CMSPASSMP18011  
A precision measurement of the W boson decay branching fractions in pp collisions at $\sqrt{s} = $ 13 TeV  
CMS Collaboration  
March 2021  
Abstract: The leptonic and inclusive hadronic decay branching fractions of the W boson are studied using 35.9 fb$^{1}$ of protonproton collision data collected at $\sqrt{s}= $ 13 TeV during the 2016 run of the CMS experiment. Events characterized by the production of two W boson, or of a W boson accompanied by jets, are selected. Multiple event categories sensitive to the signal processes are defined based on the presence of energetic isolated charged leptons, the number of hadronic jets, and the number of btagged jets. A maximum likelihood estimate of the W branching fractions is carried out by fitting to the data in each event category simultaneously. The branching fractions of the W boson decaying into electron, muon, and tau lepton final states amount to (10.83 $\pm$ 0.1 )%, (10.94 $\pm$ 0.08 )%, and (10.77 $\pm$ 0.21 )%, respectively, supporting the hypothesis of lepton universality for the weak interaction. Under the assumption of lepton universality, the inclusive leptonic and hadronic decay branching fractions are found to be (10.89 $\pm$ 0.08 )% and (67.32 $\pm$ 0.23 )%, respectively. From these results, three standard model quantities are subsequently derived: the sum square of elements in the first two rows of the CabibboKobayashiMaskawa (CKM) matrix $\sum{\mathrm{V_{ij}}^{2}} = $ 1.989 $\pm$ 0.021, the CKM element $\mathrm{V_{cs}} = $ 0.969 $\pm$ 0.011, and the strong coupling constant at the W mass scale, $\alpha_\mathrm{S}(m_\mathrm{W}) = $ 0.094 $\pm$ 0.033.  
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These preliminary results are superseded in this paper, Submitted to PRD. The superseded preliminary plots can be found here. 
Figures & Tables  Summary  Additional Figures & Tables  References  CMS Publications 

Figures  
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Figure 1:
Distributions used as inputs for the binned likelihood fits for the ee (upper) and $\mu \mu $ (lower) categories, with the requirement of one (left) or more than one (right) btagged jets. The bottom panels show the ratio of data over prefit (dotted line) and postfit (black circles) expectations, with associated statistical uncertainties (hatched area) and postfit systematic uncertainties (shaded gray). 
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Figure 1a:
Distributions used as inputs for the binned likelihood fits for the ee (upper) and $\mu \mu $ (lower) categories, with the requirement of one (left) or more than one (right) btagged jets. The bottom panels show the ratio of data over prefit (dotted line) and postfit (black circles) expectations, with associated statistical uncertainties (hatched area) and postfit systematic uncertainties (shaded gray). 
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Figure 1b:
Distributions used as inputs for the binned likelihood fits for the ee (upper) and $\mu \mu $ (lower) categories, with the requirement of one (left) or more than one (right) btagged jets. The bottom panels show the ratio of data over prefit (dotted line) and postfit (black circles) expectations, with associated statistical uncertainties (hatched area) and postfit systematic uncertainties (shaded gray). 
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Figure 1c:
Distributions used as inputs for the binned likelihood fits for the ee (upper) and $\mu \mu $ (lower) categories, with the requirement of one (left) or more than one (right) btagged jets. The bottom panels show the ratio of data over prefit (dotted line) and postfit (black circles) expectations, with associated statistical uncertainties (hatched area) and postfit systematic uncertainties (shaded gray). 
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Figure 1d:
Distributions used as inputs for the binned likelihood fits for the ee (upper) and $\mu \mu $ (lower) categories, with the requirement of one (left) or more than one (right) btagged jets. The bottom panels show the ratio of data over prefit (dotted line) and postfit (black circles) expectations, with associated statistical uncertainties (hatched area) and postfit systematic uncertainties (shaded gray). 
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Figure 2:
Distributions used as inputs for the binned likelihood fits for the e$\mu$ categories. The different panels list the varying selections on the number of jets ($N_\mathrm {j}$) and of btagged jets ($N_\mathrm{b} $) required in each case. The bottom panels show the ratio of data over prefit expectations, with the gray histograms (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
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Figure 2a:
Distributions used as inputs for the binned likelihood fits for the e$\mu$ categories. The different panels list the varying selections on the number of jets ($N_\mathrm {j}$) and of btagged jets ($N_\mathrm{b} $) required in each case. The bottom panels show the ratio of data over prefit expectations, with the gray histograms (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
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Figure 2b:
Distributions used as inputs for the binned likelihood fits for the e$\mu$ categories. The different panels list the varying selections on the number of jets ($N_\mathrm {j}$) and of btagged jets ($N_\mathrm{b} $) required in each case. The bottom panels show the ratio of data over prefit expectations, with the gray histograms (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
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Figure 2c:
Distributions used as inputs for the binned likelihood fits for the e$\mu$ categories. The different panels list the varying selections on the number of jets ($N_\mathrm {j}$) and of btagged jets ($N_\mathrm{b} $) required in each case. The bottom panels show the ratio of data over prefit expectations, with the gray histograms (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
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Figure 2d:
Distributions used as inputs for the binned likelihood fits for the e$\mu$ categories. The different panels list the varying selections on the number of jets ($N_\mathrm {j}$) and of btagged jets ($N_\mathrm{b} $) required in each case. The bottom panels show the ratio of data over prefit expectations, with the gray histograms (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
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Figure 2e:
Distributions used as inputs for the binned likelihood fits for the e$\mu$ categories. The different panels list the varying selections on the number of jets ($N_\mathrm {j}$) and of btagged jets ($N_\mathrm{b} $) required in each case. The bottom panels show the ratio of data over prefit expectations, with the gray histograms (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
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Figure 2f:
Distributions used as inputs for the binned likelihood fits for the e$\mu$ categories. The different panels list the varying selections on the number of jets ($N_\mathrm {j}$) and of btagged jets ($N_\mathrm{b} $) required in each case. The bottom panels show the ratio of data over prefit expectations, with the gray histograms (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
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Figure 3:
Distributions used as inputs for the binned likelihood fits for the e$\tau$ categories. The different panels list the varying selections on the number of jets ($N_\mathrm {j}$) and of btagged jets ($N_\mathrm{b} $) required in each case. The bottom panels show the ratio of data over prefit expectations, with the gray band (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
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Figure 3a:
Distributions used as inputs for the binned likelihood fits for the e$\tau$ categories. The different panels list the varying selections on the number of jets ($N_\mathrm {j}$) and of btagged jets ($N_\mathrm{b} $) required in each case. The bottom panels show the ratio of data over prefit expectations, with the gray band (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
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Figure 3b:
Distributions used as inputs for the binned likelihood fits for the e$\tau$ categories. The different panels list the varying selections on the number of jets ($N_\mathrm {j}$) and of btagged jets ($N_\mathrm{b} $) required in each case. The bottom panels show the ratio of data over prefit expectations, with the gray band (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
png pdf 
Figure 3c:
Distributions used as inputs for the binned likelihood fits for the e$\tau$ categories. The different panels list the varying selections on the number of jets ($N_\mathrm {j}$) and of btagged jets ($N_\mathrm{b} $) required in each case. The bottom panels show the ratio of data over prefit expectations, with the gray band (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
png pdf 
Figure 3d:
Distributions used as inputs for the binned likelihood fits for the e$\tau$ categories. The different panels list the varying selections on the number of jets ($N_\mathrm {j}$) and of btagged jets ($N_\mathrm{b} $) required in each case. The bottom panels show the ratio of data over prefit expectations, with the gray band (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
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Figure 3e:
Distributions used as inputs for the binned likelihood fits for the e$\tau$ categories. The different panels list the varying selections on the number of jets ($N_\mathrm {j}$) and of btagged jets ($N_\mathrm{b} $) required in each case. The bottom panels show the ratio of data over prefit expectations, with the gray band (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
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Figure 3f:
Distributions used as inputs for the binned likelihood fits for the e$\tau$ categories. The different panels list the varying selections on the number of jets ($N_\mathrm {j}$) and of btagged jets ($N_\mathrm{b} $) required in each case. The bottom panels show the ratio of data over prefit expectations, with the gray band (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
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Figure 3g:
Distributions used as inputs for the binned likelihood fits for the e$\tau$ categories. The different panels list the varying selections on the number of jets ($N_\mathrm {j}$) and of btagged jets ($N_\mathrm{b} $) required in each case. The bottom panels show the ratio of data over prefit expectations, with the gray band (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
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Figure 3h:
Distributions used as inputs for the binned likelihood fits for the e$\tau$ categories. The different panels list the varying selections on the number of jets ($N_\mathrm {j}$) and of btagged jets ($N_\mathrm{b} $) required in each case. The bottom panels show the ratio of data over prefit expectations, with the gray band (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
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Figure 4:
Distributions used as inputs for the binned likelihood fits for the $\mu \tau $ categories. The different panels list the varying selections on the number of jets ($N_\mathrm {j}$) and of btagged jets ($N_\mathrm{b} $) required in each case. The bottom panels show the ratio of data over prefit expectations, with the gray histograms (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
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Figure 4a:
Distributions used as inputs for the binned likelihood fits for the $\mu \tau $ categories. The different panels list the varying selections on the number of jets ($N_\mathrm {j}$) and of btagged jets ($N_\mathrm{b} $) required in each case. The bottom panels show the ratio of data over prefit expectations, with the gray histograms (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
png pdf 
Figure 4b:
Distributions used as inputs for the binned likelihood fits for the $\mu \tau $ categories. The different panels list the varying selections on the number of jets ($N_\mathrm {j}$) and of btagged jets ($N_\mathrm{b} $) required in each case. The bottom panels show the ratio of data over prefit expectations, with the gray histograms (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
png pdf 
Figure 4c:
Distributions used as inputs for the binned likelihood fits for the $\mu \tau $ categories. The different panels list the varying selections on the number of jets ($N_\mathrm {j}$) and of btagged jets ($N_\mathrm{b} $) required in each case. The bottom panels show the ratio of data over prefit expectations, with the gray histograms (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
png pdf 
Figure 4d:
Distributions used as inputs for the binned likelihood fits for the $\mu \tau $ categories. The different panels list the varying selections on the number of jets ($N_\mathrm {j}$) and of btagged jets ($N_\mathrm{b} $) required in each case. The bottom panels show the ratio of data over prefit expectations, with the gray histograms (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
png pdf 
Figure 4e:
Distributions used as inputs for the binned likelihood fits for the $\mu \tau $ categories. The different panels list the varying selections on the number of jets ($N_\mathrm {j}$) and of btagged jets ($N_\mathrm{b} $) required in each case. The bottom panels show the ratio of data over prefit expectations, with the gray histograms (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
png pdf 
Figure 4f:
Distributions used as inputs for the binned likelihood fits for the $\mu \tau $ categories. The different panels list the varying selections on the number of jets ($N_\mathrm {j}$) and of btagged jets ($N_\mathrm{b} $) required in each case. The bottom panels show the ratio of data over prefit expectations, with the gray histograms (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
png pdf 
Figure 4g:
Distributions used as inputs for the binned likelihood fits for the $\mu \tau $ categories. The different panels list the varying selections on the number of jets ($N_\mathrm {j}$) and of btagged jets ($N_\mathrm{b} $) required in each case. The bottom panels show the ratio of data over prefit expectations, with the gray histograms (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
png pdf 
Figure 4h:
Distributions used as inputs for the binned likelihood fits for the $\mu \tau $ categories. The different panels list the varying selections on the number of jets ($N_\mathrm {j}$) and of btagged jets ($N_\mathrm{b} $) required in each case. The bottom panels show the ratio of data over prefit expectations, with the gray histograms (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
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Figure 5:
Distributions used as inputs for the binned likelihood fits for the eh (upper) and $\mu$h (lower) categories, with the requirement of one (left) or more than one (right) btagged jets. The bottom panels show the ratio of data over prefit expectations, with the gray histograms (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
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Figure 5a:
Distributions used as inputs for the binned likelihood fits for the eh (upper) and $\mu$h (lower) categories, with the requirement of one (left) or more than one (right) btagged jets. The bottom panels show the ratio of data over prefit expectations, with the gray histograms (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
png pdf 
Figure 5b:
Distributions used as inputs for the binned likelihood fits for the eh (upper) and $\mu$h (lower) categories, with the requirement of one (left) or more than one (right) btagged jets. The bottom panels show the ratio of data over prefit expectations, with the gray histograms (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
png pdf 
Figure 5c:
Distributions used as inputs for the binned likelihood fits for the eh (upper) and $\mu$h (lower) categories, with the requirement of one (left) or more than one (right) btagged jets. The bottom panels show the ratio of data over prefit expectations, with the gray histograms (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
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Figure 5d:
Distributions used as inputs for the binned likelihood fits for the eh (upper) and $\mu$h (lower) categories, with the requirement of one (left) or more than one (right) btagged jets. The bottom panels show the ratio of data over prefit expectations, with the gray histograms (slanted bars) indicating MC statistical (postfit systematic) uncertainties. 
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Figure 6:
Pulls and impacts of the nuisance parameters on each W leptonic branching fraction. The impacts are calculated with respect to the uncertainty of the corresponding branching fraction component. Error bars on the pull distribution correspond to the postfit uncertainty of the corresponding nuisance parameter. 
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Figure 7:
Summary of the measured values of the W leptonic branching fractions compared to the corresponding LEP results [3]. The vertical greenyellow band shows the extracted W leptonic branching fraction assuming lepton universality (the hatched band shows the corresponding LEP result). 
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Figure 8:
Twodimensional comparisons of pairs of W leptonic branching fractions derived here, compared to LEP results and to the SM expectation. The green and yellow bands (dashed lines for the LEP results) correspond to the 68% and 95% CL for the resulting twodimensional Gaussian distribution. 
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Figure 9:
Correlation matrix between the four W boson decay branching fraction components extracted in this work. 
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Figure 10:
Twodimensional distributions of the ratios $R_{\tau /\mathrm{e}}$ versus $R_{\tau /\mu}$, compared to similar LEP and ATLAS results and to the SM expectation. The green and yellow bands (dashed lines for the LEP results) correspond to the 68% and 95% CL for the resulting twodimensional Gaussian distribution. The onedimensional (1D) 68% CL bands are also overlaid for a better visual comparison with the corresponding ATLAS $R_{\tau /\mu}$ result. 
Tables  
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Table 1:
Baseline categorization of events based on the triggering electron or muon, the presence (or vetoing) of isolated reconstructed charged leptons, plus additional jets, identified or not as originating from a b quark. Kinematic criteria required on the charged leptons and jets are listed in the last column. Categories without hadrons in the final state require also the selected leptons to have oppositesign charge. 
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Table 2:
Categorization of events with electron, muon, and/or tau leptons passing the reconstruction criteria, based on their jet and btagged jet multiplicities. 
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Table 3:
Values of the W branching fractions determined here, compared to the corresponding LEP measurements. The bottom rows list the leptonic W branching fraction derived combining the three individual decay modes assuming lepton universality. Statistical and systematics uncertainties are quoted for each branching fraction. 
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Table 4:
Ratios of different leptonic branching fractions measured in this analysis, and compared to the corresponding LEP and ATLAS results. 
Summary 
Precise measurements of the three leptonic decay branching fractions of the W boson, as well as of the inclusive leptonic and hadronic ones assuming lepton universality, have been presented. The analysis is based on a data sample of protonproton collisions at a centerofmass energy of 13 TeV corresponding to an integrated luminosity of 35.9 fb$^{1}$ recorded by the CMS experiment during the 2016 run. Events are collected online using single charged lepton triggers that require at least one prompt electron or muon with large transverse momentum. The offline analysis defines categories of final states consistent with the production of two W bosons, or a W boson plus jets, that decay leptonically. The extraction of W boson leptonic branching fractions is carried out through a binned maximum likelihood fit of multiple event categories, where the selected leptonic final states are further classified according to the number of jets as well as of the number of those jets identified as originating from bottom quarks, and binned by channeldependent kinematic information. The branching fractions for the decay of the W boson into electrons, muons, taus, and hadrons are determined to be (10.83 $\pm$ 0.10 )%, (10.94 $\pm$ 0.08 )%, (10.77 $\pm$ 0.21 )%, and (67.46 $\pm$ 0.28 )%, respectively. These results are consistent with the lepton universality hypothesis of the standard model (SM) of particle physics, with a precision that exceeds that achieved by previous measurements based on data collected by the LEP experiments. When imposing lepton universality while fitting the data, values of (10.89 $\pm$ 0.08 )% and (67.32 $\pm$ 0.23 )% are obtained for the inclusive leptonic and hadronic branching fractions, respectively. From the ratio of inclusive hadronictoleptonic branching fractions compared to the corresponding theoretical prediction, further SM quantities can be derived. First, the square sum of the elements of the first two rows of the CabibboKobayashiMaskawa (CKM) matrix are found to be $\sum_\mathrm{ij}{\mathrm{V_{ij}}}^{2} = $ 1.989 $\pm$ 0.021, thereby providing a precise test of CKM unitarity. The ${\mathrm{V_{cs}}}$ quark flavor mixing element can be fit similarly, finding ${\mathrm{V_{cs}}} = $ 0.969 $\pm$ 0.011, which is as precise as the current worldaverage of ${\mathrm{V_{cs}}} = $ 0.987 $\pm$ 0.011 obtained from direct D meson decays measurements. Finally, a value of the strong coupling constant at the W mass scale is obtained, ${\alpha_S}(m^{2}_\mathrm{W}) = $ 0.094 $\pm$ 0.033, that, although not competitive compared to the current world average value, confirms the usefulness of the W boson decays to constrain this fundamental SM parameter at future colliders. 
Additional Figures  
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Additional Figure 1:
Summary of measured values of leptonic branching fractions from this measurement, LEP, and the combination of the two results. 
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Additional Figure 2:
Two dimensional comparisons of leptonic branching fractions. For each pair shown in the panels, the branching fraction that is not shown has been marginalized over. The dashed lines correspond to 68% and 95% contour levels for the resulting two dimensional Gaussian distribution. 
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Additional Figure 3:
Two dimensional distributions of the ratios $B({\mathrm {W}}\to \tau \nu)/B({\mathrm {W}}\to \mathrm{e}/\nu)$ vs $B({\mathrm {W}}\to \tau \nu)/B({\mathrm {W}}\to \mu \nu)$ with comparisons of the CMS, LEP, the combination of CMS and LEP, and ATLAS measurements. 
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Additional Figure 4:
Measurements of $V_{\mathrm{cs}}$ from direct measurement using $\mathrm{D_{s}}^{+}\to {\mu} ^{+} {\nu} $, $\mathrm{D}\to \mathrm{K}\ell {\nu} $, and $ {\mathrm {W}}\to \mathrm{cs}$ decays compared to indirect measurements using $\mathcal {B}({\mathrm {W}}\to h)$ estimations. 
Additional Tables  
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Additional Table 1:
Percent of reconstructed final states attributable to different WW Figure decay modes. The quantities are estimated from simulated ${{\mathrm {t}\overline {\mathrm {t}}}}$ events where there are at least two jets and at least two b tags. The more significant contributions are highlighted in red. The statistical uncertainty on these quantities is negligible. 
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Additional Table 2:
Values of branching fractions from this measurement, the combined LEP measurement, and both measurements combined assuming no correlation between experiments. The quoted uncertainties combine statistical and systematics sources. The combined values are calculated taking into account the correlations of the branching fractions in the individual measurements, but assuming no correlations between the uncertainties on the LEP and CMS measurements. The branching fractions are estimated in both scenario where lepton universality (LU) is required and when each of the leptonic branching fractions is free to take on an independent value. 
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Additional Table 3:
Correlation matrices for leptonic branching fractions for both the CMS and LEP analyses. 
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Additional Table 4:
Comparison of ratios of branching fractions measured by CMS, LEP, and ATLAS. Also included is the ratios of branching fractions after combining the measurement from both CMS and LEP. 
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Additional Table 5:
The CMS and LEP results are combined assuming no correlations in the systematic uncertainties. The LEP value has been updated to account for updated values of $\alpha _{S}$ and the CKM matrix elements with respect to their originial reporting. 
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