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CMS-HIG-20-006 ; CERN-EP-2021-189

Analysis of the CP structure of the Yukawa coupling between the Higgs boson and $\tau$ leptons in proton-proton collisions at $\sqrt{s} = $ 13 TeV

CMS Collaboration

10 October 2021

JHEP 06 (2022) 012

Abstract: The first measurement of the CP structure of the Yukawa coupling between the Higgs boson and $\tau$ leptons is presented. The measurement is based on data collected in proton-proton collisions at $\sqrt{s} = $ 13 TeV by the CMS detector at the LHC, corresponding to an integrated luminosity of 137 fb$^{-1}$. The analysis uses the angular correlation between the decay planes of $\tau$ leptons produced in Higgs boson decays. The effective mixing angle between CP-even and CP-odd $\tau$ Yukawa couplings is found to be $ -1 \pm 19 ^{\circ}$, compared to an expected value of $ 0 \pm 21 ^{\circ}$ at the 68.3% confidence level. The data disfavour the pure CP-odd scenario at 3.0 standard deviations. The results are compatible with predictions for the standard model Higgs boson.

Links: e-print arXiv:2110.04836 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ;

Figures
png pdf	Figure 1: The decay planes of two $\tau$ leptons decaying to a single charged pion. The angle ${\phi _{{\textit {CP}}}}$ is the angle between the decay planes. The illustration is in the H rest frame.
png pdf	Figure 2: The normalised distribution of ${\phi _{{\textit {CP}}}}$ between the $\tau$ lepton decay planes in the H rest frame at the generator level, for both $\tau$ leptons decaying to a charged pion and a neutrino. The distributions are for a decaying scalar (CP-even, solid red), pseudoscalar (CP-odd, dash blue), a maximal mixing angle of $45^{\circ}$ (CP-mix, dash-dot-dot green), and a Z vector boson (black dash-dot). The transverse momentum of the visible $\tau$ decay products $ {p_{\mathrm {T}}} ^{\tau}$ was required to be larger than 33 GeV during the event generation.
png pdf	Figure 3: Illustration of the $\tau$ lepton decay planes and the angle ${\phi _{{\textit {CP}}}}$ for various decay configurations. The decay planes are illustrated with the shaded regions, and either the vector ${\hat{\lambda}}$ or the momentum vector of the neutral pion is in the decay plane. The illustrations are in the frame in which the sum of the momenta of the charged particles is zero. Left: the decay plane for the decays $\tau^{-} \to \pi^{-} +\nu $ and $\tau^{+} \to \pi^{+} +\bar{\nu} $. Middle: the decay plane as reconstructed from the neutral and charged pion momenta. Right: ${\phi _{{\textit {CP}}}}$ for the mixed scenario, in which one $\tau$ lepton decays to a pion while the other decays via an intermediate $\rho$ meson.
png pdf	Figure 3-a: The decay plane for the decays $\tau^{-} \to \pi^{-} +\nu $ and $\tau^{+} \to \pi^{+} +\bar{\nu} $.
png pdf	Figure 3-b: The decay plane as reconstructed from the neutral and charged pion momenta.
png pdf	Figure 3-c: ${\phi _{{\textit {CP}}}}$ for the mixed scenario, in which one $\tau$ lepton decays to a pion while the other decays via an intermediate $\rho$ meson.
png pdf	Figure 4: The decay of ${\mathrm {a_{1}^{3\text{pr}}}}$ via an intermediate ${\rho ^0}$ to three charged pions.
png pdf	Figure 5: The angle ${\phi _{{\textit {CP}}}}$ for ${\mu \to {\tau _\mathrm {h}}}$ events in which the ${\tau _\mathrm {h}}$ decays to a charged $\pi$ (upper) or a charged $\rho$ meson (lower). The distributions are decomposed in a subset in which the charged $\pi$ is "nearly coplanar" (left) or "nearly perpendicular" (right) to the production plane.
png pdf	Figure 5-a: The angle ${\phi _{{\textit {CP}}}}$ for ${\mu \to {\tau _\mathrm {h}}}$ events in which the ${\tau _\mathrm {h}}$ decays to a charged $\pi$. In this subset the charged $\pi$ is "nearly coplanar" to the production plane.
png pdf	Figure 5-b: The angle ${\phi _{{\textit {CP}}}}$ for ${\mu \to {\tau _\mathrm {h}}}$ events in which the ${\tau _\mathrm {h}}$ decays to a charged $\rho$ meson. In this subset the charged $\pi$ is "nearly perpendicular" to the production plane.
png pdf	Figure 5-c: The angle ${\phi _{{\textit {CP}}}}$ for ${\mu \to {\tau _\mathrm {h}}}$ events in which the ${\tau _\mathrm {h}}$ decays to a charged $\pi$ (upper) or a charged $\rho$ meson (lower). The distributions are decomposed in a subset in which the charged $\pi$ is "nearly coplanar" (left) or "nearly perpendicular" (right) to the production plane.
png pdf	Figure 5-d: The angle ${\phi _{{\textit {CP}}}}$ for ${\mu \to {\tau _\mathrm {h}}}$ events in which the ${\tau _\mathrm {h}}$ decays to a charged $\pi$ (upper) or a charged $\rho$ meson (lower). The distributions are decomposed in a subset in which the charged $\pi$ is "nearly coplanar" (left) or "nearly perpendicular" (right) to the production plane.
png pdf	Figure 6: The post-fit MVA score distributions for the Genuine (left) and Mis-ID categories (right) in the ${\tau _{\mu} {\tau _\mathrm {h}}}$ (upper) and ${{\tau _{\mathrm{e}}} {\tau _\mathrm {h}}}$ (lower) channels. The distributions are inclusive in ${\tau _\mathrm {h}}$ decay mode. The best fit signal distributions are overlaid. In the lower panels, the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distribution divided by the uncertainty in the background template. The uncertainty band accounts for all sources of systematic uncertainty in the background prediction, after the fit to data.
png pdf	Figure 6-a: The post-fit MVA score distribution for the Genuine category in the ${\tau _{\mu} {\tau _\mathrm {h}}}$ channel. The distribution is inclusive in ${\tau _\mathrm {h}}$ decay mode. The best fit signal distribution is overlaid. In the lower panel, the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distribution divided by the uncertainty in the background template. The uncertainty band accounts for all sources of systematic uncertainty in the background prediction, after the fit to data.
png pdf	Figure 6-b: The post-fit MVA score distribution for the Mis-ID category in the ${\tau _{\mu} {\tau _\mathrm {h}}}$ channel. The distribution is inclusive in ${\tau _\mathrm {h}}$ decay mode. The best fit signal distribution is overlaid. In the lower panel, the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distribution divided by the uncertainty in the background template. The uncertainty band accounts for all sources of systematic uncertainty in the background prediction, after the fit to data.
png pdf	Figure 6-c: The post-fit MVA score distribution for the Genuine category in the ${{\tau _{\mathrm{e}}} {\tau _\mathrm {h}}}$ channel. The distribution is inclusive in ${\tau _\mathrm {h}}$ decay mode. The best fit signal distribution is overlaid. In the lower panel, the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distribution divided by the uncertainty in the background template. The uncertainty band accounts for all sources of systematic uncertainty in the background prediction, after the fit to data.
png pdf	Figure 6-d: The post-fit MVA score distribution for the Mis-ID category in the ${{\tau _{\mathrm{e}}} {\tau _\mathrm {h}}}$ channel. The distribution is inclusive in ${\tau _\mathrm {h}}$ decay mode. The best fit signal distribution is overlaid. In the lower panel, the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distribution divided by the uncertainty in the background template. The uncertainty band accounts for all sources of systematic uncertainty in the background prediction, after the fit to data.
png pdf	Figure 7: The post-fit MVA score distributions for the Genuine (left) and Mis-ID categories (right) in the ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ channel. The distributions are inclusive in ${\tau _\mathrm {h}}$ decay mode. The best fit signal distributions are overlaid. In the lower panels, the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distribution divided by the uncertainty in the background template. The uncertainty band accounts for all sources of systematic uncertainty in the background prediction, after the fit to data.
png pdf	Figure 7-a: The post-fit MVA score distribution for the Genuine category in the ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ channel. The distribution is inclusive in ${\tau _\mathrm {h}}$ decay mode. The best fit signal distribution is overlaid. In the lower panel, the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distribution divided by the uncertainty in the background template. The uncertainty band accounts for all sources of systematic uncertainty in the background prediction, after the fit to data.
png pdf	Figure 7-b: The post-fit MVA score distribution for the Mis-ID category in the ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ channel. The distribution is inclusive in ${\tau _\mathrm {h}}$ decay mode. The best fit signal distribution is overlaid. In the lower panel, the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distribution divided by the uncertainty in the background template. The uncertainty band accounts for all sources of systematic uncertainty in the background prediction, after the fit to data.
png pdf	Figure 8: Distributions of ${\phi _{{\textit {CP}}}}$ in the ${\mu \rho}$ (upper) and ${\mu \pi}$ (lower) channels in windows of increasing MVA score, shown on top of each window. The best fit and pseudoscalar (PS) signal distributions are overlaid. The $x$-axis represents the cyclic bins in ${\phi _{{\textit {CP}}}}$ in the range of $(0, 360^{\circ})$. In the lower panels, the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distributions divided by the uncertainty in the background template. The uncertainty band accounts for all sources of systematic uncertainty in the background prediction, after the fit to data.
png pdf	Figure 8-a: Distribution of ${\phi _{{\textit {CP}}}}$ in the ${\mu \rho}$ channel in windows of increasing MVA score, shown on top of the window. The best fit and pseudoscalar (PS) signal distributions are overlaid. The $x$-axis represents the cyclic bins in ${\phi _{{\textit {CP}}}}$ in the range of $(0, 360^{\circ})$. In the lower panel, the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distributions divided by the uncertainty in the background template. The uncertainty band accounts for all sources of systematic uncertainty in the background prediction, after the fit to data.
png pdf	Figure 8-b: Distribution of ${\phi _{{\textit {CP}}}}$ in the ${\mu \pi}$ channel in windows of increasing MVA score, shown on top of the window. The best fit and pseudoscalar (PS) signal distributions are overlaid. The $x$-axis represents the cyclic bins in ${\phi _{{\textit {CP}}}}$ in the range of $(0, 360^{\circ})$. In the lower panel, the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distributions divided by the uncertainty in the background template. The uncertainty band accounts for all sources of systematic uncertainty in the background prediction, after the fit to data.
png pdf	Figure 9: Distributions of ${\phi _{{\textit {CP}}}}$ in the ${\rho \rho}$ (upper) and ${\pi \rho}$ (lower) channels in windows of increasing MVA score, shown on top of each window. The best fit and pseudoscalar (PS) signal distributions are overlaid. The $x$-axis represents the cyclic bins in ${\phi _{{\textit {CP}}}}$ in the range of $(0, 360^{\circ})$. In the lower panels, the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distributions divided by the uncertainty in the background template. The uncertainty band accounts for all sources of systematic uncertainty in the background prediction, after the fit to data.
png pdf	Figure 9-a: Distribution of ${\phi _{{\textit {CP}}}}$ in the ${\rho \rho}$ channel in windows of increasing MVA score, shown on top of the window. The best fit and pseudoscalar (PS) signal distributions are overlaid. The $x$-axis represents the cyclic bins in ${\phi _{{\textit {CP}}}}$ in the range of $(0, 360^{\circ})$. In the lower panel, the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distributions divided by the uncertainty in the background template. The uncertainty band accounts for all sources of systematic uncertainty in the background prediction, after the fit to data.
png pdf	Figure 9-b: Distribution of ${\phi _{{\textit {CP}}}}$ in the ${\pi \rho}$ channel in windows of increasing MVA score, shown on top of the window. The best fit and pseudoscalar (PS) signal distributions are overlaid. The $x$-axis represents the cyclic bins in ${\phi _{{\textit {CP}}}}$ in the range of $(0, 360^{\circ})$. In the lower panel, the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distributions divided by the uncertainty in the background template. The uncertainty band accounts for all sources of systematic uncertainty in the background prediction, after the fit to data.
png pdf	Figure 10: Distributions of ${\phi _{{\textit {CP}}}}$ in the ${\mathrm{e} \rho}$ (upper) and ${\mathrm{e} \pi}$ (lower) channels in windows of increasing MVA score, shown on top of each window. The best fit and pseudoscalar (PS) signal distributions are overlaid. The $x$-axis represents the cyclic bins in ${\phi _{{\textit {CP}}}}$ in the range of $(0, 360^{\circ})$. In the lower panels, the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distributions divided by the uncertainty in the background template. The uncertainty band accounts for all sources of systematic uncertainty in the background prediction, after the fit to data.
png pdf	Figure 10-a: Distribution of ${\phi _{{\textit {CP}}}}$ in the ${\mathrm{e} \rho}$ channel in windows of increasing MVA score, shown on top of the window. The best fit and pseudoscalar (PS) signal distributions are overlaid. The $x$-axis represents the cyclic bins in ${\phi _{{\textit {CP}}}}$ in the range of $(0, 360^{\circ})$. In the lower panel, the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distributions divided by the uncertainty in the background template. The uncertainty band accounts for all sources of systematic uncertainty in the background prediction, after the fit to data.
png pdf	Figure 10-b: Distribution of ${\phi _{{\textit {CP}}}}$ in the ${\mathrm{e} \pi}$ channel in windows of increasing MVA score, shown on top of the window. The best fit and pseudoscalar (PS) signal distributions are overlaid. The $x$-axis represents the cyclic bins in ${\phi _{{\textit {CP}}}}$ in the range of $(0, 360^{\circ})$. In the lower panel, the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distributions divided by the uncertainty in the background template. The uncertainty band accounts for all sources of systematic uncertainty in the background prediction, after the fit to data.
png pdf	Figure 11: Negative log-likelihood scan for the combination of the ${{\tau _{\mathrm{e}}} {\tau _\mathrm {h}}}$, ${\tau _{\mu} {\tau _\mathrm {h}}}$, and ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ channels. The observed (expected) sensitivity to distinguish between the scalar and pseudoscalar hypotheses, defined at $ {\alpha ^{\mathrm{H} \tau \tau}} = $ 0 and $ \pm 90 ^{\circ}$, respectively, is 3.0$\sigma $ (2.6$\sigma $). The observed (expected) value for ${\alpha ^{\mathrm{H} \tau \tau}}$ is $-1 \pm 19 ^{\circ}$ ($0 \pm 21 ^{\circ}$) at the 68.3% CL. At 95.5% CL the range is $ \pm 41 ^{\circ}$ ($ \pm 49 ^{\circ}$), and at the 99.7% CL the observed range is $ \pm 84 ^{\circ}$.
png pdf	Figure 12: The 2-D scan of the signal strength modifier $\mu $ versus ${\alpha ^{\mathrm{H} \tau \tau}}$. The 68.3, 95.5, and 99.7% confidence regions are overlaid.
png pdf	Figure 13: The 2-D scan of the (reduced) CP-even (${\kappa _\tau}$) and CP-odd (${\tilde{\kappa}_\tau}$) $\tau$ Yukawa couplings. The 68.3, 95.5, and 99.7% confidence regions are overlaid.
png pdf	Figure 14: The ${\phi _{{\textit {CP}}}}$ distributions for the ${\rho \rho}$, ${\pi \rho}$, ${\mu \rho}$, and ${\mathrm{e} \rho}$ channels weighed by A S/(S+B) are combined. Events are included from all MVA score bins in the four signal categories. The background is subtracted from the data. The scalar distribution is depicted in red, while the pseudoscalar is displayed in blue. In the predictions, the rate parameters are taken from their best fit values. The grey uncertainty band indicates the uncertainty in the subtracted background component. In combining the channels, a phase-shift of 180$^{\circ}$ was applied to the channels involving a lepton since this channel has a phase difference of 180$^{\circ}$ with respect to the two hadronic channels due to a sign-flip in the spectral function of the light lepton.

Tables
png pdf	Table 1: Decay modes of $\tau$ leptons used in this analysis and their branching fractions $\mathcal {B}$ [38]. Where appropriate, we indicate the known intermediate resonances. The last row gives the shorthand notation for the decays used throughout this paper.
png pdf	Table 2: Kinematic trigger and offline requirements applied to the ${{\tau _{\mathrm{e}}} {\tau _\mathrm {h}}}$, ${\tau _{\mu} {\tau _\mathrm {h}}}$, and ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ channels. The trigger ${p_{\mathrm {T}}}$ requirement is indicated in parentheses (in GeV). The ${p_{\mathrm {T}}}$ thresholds indicated for the ${\tau _\mathrm {h}}$ apply only for the object matched to the hadronic trigger or to the hadronic leg from the cross trigger.
png pdf	Table 3: The different sources of backgrounds in the ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ channel are shown in the rows and columns. The entries in the table represent the possible $\tau$ lepton pair background contribution from different processes and misidentifications and encapsulate the different experimental techniques that are deployed to estimate the background contributions.
png pdf	Table 4: The different sources of backgrounds in the ${{\tau _{\ell}} {\tau _\mathrm {h}}}$ channel are shown in the rows and columns. The entries in the table represent the possible $\tau$ lepton pair background contribution from different processes and misidentifications and encapsulate the different experimental techniques that are deployed to estimate the background contributions.
png pdf	Table 5: Input variables to the MVA discriminants for the ${{\tau _{\ell}} {\tau _\mathrm {h}}}$ and ${{\tau _\mathrm {h}} {\tau _\mathrm {h}}}$ channels. The {Svfit} algorithm is used to estimate the di-$\tau$ mass.
png pdf	Table 6: Overview of the systematic uncertainties. The third column indicates if the source of uncertainty was treated as being correlated between the years in the fit described in Section 12. The forth column indicates if the uncertainty affects the shapes of the distributions.

Summary

The first measurement of the effective mixing angle $\alpha^{\mathrm{H \to \tau\tau}}$ between scalar and pseudoscalar $\mathrm{H\tau\tau}$ couplings has been presented for a data set of proton-proton collisions at $\sqrt{s} = $ 13 TeV corresponding to an integrated luminosity of 137 fb$^{-1}$. The data were collected with the CMS experiment at the LHC in the period 2016-2018. The following $\tau$ lepton decay modes were included: $\mathrm{e^{\pm}}$, $\mu^{\pm}$, $\pi^{\pm}$, $\rho^{\pm} \to \pi^{\pm}\pi^{0}$, $\mathrm{q}_{1}^\pm\to\pi^{\pm}\pi^{0}\pi^{0}$, and $\mathrm{q}_{1}^\pm\to\pi^{\pm}\pi^{\mp}\pi^{\pm}$. Dedicated strategies were adopted to reconstruct the angle $\phi_{\text{CP}}$ between the $\tau$ decay planes for the various $\tau$ decay modes. The data disfavour the pure CP-odd scenario at 3.0 standard deviations. The observed effective mixing angle is found to be $-1 \pm 19 ^{\circ}$, while the expected value is $0 \pm 21 ^{\circ}$ at the 68.3% confidence level (CL). The observed and expected uncertainties are found to be $ \pm 41 ^{\circ}$ and $ \pm 49 ^{\circ}$ at the 95.5% CL, respectively, and the observed sensitivity at the 99.7% CL is $ \pm 84 ^{\circ}$. The leading uncertainty in the measurement is statistical, implying that the precision of the measurement will increase with the accumulation of more collision data. The measurement is consistent with the standard model expectation, and reduces the allowed parameter space for its extensions. Tabulated results are provided in HEPDATA [110].

Additional Figures
png pdf	Additional Figure 1: The normalised distribution of $\phi _{\textit {CP}}$ between the ${\tau}$ decay planes in the visible rest frame in the $ {{\mu}} {\pi}$ channel. The distributions are for a decaying scalar (CP-even, solid red), pseudoscalar (CP-odd, dash blue), a maximal mixing angle of 45$^{\circ}$ (CP-mix, dash-dot-dot green), and a Z vector boson (black dash-dot). A ${p_{\mathrm {T}}}$ cutoff of 19 (16) GeV is applied on the visible leptonic (hadronic) tau decay products.
png pdf	Additional Figure 2: The normalised distribution of $\phi _{\textit {CP}}$ between the ${\tau}$ decay planes in the visible rest frame in the $ {\pi} {\rho} $ channel. The distributions are for a decaying scalar (CP-even, solid red), pseudoscalar (CP-odd, dash blue), a maximal mixing angle of 45$^{\circ}$ (CP-mix, dash-dot-dot green), and a Z vector boson (black dash-dot). A ${p_{\mathrm {T}}}$ cutoff of 33 GeV is applied on the visible tau decay products.
png pdf	Additional Figure 3: The normalised distribution of $\phi _{\textit {CP}}$ between the ${\tau}$ decay planes in visible rest frame in the $ {\rho} {\rho} $ channel. The distributions are for a decaying scalar (CP-even, solid red), pseudoscalar (CP-odd, dash blue), a maximal mixing angle of 45$^{\circ}$ (CP-mix, dash-dot-dot green), and a Z vector boson (black dash-dot). A ${p_{\mathrm {T}}}$ cutoff of 33 GeV is applied on the visible tau decay products.
png pdf	Additional Figure 4: The $\phi _{\textit {CP}}$ distribution in the $ {{\mu}} {\rho} $ channel. Events were collected from all years and MVA score bins. The background is subtracted from the data. The events are reweighed via AS/(S+B), in which S and B are the signal and background rates, respectively, and A is a measure for the average asymmetry between the scalar and pseudoscalar distributions. The definition of the value of A per bin is $ {| \textit {CP}^{\text {even}}-\textit {CP}^{\text {odd}} |}/(\textit {CP}^{\text {even}}+\textit {CP}^{\text {odd}})$, and A is normalised to the total number of bins. In this equation $\textit {CP}^{\text {even}}$ and $\textit {CP}^{\text {odd}}$ are the scalar and pseudoscalar contributions per bin. The scalar distribution is depicted in red, while the pseudoscalar is displayed in blue. In the predictions the rate parameters are taken from their best fit values. The grey uncertainty band indicates the uncertainty in the subtracted background component. It should be noted that an overall phase-shift of 180$^{\circ}$ was applied to the channel.
png pdf	Additional Figure 5: The $\phi _{\textit {CP}}$ distribution in the $ {\pi} {\rho} $ channel. Events were collected from all years and MVA score bins. The background is subtracted from the data. The events are reweighed via AS/(S+B), in which S and B are the signal and background rates, respectively, and A is a measure for the average asymmetry between the scalar and pseudoscalar distributions. The definition of the value of A per bin is $ {| \textit {CP}^{\text {even}}-\textit {CP}^{\text {odd}} |}/(\textit {CP}^{\text {even}}+\textit {CP}^{\text {odd}})$, and A is normalised to the total number of bins. In this equation $\textit {CP}^{\text {even}}$ and $\textit {CP}^{\text {odd}}$ are the scalar and pseudoscalar contributions per bin. The scalar distribution is depicted in red, while the pseudoscalar is displayed in blue. In the predictions the rate parameters are taken from their best fit values. The grey uncertainty band indicates the uncertainty in the subtracted background component.
png pdf	Additional Figure 6: The $\phi _{\textit {CP}}$ distribution in the $ {\rho} {\rho} $ channel. Events were collected from all years and MVA score bins. The background is subtracted from the data. The events are reweighed via AS/(S+B), in which S and B are the signal and background rates, respectively, and A is a measure for the average asymmetry between the scalar and pseudoscalar distributions. The definition of the value of A per bin is $ {| \textit {CP}^{\text {even}}-\textit {CP}^{\text {odd}} |}/(\textit {CP}^{\text {even}}+\textit {CP}^{\text {odd}})$, and A is normalised to the total number of bins. In this equation $\textit {CP}^{\text {even}}$ and $\textit {CP}^{\text {odd}}$ are the scalar and pseudoscalar contributions per bin. The scalar distribution is depicted in red, while the pseudoscalar is displayed in blue. In the predictions the rate parameters are taken from their best fit values. The grey uncertainty band indicates the uncertainty in the subtracted background component.
png pdf	Additional Figure 7: The $\phi _{\textit {CP}}$ distribution in the $ {\mathrm {e}} {\rho} $ channel. Events were collected from all years and MVA score bins. The background is subtracted from the data. The events are reweighed via AS/(S+B), in which S and B are the signal and background rates, respectively, and A is a measure for the average asymmetry between the scalar and pseudoscalar distributions. The definition of the value of A per bin is $ {| \textit {CP}^{\text {even}}-\textit {CP}^{\text {odd}} |}/(\textit {CP}^{\text {even}}+\textit {CP}^{\text {odd}})$, and A is normalised to the total number of bins. In this equation $\textit {CP}^{\text {even}}$ and $\textit {CP}^{\text {odd}}$ are the scalar and pseudoscalar contributions per bin. The scalar distribution is depicted in red, while the pseudoscalar is displayed in blue. In the predictions the rate parameters are taken from their best fit values. The grey uncertainty band indicates the uncertainty in the subtracted background component. It should be noted that an overall phase-shift of 180$^{\circ}$ was applied to the channel.
png pdf	Additional Figure 8: The $\phi _{\textit {CP}}$ distribution for combination of the 13 least sensitive $\tau _{l}\tau _{\mathrm {h}}$ and $\tau _{\mathrm {h}}\tau _{\mathrm {h}}$ channels added together. Events were collected from all years and MVA score bins. The background is subtracted from the data. The events are reweighed via AS/(S+B), in which S and B are the signal and background rates, respectively, and A is a measure for the average asymmetry between the scalar and pseudoscalar distributions. The definition of the value of A per bin is $ {| \textit {CP}^{\text {even}}-\textit {CP}^{\text {odd}} |}/(\textit {CP}^{\text {even}}+\textit {CP}^{\text {odd}})$, and A is normalised to the total number of bins. In this equation $\textit {CP}^{\text {even}}$ and $\textit {CP}^{\text {odd}}$ are the scalar and pseudoscalar contributions per bin. The scalar distribution is depicted in red, while the pseudoscalar is displayed in blue. In the predictions the rate parameters are taken from their best fit values. The grey uncertainty band indicates the uncertainty in the subtracted background component. In combining the channels, a phase-shift of 180$^{\circ}$ was applied to a subset of the channels such that the distributions are all in phase.
png pdf	Additional Figure 9: Distributions of $\phi _{\textit {CP}}$ in the $ {{\mu}}\mathrm {a_{1}^{3pr}}$ channel for an event sample dominated by Drell-Yan events. Events were selected for which $\alpha ^{\rho}_{-}\geq \pi /4$ for the intermediate ${\rho}$. The Drell-Yan background template is extracted from simulation, while the $\text {jet}\to \tau _{\mathrm {h}}$ background is obtained from the $F_{\text {F}}$ method. The remaining backgrounds are summarised in the template named Other. In the lower plot the ratio between data and the prediction is displayed together with the systematic uncertainty band.
png pdf	Additional Figure 10: Distributions of $\phi _{\textit {CP}}$ in the $ {{\mu}}\mathrm {a_{1}^{1pr}}$ channel for an event sample dominated by Drell-Yan events. Events were selected for which $\alpha ^{\rho}_{-}$, calculated for the intermediate $\mathrm {a_{1}^{1pr}}$, was $\geq \pi /4$. The Drell-Yan background template is extracted from simulation, while the $\text {jet}\to \tau _{\mathrm {h}}$ background is obtained from the $F_{\text {F}}$ method. The remaining backgrounds are summarised in the template named Other. In the lower plot the ratio between data and the prediction is displayed together with the systematic uncertainty band.
png pdf	Additional Figure 11: Distributions of $\phi _{\textit {CP}}$ in the $ {{\mu}}\mathrm {a_{1}^{3pr}}$ channel for an event sample dominated by Drell-Yan events. Events were selected for which $\alpha ^{\rho}_{-} < \pi /4$ for the intermediate ${\rho}$. The Drell-Yan background template is extracted from simulation, while the $\text {jet}\to \tau _{\mathrm {h}}$ background is obtained from the $F_{\text {F}}$ method. The remaining backgrounds are summarised in the template named Other. In the lower plot the ratio between data and the prediction is displayed together with the systematic uncertainty band.
png pdf	Additional Figure 12: Distributions of $\phi _{\textit {CP}}$ in the $ {{\mu}}\mathrm {a_{1}^{1pr}}$ channel for an event sample dominated by Drell-Yan events. Events were selected for which $\alpha ^{\rho}_{-}$, calculated for the intermediate $\mathrm {a_{1}^{1pr}}$, was $ < \pi /4$. The Drell-Yan background template is extracted from simulation, while the $\text {jet}\to \tau _{\mathrm {h}}$ background is obtained from the $F_{\text {F}}$ method. The remaining backgrounds are summarised in the template named Other. In the lower plot the ratio between data and the prediction is displayed together with the systematic uncertainty band.
png pdf	Additional Figure 13: Distributions of $\phi _{\textit {CP}}$ in the $ {{\mu}}\mathrm {a_{1}^{3pr}}$ channel in windows of increasing MVA score, shown on top of each window. The best fit and pseudoscalar signal distributions are overlaid. The $x$ axis represents the cyclic bins in $\phi _{\textit {CP}}$ in the range of (0, 360$^{\circ}$). In the bottom plot the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distributions divided by the uncertainty in the background template. The uncertainty band consists of the sum of the post-fit uncertainties in the background templates.
png pdf	Additional Figure 14: Distributions of $\phi _{\textit {CP}}$ in the $ {{\mu}}\mathrm {a_{1}^{1pr}}$ channel in windows of increasing MVA score, shown on top of each window. The best fit and pseudoscalar signal distributions are overlaid. The $x$ axis represents the cyclic bins in $\phi _{\textit {CP}}$ in the range of (0, 360$^{\circ}$). In the bottom plot the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distributions divided by the uncertainty in the background template. The uncertainty band consists of the sum of the post-fit uncertainties in the background templates.
png pdf	Additional Figure 15: Distributions of $\phi _{\textit {CP}}$ in the $\mathrm {a_{1}^{1pr}} {\rho} +\mathrm {a_{1}^{1pr}}\mathrm {a_{1}^{1pr}}$ channels in windows of increasing MVA score, shown on top of each window. The best fit and pseudoscalar signal distributions are overlaid. The $x$ axis represents the cyclic bins in $\phi _{\textit {CP}}$ in the range of (0, 360$^{\circ}$). In the bottom plot the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distributions divided by the uncertainty in the background template. The uncertainty band consists of the sum of the post-fit uncertainties in the background templates.
png pdf	Additional Figure 16: Distributions of $\phi _{\textit {CP}}$ in the $\mathrm {a_{1}^{3pr}}\mathrm {a_{1}^{1pr}}$ channel in windows of increasing MVA score, shown on top of each window. The best fit and pseudoscalar signal distributions are overlaid. The $x$ axis represents the cyclic bins in $\phi _{\textit {CP}}$ in the range of (0, 360$^{\circ}$). In the bottom plot the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distributions divided by the uncertainty in the background template. The uncertainty band consists of the sum of the post-fit uncertainties in the background templates.
png pdf	Additional Figure 17: Distributions of $\phi _{\textit {CP}}$ in the $ {\pi}\mathrm {a_{1}^{1pr}}$ channel in windows of increasing MVA score, shown on top of each window. The best fit and pseudoscalar signal distributions are overlaid. The $x$ axis represents the cyclic bins in $\phi _{\textit {CP}}$ in the range of (0, 360$^{\circ}$). In the bottom plot the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distributions divided by the uncertainty in the background template. The uncertainty band consists of the sum of the post-fit uncertainties in the background templates.
png pdf	Additional Figure 18: Distributions of $\phi _{\textit {CP}}$ in the $\mathrm {a_{1}^{3pr}}\mathrm {a_{1}^{3pr}}$ channel in windows of increasing MVA score, shown on top of each window. The polarimetric vector method was deployed to reconstruct $\phi _{\textit {CP}}$. The best fit and pseudoscalar signal distributions are overlaid. The $x$ axis represents the cyclic bins in $\phi _{\textit {CP}}$ in the range of (0, 360$^{\circ}$). In the bottom plot the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distributions divided by the uncertainty in the background template. The uncertainty band consists of the sum of the post-fit uncertainties in the background templates.
png pdf	Additional Figure 19: Distributions of $\phi _{\textit {CP}}$ in the $ {\pi}\mathrm {a_{1}^{3pr}}$ channel in windows of increasing MVA score, shown on top of each window. The best fit and pseudoscalar signal distributions are overlaid. The $x$ axis represents the cyclic bins in $\phi _{\textit {CP}}$ in the range of (0, 360$^{\circ}$). In the bottom plot the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distributions divided by the uncertainty in the background template. The uncertainty band consists of the sum of the post-fit uncertainties in the background templates.
png pdf	Additional Figure 20: Distributions of $\phi _{\textit {CP}}$ in the $\mathrm {a_{1}^{3pr}} {\rho} $ channel in windows of increasing MVA score, shown on top of each window. The best fit and pseudoscalar signal distributions are overlaid. The $x$ axis represents the cyclic bins in $\phi _{\textit {CP}}$ in the range of (0, 360$^{\circ}$). In the bottom plot the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distributions divided by the uncertainty in the background template. The uncertainty band consists of the sum of the post-fit uncertainties in the background templates.
png pdf	Additional Figure 21: Distributions of $\phi _{\textit {CP}}$ in the $ {\pi} {\pi}$ channel in windows of increasing MVA score, shown on top of each window. The best fit and pseudoscalar signal distributions are overlaid. The $x$ axis represents the cyclic bins in $\phi _{\textit {CP}}$ in the range of (0, 360$^{\circ}$). In the bottom plot the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distributions divided by the uncertainty in the background template. The uncertainty band consists of the sum of the post-fit uncertainties in the background templates.
png pdf	Additional Figure 22: Distributions of $\phi _{\textit {CP}}$ in the $ {\mathrm {e}}\mathrm {a_{1}^{3pr}}$ channel in windows of increasing MVA score, shown on top of each window. The best fit and pseudoscalar signal distributions are overlaid. The $x$ axis represents the cyclic bins in $\phi _{\textit {CP}}$ in the range of (0, 360$^{\circ}$). In the bottom plot the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distributions divided by the uncertainty in the background template. The uncertainty band consists of the sum of the post-fit uncertainties in the background templates.
png pdf	Additional Figure 23: Distributions of $\phi _{\textit {CP}}$ in the $ {\mathrm {e}}\mathrm {a_{1}^{1pr}}$ channel in windows of increasing MVA score, shown on top of each window. The best fit and pseudoscalar signal distributions are overlaid. The $x$ axis represents the cyclic bins in $\phi _{\textit {CP}}$ in the range of (0, 360$^{\circ}$). In the bottom plot the data minus the background template divided by the uncertainty in the background template is displayed, as well as the signal distributions divided by the uncertainty in the background template. The uncertainty band consists of the sum of the post-fit uncertainties in the background templates.
png pdf	Additional Figure 24: A candidate event featuring a Higgs decaying into two ${\tau}$ leptons is depicted. The ${\tau}$ leptons decay into a muon (in red) and a $\mathrm {a_{1}}$ that decays in three charged pions (indicated by the orange cone and the calorimeter cells).
png pdf	Additional Figure 25: A zoomed view of a candidate event featuring a Higgs decaying into two ${\tau}$ leptons. The ${\tau}$ leptons decay into a muon (in red) and a $\mathrm {a_{1}}$ that decays into three charged pions. The displaced secondary vertex from which the tracks of the three charged pions candidates are emerging is indicated by the red circle. The pileup vertices are also indicated.
png pdf	Additional Figure 26: The resolution of the x (left), y (middle) and z (right) coordinate of the nominal primary vertex (blue), and the refitted beamspot-corrected primary vertex (red). The width of the distributions is indicated in the legend. Event samples were utilised in which a Higgs boson was produced in the gluon fusion and vector boson fusion process, and the samples were reweighed to their standard model cross section.
png pdf	Additional Figure 27: Expected negative log-likelihood scan for the combination of the $\tau _{{\mathrm {e}}}\tau _{\mathrm {h}}$, $\tau _{{{\mu}}}\tau _{\mathrm {h}}$ and $\tau _{\mathrm {h}}\tau _{\mathrm {h}}$ channels, including predictions for LHC Run 3 and Phase 2 integrated luminosities. The extrapolations have been made assuming systematic uncertainties as derived for the main analysis, while the statistical uncertainties were adjusted to different luminosity scenarios. The expected sensitivity to distinguish between the scalar and pseudo-scalar hypotheses, defined at $\alpha ^{{\mathrm {H}} \tau \tau} = $ 0 and $ \pm $ 90$ ^{\circ}$, respectively, exceeds 5 standard deviations for the Phase 2 scenario.
png pdf	Additional Figure 28: The ratio of $\phi _{\textit {CP}}$ for simulated events and events from the embedded samples in the $ {{\mu}} {\pi}$ final state are displayed. The shapes are consistent within statistical fluctuations.
png pdf	Additional Figure 29: The ratio of $\phi _{\textit {CP}}$ for simulated events and events from the embedded samples in the $ {{\mu}} {\rho} $ final state are displayed. A minor residual effect is present in the embedded sample that is a consequence of misalignment effects in the embedding procedure. These effects cancel in the bin flattening procedure that is applied.
png pdf	Additional Figure 30: Observed correlations between $\alpha ^{{\mathrm {H}} \tau \tau}$ and the signal strength modifiers.
png pdf	Additional Figure 31: Two-dimensional scan of the $ {\mathrm {g}} {\mathrm {g}} {\mathrm {H}} $ signal strength modifier versus $\alpha ^{{\mathrm {H}} \tau \tau}$. The VBF+$ {\mathrm {H}} $ signal strength modifier is profiled.
png pdf	Additional Figure 32: Two-dimensional scan of the VBF+$ {\mathrm {H}} $ signal strength modifier versus $\alpha ^{{\mathrm {H}} \tau \tau}$. The $ {\mathrm {g}} {\mathrm {g}} {\mathrm {H}} $ signal strength modifier is profiled.
png pdf	Additional Figure 33: Two-dimensional scan of the $ {\mathrm {g}} {\mathrm {g}} {\mathrm {H}} $ and VBF+$ {\mathrm {H}} $ signal strength modifiers. The value of $\alpha ^{{\mathrm {H}} \tau \tau}$ is profiled.
png pdf	Additional Figure 34: Observed and expected distribution of the ${\pi ^{\pm}}$ energy from the $ {\tau}\rightarrow {\rho} \nu \rightarrow {\pi ^{\pm}} {\pi ^0}\nu $ decay chain in the $\tau _{{{\mu}}}\tau _{\mathrm {h}}$ channel, produced using the 2018 dataset prior to the fit used for the signal extraction. The invariant mass of the visible $ {\tau} {\tau}$ decay products is required to be smaller than 90 GeV in order to select a large fraction of $ {\mathrm {Z}} \rightarrow \tau \tau $ events. The uncertainty band includes statistical uncertainties and systematic uncertainties that affect the normalisation of the background distribution.
png pdf	Additional Figure 35: Observed and expected distribution of the ${\pi ^{\pm}}$ azimuthal angle $\phi $ from the $ {\tau}\rightarrow {\rho} \nu \rightarrow {\pi ^{\pm}} {\pi ^0}\nu $ decay chain in the $\tau _{{{\mu}}}\tau _{\mathrm {h}}$ channel, produced using the 2018 dataset prior to the fit used for the signal extraction. The invariant mass of the visible $ {\tau} {\tau}$ decay products is required to be smaller than 90 GeV in order to select a large fraction of $ {\mathrm {Z}} \rightarrow \tau \tau $ events. The uncertainty band includes statistical uncertainties and systematic uncertainties that affect the normalisation of the background distribution.
png pdf	Additional Figure 36: Observed and expected distribution of the ${\pi ^{\pm}}$ pseudorapidity $\eta $ from the $ {\tau}\rightarrow {\rho} \nu \rightarrow {\pi ^{\pm}} {\pi ^0}\nu $ decay chain in the $\tau _{{{\mu}}}\tau _{\mathrm {h}}$ channel, produced using the 2018 dataset prior to the fit used for the signal extraction. The invariant mass of the visible $ {\tau} {\tau}$ decay products is required to be smaller than 90 GeV in order to select a large fraction of $ {\mathrm {Z}} \rightarrow \tau \tau $ events. The uncertainty band includes statistical uncertainties and systematic uncertainties that affect the normalisation of the background distribution.
png pdf	Additional Figure 37: Observed and expected distribution of the ${\pi ^0}$ energy from the $ {\tau}\rightarrow {\rho} \nu \rightarrow {\pi ^{\pm}} {\pi ^0}\nu $ decay chain in the $\tau _{{{\mu}}}\tau _{\mathrm {h}}$ channel, produced using the 2018 dataset prior to the fit used for the signal extraction. The invariant mass of the visible $ {\tau} {\tau}$ decay products is required to be smaller than 90 GeV in order to select a large fraction of $ {\mathrm {Z}} \rightarrow \tau \tau $ events. The uncertainty band includes statistical uncertainties and systematic uncertainties that affect the normalisation of the background distribution.
png pdf	Additional Figure 38: Observed and expected distribution of the ${\pi ^0}$ azimuthal angle $\phi $ from the $ {\tau}\rightarrow {\rho} \nu \rightarrow {\pi ^{\pm}} {\pi ^0}\nu $ decay chain in the $\tau _{{{\mu}}}\tau _{\mathrm {h}}$ channel, produced using the 2018 dataset prior to the fit used for the signal extraction. The invariant mass of the visible $ {\tau} {\tau}$ decay products is required to be smaller than 90 GeV in order to select a large fraction of $ {\mathrm {Z}} \rightarrow \tau \tau $ events. The uncertainty band includes statistical uncertainties and systematic uncertainties that affect the normalisation of the background distribution.
png pdf	Additional Figure 39: Observed and expected distribution of the ${\pi ^0}$ pseudorapidity $\eta $ from the $ {\tau}\rightarrow {\rho} \nu \rightarrow {\pi ^{\pm}} {\pi ^0}\nu $ decay chain in the $\tau _{{{\mu}}}\tau _{\mathrm {h}}$ channel, produced using the 2018 dataset prior to the fit used for the signal extraction. The invariant mass of the visible $ {\tau} {\tau}$ decay products is required to be smaller than 90 GeV in order to select a large fraction of $ {\mathrm {Z}} \rightarrow \tau \tau $ events. The uncertainty band includes statistical uncertainties and systematic uncertainties that affect the normalisation of the background distribution.
png pdf	Additional Figure 40: Observed and expected distribution of the ${\pi ^{\pm}}$ impact parameter ($\lambda $) magnitude from $ {\tau}\rightarrow {\pi ^{\pm}} \nu $ decays in the $\tau _{{{\mu}}}\tau _{\mathrm {h}}$ channel, produced using the 2018 dataset prior to the fit used for the signal extraction. The invariant mass of the visible $ {\tau} {\tau}$ decay products is required to be smaller than 90 GeV in order to select a large fraction of $ {\mathrm {Z}} \rightarrow \tau \tau $ events. The uncertainty band includes statistical uncertainties and systematic uncertainties that affect the normalisation of the background distribution.
png pdf	Additional Figure 41: Observed and expected distribution of the ${\pi ^{\pm}}$ impact parameter ($\lambda $) azimuthal angle $\phi $ from $ {\tau}\rightarrow {\pi ^{\pm}} \nu $ decays in the $\tau _{{{\mu}}}\tau _{\mathrm {h}}$ channel, produced using the 2018 dataset prior to the fit used for the signal extraction. The invariant mass of the visible $ {\tau} {\tau}$ decay products is required to be smaller than 90 GeV in order to select a large fraction of $ {\mathrm {Z}} \rightarrow \tau \tau $ events. The uncertainty band includes statistical uncertainties and systematic uncertainties that affect the normalisation of the background distribution.
png pdf	Additional Figure 42: Observed and expected distribution of the ${\pi ^{\pm}}$ impact parameter ($\lambda $) pseudorapidity $\eta $ from $ {\tau}\rightarrow {\pi ^{\pm}} \nu $ decays in the $\tau _{{{\mu}}}\tau _{\mathrm {h}}$ channel, produced using the 2018 dataset prior to the fit used for the signal extraction. The invariant mass of the visible $ {\tau} {\tau}$ decay products is required to be smaller than 90 GeV in order to select a large fraction of $ {\mathrm {Z}} \rightarrow \tau \tau $ events. The uncertainty band includes statistical uncertainties and systematic uncertainties that affect the normalisation of the background distribution.
png pdf	Additional Figure 43: Observed and expected distribution of the ${\tau}$ secondary vertex (SV) length relative to the primary vertex (PV) position from the $ {\tau}\rightarrow \mathrm {a_{1}}\nu \rightarrow {\pi ^{\pm}} {\pi^{\mp}} {\pi ^{\pm}} \nu $ decay chain in the $\tau _{{{\mu}}}\tau _{\mathrm {h}}$ channel, produced using the 2018 dataset prior to the fit used for the signal extraction. The invariant mass of the visible $ {\tau} {\tau}$ decay products is required to be smaller than 90 GeV in order to select a large fraction of $ {\mathrm {Z}} \rightarrow \tau \tau $ events. The uncertainty band includes statistical uncertainties and systematic uncertainties that affect the normalisation of the background distribution.
png pdf	Additional Figure 44: Observed and expected distribution of the ${\tau}$ secondary vertex (SV) azimuthal angle $\phi $ relative to the primary vertex (PV) position from the $ {\tau}\rightarrow \mathrm {a_{1}}\nu \rightarrow {\pi ^{\pm}} {\pi^{\mp}} {\pi ^{\pm}} \nu $ decay chain in the $\tau _{{{\mu}}}\tau _{\mathrm {h}}$ channel, produced using the 2018 dataset prior to the fit used for the signal extraction. The invariant mass of the visible $ {\tau} {\tau}$ decay products is required to be smaller than 90 GeV in order to select a large fraction of $ {\mathrm {Z}} \rightarrow \tau \tau $ events. The uncertainty band includes statistical uncertainties and systematic uncertainties that affect the normalisation of the background distribution.
png pdf	Additional Figure 45: Observed and expected distribution of the ${\tau}$ secondary vertex (SV) pseudorapidity $\eta $ relative to the primary vertex (PV) position from the $ {\tau}\rightarrow \mathrm {a_{1}}\nu \rightarrow {\pi ^{\pm}} {\pi^{\mp}} {\pi ^{\pm}} \nu $ decay chain in the $\tau _{{{\mu}}}\tau _{\mathrm {h}}$ channel, produced using the 2018 dataset prior to the fit used for the signal extraction. The invariant mass of the visible $ {\tau} {\tau}$ decay products is required to be smaller than 90 GeV in order to select a large fraction of $ {\mathrm {Z}} \rightarrow \tau \tau $ events. The uncertainty band includes statistical uncertainties and systematic uncertainties that affect the normalisation of the background distribution.
png pdf	Additional Figure 46: Projections of the expected negative log-likelihood scans based on the Run 2 CMS analysis to an integrated luminosity, $\mathcal {L}$, of 3 ab$^{-1}$. The extrapolations have been made using different assumptions about the systematic uncertainties: no systematic uncertainties (red), assuming the same systematic uncertainties as for the Run 2 analysis (blue), systematic uncertainties scaled following the scheme used for the YR18 (arXiv:1902.00134) HL-LHC projections (black), and with "bin-by-bin" systematic uncertainties related to the finite statistics in the signal and background histograms scaled by 1/$\sqrt {\mathcal {L}}$ while all other systematic uncertainties are scaled following the YR18 scheme (magenta).
png pdf	Additional Figure 47: Projections of the expected negative log-likelihood scans based on the Run 2 CMS analysis to an integrated luminosity, $\mathcal {L}$, of 3 ab$^{-1}$. The extrapolations have been made using different assumptions about the systematic uncertainties: no systematic uncertainties (red), assuming the same systematic uncertainties as for the Run 2 analysis (blue), systematic uncertainties scaled following the scheme used for the YR18 (arXiv:1902.00134) HL-LHC projections (black), and with "bin-by-bin" systematic uncertainties related to the finite statistics in the signal and background histograms scaled by 1/$\sqrt {\mathcal {L}}$ while all other systematic uncertainties are scaled following the YR18 scheme (magenta). The range $|\alpha ^{{\mathrm {H}} \tau \tau}| < $ 40$^{\circ}$ is shown.

Additional Tables
png pdf	Additional Table 1: The obtained expected sensitivities in standard deviations to distinguish between a CP-even and CP-odd $ {\mathrm {H}} {\tau} {\tau}$ coupling. Results are displayed for the individual decay modes (combined with their background categories), the combined $\tau _{{\mathrm {e}}}\tau _{\mathrm {h}}$, $\tau _{{{\mu}}}\tau _{\mathrm {h}}$ and $\tau _{\mathrm {h}}\tau _{\mathrm {h}}$ channels with their background categories, and the overall combination.
png pdf	Additional Table 2: The expected and observed values of $\alpha ^{{\mathrm {H}} \tau \tau}$ and the signal strength modifiers.

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