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CMS-TAU-18-001 ; CERN-EP-2019-012

An embedding technique to determine $\tau\tau$ backgrounds in proton-proton collision data

CMS Collaboration

3 March 2019

JINST 14 (2019) P06032

Abstract: An embedding technique is presented to estimate standard model ${\tau_{\mathrm{h}} \tau_{\mathrm{h}} }$ backgrounds from data with minimal simulation input. In the data, the muons are removed from reconstructed $\mu\mu$ events and replaced with simulated tau leptons with the same kinematic properties. In this way a set of hybrid events is obtained that does not rely on simulation except for the decay of the tau leptons. The challenges in describing the underlying event or the production of associated jets in the simulation are avoided. The technique described in this paper was developed for CMS. Its validation and the inherent uncertainties are also discussed. The demonstration of the performance of the technique is based on a sample of proton-proton collisions collected by CMS in 2017 at $\sqrt{s} = $ 13 TeV corresponding to an integrated luminosity of 41.5 fb$^{-1}$.

Links: e-print arXiv:1903.01216 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ;

Figures
png pdf	Figure 1: Schematic view of the four main steps of the $ {\tau}$-embedding technique, as described in Section 5. A ${{{\mathrm {Z}} \to {{\mu}} {{\mu}}}}$ candidate event is selected in data ("${{{\mathrm {Z}} \to {{\mu}} {{\mu}}}}$ Selection''), all energy deposits associated with the muons are removed from the event record ("${{{\mathrm {Z}} \to {{\mu}} {{\mu}}}}$ Cleaning''), and two tau lepton decays are simulated in an otherwise empty detector ("${{{\mathrm {Z}} \to {\tau} {\tau}}}$ Simulation''). Finally all energy deposits of the simulated tau lepton decays are combined with the original reconstructed event record ("${{{\mathrm {Z}} \to {\tau} {\tau}}}$ Hybrid''). In the example, one of the simulated tau leptons decays into a muon and the other one into hadrons.
png pdf	Figure 2: (Left) invariant mass, $ {m_{\mu \mu}} $, of the selected dimuon Z boson candidates and (right) $ {p_{\mathrm {T}}} $ of the trailing muon after the event selection, as described in Section 5.1.
png pdf	Figure 2-a: Invariant mass, $ {m_{\mu \mu}} $, of the selected dimuon Z boson candidates, as described in Section 5.1.
png pdf	Figure 2-b: $ {p_{\mathrm {T}}} $ of the trailing muon after the event selection, as described in Section 5.1.
png pdf	Figure 3: Display of a ${{{\mathrm {Z}} \to {{\mu}} {{\mu}}}}$ candidate event in the 2017 data set, in the $\eta $-$\phi $ plane at the surface of the calorimeters (left) before and (right) after the hits and energy deposits associated with the muons have been removed from the reconstructed event record. The red crosses indicate the intercepts of the reconstructed muon trajectories with the calorimeter surface. The red (blue) boxes correspond to clusters in the ECAL (HCAL).
png pdf	Figure 3-a: Display of a ${{{\mathrm {Z}} \to {{\mu}} {{\mu}}}}$ candidate event in the 2017 data set, in the $\eta $-$\phi $ plane at the surface of the calorimeters before the hits and energy deposits associated with the muons have been removed from the reconstructed event record. The red crosses indicate the intercepts of the reconstructed muon trajectories with the calorimeter surface. The red (blue) boxes correspond to clusters in the ECAL (HCAL).
png pdf	Figure 3-b: Display of a ${{{\mathrm {Z}} \to {{\mu}} {{\mu}}}}$ candidate event in the 2017 data set, in the $\eta $-$\phi $ plane at the surface of the calorimeters after the hits and energy deposits associated with the muons have been removed from the reconstructed event record. The red crosses indicate the intercepts of the reconstructed muon trajectories with the calorimeter surface. The red (blue) boxes correspond to clusters in the ECAL (HCAL).
png pdf	Figure 4: Comparison of the reconstructed invariant mass, $ {m_{\mu \mu}} $, of the selected muons from a simulated ${{{\mathrm {Z}} \to {{\mu}} {{\mu}}}}$ sample with the corresponding $ {{\mu}}$-embedded event sample. On the left the (red histogram) simulated ${{{\mathrm {Z}} \to {{\mu}} {{\mu}}}}$ sample and the $ {{\mu}}$-embedded event sample (blue dots) with and (green dots) without the correction for the effects of the finite detector resolution, as described in the text, are shown. On the right (magenta histogram) $ {m_{\mu \mu}} $ from the simulated ${{{\mathrm {Z}} \to {{\mu}} {{\mu}}}}$ sample before FSR is shown in addition, to illustrate the effect.
png pdf	Figure 4-a: Comparison of the reconstructed invariant mass, $ {m_{\mu \mu}} $, of the selected muons from a simulated ${{{\mathrm {Z}} \to {{\mu}} {{\mu}}}}$ sample with the corresponding $ {{\mu}}$-embedded event sample. The (red histogram) simulated ${{{\mathrm {Z}} \to {{\mu}} {{\mu}}}}$ sample and the $ {{\mu}}$-embedded event sample (blue dots) with and (green dots) without the correction for the effects of the finite detector resolution, as described in the text, are shown.
png pdf	Figure 4-b: Comparison of the reconstructed invariant mass, $ {m_{\mu \mu}} $, of the selected muons from a simulated ${{{\mathrm {Z}} \to {{\mu}} {{\mu}}}}$ sample with the corresponding $ {{\mu}}$-embedded event sample. The (magenta histogram) $ {m_{\mu \mu}} $ from the simulated ${{{\mathrm {Z}} \to {{\mu}} {{\mu}}}}$ sample before FSR is shown to illustrate the effect.
png pdf	Figure 5: Comparison of $ {{\mu}}$-embedded events with exactly the same ${{{\mathrm {Z}} \to {{\mu}} {{\mu}}}}$ events from simulation. Shown are the (upper left) $\eta $ and (upper right) $ {p_{\mathrm {T}}} $ distributions of the leading muon in $ {p_{\mathrm {T}}} $, (middle left) $ {{p_{\mathrm {T}}} ^\text {miss}} $, (middle right) $ {m_{\text {jj}}} $, (lower left) jet and, (lower right) b jet multiplicities, as described in the text.
png pdf	Figure 5-a: Comparison of $ {{\mu}}$-embedded events with exactly the same ${{{\mathrm {Z}} \to {{\mu}} {{\mu}}}}$ events from simulation. Shown is the $\eta $ distribution of the leading muon in $ {p_{\mathrm {T}}} $, as described in the text.
png pdf	Figure 5-b: Comparison of $ {{\mu}}$-embedded events with exactly the same ${{{\mathrm {Z}} \to {{\mu}} {{\mu}}}}$ events from simulation. Shown is the $ {p_{\mathrm {T}}} $ distribution of the leading muon in $ {p_{\mathrm {T}}} $, as described in the text.
png pdf	Figure 5-c: Comparison of $ {{\mu}}$-embedded events with exactly the same ${{{\mathrm {Z}} \to {{\mu}} {{\mu}}}}$ events from simulation. Shown is $ {{p_{\mathrm {T}}} ^\text {miss}} $, as described in the text.
png pdf	Figure 5-d: Comparison of $ {{\mu}}$-embedded events with exactly the same ${{{\mathrm {Z}} \to {{\mu}} {{\mu}}}}$ events from simulation. Shown is $ {m_{\text {jj}}} $, as described in the text.
png pdf	Figure 5-e: Comparison of $ {{\mu}}$-embedded events with exactly the same ${{{\mathrm {Z}} \to {{\mu}} {{\mu}}}}$ events from simulation. Shown is the jet multiplicity, as described in the text.
png pdf	Figure 5-f: Comparison of $ {{\mu}}$-embedded events with exactly the same ${{{\mathrm {Z}} \to {{\mu}} {{\mu}}}}$ events from simulation. Shown is the b-jet multiplicity, as described in the text.
png pdf	Figure 6: Comparison of $ {{\mu}}$-embedded events with exactly the same ${{{\mathrm {Z}} \to {{\mu}} {{\mu}}}}$ events from simulation. Shown is the mean transverse momentum (energy) flux per muon, from all reconstructed particles with the distance $R$ from the muon, split by (upper left) charged hadrons from the PV and (upper right) PU vertices, (lower left) photons, and (lower right) neutral hadrons. The distributions are shown for the $ {\mu ^-} $ and for events with $ {m_{\mu \mu}} $ close to the nominal Z boson mass.
png pdf	Figure 6-a: Comparison of $ {{\mu}}$-embedded events with exactly the same ${{{\mathrm {Z}} \to {{\mu}} {{\mu}}}}$ events from simulation. Shown is the mean transverse momentum (energy) flux per muon, from all reconstructed particles with the distance $R$ from the muon, split by charged hadrons from the PV vertices. The distribution is shown for the $ {\mu ^-} $ and for events with $ {m_{\mu \mu}} $ close to the nominal Z boson mass.
png pdf	Figure 6-b: Comparison of $ {{\mu}}$-embedded events with exactly the same ${{{\mathrm {Z}} \to {{\mu}} {{\mu}}}}$ events from simulation. Shown is the mean transverse momentum (energy) flux per muon, from all reconstructed particles with the distance $R$ from the muon, split by charged hadrons from the PU vertices. The distribution is shown for the $ {\mu ^-} $ and for events with $ {m_{\mu \mu}} $ close to the nominal Z boson mass.
png pdf	Figure 6-c: Comparison of $ {{\mu}}$-embedded events with exactly the same ${{{\mathrm {Z}} \to {{\mu}} {{\mu}}}}$ events from simulation. Shown is the mean transverse momentum (energy) flux per muon, from all reconstructed particles with the distance $R$ from the muon, split by photons. The distribution is shown for the $ {\mu ^-} $ and for events with $ {m_{\mu \mu}} $ close to the nominal Z boson mass.
png pdf	Figure 6-d: Comparison of $ {{\mu}}$-embedded events with exactly the same ${{{\mathrm {Z}} \to {{\mu}} {{\mu}}}}$ events from simulation. Shown is the mean transverse momentum (energy) flux per muon, from all reconstructed particles with the distance $R$ from the muon, split by neutral hadrons. The distribution is shown for the $ {\mu ^-} $ and for events with $ {m_{\mu \mu}} $ close to the nominal Z boson mass.
png pdf	Figure 7: Comparison of e-embedded events with a statistically independent sample of simulated ${{{\mathrm {Z}} \to {\mathrm {e}} {\mathrm {e}}}}$ events. Shown are distributions of the energy-weighted standard deviations of a 5$\times $5 crystal array in (upper left) $\eta $, $\sigma _{i\eta i\eta}$, and (upper right) $\phi $, $\sigma _{i\phi i\phi}$, as described in the text, (lower left) the number $N_{\mathrm {GSF}}$ of detector hits, used for the Gaussian Sum Filter algorithm [27] as described in Section 3, and (lower right) the multivariate discriminator for the identification of electrons (electron-ID BDT). The black arrow, shown in addition to the electron-ID BDT distribution, indicates the working point with 80% efficiency in the displayed electron $\eta $ region. For better visibility, the statistical uncertainties of both samples, red-shaded band for simulated ${{{\mathrm {Z}} \to {\mathrm {e}} {\mathrm {e}}}}$ events, and blue vertical bars for e-embedded events, are multiplied by 10 for the figures.
png pdf	Figure 7-a: Comparison of e-embedded events with a statistically independent sample of simulated ${{{\mathrm {Z}} \to {\mathrm {e}} {\mathrm {e}}}}$ events. Shown are distributions of the energy-weighted standard deviations of a 5$\times $5 crystal array in $\eta $, $\sigma _{i\eta i\eta}$, as described in the text. For better visibility, the statistical uncertainties of both samples, red-shaded band for simulated ${{{\mathrm {Z}} \to {\mathrm {e}} {\mathrm {e}}}}$ events, and blue vertical bars for e-embedded events, are multiplied by 10.
png pdf	Figure 7-b: Comparison of e-embedded events with a statistically independent sample of simulated ${{{\mathrm {Z}} \to {\mathrm {e}} {\mathrm {e}}}}$ events. Shown are distributions of the energy-weighted standard deviations of a 5$\times $5 crystal array in $\phi $, $\sigma _{i\phi i\phi}$, as described in the text. For better visibility, the statistical uncertainties of both samples, red-shaded band for simulated ${{{\mathrm {Z}} \to {\mathrm {e}} {\mathrm {e}}}}$ events, and blue vertical bars for e-embedded events, are multiplied by 10.
png pdf	Figure 7-c: Comparison of e-embedded events with a statistically independent sample of simulated ${{{\mathrm {Z}} \to {\mathrm {e}} {\mathrm {e}}}}$ events. Shown are distributions of the energy-weighted standard deviations of a 5$\times $5 crystal array in the number $N_{\mathrm {GSF}}$ of detector hits, used for the Gaussian Sum Filter algorithm [27] as described in Section 3. For better visibility, the statistical uncertainties of both samples, red-shaded band for simulated ${{{\mathrm {Z}} \to {\mathrm {e}} {\mathrm {e}}}}$ events, and blue vertical bars for e-embedded events, are multiplied by 10.
png pdf	Figure 7-d: Comparison of e-embedded events with a statistically independent sample of simulated ${{{\mathrm {Z}} \to {\mathrm {e}} {\mathrm {e}}}}$ events. Shown are distributions of the energy-weighted standard deviations of a 5$\times $5 crystal array in the multivariate discriminator for the identification of electrons (electron-ID BDT). The black arrow, shown in addition to the electron-ID BDT distribution, indicates the working point with 80% efficiency in the displayed electron $\eta $ region. For better visibility, the statistical uncertainties of both samples, red-shaded band for simulated ${{{\mathrm {Z}} \to {\mathrm {e}} {\mathrm {e}}}}$ events, and blue vertical bars for e-embedded events, are multiplied by 10.
png pdf	Figure 8: Comparison of the e-embedded events with a statistically independent sample of simulated ${{{\mathrm {Z}} \to {\mathrm {e}} {\mathrm {e}}}}$ events. Shown are the distributions of (left) $m_{{{\mathrm {e}} {\mathrm {e}}}}$ and (right) $ {p_{\mathrm {T}}} $ of the leading electron in $ {p_{\mathrm {T}}} $. The blue vertical bars and red-shaded bands correspond to the statistical uncertainty of each sample. The effect of a variation of the electron energy scale of $\pm $1% is also shown by the green lines.
png pdf	Figure 8-a: Comparison of the e-embedded events with a statistically independent sample of simulated ${{{\mathrm {Z}} \to {\mathrm {e}} {\mathrm {e}}}}$ events. Shown is the distribution of $m_{{{\mathrm {e}} {\mathrm {e}}}}$. The blue vertical bars and red-shaded bands correspond to the statistical uncertainty of each sample. The effect of a variation of the electron energy scale of $\pm $1% is also shown by the green lines.
png pdf	Figure 8-b: Comparison of the e-embedded events with a statistically independent sample of simulated ${{{\mathrm {Z}} \to {\mathrm {e}} {\mathrm {e}}}}$ events. Shown is the distribution of the $ {p_{\mathrm {T}}} $ of the leading electron in $ {p_{\mathrm {T}}} $. The blue vertical bars and red-shaded bands correspond to the statistical uncertainty of each sample. The effect of a variation of the electron energy scale of $\pm $1% is also shown by the green lines.
png pdf	Figure 9: Comparison of $ {\tau}$-embedded events with a statistically independent sample of simulated ${{{\mathrm {Z}} \to {\tau} {\tau}}}$ events. Shown are the (left) $\eta $ and (right) $ {p_{\mathrm {T}}} $ distributions of the (upper row) electron in the $ {{\mathrm {e}} {\mu}} {+} {{\mathrm {e}} {\tau}_{\text {h}}} $ final states, (middle row) muon in $ {{\mathrm {e}} {\mu}} {+} {{\mu} {\tau}_{\text {h}}} $ final states, and (lower row) $ {\tau}_{\text {h}} $ candidate in the $ {{\mathrm {e}} {\tau}_{\text {h}}} {+} {{\mu} {\tau}_{\text {h}}} $ final states. The blue vertical bars and red-shaded bands correspond to the statistical uncertainty of each sample. The effect of a variation of the electron ($ {\tau}_{\text {h}} $) energy scale of $\pm $1.0% ($\pm $1.2%) is shown by the green lines.
png pdf	Figure 9-a: Comparison of $ {\tau}$-embedded events with a statistically independent sample of simulated ${{{\mathrm {Z}} \to {\tau} {\tau}}}$ events. Shown is the $\eta $ distribution of the electron in the $ {{\mathrm {e}} {\mu}} {+} {{\mathrm {e}} {\tau}_{\text {h}}} $ final states. The blue vertical bars and red-shaded bands correspond to the statistical uncertainty of each sample.
png pdf	Figure 9-b: Comparison of $ {\tau}$-embedded events with a statistically independent sample of simulated ${{{\mathrm {Z}} \to {\tau} {\tau}}}$ events. Shown is the $ {p_{\mathrm {T}}} $ distribution of the electron in the $ {{\mathrm {e}} {\mu}} {+} {{\mathrm {e}} {\tau}_{\text {h}}} $ final states. The blue vertical bars and red-shaded bands correspond to the statistical uncertainty of each sample. The effect of a variation of the electron ($ {\tau}_{\text {h}} $) energy scale of $\pm $1.0% ($\pm $1.2%) is shown by the green lines.
png pdf	Figure 9-c: Comparison of $ {\tau}$-embedded events with a statistically independent sample of simulated ${{{\mathrm {Z}} \to {\tau} {\tau}}}$ events. Shown is the $\eta $ distribution of the muon in $ {{\mathrm {e}} {\mu}} {+} {{\mu} {\tau}_{\text {h}}} $ final states. The blue vertical bars and red-shaded bands correspond to the statistical uncertainty of each sample.
png pdf	Figure 9-d: Comparison of $ {\tau}$-embedded events with a statistically independent sample of simulated ${{{\mathrm {Z}} \to {\tau} {\tau}}}$ events. Shown is the $ {p_{\mathrm {T}}} $ distribution of the muon in $ {{\mathrm {e}} {\mu}} {+} {{\mu} {\tau}_{\text {h}}} $ final states. The blue vertical bars and red-shaded bands correspond to the statistical uncertainty of each sample.
png pdf	Figure 9-e: Comparison of $ {\tau}$-embedded events with a statistically independent sample of simulated ${{{\mathrm {Z}} \to {\tau} {\tau}}}$ events. Shown is the $\eta $ distribution of the $ {\tau}_{\text {h}} $ candidate in the $ {{\mathrm {e}} {\tau}_{\text {h}}} {+} {{\mu} {\tau}_{\text {h}}} $ final states. The blue vertical bars and red-shaded bands correspond to the statistical uncertainty of each sample.
png pdf	Figure 9-f: Comparison of $ {\tau}$-embedded events with a statistically independent sample of simulated ${{{\mathrm {Z}} \to {\tau} {\tau}}}$ events. Shown is the $ {p_{\mathrm {T}}} $ distribution of the $ {\tau}_{\text {h}} $ candidate in the $ {{\mathrm {e}} {\tau}_{\text {h}}} {+} {{\mu} {\tau}_{\text {h}}} $ final states. The blue vertical bars and red-shaded bands correspond to the statistical uncertainty of each sample. The effect of a variation of the electron ($ {\tau}_{\text {h}} $) energy scale of $\pm $1.0% ($\pm $1.2%) is shown by the green lines.
png pdf	Figure 10: Comparison of $ {\tau}$-embedded events with a statistically independent sample of simulated ${{{\mathrm {Z}} \to {\tau} {\tau}}}$ events. Shown are distributions of (upper left) $ {I_{\text {rel}}^{{\mathrm {e}}}} $, (upper right) $ {{p_{\mathrm {T}}} ^\text {miss}} $, (middle left) $ {I_{\text {rel}}^{{\mu}}} $, (middle right) $ {m_{\text {jj}}} $, (lower left) $ {\tau}_{\text {h}} $-ID BDT, and $ {m_{\text {vis}}} $, as discussed in the text. The black arrows indicate the working points usually used in the target analyses. The blue vertical bars and red-shaded bands correspond to the statistical uncertainty of each sample. The effect of a variation of the $ {\tau}_{\text {h}} $ energy scale of $\pm $1.2% is shown by the green lines.
png pdf	Figure 10-a: Comparison of $ {\tau}$-embedded events with a statistically independent sample of simulated ${{{\mathrm {Z}} \to {\tau} {\tau}}}$ events. Shown is the distribution of $ {I_{\text {rel}}^{{\mathrm {e}}}} $, as discussed in the text. The black arrow indicates the working points usually used in the target analyses. The blue vertical bars and red-shaded bands correspond to the statistical uncertainty of each sample.
png pdf	Figure 10-b: Comparison of $ {\tau}$-embedded events with a statistically independent sample of simulated ${{{\mathrm {Z}} \to {\tau} {\tau}}}$ events. Shown is the distribution of $ {{p_{\mathrm {T}}} ^\text {miss}} $, as discussed in the text. The blue vertical bars and red-shaded bands correspond to the statistical uncertainty of each sample.
png pdf	Figure 10-c: Comparison of $ {\tau}$-embedded events with a statistically independent sample of simulated ${{{\mathrm {Z}} \to {\tau} {\tau}}}$ events. Shown is the distribution of $ {I_{\text {rel}}^{{\mu}}} $, as discussed in the text. The black arrow indicates the working points usually used in the target analyses. The blue vertical bars and red-shaded bands correspond to the statistical uncertainty of each sample.
png pdf	Figure 10-d: Comparison of $ {\tau}$-embedded events with a statistically independent sample of simulated ${{{\mathrm {Z}} \to {\tau} {\tau}}}$ events. Shown is the distribution of $ {m_{\text {jj}}} $, as discussed in the text. The blue vertical bars and red-shaded bands correspond to the statistical uncertainty of each sample.
png pdf	Figure 10-e: Comparison of $ {\tau}$-embedded events with a statistically independent sample of simulated ${{{\mathrm {Z}} \to {\tau} {\tau}}}$ events. Shown is the distribution of $ {\tau}_{\text {h}} $-ID BDT, as discussed in the text. The black arrow indicates the working points usually used in the target analyses. The blue vertical bars and red-shaded bands correspond to the statistical uncertainty of each sample.
png pdf	Figure 10-f: Comparison of $ {\tau}$-embedded events with a statistically independent sample of simulated ${{{\mathrm {Z}} \to {\tau} {\tau}}}$ events. Shown is the distribution of $ {m_{\text {vis}}} $, as discussed in the text. The blue vertical bars and red-shaded bands correspond to the statistical uncertainty of each sample. The effect of a variation of the $ {\tau}_{\text {h}} $ energy scale of $\pm $1.2% is shown by the green lines.
png pdf	Figure 11: (Left column) muon and (right column) electron (upper row) identification and (lower row) isolation efficiencies as a function of the $ {p_{\mathrm {T}}} $ of the corresponding lepton in the central region of the detector. The black arrows indicate typical trigger thresholds of the target analyses. In the upper panel of each subfigure, the black dots correspond to the efficiencies obtained in data, the blue dots to the efficiencies obtained in the corresponding embedded event sample, and the red dots to the efficiencies obtained from the simulation. The lower panels show the ratios of the (blue) embedded event sample and (red) simulation, to the efficiency observed in data, which corresponds to the correction factors.
png pdf	Figure 11-a: Muon identification efficiency as a function of the $ {p_{\mathrm {T}}} $ of the corresponding lepton in the central region of the detector. The black arrow indicates a typical trigger threshold of the target analyses. In the upper panel, the black dots correspond to the efficiencies obtained in data, the blue dots to the efficiencies obtained in the corresponding embedded event sample, and the red dots to the efficiencies obtained from the simulation. The lower panel shows the ratios of the (blue) embedded event sample and (red) simulation, to the efficiency observed in data, which corresponds to the correction factors.
png pdf	Figure 11-b: Electron identification efficiency as a function of the $ {p_{\mathrm {T}}} $ of the corresponding lepton in the central region of the detector. The black arrow indicates a typical trigger threshold of the target analyses. In the upper panel, the black dots correspond to the efficiencies obtained in data, the blue dots to the efficiencies obtained in the corresponding embedded event sample, and the red dots to the efficiencies obtained from the simulation. The lower panel shows the ratios of the (blue) embedded event sample and (red) simulation, to the efficiency observed in data, which corresponds to the correction factors.
png pdf	Figure 11-c: Muon isolation efficiency as a function of the $ {p_{\mathrm {T}}} $ of the corresponding lepton in the central region of the detector. The black arrow indicates a typical trigger threshold of the target analyses. In the upper panel, the black dots correspond to the efficiencies obtained in data, the blue dots to the efficiencies obtained in the corresponding embedded event sample, and the red dots to the efficiencies obtained from the simulation. The lower panel shows the ratios of the (blue) embedded event sample and (red) simulation, to the efficiency observed in data, which corresponds to the correction factors.
png pdf	Figure 11-d: Electron isolation efficiency as a function of the $ {p_{\mathrm {T}}} $ of the corresponding lepton in the central region of the detector. The black arrow indicates a typical trigger threshold of the target analyses. In the upper panel, the black dots correspond to the efficiencies obtained in data, the blue dots to the efficiencies obtained in the corresponding embedded event sample, and the red dots to the efficiencies obtained from the simulation. The lower panel shows the ratios of the (blue) embedded event sample and (red) simulation, to the efficiency observed in data, which corresponds to the correction factors.
png pdf	Figure 12: Distributions of (upper left) $ {{p_{\mathrm {T}}} ^\text {miss}} $ in the $ {{\mu} {\tau}_{\text {h}}} $ final state, (upper right) $ {D_{\zeta}} $ in the $ {{\mathrm {e}} {\mu}} $ final state, (lower left) $ {m_{\text {T}}^{{\mathrm {e}}}} $ in the $ {{\mathrm {e}} {\tau}_{\text {h}}} $ final state, and (lower right) $ {m_{\text {T}}^{{\mu}}} $ in the $ {{\mu} {\tau}_{\text {h}}} $ final state. The distributions are shown prior to the maximum likelihood fit described in the text. For these figures, no uncertainties that affect the shape of the distributions have been included in the uncertainty model. The background estimation purely from the CMS simulation is shown as an additional red line.
png pdf	Figure 12-a: Distribution of $ {{p_{\mathrm {T}}} ^\text {miss}} $ in the $ {{\mu} {\tau}_{\text {h}}} $ final state. The distribution is shown prior to the maximum likelihood fit described in the text. No uncertainties that affect the shape of the distribution have been included in the uncertainty model. The background estimation purely from the CMS simulation is shown as an additional red line.
png pdf	Figure 12-b: Distribution of $ {D_{\zeta}} $ in the $ {{\mathrm {e}} {\mu}} $ final state. The distribution is shown prior to the maximum likelihood fit described in the text. No uncertainties that affect the shape of the distribution have been included in the uncertainty model. The background estimation purely from the CMS simulation is shown as an additional red line.
png pdf	Figure 12-c: Distribution of $ {m_{\text {T}}^{{\mathrm {e}}}} $ in the $ {{\mathrm {e}} {\tau}_{\text {h}}} $ final state. The distribution is shown prior to the maximum likelihood fit described in the text. No uncertainties that affect the shape of the distribution have been included in the uncertainty model. The background estimation purely from the CMS simulation is shown as an additional red line.
png pdf	Figure 12-d: Distribution of $ {m_{\text {T}}^{{\mu}}} $ in the $ {{\mu} {\tau}_{\text {h}}} $ final state. The distribution is shown prior to the maximum likelihood fit described in the text. No uncertainties that affect the shape of the distribution have been included in the uncertainty model. The background estimation purely from the CMS simulation is shown as an additional red line.
png pdf	Figure 13: Invariant mass distribution of the visible $ {\tau} {\tau}$ decay products, $ {m_{\text {vis}}} $, in the (upper left) $ {{\mathrm {e}} {\mu}} $, (upper right) $ {{\mathrm {e}} {\tau}_{\text {h}}} $, (lower left) $ {{\mu} {\tau}_{\text {h}}} $, and (lower right) $ {{\tau}_{\text {h}} {\tau}_{\text {h}}} $ final states, after a fit to the data exploiting a typical uncertainty model as, {e.g.}, discussed in Ref. [45].
png pdf	Figure 13-a: Invariant mass distribution of the visible $ {\tau} {\tau}$ decay products, $ {m_{\text {vis}}} $, in the $ {{\mathrm {e}} {\mu}} $ final state, after a fit to the data exploiting a typical uncertainty model as, {e.g.}, discussed in Ref. [45].
png pdf	Figure 13-b: Invariant mass distribution of the visible $ {\tau} {\tau}$ decay products, $ {m_{\text {vis}}} $, in the $ {{\mathrm {e}} {\tau}_{\text {h}}} $ final state, after a fit to the data exploiting a typical uncertainty model as, {e.g.}, discussed in Ref. [45].
png pdf	Figure 13-c: Invariant mass distribution of the visible $ {\tau} {\tau}$ decay products, $ {m_{\text {vis}}} $, in the $ {{\mu} {\tau}_{\text {h}}} $ final state, after a fit to the data exploiting a typical uncertainty model as, {e.g.}, discussed in Ref. [45].
png pdf	Figure 13-d: Invariant mass distribution of the visible $ {\tau} {\tau}$ decay products, $ {m_{\text {vis}}} $, in the $ {{\tau}_{\text {h}} {\tau}_{\text {h}}} $ final state, after a fit to the data exploiting a typical uncertainty model as, {e.g.}, discussed in Ref. [45].
png pdf	Figure 14: Distributions of (left) $ {m_{\text {jj}}} $ and (right) the number of reconstructed primary vertices $N_{\text {vtx}}$ in the $ {{\mu} {\tau}_{\text {h}}} $ final state.
png pdf	Figure 14-a: Distribution of $ {m_{\text {jj}}} $ in the $ {{\mu} {\tau}_{\text {h}}} $ final state.
png pdf	Figure 14-b: Distribution of the number of reconstructed primary vertices $N_{\text {vtx}}$ in the $ {{\mu} {\tau}_{\text {h}}} $ final state.
png pdf	Figure 15: Distributions of the (left) jet and (right) b-jet multiplicity, as described in the text, in the $ {{\mu} {\tau}_{\text {h}}} $ final state.
png pdf	Figure 15-a: Distribution of the jet multiplicity, as described in the text, in the $ {{\mu} {\tau}_{\text {h}}} $ final state.
png pdf	Figure 15-b: Distribution of the b-jet multiplicity, as described in the text, in the $ {{\mu} {\tau}_{\text {h}}} $ final state.
png pdf	Figure 16: Distributions of the $ {p_{\mathrm {T}}} $ of the (left) leading and (right) trailing jet for events with more than one jet in the $ {{\mu} {\tau}_{\text {h}}} $ final state.
png pdf	Figure 16-a: Distribution of the $ {p_{\mathrm {T}}} $ of the leading jet for events with more than one jet in the $ {{\mu} {\tau}_{\text {h}}} $ final state.
png pdf	Figure 16-b: Distribution of the $ {p_{\mathrm {T}}} $ of the trailing jet for events with more than one jet in the $ {{\mu} {\tau}_{\text {h}}} $ final state.

Tables
png pdf	Table 1: Expected event composition after the selection of two muons, as described in Section 5.1. The compositions after adding selections on $ {m_{\mu \mu}} > $ 70 GeV or on the number of b jets with $ {p_{\mathrm {T}}} > $ 20 GeV in the event are shown in column 3 and 4 respectively. In the second column the fraction of events where the corresponding process has two genuine muons in the final state is given in parentheses.
png pdf	Table 2: Kinematic range of eligibility for each $ {\tau}$-embedded event sample in the $ {{\mathrm {e}} {\mu}} $, $ {{\mathrm {e}} {\tau}_{\text {h}}} $, $ {{\mu} {\tau}_{\text {h}}} $, and $ {{\tau}_{\text {h}} {\tau}_{\text {h}}} $ final states. The expression "First/Second object'' refers to the final state label used in the first column. Also given are the probability of the simulated tau lepton pair to pass the kinematic filtering ($\epsilon _{\text {kin}}$), described in the text, and the equivalent of the integrated luminosity $\mathcal {L}_{\text {int}}$, of the corresponding $ {\tau}$-embedded event sample, in multiples of the data set, from which the embedded event sample has been created.
png pdf	Table 3: Normalization of the $ {\tau}$-embedded event samples and $p$-values of the saturated model (SAT), Kolmogorov-Smirnov (KS) and Anderson-Darling (AD) test, as discussed in the text, separated by $ {\tau} {\tau}$ final state, as introduced in Section 5 and (where applicable) for all channels combined. The $p$-values have a statistical precision better than 0.5%.

Summary

The $\tau$-embedding technique developed for the CMS experiment is described and its validation and relevant uncertainties are discussed. The 13 TeV proton-proton collisions collected by CMS in 2017 are used to demonstrate the performance of the technique with the data sample corresponding to an integrated luminosity of 41.5 fb$^{-1}$. The main goal of the procedure is to estimate the background from $\mathrm{Z} \to \tau\tau$ events using recorded $\mathrm{Z} \to \mu\mu$ events. The estimate also includes events from $\mathrm{t\bar{t}}$ and diboson production with two tau leptons in the final state. Recorded $\mu\mu$ events are selected, the muons are removed from the reconstructed event record, and replaced with simulated tau leptons with the same kinematic properties as the removed muons. In that way hybrid events are obtained, which rely on the simulation only for the decay of the tau leptons. Challenges in describing the underlying event or the production of associated jets in the simulation, as well as the costly simulation of PU events thus are avoided. The embedding technique decreases the uncertainties inherent in a typical simulation process, such as the uncertainties in the missing transverse momentum, jet energy scale and resolution, b tagging efficiency, and misidentification probability. A number of validation tests for $\mu$-, e-, and $\tau$-embedding, as well as several goodness-of-fit tests, show good agreement of embedded distributions with those obtained using simulated and recorded data events. The embedding technique avoids time-consuming simulations of events that becomes critical for the planned High-Luminosity LHC upgrade, where typical pileup of 140-200 collisions per bunch crossing is expected.

Additional Figures
png pdf	Additional Figure 1: Event overlap between the $ {{{\mu}} {\tau}_{\text {h}}} $ and $ {{\mathrm {e}} {\tau}_{\text {h}}} $ final states after the event selections described in Section 7.3 of the paper, presented in form of a Venn diagram. The sizes of the circles correspond to the number of events passing the selection requirements of each final state. For the overlapping events, the same recorded $ {{\mu}} {{\mu}}$ event is used. As only the muons are replaced by corresponding tau lepton decays the rest of the event is expected to be identical, when compared on an event-by-event basis.
png pdf	Additional Figure 2: Event overlap between the $ {{{\mu}} {\tau}_{\text {h}}} $ and $ {{\mathrm {e}} {\mu}} $ final states after the event selections described in Section 7.3 of the paper, presented in form of a Venn diagram. The sizes of the circles correspond to the number of events passing the selection requirements of each final state. For the overlapping events, the same recorded $ {{\mu}} {{\mu}}$ event is used. As only the muons are replaced by corresponding tau lepton decays the rest of the event is expected to be identical, when compared on an event-by-event basis.
png pdf	Additional Figure 3: Event overlap between the $ {{{\mu}} {\tau}_{\text {h}}} $ and $ {{\tau}_{\text {h}} {\tau}_{\text {h}}} $ final states after the event selections described in Section 7.3 of the paper, presented in form of a Venn diagram. The sizes of the circles correspond to the number of events passing the selection requirements of each final state. For the overlapping events, the same recorded $ {{\mu}} {{\mu}}$ event is used. As only the muons are replaced by corresponding tau lepton decays the rest of the event is expected to be identical, when compared on an event-by-event basis.
png pdf	Additional Figure 4: Event overlap between the $ {{\mathrm {e}} {\tau}_{\text {h}}} $ and $ {{\mathrm {e}} {\mu}} $ final states after the event selections described in Section 7.3 of the paper, presented in form of a Venn diagram. The sizes of the circles correspond to the number of events passing the selection requirements of each final state. For the overlapping events, the same recorded $ {{\mu}} {{\mu}}$ event is used. As only the muons are replaced by corresponding tau lepton decays the rest of the event is expected to be identical, when compared on an event-by-event basis.
png pdf	Additional Figure 5: Event overlap between the $ {{\mathrm {e}} {\tau}_{\text {h}}} $ and $ {{\tau}_{\text {h}} {\tau}_{\text {h}}} $ final states after the event selections described in Section 7.3 of the paper, presented in form of a Venn diagram. The sizes of the circles correspond to the number of events passing the selection requirements of each final state. For the overlapping events, the same recorded $ {{\mu}} {{\mu}}$ event is used. As only the muons are replaced by corresponding tau lepton decays the rest of the event is expected to be identical, when compared on an event-by-event basis.
png pdf	Additional Figure 6: Event overlap between the $ {{\tau}_{\text {h}} {\tau}_{\text {h}}} $ and $ {{\mathrm {e}} {\mu}} $ final states after the event selections described in Section 7.3 of the paper, presented in form of a Venn diagram. The sizes of the circles correspond to the number of events passing the selection requirements of each corresponding final state. Since the selection for the $ {{\tau}_{\text {h}} {\tau}_{\text {h}}} $ ($ {{\mathrm {e}} {\mu}} $) final state is tightest (loosest), the corresponding number of selected events is smallest (largest). Here 72.2% of the selected events in the $ {{\tau}_{\text {h}} {\tau}_{\text {h}}} $ final state are also selected in the $ {{\mathrm {e}} {\mu}} $ final state, while the same events constitute only 1.8% of all selected events in the $ {{\mathrm {e}} {\mu}} $ final state. For the overlapping events, the same recorded $ {{\mu}} {{\mu}}$ event is used. As only the muons are replaced by corresponding tau lepton decays the rest of the event is expected to be identical, when compared on an event-by-event basis.
png pdf	Additional Figure 7: Event-by-event comparison of the mass of the two leading jets in $ {p_{\mathrm {T}}} $, $ {m_{\text {jj}}} $, for those events that are selected in both, the $ {{{\mu}} {\tau}_{\text {h}}} $ and $ {{\mathrm {e}} {\tau}_{\text {h}}} $ final state, where $ {m_{\text {jj}}} $ is calculated from the remaining part of the same recorded $ {{\mu}} {{\mu}}$ event. The overlap is 24.9% of the selected $ {{{\mu}} {\tau}_{\text {h}}} $ events and 41.1% of the selected $ {{\mathrm {e}} {\tau}_{\text {h}}} $ events. The linear correlation coefficient is $0.98$. In the target analyses quantities are not compared on an event-by-event basis, but based on unsorted distributions, to which also non-overlapping events contribute.
png pdf	Additional Figure 8: Event-by-event comparison of the absolute value of the difference in $\eta $ between the two leading jets in $ {p_{\mathrm {T}}} $, $ {| \Delta \eta _{jj} |}$, for those events that are selected in both, the $ {{{\mu}} {\tau}_{\text {h}}} $ and $ {{\mathrm {e}} {\tau}_{\text {h}}} $ final state, where $ {| \Delta \eta _{\text {jj}} |}$ is calculated from the remaining part of the same recorded $ {{\mu}} {{\mu}}$ event. The overlap is 24.9% of the selected $ {{{\mu}} {\tau}_{\text {h}}} $ events and 41.1% of the selected $ {{\mathrm {e}} {\tau}_{\text {h}}} $ events. The linear correlation coefficient is 0.98. In the target analyses quantities are not compared on an event-by-event basis, but based on unsorted distributions, to which also non-overlapping events contribute.
png pdf	Additional Figure 9: Event-by-event comparison of the visible mass of the tau lepton decay products, $ {m_{\text {vis}}} $, for those events that are selected in both, the $ {{{\mu}} {\tau}_{\text {h}}} $ and $ {{\mathrm {e}} {\tau}_{\text {h}}} $ final state. The overlap is 24.9% of the selected $ {{{\mu}} {\tau}_{\text {h}}} $ events and 41.1% of the selected $ {{\mathrm {e}} {\tau}_{\text {h}}} $ events. The linear correlation coefficient is 0.61. The reduction of the correlation originates from a partial randomization due to the independent simulation of the tau lepton decays. In the target analyses quantities are not compared on an event-by-event basis, but based on unsorted distributions, to which also non-overlapping events contribute.
png pdf	Additional Figure 10: Comparison of the distributions of $ {m_{\text {jj}}} $ for all events passing the selection in the $ {{\mathrm {e}} {\tau}_{\text {h}}} $ and $ {{{\mu}} {\tau}_{\text {h}}} $ final states. Both distributions are scaled to unity. The $\chi _{\text {obs}}^{2}$ divided by the number of degrees of freedom (ndf) indicating the statistical compatibility of both distributions is also given.
png pdf	Additional Figure 11: Comparison of the distributions of $ {| \Delta \eta _{\text {jj}} |}$ for all events passing the selection in the $ {{\mathrm {e}} {\tau}_{\text {h}}} $ and $ {{{\mu}} {\tau}_{\text {h}}} $ final states. The distributions are scaled to unity. The $\chi _{\text {obs}}^{2}$ divided by the number of degrees of freedom (ndf) indicating the statistical compatibility of both distributions is also given.
png pdf	Additional Figure 12: Quantification of the remaining correlation between the distributions shown in Addtional Figure 10. The histogram results from 100000 pseudo-experiments derived from a Poisson randomization in each bin of the $ {m_{\text {jj}}} $ distribution in the $ {{{\mu}} {\tau}_{\text {h}}} $ final state. For each pseudo-experiment the value of $\chi ^{2}/\text {ndf}$ with respect to the original distribution is calculated. The $\chi _{\text {obs}}^{2}/\text {ndf}$ as observed for the comparison of the distributions in the $ {{\mathrm {e}} {\tau}_{\text {h}}} $ and $ {{{\mu}} {\tau}_{\text {h}}} $ final states in Addtional Figure 10 is indicated by the blue arrow. The integral over the histogram from $\chi _{\text {obs}}^{2}/\text {ndf}$ to $+\infty $ (illustrated by the gray shaded area) results in a p-value of 0.553, revealing good compatibility and no remaining correlation across the distributions in the $ {{\mathrm {e}} {\tau}_{\text {h}}} $ and $ {{{\mu}} {\tau}_{\text {h}}} $ final states. Such a correlation would have resulted in a systematically higher p-value.
png pdf	Additional Figure 13: Quantification of the remaining correlation between the distributions shown in Addtional Figure 11. The histogram results from 100000 pseudo-experiments derived from a Poisson randomization in each bin of the $ {| \Delta \eta _{\text {jj}} |}$ distribution in the $ {{{\mu}} {\tau}_{\text {h}}} $ final state. For each pseudo-experiment the value of $\chi ^{2}/\text {ndf}$ with respect to the original distribution is calculated. The $\chi _{\text {obs}}^{2}/\text {ndf}$ as observed for the comparison of the distributions in the $ {{\mathrm {e}} {\tau}_{\text {h}}} $ and $ {{{\mu}} {\tau}_{\text {h}}} $ final states in Addtional Figure 11 is indicated by the blue arrow. The integral over the histogram from $\chi _{\text {obs}}^{2}/\text {ndf}$ to $+\infty $ (illustrated by the gray shaded area) results in a p-value of 0.488, revealing good compatibility and no remaining correlation across the distributions in the $ {{\mathrm {e}} {\tau}_{\text {h}}} $ and $ {{{\mu}} {\tau}_{\text {h}}} $ final states. Such a correlation would have resulted in a systematically higher p-value.

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