium, loose, and very loose, respectively.
png pdf	Figure 3-a: Misidentification probabilities for $ {{\tau} _\mathrm {h}} $ as a function of their identification efficiency, evaluated using $ {\mathrm {H}} \to {\tau} {\tau}$ and QCD multijet MC events. The MVA-based discriminants trained on their corresponding MC events are compared to each other, as well as to the isolation-sum discriminants. The points correspond to different working points of the discriminants. The three points for the isolation-sum discriminants from left to right correspond to the tight, medium, and loose WPs. Similarly, the six points of the MVA-based discriminants define the WP as very-very tight, very tight, tight, medium, loose, and very loose, respectively.
png pdf	Figure 3-b: Misidentification probabilities for $ {{\tau} _\mathrm {h}} $ as a function of their identification efficiency, evaluated using $ {\mathrm {Z}}^{'}(2 TeV) \to {\tau} {\tau}$ and QCD multijet MC events. The MVA-based discriminants trained on their corresponding MC events are compared to each other, as well as to the isolation-sum discriminants. The points correspond to different working points of the discriminants. The three points for the isolation-sum discriminants from left to right correspond to the tight, medium, and loose WPs. Similarly, the six points of the MVA-based discriminants define the WP as very-very tight, very tight, tight, medium, loose, and very loose, respectively.
png pdf	Figure 4: Efficiency of $ {{\tau} _\mathrm {h}} $ identification, estimated using simulated $ {\mathrm {Z}}/ {\gamma ^{*}} \to {\tau} {\tau}$ events (left), and the misidentification probability estimated using simulated QCD multijet events (right) are given, for the very loose, loose, medium, tight, very tight, and very-very tight WPs of the MVA-based $ {{\tau} _\mathrm {h}} $ isolation algorithm. The efficiency and misidentification probabilities are shown as a function of ${p_{\mathrm {T}}}$ of the generated $ {{\tau} _\mathrm {h}} $ and of the reconstructed jet, respectively. Vertical bars (often smaller than the symbol size) correspond to the statistical uncertainties (the 68% Clopper-Pearson intervals [61]), while horizontal bars indicate the bin widths.
png pdf	Figure 4-a: Efficiency of $ {{\tau} _\mathrm {h}} $ identification, estimated using simulated $ {\mathrm {Z}}/ {\gamma ^{*}} \to {\tau} {\tau}$ events is given, for the very loose, loose, medium, tight, very tight, and very-very tight WPs of the MVA-based $ {{\tau} _\mathrm {h}} $ isolation algorithm. The probability is shown as a function of ${p_{\mathrm {T}}}$ of the generated $ {{\tau} _\mathrm {h}} $ and of the reconstructed jet, respectively. Vertical bars (often smaller than the symbol size) correspond to the statistical uncertainties (the 68% Clopper-Pearson intervals [61]), while horizontal bars indicate the bin widths.
png pdf	Figure 4-b: Misidentification probability estimated using simulated QCD multijet events is given, for the very loose, loose, medium, tight, very tight, and very-very tight WPs of the MVA-based $ {{\tau} _\mathrm {h}} $ isolation algorithm. The probability is shown as a function of ${p_{\mathrm {T}}}$ of the generated $ {{\tau} _\mathrm {h}} $ and of the reconstructed jet, respectively. Vertical bars (often smaller than the symbol size) correspond to the statistical uncertainties (the 68% Clopper-Pearson intervals [61]), while horizontal bars indicate the bin widths.
png pdf	Figure 5: Efficiencies of $ {{\tau} _\mathrm {h}} $ identification estimated via simulated $ {\mathrm {Z}}/ {\gamma ^{*}} \to {\tau} {\tau}$ events (left), and the $ {\mathrm {e}} \rightarrow {{\tau} _\mathrm {h}} $ misidentification probability estimated using simulated $ {\mathrm {Z}}/ {\gamma ^{*}} \to {\mathrm {e}} {\mathrm {e}}$ events (right) for the very loose, loose, medium, tight, and very tight WPs of the MVA-based electron discrimination algorithm. The efficiency is shown as a function of ${p_{\mathrm {T}}}$ of the reconstructed $ {{\tau} _\mathrm {h}} $ candidate, while the misidentification probability is shown as a function of the generated electron ${p_{\mathrm {T}}}$. The efficiency is calculated for $ {{\tau} _\mathrm {h}} $ candidates with a reconstructed decay mode that pass the loose WP of the isolation-sum discriminant, while the misidentification probability is calculated for generated electrons of $ {p_{\mathrm {T}}} > $ 20 GeV and $ {| \eta |} < 2.3$, excluding the less sensitive detector region of 1.46 $ < {| \eta |} < $ 1.56 between the barrel and endcap ECAL regions. Vertical bars (often smaller than the symbol size) indicate the statistical uncertainties (the 68% Clopper-Pearson intervals), while horizontal bars indicate the bin widths.
png pdf	Figure 5-a: Efficiencies of $ {{\tau} _\mathrm {h}} $ identification estimated via simulated $ {\mathrm {Z}}/ {\gamma ^{*}} \to {\tau} {\tau}$ events for the very loose, loose, medium, tight, and very tight WPs of the MVA-based electron discrimination algorithm. The efficiency is shown as a function of ${p_{\mathrm {T}}}$ of the reconstructed $ {{\tau} _\mathrm {h}} $ candidate. The efficiency is calculated for $ {{\tau} _\mathrm {h}} $ candidates with a reconstructed decay mode that pass the loose WP of the isolation-sum discriminant. Vertical bars (often smaller than the symbol size) indicate the statistical uncertainties (the 68% Clopper-Pearson intervals), while horizontal bars indicate the bin widths.
png pdf	Figure 5-b: The $ {\mathrm {e}} \rightarrow {{\tau} _\mathrm {h}} $ misidentification probability estimated using simulated $ {\mathrm {Z}}/ {\gamma ^{*}} \to {\mathrm {e}} {\mathrm {e}}$ events for the very loose, loose, medium, tight, and very tight WPs of the MVA-based electron discrimination algorithm. The misidentification probability is shown as a function of the generated electron ${p_{\mathrm {T}}}$. The misidentification probability is calculated for generated electrons of $ {p_{\mathrm {T}}} > $ 20 GeV and $ {| \eta |} < $ 2.3, excluding the less sensitive detector region of 1.46 $ < {| \eta |} < $ 1.56 between the barrel and endcap ECAL regions. Vertical bars (often smaller than the symbol size) indicate the statistical uncertainties (the 68% Clopper-Pearson intervals), while horizontal bars indicate the bin widths.
png pdf	Figure 6: Reconstruction and identification efficiencies for the $ {{\tau} _\mathrm {h}} $ in the $ {{\mu}} {{\tau} _\mathrm {h}} $ (upper left) and $ {{\tau} _\mathrm {h}} {{\tau} _\mathrm {h}} $ (upper right) final states, and for the $ {{\tau} _\mathrm {h}} {{\tau} _\mathrm {h}} $ pair (lower left), as a function of the generated $ {p_{\mathrm {T}}} $ of the Higgs boson, and the probability for large-radius jets in QCD multijet events to be misidentified as $ {{\tau} _\mathrm {h}} {{\tau} _\mathrm {h}} $ final states (lower right), as a function of the large-radius jet $ {p_{\mathrm {T}}}$. Vertical bars correspond to the statistical uncertainties (the 68% Clopper-Pearson intervals), while horizontal bars indicate the bin widths.
png pdf	Figure 6-a: Reconstruction and identification efficiencies for the $ {{\tau} _\mathrm {h}} $ in the $ {{\mu}} {{\tau} _\mathrm {h}} $ final state, as a function of the generated $ {p_{\mathrm {T}}} $ of the Higgs boson. Vertical bars correspond to the statistical uncertainties (the 68% Clopper-Pearson intervals), while horizontal bars indicate the bin widths.
png pdf	Figure 6-b: Reconstruction and identification efficiencies for the $ {{\tau} _\mathrm {h}} $ in the $ {{\tau} _\mathrm {h}} {{\tau} _\mathrm {h}} $ final state, as a function of the generated $ {p_{\mathrm {T}}} $ of the Higgs boson. Vertical bars correspond to the statistical uncertainties (the 68% Clopper-Pearson intervals), while horizontal bars indicate the bin widths.
png pdf	Figure 6-c: Reconstruction and identification efficiencies for the $ {{\tau} _\mathrm {h}} {{\tau} _\mathrm {h}} $ pair, as a function of the generated $ {p_{\mathrm {T}}} $ of the Higgs boson. Vertical bars correspond to the statistical uncertainties (the 68% Clopper-Pearson intervals), while horizontal bars indicate the bin widths.
png pdf	Figure 6-d: The probability for large-radius jets in QCD multijet events to be misidentified as $ {{\tau} _\mathrm {h}} {{\tau} _\mathrm {h}} $ final states, as a function of the large-radius jet $ {p_{\mathrm {T}}}$. Vertical bars correspond to the statistical uncertainties (the 68% Clopper-Pearson intervals), while horizontal bars indicate the bin widths.
png pdf	Figure 7: The fitted distribution in $ {m_\text {vis}}$ in the passing (left) and failing (right) categories for the tight WP of the MVA-based isolation. The electroweak background includes contributions from W+jets (dominating), diboson, and single top quark events. Vertical bars correspond to the statistical uncertainties in the data points (68% frequentist confidence intervals), while shaded bands to the quadratic sum of the fitted statistical and systematic uncertainties.
png pdf	Figure 7-a: The fitted distribution in $ {m_\text {vis}}$ in the passing category for the tight WP of the MVA-based isolation. The electroweak background includes contributions from W+jets (dominating), diboson, and single top quark events. Vertical bars correspond to the statistical uncertainties in the data points (68% frequentist confidence intervals), while shaded bands to the quadratic sum of the fitted statistical and systematic uncertainties.
png pdf	Figure 7-b: The fitted distribution in $ {m_\text {vis}}$ in the failing category for the tight WP of the MVA-based isolation. The electroweak background includes contributions from W+jets (dominating), diboson, and single top quark events. Vertical bars correspond to the statistical uncertainties in the data points (68% frequentist confidence intervals), while shaded bands to the quadratic sum of the fitted statistical and systematic uncertainties.
png pdf	Figure 8: Fitted distributions for the signal (upper), $ {\mathrm {e}} {{\mu}}$ passing (lower left), and the $ {\mathrm {e}} {{\mu}}$ failing (lower right) categories, using the $ {m_{\mathrm {T}}} $ for the $ {\vec{p}_{\mathrm {T}}} ^{\mu}$ and ${\vec{p}_{\mathrm {T}}^{\,\text {miss}}}$ vectors as observables for the tight WP of the MVA-based isolation with $ {p_{\mathrm {T}}} ^{{{\tau} _\mathrm {h}}}$ between 30 and 40 GeV. The electroweak background includes contributions from W+jets (dominating), diboson, and single top quark events. Vertical bars correspond to the statistical uncertainties in the data points (68% frequentist confidence intervals), while the shaded bands reflect the quadratic sum of the statistical and systematic uncertainties after the fit.
png pdf	Figure 8-a: Fitted distribution for the signal category, using the $ {m_{\mathrm {T}}} $ for the $ {\vec{p}_{\mathrm {T}}} ^{\mu}$ and ${\vec{p}_{\mathrm {T}}^{\,\text {miss}}}$ vectors as observables for the tight WP of the MVA-based isolation with $ {p_{\mathrm {T}}} ^{{{\tau} _\mathrm {h}}}$ between 30 and 40 GeV. The electroweak background includes contributions from W+jets (dominating), diboson, and single top quark events. Vertical bars correspond to the statistical uncertainties in the data points (68% frequentist confidence intervals), while the shaded bands reflect the quadratic sum of the statistical and systematic uncertainties after the fit.
png pdf	Figure 8-b: Fitted distribution for the $ {\mathrm {e}} {{\mu}}$ passing category, using the $ {m_{\mathrm {T}}} $ for the $ {\vec{p}_{\mathrm {T}}} ^{\mu}$ and ${\vec{p}_{\mathrm {T}}^{\,\text {miss}}}$ vectors as observables for the tight WP of the MVA-based isolation with $ {p_{\mathrm {T}}} ^{{{\tau} _\mathrm {h}}}$ between 30 and 40 GeV. The electroweak background includes contributions from W+jets (dominating), diboson, and single top quark events. Vertical bars correspond to the statistical uncertainties in the data points (68% frequentist confidence intervals), while the shaded bands reflect the quadratic sum of the statistical and systematic uncertainties after the fit.
png pdf	Figure 8-c: Fitted distribution for the $ {\mathrm {e}} {{\mu}}$ failing category, using the $ {m_{\mathrm {T}}} $ for the $ {\vec{p}_{\mathrm {T}}} ^{\mu}$ and ${\vec{p}_{\mathrm {T}}^{\,\text {miss}}}$ vectors as observables for the tight WP of the MVA-based isolation with $ {p_{\mathrm {T}}} ^{{{\tau} _\mathrm {h}}}$ between 30 and 40 GeV. The electroweak background includes contributions from W+jets (dominating), diboson, and single top quark events. Vertical bars correspond to the statistical uncertainties in the data points (68% frequentist confidence intervals), while the shaded bands reflect the quadratic sum of the statistical and systematic uncertainties after the fit.
png pdf	Figure 9: The $ {m_{\mathrm {T}}} $ distribution for selected $ {\mathrm {W}}\to {\tau} {\nu}$ (left) and $ {\mathrm {W}}\to {{\mu}} {\nu}$ (right) events after the maximum likelihood fit. The medium WP of the MVA-based isolation discriminant is applied to select $ {\mathrm {W}}\to {\tau} {\nu}$ events. The electroweak background contribution includes diboson and single top quark events. Vertical bars correspond to the statistical uncertainties in the data points (68% frequentist confidence intervals), while the shaded bands to the quadratic sum of the statistical and systematic uncertainties after the fit.
png pdf	Figure 9-a: The $ {m_{\mathrm {T}}} $ distribution for selected $ {\mathrm {W}}\to {\tau} {\nu}$ events after the maximum likelihood fit. The medium WP of the MVA-based isolation discriminant is applied to select $ {\mathrm {W}}\to {\tau} {\nu}$ events. The electroweak background contribution includes diboson and single top quark events. Vertical bars correspond to the statistical uncertainties in the data points (68% frequentist confidence intervals), while the shaded bands to the quadratic sum of the statistical and systematic uncertainties after the fit.
png pdf	Figure 9-b: The $ {m_{\mathrm {T}}} $ distribution for selected $ {\mathrm {W}}\to {{\mu}} {\nu}$ events after the maximum likelihood fit. The electroweak background contribution includes diboson and single top quark events. Vertical bars correspond to the statistical uncertainties in the data points (68% frequentist confidence intervals), while the shaded bands to the quadratic sum of the statistical and systematic uncertainties after the fit.
png pdf	Figure 10: Fit of the measured scale factors to a constant value in the $ {{\tau} _\mathrm {h}} $ identification efficiency, for the tight WP of the MVA-based isolation discriminant in $ {\mathrm {Z}}/ {\gamma ^{*}} $, $ {{\mathrm {t}\overline {\mathrm {t}}}} $, and W events, as a function of $ {p_{\mathrm {T}}} ^{{{\tau} _\mathrm {h}}}$. The shaded band represents the uncertainties in the fit, where the result is combined with the difference obtained using a first-order polynomial instead of a constant for the downward deviations, which also contain an additional contribution from the uncertainty in track-reconstruction efficiency.
png pdf	Figure 11: Fitted distributions to the passing (left) and failing (right) events for $ {{\tau} _\mathrm {h}} $ from highly boosted $ {\tau}$ lepton pairs that pass the medium WP of the MVA-based isolation discriminant. The electroweak background includes contributions from W+jets (dominating), diboson, and single top quark events. Vertical bars correspond to the statistical uncertainties in the data points (68% frequentist confidence intervals), while the shaded bands provide the quadratic sum of the statistical and systematic uncertainties after the fit.
png pdf	Figure 11-a: Fitted distributions to the passing events for $ {{\tau} _\mathrm {h}} $ from highly boosted $ {\tau}$ lepton pairs that pass the medium WP of the MVA-based isolation discriminant. The electroweak background includes contributions from W+jets (dominating), diboson, and single top quark events. Vertical bars correspond to the statistical uncertainties in the data points (68% frequentist confidence intervals), while the shaded bands provide the quadratic sum of the statistical and systematic uncertainties after the fit.
png pdf	Figure 11-b: Fitted distributions to the failing events for $ {{\tau} _\mathrm {h}} $ from highly boosted $ {\tau}$ lepton pairs that pass the medium WP of the MVA-based isolation discriminant. The electroweak background includes contributions from W+jets (dominating), diboson, and single top quark events. Vertical bars correspond to the statistical uncertainties in the data points (68% frequentist confidence intervals), while the shaded bands provide the quadratic sum of the statistical and systematic uncertainties after the fit.
png pdf	Figure 12: Probabilities for quark and gluon jets in W+jet events to pass the loose (uppermost), medium (middle), and tight (lowest) WPs of the MVA-based isolation discriminant as a function of $ {p_{\mathrm {T}}} ^\text {jet}$ (left) and $\eta ^\text {jet}$ (right). The misidentification probabilities in data are compared to expectations from simulation. The vertical bars in the simulated and observed misidentification probabilities include statistical uncertainties from the limited event count in both data and simulated samples, including the background subtraction. The shaded bands contain the systematic uncertainties related to background subtraction and the jet energy scale.
png pdf	Figure 12-a: Probability for quark and gluon jets in W+jet events to pass the loose WP of the MVA-based isolation discriminant as a function of $ {p_{\mathrm {T}}} ^\text {jet}$. The misidentification probabilities in data are compared to expectations from simulation. The vertical bars in the simulated and observed misidentification probabilities include statistical uncertainties from the limited event count in both data and simulated samples, including the background subtraction. The shaded bands contain the systematic uncertainties related to background subtraction and the jet energy scale.
png pdf	Figure 12-b: Probability for quark and gluon jets in W+jet events to pass the loose WP of the MVA-based isolation discriminant as a function of $\eta ^\text {jet}$. The misidentification probabilities in data are compared to expectations from simulation. The vertical bars in the simulated and observed misidentification probabilities include statistical uncertainties from the limited event count in both data and simulated samples, including the background subtraction. The shaded bands contain the systematic uncertainties related to background subtraction and the jet energy scale.
png pdf	Figure 12-c: Probability for quark and gluon jets in W+jet events to pass the medium WP of the MVA-based isolation discriminant as a function of $ {p_{\mathrm {T}}} ^\text {jet}$. The misidentification probabilities in data are compared to expectations from simulation. The vertical bars in the simulated and observed misidentification probabilities include statistical uncertainties from the limited event count in both data and simulated samples, including the background subtraction. The shaded bands contain the systematic uncertainties related to background subtraction and the jet energy scale.
png pdf	Figure 12-d: Probability for quark and gluon jets in W+jet events to pass the medium WP of the MVA-based isolation discriminant as a function of $\eta ^\text {jet}$. The misidentification probabilities in data are compared to expectations from simulation. The vertical bars in the simulated and observed misidentification probabilities include statistical uncertainties from the limited event count in both data and simulated samples, including the background subtraction. The shaded bands contain the systematic uncertainties related to background subtraction and the jet energy scale.
png pdf	Figure 12-e: Probability for quark and gluon jets in W+jet events to pass the tight WP of the MVA-based isolation discriminant as a function of $ {p_{\mathrm {T}}} ^\text {jet}$. The misidentification probabilities in data are compared to expectations from simulation. The vertical bars in the simulated and observed misidentification probabilities include statistical uncertainties from the limited event count in both data and simulated samples, including the background subtraction. The shaded bands contain the systematic uncertainties related to background subtraction and the jet energy scale.
png pdf	Figure 12-f: Probability for quark and gluon jets in W+jet events to pass the ltight WP of the MVA-based isolation discriminant as a function of $\eta ^\text {jet}$. The misidentification probabilities in data are compared to expectations from simulation. The vertical bars in the simulated and observed misidentification probabilities include statistical uncertainties from the limited event count in both data and simulated samples, including the background subtraction. The shaded bands contain the systematic uncertainties related to background subtraction and the jet energy scale.
png pdf	Figure 13: Probabilities for quark and gluon jets in $ {\mathrm {e}} {{\mu}}$+jets events to pass the loose (uppermost), medium (middle), and tight (lowest) WPs of the MVA-based isolation discriminant as a function of $ {p_{\mathrm {T}}} ^\text {jet}$ (left) and $\eta ^\text {jet}$ (right). The misidentification probabilities in data are compared to expectations from simulation. The vertical bars in the simulated and observed misidentification probabilities include statistical uncertainties from the limited event count in both data and simulated samples, including the background subtraction. The shaded bands contain the systematic uncertainties related to background subtraction and the jet energy scale.
png pdf	Figure 13-a: Probability for quark and gluon jets in $ {\mathrm {e}} {{\mu}}$+jets events to pass the loose WP of the MVA-based isolation discriminant as a function of $ {p_{\mathrm {T}}} ^\text {jet}$. The misidentification probabilities in data are compared to expectations from simulation. The vertical bars in the simulated and observed misidentification probabilities include statistical uncertainties from the limited event count in both data and simulated samples, including the background subtraction. The shaded bands contain the systematic uncertainties related to background subtraction and the jet energy scale.
png pdf	Figure 13-b: Probability for quark and gluon jets in $ {\mathrm {e}} {{\mu}}$+jets events to pass the loose WP of the MVA-based isolation discriminant as a function of $\eta ^\text {jet}$. The misidentification probabilities in data are compared to expectations from simulation. The vertical bars in the simulated and observed misidentification probabilities include statistical uncertainties from the limited event count in both data and simulated samples, including the background subtraction. The shaded bands contain the systematic uncertainties related to background subtraction and the jet energy scale.
png pdf	Figure 13-c: Probability for quark and gluon jets in $ {\mathrm {e}} {{\mu}}$+jets events to pass the medium WP of the MVA-based isolation discriminant as a function of $ {p_{\mathrm {T}}} ^\text {jet}$. The misidentification probabilities in data are compared to expectations from simulation. The vertical bars in the simulated and observed misidentification probabilities include statistical uncertainties from the limited event count in both data and simulated samples, including the background subtraction. The shaded bands contain the systematic uncertainties related to background subtraction and the jet energy scale.
png pdf	Figure 13-d: Probability for quark and gluon jets in $ {\mathrm {e}} {{\mu}}$+jets events to pass the medium WP of the MVA-based isolation discriminant as a function of $\eta ^\text {jet}$. The misidentification probabilities in data are compared to expectations from simulation. The vertical bars in the simulated and observed misidentification probabilities include statistical uncertainties from the limited event count in both data and simulated samples, including the background subtraction. The shaded bands contain the systematic uncertainties related to background subtraction and the jet energy scale.
png pdf	Figure 13-e: Probability for quark and gluon jets in $ {\mathrm {e}} {{\mu}}$+jets events to pass the tight WP of the MVA-based isolation discriminant as a function of $ {p_{\mathrm {T}}} ^\text {jet}$. The misidentification probabilities in data are compared to expectations from simulation. The vertical bars in the simulated and observed misidentification probabilities include statistical uncertainties from the limited event count in both data and simulated samples, including the background subtraction. The shaded bands contain the systematic uncertainties related to background subtraction and the jet energy scale.
png pdf	Figure 13-f: Probability for quark and gluon jets in $ {\mathrm {e}} {{\mu}}$+jets events to pass the tight WP of the MVA-based isolation discriminant as a function of $\eta ^\text {jet}$. The misidentification probabilities in data are compared to expectations from simulation. The vertical bars in the simulated and observed misidentification probabilities include statistical uncertainties from the limited event count in both data and simulated samples, including the background subtraction. The shaded bands contain the systematic uncertainties related to background subtraction and the jet energy scale.
png pdf	Figure 14: Fitted distributions in $ {m_\text {vis}}$ in the passing category for the medium (left) and very tight (right) WPs of the against-$ {\mathrm {e}}$ discriminant in the barrel region. The electroweak background includes contributions from W+jets (dominating), diboson, and single top quark events. Vertical bars correspond to the small (not visible) statistical uncertainties in the data points (68% frequentist confidence intervals), while the shaded bands provide the quadratic sum of the statistical and systematic uncertainties after the fit.
png pdf	Figure 14-a: Fitted distribution in $ {m_\text {vis}}$ in the passing category for the medium WP of the against-$ {\mathrm {e}}$ discriminant in the barrel region. The electroweak background includes contributions from W+jets (dominating), diboson, and single top quark events. Vertical bars correspond to the small (not visible) statistical uncertainties in the data points (68% frequentist confidence intervals), while the shaded bands provide the quadratic sum of the statistical and systematic uncertainties after the fit.
png pdf	Figure 14-b: Fitted distribution in $ {m_\text {vis}}$ in the passing category for the very tight WP of the against-$ {\mathrm {e}}$ discriminant in the barrel region. The electroweak background includes contributions from W+jets (dominating), diboson, and single top quark events. Vertical bars correspond to the small (not visible) statistical uncertainties in the data points (68% frequentist confidence intervals), while the shaded bands provide the quadratic sum of the statistical and systematic uncertainties after the fit.
png pdf	Figure 15: Probability for electrons to pass different working points of the against-$ {\mathrm {e}}$ discriminant, split into the barrel (left) and endcap (right) regions. For each working point, the $ {\mathrm {e}} \rightarrow {{\tau} _\mathrm {h}} $ misidentification probability is defined as the fraction of probes passing that working point relative to the total number of probes. Vertical bars correspond to the statistical and the quadratic sum of the statistical and systematic uncertainties, respectively, for simulated and observed data.
png pdf	Figure 15-a: Probability for electrons to pass different working points of the against-$ {\mathrm {e}}$ discriminant, in the barrel region. For each working point, the $ {\mathrm {e}} \rightarrow {{\tau} _\mathrm {h}} $ misidentification probability is defined as the fraction of probes passing that working point relative to the total number of probes. Vertical bars correspond to the statistical and the quadratic sum of the statistical and systematic uncertainties, respectively, for simulated and observed data.
png pdf	Figure 15-b: Probability for electrons to pass different working points of the against-$ {\mathrm {e}}$ discriminant, in the endcap region. For each working point, the $ {\mathrm {e}} \rightarrow {{\tau} _\mathrm {h}} $ misidentification probability is defined as the fraction of probes passing that working point relative to the total number of probes. Vertical bars correspond to the statistical and the quadratic sum of the statistical and systematic uncertainties, respectively, for simulated and observed data.
png pdf	Figure 16: Fitted distribution in $ {m_\text {vis}}$ in the passing category for the loose (left) and tight (right) WPs of the against-$ {{\mu}}$ discriminant in the region of $ {| \eta |} < $ 0.4. The electroweak background includes contributions from W+jets (dominating), diboson, and single top quark events. Vertical bars correspond to the small (not visible) statistical uncertainties in the data points (68% frequentist confidence intervals), while the shaded bands provide the quadratic sum of the statistical and systematic uncertainties after the fit.
png pdf	Figure 16-a: Fitted distribution in $ {m_\text {vis}}$ in the passing category for the loose WP of the against-$ {{\mu}}$ discriminant in the region of $ {| \eta |} < $ 0.4. The electroweak background includes contributions from W+jets (dominating), diboson, and single top quark events. Vertical bars correspond to the small (not visible) statistical uncertainties in the data points (68% frequentist confidence intervals), while the shaded bands provide the quadratic sum of the statistical and systematic uncertainties after the fit.
png pdf	Figure 16-b: Fitted distribution in $ {m_\text {vis}}$ in the passing category for the tight WP of the against-$ {{\mu}}$ discriminant in the region of $ {| \eta |} < $ 0.4. The electroweak background includes contributions from W+jets (dominating), diboson, and single top quark events. Vertical bars correspond to the small (not visible) statistical uncertainties in the data points (68% frequentist confidence intervals), while the shaded bands provide the quadratic sum of the statistical and systematic uncertainties after the fit.
png pdf	Figure 17: Probability for muons to pass the loose (left) and tight (right) WPs of the against-$ {{\mu}}$ discriminant, as a function of the $ {| \eta |}$ of the probe. For each working point, the $ {{\mu}} \rightarrow {{\tau} _\mathrm {h}} $ misidentification probability is defined as the fraction of probes passing that working point relative to the total number of probes. Vertical bars correspond to the statistical and the quadratic sum of the statistical and systematic uncertainties, respectively, for simulated and observed data.
png pdf	Figure 17-a: Probability for muons to pass the loose WP of the against-$ {{\mu}}$ discriminant, as a function of the $ {| \eta |}$ of the probe. The $ {{\mu}} \rightarrow {{\tau} _\mathrm {h}} $ misidentification probability is defined as the fraction of probes passing that working point relative to the total number of probes. Vertical bars correspond to the statistical and the quadratic sum of the statistical and systematic uncertainties, respectively, for simulated and observed data.
png pdf	Figure 17-b: Probability for muons to pass the tight WP of the against-$ {{\mu}}$ discriminant, as a function of the $ {| \eta |}$ of the probe. The $ {{\mu}} \rightarrow {{\tau} _\mathrm {h}} $ misidentification probability is defined as the fraction of probes passing that working point relative to the total number of probes. Vertical bars correspond to the statistical and the quadratic sum of the statistical and systematic uncertainties, respectively, for simulated and observed data.
png pdf	Figure 18: The distributions in $m_{{{\tau} _\mathrm {h}}}$ for $ {{\mu}} {{\tau} _\mathrm {h}} $ events in the $ {\mathrm {h}^{\pm} {\pi ^0}} $ decay channel. The data are compared to predictions with different shifts applied to the $ {{\tau} _\mathrm {h}} $ energy scale: 0% (upper), $-$6% (lower left), and $+$6% (lower right). The electroweak background includes contributions from W+jets (dominating), diboson, and single top quark events. Vertical bars (smaller than the symbol size) correspond to the statistical uncertainty in the data points (68% frequentist confidence intervals), while the shaded bands provide the expected systematic uncertainties.
png pdf	Figure 18-a: The distributions in $m_{{{\tau} _\mathrm {h}}}$ for $ {{\mu}} {{\tau} _\mathrm {h}} $ events in the $ {\mathrm {h}^{\pm} {\pi ^0}} $ decay channel. The data are compared to predictions with 0% shift applied to the $ {{\tau} _\mathrm {h}} $ energy scale. The electroweak background includes contributions from W+jets (dominating), diboson, and single top quark events. Vertical bars (smaller than the symbol size) correspond to the statistical uncertainty in the data points (68% frequentist confidence intervals), while the shaded bands provide the expected systematic uncertainties.
png pdf	Figure 18-b: The distributions in $m_{{{\tau} _\mathrm {h}}}$ for $ {{\mu}} {{\tau} _\mathrm {h}} $ events in the $ {\mathrm {h}^{\pm} {\pi ^0}} $ decay channel. The data are compared to predictions with $-$6% shift applied to the $ {{\tau} _\mathrm {h}} $ energy scale. The electroweak background includes contributions from W+jets (dominating), diboson, and single top quark events. Vertical bars (smaller than the symbol size) correspond to the statistical uncertainty in the data points (68% frequentist confidence intervals), while the shaded bands provide the expected systematic uncertainties.
png pdf	Figure 18-c: The distributions in $m_{{{\tau} _\mathrm {h}}}$ for $ {{\mu}} {{\tau} _\mathrm {h}} $ events in the $ {\mathrm {h}^{\pm} {\pi ^0}} $ decay channel. The data are compared to predictions with $+$6% shift applied to the $ {{\tau} _\mathrm {h}} $ energy scale. The electroweak background includes contributions from W+jets (dominating), diboson, and single top quark events. Vertical bars (smaller than the symbol size) correspond to the statistical uncertainty in the data points (68% frequentist confidence intervals), while the shaded bands provide the expected systematic uncertainties.
png pdf	Figure 19: Single-$ {{\tau} _\mathrm {h}} $ efficiency of the $ {{\mu}} {{\tau} _\mathrm {h}} $ (left) and $ {{\tau} _\mathrm {h}} {{\tau} _\mathrm {h}} $ (right) triggers. The efficiency is computed per single $ {{\tau} _\mathrm {h}} $, using the tag-and-probe method as a function of the offline-reconstructed $ {p_{\mathrm {T}}} ^{{{\tau} _\mathrm {h}}}$. Observed data are compared to simulated $ {\mathrm {Z}}/ {\gamma ^{*}} \to {\tau} {\tau}$ events selected through the same procedure. Vertical bars correspond to the statistical uncertainties. The plot on the right has data points fitted using a cumulative (integral) distribution of the Crystal Ball function [76].
png pdf	Figure 19-a: Single-$ {{\tau} _\mathrm {h}} $ efficiency of the $ {{\mu}} {{\tau} _\mathrm {h}} $ trigger. The efficiency is computed per single $ {{\tau} _\mathrm {h}} $, using the tag-and-probe method as a function of the offline-reconstructed $ {p_{\mathrm {T}}} ^{{{\tau} _\mathrm {h}}}$. Observed data are compared to simulated $ {\mathrm {Z}}/ {\gamma ^{*}} \to {\tau} {\tau}$ events selected through the same procedure. Vertical bars correspond to the statistical uncertainties.
png pdf	Figure 19-b: Single-$ {{\tau} _\mathrm {h}} $ efficiency of the $ {{\tau} _\mathrm {h}} {{\tau} _\mathrm {h}} $ trigger. The efficiency is computed per single $ {{\tau} _\mathrm {h}} $, using the tag-and-probe method as a function of the offline-reconstructed $ {p_{\mathrm {T}}} ^{{{\tau} _\mathrm {h}}}$. Observed data are compared to simulated $ {\mathrm {Z}}/ {\gamma ^{*}} \to {\tau} {\tau}$ events selected through the same procedure. Vertical bars correspond to the statistical uncertainties. Data points are fitted using a cumulative (integral) distribution of the Crystal Ball function [76].

Tables
png pdf	Table 1: Tau lepton decays and their branching fractions.
png pdf	Table 2: Systematic uncertainties affecting the measurements described in Sections 9-12. Given are the source of the uncertainty and whether the distribution in question is affected.
png pdf	Table 3: Data-to-simulation scale factors for different MVA-based isolation working points with $\Delta R=$ 0.5, measured using $ {\mathrm {Z}}/ {\gamma ^{*}} $ events. An uncertainty of 3.9% is added in quadrature to the uncertainty returned by the fit to account for the uncertainty in track reconstruction efficiency.
png pdf	Table 4: Data-to-simulation scale factors for different MVA-based isolation working points obtained from $ {{\mathrm {t}\overline {\mathrm {t}}}} $ events.
png pdf	Table 5: The scale factor in the $ {{\tau} _\mathrm {h}} $ identification efficiency, the normalization of W boson production with $m_{{\mathrm {W}}} > $ 200 GeV, $r_{{\mathrm {W}}}$, and the correlation coefficient between the two quantities obtained from the fit, measured for MVA-based discriminants using $\Delta R =$ 0.5 in $ {\mathrm {W}}\to {\tau} {\nu}$ events.
png pdf	Table 6: Data-to-simulation scale factors for different working points of the MVA-based isolation discriminant, using highly boosted $ {\mathrm {Z}}/ {\gamma ^{*}} $ events decaying to $ {\tau}$ lepton pairs.
png pdf	Table 7: Numerical results of the tau energy scale measurements.
png pdf	Table 8: Triggers with $ {{\tau} _\mathrm {h}} $ candidates used to record pp collisions in 2016: the final state (Channel), HLT $ {p_{\mathrm {T}}} $ thresholds and $ {{\tau} _\mathrm {h}} $ isolation working point, L1 $ {p_{\mathrm {T}}} $ thresholds, peak instantaneous luminosity ($ {\mathcal {L}} _\text {peak}$) in the period of operation as main trigger, and integrated luminosity (${\mathcal {L}} $) collected with the trigger. The $ {{\tau} _\mathrm {h}} {{\tau} _\mathrm {h}} $ and $ {{\tau} _\mathrm {h}} {{p_{\mathrm {T}}} ^\text {miss}} $ triggers are seeded by sets of L1 triggers with thresholds dynamically adjusted as a function of the instantaneous luminosity to maintain a constant L1 rate, given by the ranges in $ {p_{\mathrm {T}}}$. The trigger $ {p_{\mathrm {T}}} $ thresholds and isolation criteria were successively tightened over the data-taking period to keep the rate of events passing HLT approximately constant with increasing instantaneous luminosity.

Summary

The "hadron-plus-strips'' algorithm developed at the CMS experiment to reconstruct and identify $\tau\to\text{hadrons}+\nu_{\tau}$ decays in proton-proton collisions at $\sqrt{s}=$ 7 and 8 TeV, as presented in Ref. [24], has been improved. The changes include a dynamic strip reconstruction, the reconstruction of highly boosted $\tau$ lepton pairs, and the introduction of additional variables in the multivariate-analysis discriminants used to reject jets and electrons. The isolation discriminants have also been optimized to cope with the large pileup of events in $\sqrt{s} = $ 13 TeV proton-proton runs. The performance of the improved algorithm has been measured using 35.9 fb$^{-1}$ of data recorded during 2016 at $\sqrt{s} = $ 13 TeV. The ${\tau_\mathrm{h}}$ identification efficiency in data at low, intermediate, and high transverse momenta, as well as for highly Lorentz-boosted $\tau$ lepton pairs, is similar to that expected from Monte Carlo simulation, while differences of 10-20% are found between data and simulation for the $\text{jet} \mapsto {\tau_\mathrm{h}}$ misidentification probability. The $\mathrm{e} \mapsto {\tau_\mathrm{h}}$ and $\mu \mapsto {\tau_\mathrm{h}}$ misidentification probabilities are smaller than those of the previous version of the algorithm under the same running conditions, while maintaining a high efficiency for the selection of genuine ${\tau_\mathrm{h}}$ candidates. The corresponding data-to-simulation scale factors have also been determined. The energy scale of ${\tau_\mathrm{h}}$ candidates is measured, and its response relative to Monte Carlo simulation is found to be close to unity. Finally, a specialized ${\tau_\mathrm{h}}$ reconstruction and identification algorithm has been used in the high-level trigger, and its performance has been presented.

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