Test of the universality of $\tau$ and $\mu$ lepton couplings in $W$-boson decays with the ATLAS detector

Content	Preview
Test of the universality of $\tau$ and $\mu$ lepton couplings in $W$-boson decays with the ATLAS detector Nature Phys. 17 (2021) 813 28 July 2020
Contact: ATLAS Top conveners
e-print arXiv:2007.14040, Physics Briefing - internal	pdf from arXiv
Inspire record	-
Figures Tables Auxiliary Material	-
Abstract
The Standard Model of particle physics encapsulates our current best understanding of physics at the smallest scales. A fundamental axiom of this theory is the universality of the couplings of the different generations of leptons to the electroweak gauge bosons. The measurement of the ratio of the rate of decay of $W$ bosons to $\tau$-leptons and muons, $R(\tau/\mu) = B(W \to \tau \nu_\tau)/B(W \to \mu \nu_\mu)$, constitutes an important test of this axiom. A measurement of this quantity with a novel technique using di-leptonic $t\bar{t}$ events is presented based on 139 fb$^{-1}$ of data recorded with the ATLAS detector in proton--proton collisions at $\sqrt{s}=13$ TeV. Muons originating from $W$ bosons and those originating from an intermediate $\tau$-lepton are distinguished using the lifetime of the $\tau$-lepton, through the muon transverse impact parameter, and differences in the muon transverse momentum spectra. The value of $R(\tau/\mu)$ is found to be $0.992 \pm 0.013 [\pm 0.007 (stat) \pm 0.011 (syst)]$ and is in agreement with the hypothesis of universal lepton couplings as postulated in the Standard Model. This is the most precise measurement of this ratio, and the only such measurement from the Large Hadron Collider, to date.
Figures
Figure 01: The m(μμ) distribution in the Z→μμ control region used to extract the Z→μμ normalisation, which is applied in the signal region. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit of the signal region data applied. png (231kB) pdf (25kB)
Figure 02a: The probe muon \|d₀^μ\| (a) and p_T^μ (b) distributions in the μ–μchannel same-sign μ(hadron decay) control region. The extracted normalisation factors have been applied. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit of the signal region data applied. png (203kB) pdf (19kB)
Figure 02b: The probe muon \|d₀^μ\| (a) and p_T^μ (b) distributions in the μ–μchannel same-sign μ(hadron decay) control region. The extracted normalisation factors have been applied. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit of the signal region data applied. png (224kB) pdf (20kB)
Figure 03a: The \|d₀^μ\| distributions for each channel ((a),(c),(e): e–μ channel, (b),(d),(f): μ–μ channel) and probe muon p_T^μ bin ((a)-(b): 5<p_T^μ<10 GeV, (c)-(d): 10<p_T^μ<20 GeV, (e)-(f): 20<p_T^μ<250 GeV) used in the analysis. Plots are shown after the fit has been performed. The data are represented by points and a stacked histogram represents the different simulated processes. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit applied. Different components are labelled according to the muon source and process. The contribution from 'other SM processes' is dominated by di-boson and tt̄+V production. png (198kB) pdf (19kB)
Figure 03b: The \|d₀^μ\| distributions for each channel ((a),(c),(e): e–μ channel, (b),(d),(f): μ–μ channel) and probe muon p_T^μ bin ((a)-(b): 5<p_T^μ<10 GeV, (c)-(d): 10<p_T^μ<20 GeV, (e)-(f): 20<p_T^μ<250 GeV) used in the analysis. Plots are shown after the fit has been performed. The data are represented by points and a stacked histogram represents the different simulated processes. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit applied. Different components are labelled according to the muon source and process. The contribution from 'other SM processes' is dominated by di-boson and tt̄+V production. png (201kB) pdf (20kB)
Figure 03c: The \|d₀^μ\| distributions for each channel ((a),(c),(e): e–μ channel, (b),(d),(f): μ–μ channel) and probe muon p_T^μ bin ((a)-(b): 5<p_T^μ<10 GeV, (c)-(d): 10<p_T^μ<20 GeV, (e)-(f): 20<p_T^μ<250 GeV) used in the analysis. Plots are shown after the fit has been performed. The data are represented by points and a stacked histogram represents the different simulated processes. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit applied. Different components are labelled according to the muon source and process. The contribution from 'other SM processes' is dominated by di-boson and tt̄+V production. png (196kB) pdf (19kB)
Figure 03d: The \|d₀^μ\| distributions for each channel ((a),(c),(e): e–μ channel, (b),(d),(f): μ–μ channel) and probe muon p_T^μ bin ((a)-(b): 5<p_T^μ<10 GeV, (c)-(d): 10<p_T^μ<20 GeV, (e)-(f): 20<p_T^μ<250 GeV) used in the analysis. Plots are shown after the fit has been performed. The data are represented by points and a stacked histogram represents the different simulated processes. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit applied. Different components are labelled according to the muon source and process. The contribution from 'other SM processes' is dominated by di-boson and tt̄+V production. png (200kB) pdf (20kB)
Figure 03e: The \|d₀^μ\| distributions for each channel ((a),(c),(e): e–μ channel, (b),(d),(f): μ–μ channel) and probe muon p_T^μ bin ((a)-(b): 5<p_T^μ<10 GeV, (c)-(d): 10<p_T^μ<20 GeV, (e)-(f): 20<p_T^μ<250 GeV) used in the analysis. Plots are shown after the fit has been performed. The data are represented by points and a stacked histogram represents the different simulated processes. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit applied. Different components are labelled according to the muon source and process. The contribution from 'other SM processes' is dominated by di-boson and tt̄+V production. png (202kB) pdf (19kB)
Figure 03f: The \|d₀^μ\| distributions for each channel ((a),(c),(e): e–μ channel, (b),(d),(f): μ–μ channel) and probe muon p_T^μ bin ((a)-(b): 5<p_T^μ<10 GeV, (c)-(d): 10<p_T^μ<20 GeV, (e)-(f): 20<p_T^μ<250 GeV) used in the analysis. Plots are shown after the fit has been performed. The data are represented by points and a stacked histogram represents the different simulated processes. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit applied. Different components are labelled according to the muon source and process. The contribution from 'other SM processes' is dominated by di-boson and tt̄+V production. png (206kB) pdf (20kB)
Figure 04: The measurement of R(τ/μ) is shown (black circular marker) and compared with the previous LEP result (red square marker). The statistical and systematic errors are shown separately and also the total error of the measurement. The vertical dashed line indicates the Standard Model's prediction lepton-flavour universality, with equal W boson branching ratios to different lepton flavours. png (127kB) pdf (12kB)
Tables
Table 01: The alternative settings and, in the case of the parton shower and hadronisation model, the alternative sample which are used to assess the theoretical uncertainties in the modelling of tt̄. In the cases where a single alternative is given, the uncertainty is taken to be the deviation from the nominal result and then symmetrised. png (121kB) pdf (68kB)
Table 02: A list of the sources of uncertainty affecting the measurement. The impact on R(τ/μ) is assessed by fixing the relevant fit parameters for a given uncertainty and re-fitting to data. The size of the uncertainty reduction in this modified fit is the quoted impact. Different individual components used in the fit are combined into categories such that the leading sources can be seen clearly. png (165kB) pdf (97kB)
Auxiliary figures and tables
Figure 01a: The probe muon \|d₀^μ\| (a) and p_T^μ (b) distributions in the e-μ same-sign μ (hadron decay) control region. The black markers represent the measured data while the histograms correspond to the expectation from simulation with the extracted normalisation factors applied. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit of the signal region data applied. Different components are labelled according to the muon source and process. The other backgrounds contribution is dominated by Z→ττ production. png (210kB) pdf (19kB)
Figure 01b: The probe muon \|d₀^μ\| (a) and p_T^μ (b) distributions in the e-μ same-sign μ (hadron decay) control region. The black markers represent the measured data while the histograms correspond to the expectation from simulation with the extracted normalisation factors applied. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit of the signal region data applied. Different components are labelled according to the muon source and process. The other backgrounds contribution is dominated by Z→ττ production. png (222kB) pdf (20kB)
Figure 02a: The \|d₀^μ\| distributions for each tag lepton channel ((a),(c),(e): e–μ channel, (b),(d),(f): μ–μ channel) and probe muon p_T^μ bin ((a)-(b): 5<p_T^μ<10 GeV, (c)-(d): 10<p_T^μ<20 GeV, (e)-(f): 20<p_T^μ<250 GeV) that enter the analysis fit. Plots are shown before the fit has been performed, but after the control region normalisations have been applied. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties. Note that uncertainties on the tt̄ normalisation have not been included as this is a free parameter in the fit. png (202kB) pdf (20kB)
Figure 02b: The \|d₀^μ\| distributions for each tag lepton channel ((a),(c),(e): e–μ channel, (b),(d),(f): μ–μ channel) and probe muon p_T^μ bin ((a)-(b): 5<p_T^μ<10 GeV, (c)-(d): 10<p_T^μ<20 GeV, (e)-(f): 20<p_T^μ<250 GeV) that enter the analysis fit. Plots are shown before the fit has been performed, but after the control region normalisations have been applied. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties. Note that uncertainties on the tt̄ normalisation have not been included as this is a free parameter in the fit. png (203kB) pdf (20kB)
Figure 02c: The \|d₀^μ\| distributions for each tag lepton channel ((a),(c),(e): e–μ channel, (b),(d),(f): μ–μ channel) and probe muon p_T^μ bin ((a)-(b): 5<p_T^μ<10 GeV, (c)-(d): 10<p_T^μ<20 GeV, (e)-(f): 20<p_T^μ<250 GeV) that enter the analysis fit. Plots are shown before the fit has been performed, but after the control region normalisations have been applied. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties. Note that uncertainties on the tt̄ normalisation have not been included as this is a free parameter in the fit. png (200kB) pdf (20kB)
Figure 02d: The \|d₀^μ\| distributions for each tag lepton channel ((a),(c),(e): e–μ channel, (b),(d),(f): μ–μ channel) and probe muon p_T^μ bin ((a)-(b): 5<p_T^μ<10 GeV, (c)-(d): 10<p_T^μ<20 GeV, (e)-(f): 20<p_T^μ<250 GeV) that enter the analysis fit. Plots are shown before the fit has been performed, but after the control region normalisations have been applied. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties. Note that uncertainties on the tt̄ normalisation have not been included as this is a free parameter in the fit. png (204kB) pdf (20kB)
Figure 02e: The \|d₀^μ\| distributions for each tag lepton channel ((a),(c),(e): e–μ channel, (b),(d),(f): μ–μ channel) and probe muon p_T^μ bin ((a)-(b): 5<p_T^μ<10 GeV, (c)-(d): 10<p_T^μ<20 GeV, (e)-(f): 20<p_T^μ<250 GeV) that enter the analysis fit. Plots are shown before the fit has been performed, but after the control region normalisations have been applied. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties. Note that uncertainties on the tt̄ normalisation have not been included as this is a free parameter in the fit. png (207kB) pdf (20kB)
Figure 02f: The \|d₀^μ\| distributions for each tag lepton channel ((a),(c),(e): e–μ channel, (b),(d),(f): μ–μ channel) and probe muon p_T^μ bin ((a)-(b): 5<p_T^μ<10 GeV, (c)-(d): 10<p_T^μ<20 GeV, (e)-(f): 20<p_T^μ<250 GeV) that enter the analysis fit. Plots are shown before the fit has been performed, but after the control region normalisations have been applied. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties. Note that uncertainties on the tt̄ normalisation have not been included as this is a free parameter in the fit. png (210kB) pdf (20kB)
Figure 03a: The \|d₀^μ\| distributions for each tag lepton channel ((a): e–μ channel, (b): μ–μ channel) inclusive in probe muon p_T^μ after the fit to data has been performed. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit applied. png (192kB) pdf (19kB)
Figure 03b: The \|d₀^μ\| distributions for each tag lepton channel ((a): e–μ channel, (b): μ–μ channel) inclusive in probe muon p_T^μ after the fit to data has been performed. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit applied. png (197kB) pdf (20kB)
Figure 04a: The probe muon p_T^μ inclusive in \|d₀^μ\| for the signal region selection after the fit to data has been performed. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit applied. png (219kB) pdf (20kB)
Figure 04b: The probe muon p_T^μ inclusive in \|d₀^μ\| for the signal region selection after the fit to data has been performed. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit applied. png (220kB) pdf (20kB)
Figure 05a: Impact of the data-driven corrections to the \|d₀^μ\| distributions, inclusive in p_T^μ, of prompt muons. Figures (a) and (c) show the distribution before the application of the \|d₀^μ\| corrections to prompt muons. Figures (b) and (d) are after these corrections have been applied. In all cases the Z→μμ normalisation and μ (hadron decay) normalisation has been applied. Additionally the tt̄ and Wt processes are scaled by their post-fit scale factors. Only statistical uncertainties are shown. png (192kB) pdf (15kB)
Figure 05b: Impact of the data-driven corrections to the \|d₀^μ\| distributions, inclusive in p_T^μ, of prompt muons. Figures (a) and (c) show the distribution before the application of the \|d₀^μ\| corrections to prompt muons. Figures (b) and (d) are after these corrections have been applied. In all cases the Z→μμ normalisation and μ (hadron decay) normalisation has been applied. Additionally the tt̄ and Wt processes are scaled by their post-fit scale factors. Only statistical uncertainties are shown. png (190kB) pdf (15kB)
Figure 05c: Impact of the data-driven corrections to the \|d₀^μ\| distributions, inclusive in p_T^μ, of prompt muons. Figures (a) and (c) show the distribution before the application of the \|d₀^μ\| corrections to prompt muons. Figures (b) and (d) are after these corrections have been applied. In all cases the Z→μμ normalisation and μ (hadron decay) normalisation has been applied. Additionally the tt̄ and Wt processes are scaled by their post-fit scale factors. Only statistical uncertainties are shown. png (197kB) pdf (16kB)
Figure 05d: Impact of the data-driven corrections to the \|d₀^μ\| distributions, inclusive in p_T^μ, of prompt muons. Figures (a) and (c) show the distribution before the application of the \|d₀^μ\| corrections to prompt muons. Figures (b) and (d) are after these corrections have been applied. In all cases the Z→μμ normalisation and μ (hadron decay) normalisation has been applied. Additionally the tt̄ and Wt processes are scaled by their post-fit scale factors. Only statistical uncertainties are shown. png (195kB) pdf (16kB)
Figure 06: The leading individual systematic uncertainties ranked by their post-fit impact on R(τ/μ). Solid (outlined) bars indicate the post-fit (pre-fit) impact on R(τ/μ) as indicated by the legend at the top of the plot. The difference between the pre- and post-fit reflects the constraint of the nuisance parameter, θ. The post-fit values of the nuisance parameters (pulls) and their post-fit uncertainties normalised to the pre-fit uncertainties are shown by the black point with errors. The "tt̄ PS" uncertainty corresponds to the parton shower and hadronisation model variation. png (238kB) pdf (17kB)
Figure 07: The measured value of R(τ/μ) with previous measurements, as well as previous measurements of R(μ/e) and R(τ/e). The statistical (yellow box) and systematic (purple box) errors are shown separately as well as the total error on the measurement (black circular marker). A vertical dashed line indicates the Standard Model prediction of equal branching ratios to different lepton flavours. png (256kB) pdf (16kB)
Figure 08: The nominal result (bottom) and the results when separate values of R(τ/μ) are fitted in the μ-μ (top) and e-μ (middle) channels. A single fit is performed with the same correlation model as the nominal fit but with two parameters of interest for R(τ/μ); one applied only the e-μ regions and one applied only the μ-μ regions. png (124kB) pdf (12kB)
Figure 09: The nominal result (bottom) and the results of independent fits when only considering negatively (top) and positively (middle) charged muons. In these tests the theory errors are computed using the inclusive sample and the \|d₀^μ\| templates are also formed inclusive of charge. png (134kB) pdf (12kB)

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2024-05-04 00:56:26

Content	Preview
Test of the universality of $\tau$ and $\mu$ lepton couplings in $W$-boson decays with the ATLAS detector Nature Phys. 17 (2021) 813 28 July 2020
Contact: ATLAS Top conveners
e-print arXiv:2007.14040, Physics Briefing - internal	pdf from arXiv
Inspire record	-
Figures Tables Auxiliary Material	-
Abstract
The Standard Model of particle physics encapsulates our current best understanding of physics at the smallest scales. A fundamental axiom of this theory is the universality of the couplings of the different generations of leptons to the electroweak gauge bosons. The measurement of the ratio of the rate of decay of $W$ bosons to $\tau$-leptons and muons, $R(\tau/\mu) = B(W \to \tau \nu_\tau)/B(W \to \mu \nu_\mu)$, constitutes an important test of this axiom. A measurement of this quantity with a novel technique using di-leptonic $t\bar{t}$ events is presented based on 139 fb$^{-1}$ of data recorded with the ATLAS detector in proton--proton collisions at $\sqrt{s}=13$ TeV. Muons originating from $W$ bosons and those originating from an intermediate $\tau$-lepton are distinguished using the lifetime of the $\tau$-lepton, through the muon transverse impact parameter, and differences in the muon transverse momentum spectra. The value of $R(\tau/\mu)$ is found to be $0.992 \pm 0.013 [\pm 0.007 (stat) \pm 0.011 (syst)]$ and is in agreement with the hypothesis of universal lepton couplings as postulated in the Standard Model. This is the most precise measurement of this ratio, and the only such measurement from the Large Hadron Collider, to date.
Figures
Figure 01: The m(μμ) distribution in the Z→μμ control region used to extract the Z→μμ normalisation, which is applied in the signal region. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit of the signal region data applied. png (231kB) pdf (25kB)
Figure 02a: The probe muon \|d₀^μ\| (a) and p_T^μ (b) distributions in the μ–μchannel same-sign μ(hadron decay) control region. The extracted normalisation factors have been applied. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit of the signal region data applied. png (203kB) pdf (19kB)
Figure 02b: The probe muon \|d₀^μ\| (a) and p_T^μ (b) distributions in the μ–μchannel same-sign μ(hadron decay) control region. The extracted normalisation factors have been applied. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit of the signal region data applied. png (224kB) pdf (20kB)
Figure 03a: The \|d₀^μ\| distributions for each channel ((a),(c),(e): e–μ channel, (b),(d),(f): μ–μ channel) and probe muon p_T^μ bin ((a)-(b): 5<p_T^μ<10 GeV, (c)-(d): 10<p_T^μ<20 GeV, (e)-(f): 20<p_T^μ<250 GeV) used in the analysis. Plots are shown after the fit has been performed. The data are represented by points and a stacked histogram represents the different simulated processes. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit applied. Different components are labelled according to the muon source and process. The contribution from 'other SM processes' is dominated by di-boson and tt̄+V production. png (198kB) pdf (19kB)
Figure 03b: The \|d₀^μ\| distributions for each channel ((a),(c),(e): e–μ channel, (b),(d),(f): μ–μ channel) and probe muon p_T^μ bin ((a)-(b): 5<p_T^μ<10 GeV, (c)-(d): 10<p_T^μ<20 GeV, (e)-(f): 20<p_T^μ<250 GeV) used in the analysis. Plots are shown after the fit has been performed. The data are represented by points and a stacked histogram represents the different simulated processes. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit applied. Different components are labelled according to the muon source and process. The contribution from 'other SM processes' is dominated by di-boson and tt̄+V production. png (201kB) pdf (20kB)
Figure 03c: The \|d₀^μ\| distributions for each channel ((a),(c),(e): e–μ channel, (b),(d),(f): μ–μ channel) and probe muon p_T^μ bin ((a)-(b): 5<p_T^μ<10 GeV, (c)-(d): 10<p_T^μ<20 GeV, (e)-(f): 20<p_T^μ<250 GeV) used in the analysis. Plots are shown after the fit has been performed. The data are represented by points and a stacked histogram represents the different simulated processes. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit applied. Different components are labelled according to the muon source and process. The contribution from 'other SM processes' is dominated by di-boson and tt̄+V production. png (196kB) pdf (19kB)
Figure 03d: The \|d₀^μ\| distributions for each channel ((a),(c),(e): e–μ channel, (b),(d),(f): μ–μ channel) and probe muon p_T^μ bin ((a)-(b): 5<p_T^μ<10 GeV, (c)-(d): 10<p_T^μ<20 GeV, (e)-(f): 20<p_T^μ<250 GeV) used in the analysis. Plots are shown after the fit has been performed. The data are represented by points and a stacked histogram represents the different simulated processes. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit applied. Different components are labelled according to the muon source and process. The contribution from 'other SM processes' is dominated by di-boson and tt̄+V production. png (200kB) pdf (20kB)
Figure 03e: The \|d₀^μ\| distributions for each channel ((a),(c),(e): e–μ channel, (b),(d),(f): μ–μ channel) and probe muon p_T^μ bin ((a)-(b): 5<p_T^μ<10 GeV, (c)-(d): 10<p_T^μ<20 GeV, (e)-(f): 20<p_T^μ<250 GeV) used in the analysis. Plots are shown after the fit has been performed. The data are represented by points and a stacked histogram represents the different simulated processes. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit applied. Different components are labelled according to the muon source and process. The contribution from 'other SM processes' is dominated by di-boson and tt̄+V production. png (202kB) pdf (19kB)
Figure 03f: The \|d₀^μ\| distributions for each channel ((a),(c),(e): e–μ channel, (b),(d),(f): μ–μ channel) and probe muon p_T^μ bin ((a)-(b): 5<p_T^μ<10 GeV, (c)-(d): 10<p_T^μ<20 GeV, (e)-(f): 20<p_T^μ<250 GeV) used in the analysis. Plots are shown after the fit has been performed. The data are represented by points and a stacked histogram represents the different simulated processes. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit applied. Different components are labelled according to the muon source and process. The contribution from 'other SM processes' is dominated by di-boson and tt̄+V production. png (206kB) pdf (20kB)
Figure 04: The measurement of R(τ/μ) is shown (black circular marker) and compared with the previous LEP result (red square marker). The statistical and systematic errors are shown separately and also the total error of the measurement. The vertical dashed line indicates the Standard Model's prediction lepton-flavour universality, with equal W boson branching ratios to different lepton flavours. png (127kB) pdf (12kB)
Tables
Table 01: The alternative settings and, in the case of the parton shower and hadronisation model, the alternative sample which are used to assess the theoretical uncertainties in the modelling of tt̄. In the cases where a single alternative is given, the uncertainty is taken to be the deviation from the nominal result and then symmetrised. png (121kB) pdf (68kB)
Table 02: A list of the sources of uncertainty affecting the measurement. The impact on R(τ/μ) is assessed by fixing the relevant fit parameters for a given uncertainty and re-fitting to data. The size of the uncertainty reduction in this modified fit is the quoted impact. Different individual components used in the fit are combined into categories such that the leading sources can be seen clearly. png (165kB) pdf (97kB)
Auxiliary figures and tables
Figure 01a: The probe muon \|d₀^μ\| (a) and p_T^μ (b) distributions in the e-μ same-sign μ (hadron decay) control region. The black markers represent the measured data while the histograms correspond to the expectation from simulation with the extracted normalisation factors applied. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit of the signal region data applied. Different components are labelled according to the muon source and process. The other backgrounds contribution is dominated by Z→ττ production. png (210kB) pdf (19kB)
Figure 01b: The probe muon \|d₀^μ\| (a) and p_T^μ (b) distributions in the e-μ same-sign μ (hadron decay) control region. The black markers represent the measured data while the histograms correspond to the expectation from simulation with the extracted normalisation factors applied. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit of the signal region data applied. Different components are labelled according to the muon source and process. The other backgrounds contribution is dominated by Z→ττ production. png (222kB) pdf (20kB)
Figure 02a: The \|d₀^μ\| distributions for each tag lepton channel ((a),(c),(e): e–μ channel, (b),(d),(f): μ–μ channel) and probe muon p_T^μ bin ((a)-(b): 5<p_T^μ<10 GeV, (c)-(d): 10<p_T^μ<20 GeV, (e)-(f): 20<p_T^μ<250 GeV) that enter the analysis fit. Plots are shown before the fit has been performed, but after the control region normalisations have been applied. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties. Note that uncertainties on the tt̄ normalisation have not been included as this is a free parameter in the fit. png (202kB) pdf (20kB)
Figure 02b: The \|d₀^μ\| distributions for each tag lepton channel ((a),(c),(e): e–μ channel, (b),(d),(f): μ–μ channel) and probe muon p_T^μ bin ((a)-(b): 5<p_T^μ<10 GeV, (c)-(d): 10<p_T^μ<20 GeV, (e)-(f): 20<p_T^μ<250 GeV) that enter the analysis fit. Plots are shown before the fit has been performed, but after the control region normalisations have been applied. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties. Note that uncertainties on the tt̄ normalisation have not been included as this is a free parameter in the fit. png (203kB) pdf (20kB)
Figure 02c: The \|d₀^μ\| distributions for each tag lepton channel ((a),(c),(e): e–μ channel, (b),(d),(f): μ–μ channel) and probe muon p_T^μ bin ((a)-(b): 5<p_T^μ<10 GeV, (c)-(d): 10<p_T^μ<20 GeV, (e)-(f): 20<p_T^μ<250 GeV) that enter the analysis fit. Plots are shown before the fit has been performed, but after the control region normalisations have been applied. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties. Note that uncertainties on the tt̄ normalisation have not been included as this is a free parameter in the fit. png (200kB) pdf (20kB)
Figure 02d: The \|d₀^μ\| distributions for each tag lepton channel ((a),(c),(e): e–μ channel, (b),(d),(f): μ–μ channel) and probe muon p_T^μ bin ((a)-(b): 5<p_T^μ<10 GeV, (c)-(d): 10<p_T^μ<20 GeV, (e)-(f): 20<p_T^μ<250 GeV) that enter the analysis fit. Plots are shown before the fit has been performed, but after the control region normalisations have been applied. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties. Note that uncertainties on the tt̄ normalisation have not been included as this is a free parameter in the fit. png (204kB) pdf (20kB)
Figure 02e: The \|d₀^μ\| distributions for each tag lepton channel ((a),(c),(e): e–μ channel, (b),(d),(f): μ–μ channel) and probe muon p_T^μ bin ((a)-(b): 5<p_T^μ<10 GeV, (c)-(d): 10<p_T^μ<20 GeV, (e)-(f): 20<p_T^μ<250 GeV) that enter the analysis fit. Plots are shown before the fit has been performed, but after the control region normalisations have been applied. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties. Note that uncertainties on the tt̄ normalisation have not been included as this is a free parameter in the fit. png (207kB) pdf (20kB)
Figure 02f: The \|d₀^μ\| distributions for each tag lepton channel ((a),(c),(e): e–μ channel, (b),(d),(f): μ–μ channel) and probe muon p_T^μ bin ((a)-(b): 5<p_T^μ<10 GeV, (c)-(d): 10<p_T^μ<20 GeV, (e)-(f): 20<p_T^μ<250 GeV) that enter the analysis fit. Plots are shown before the fit has been performed, but after the control region normalisations have been applied. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties. Note that uncertainties on the tt̄ normalisation have not been included as this is a free parameter in the fit. png (210kB) pdf (20kB)
Figure 03a: The \|d₀^μ\| distributions for each tag lepton channel ((a): e–μ channel, (b): μ–μ channel) inclusive in probe muon p_T^μ after the fit to data has been performed. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit applied. png (192kB) pdf (19kB)
Figure 03b: The \|d₀^μ\| distributions for each tag lepton channel ((a): e–μ channel, (b): μ–μ channel) inclusive in probe muon p_T^μ after the fit to data has been performed. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit applied. png (197kB) pdf (20kB)
Figure 04a: The probe muon p_T^μ inclusive in \|d₀^μ\| for the signal region selection after the fit to data has been performed. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit applied. png (219kB) pdf (20kB)
Figure 04b: The probe muon p_T^μ inclusive in \|d₀^μ\| for the signal region selection after the fit to data has been performed. The bottom panel shows the ratio of the data to the expectation. Blue bands indicate the systematic uncertainties with the constraints from the analysis fit applied. png (220kB) pdf (20kB)
Figure 05a: Impact of the data-driven corrections to the \|d₀^μ\| distributions, inclusive in p_T^μ, of prompt muons. Figures (a) and (c) show the distribution before the application of the \|d₀^μ\| corrections to prompt muons. Figures (b) and (d) are after these corrections have been applied. In all cases the Z→μμ normalisation and μ (hadron decay) normalisation has been applied. Additionally the tt̄ and Wt processes are scaled by their post-fit scale factors. Only statistical uncertainties are shown. png (192kB) pdf (15kB)
Figure 05b: Impact of the data-driven corrections to the \|d₀^μ\| distributions, inclusive in p_T^μ, of prompt muons. Figures (a) and (c) show the distribution before the application of the \|d₀^μ\| corrections to prompt muons. Figures (b) and (d) are after these corrections have been applied. In all cases the Z→μμ normalisation and μ (hadron decay) normalisation has been applied. Additionally the tt̄ and Wt processes are scaled by their post-fit scale factors. Only statistical uncertainties are shown. png (190kB) pdf (15kB)
Figure 05c: Impact of the data-driven corrections to the \|d₀^μ\| distributions, inclusive in p_T^μ, of prompt muons. Figures (a) and (c) show the distribution before the application of the \|d₀^μ\| corrections to prompt muons. Figures (b) and (d) are after these corrections have been applied. In all cases the Z→μμ normalisation and μ (hadron decay) normalisation has been applied. Additionally the tt̄ and Wt processes are scaled by their post-fit scale factors. Only statistical uncertainties are shown. png (197kB) pdf (16kB)
Figure 05d: Impact of the data-driven corrections to the \|d₀^μ\| distributions, inclusive in p_T^μ, of prompt muons. Figures (a) and (c) show the distribution before the application of the \|d₀^μ\| corrections to prompt muons. Figures (b) and (d) are after these corrections have been applied. In all cases the Z→μμ normalisation and μ (hadron decay) normalisation has been applied. Additionally the tt̄ and Wt processes are scaled by their post-fit scale factors. Only statistical uncertainties are shown. png (195kB) pdf (16kB)
Figure 06: The leading individual systematic uncertainties ranked by their post-fit impact on R(τ/μ). Solid (outlined) bars indicate the post-fit (pre-fit) impact on R(τ/μ) as indicated by the legend at the top of the plot. The difference between the pre- and post-fit reflects the constraint of the nuisance parameter, θ. The post-fit values of the nuisance parameters (pulls) and their post-fit uncertainties normalised to the pre-fit uncertainties are shown by the black point with errors. The "tt̄ PS" uncertainty corresponds to the parton shower and hadronisation model variation. png (238kB) pdf (17kB)
Figure 07: The measured value of R(τ/μ) with previous measurements, as well as previous measurements of R(μ/e) and R(τ/e). The statistical (yellow box) and systematic (purple box) errors are shown separately as well as the total error on the measurement (black circular marker). A vertical dashed line indicates the Standard Model prediction of equal branching ratios to different lepton flavours. png (256kB) pdf (16kB)
Figure 08: The nominal result (bottom) and the results when separate values of R(τ/μ) are fitted in the μ-μ (top) and e-μ (middle) channels. A single fit is performed with the same correlation model as the nominal fit but with two parameters of interest for R(τ/μ); one applied only the e-μ regions and one applied only the μ-μ regions. png (124kB) pdf (12kB)
Figure 09: The nominal result (bottom) and the results of independent fits when only considering negatively (top) and positively (middle) charged muons. In these tests the theory errors are computed using the inclusive sample and the \|d₀^μ\| templates are also formed inclusive of charge. png (134kB) pdf (12kB)