CMS-SMP-18-011

CMS-SMP-18-011 ; CERN-EP-2021-240
Precision measurement of the W boson decay branching fractions in proton-proton collisions at $\sqrt{s} =$ 13 TeV
CMS Collaboration
19 January 2022
Phys. Rev. D 105 (2022) 072008
Abstract: The leptonic and inclusive hadronic decay branching fractions of the W boson are measured using proton-proton collision data collected at $\sqrt{s} =$ 13 TeV by the CMS experiment at the CERN LHC, corresponding to an integrated luminosity of 35.9 fb $^{-1}$ . Events characterized by the production of one or two W bosons are selected and categorized based on the multiplicity and flavor of reconstructed leptons, the number of jets, and the number of jets identified as originating from the hadronization of b quarks. A binned maximum likelihood estimate of the W boson branching fractions is performed simultaneously in each event category. The measured branching fractions of the W boson decaying into electron, muon, and tau lepton final states are (10.83 $\pm$ 0.10)%, (10.94 $\pm$ 0.08)%, and (10.77 $\pm$ 0.21)%, respectively, consistent with lepton flavor universality for the weak interaction. The average leptonic and inclusive hadronic decay branching fractions are estimated to be (10.89 $\pm$ 0.08)% and (67.32 $\pm$ 0.23)%, respectively. Based on the hadronic branching fraction, three standard model quantities are subsequently derived: the sum of squared elements in the first two rows of the Cabibbo-Kobayashi-Maskawa (CKM) matrix $\sum_{ij}\|{V_{ij}} \|^{2} =$ 1.984 $\pm$ 0.021, the CKM element $\|{V_{\mathrm{c}\mathrm{s}}} \| =$ 0.967 $\pm$ 0.011, and the strong coupling constant at the W boson mass scale, ${\alpha_S}(m^2_{\mathrm{W}}) =$ 0.095 $\pm$ 0.033.
Links: e-print arXiv:2201.07861 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Subleading electron and muon ${p_{\mathrm {T}}}$ distributions used as inputs for the binned likelihood fits for the $\mathrm{e} \mathrm{e}$ (upper) and $\mu \mu$ (lower) categories, respectively, with the requirement of one (left) or more than one (right) b-tagged jets. The lower subpanels show the ratio of data over pre-fit (dotted line) and post-fit (black circles) expectations, with associated MC statistical uncertainties (hatched area) and post-fit systematic uncertainties (shaded gray). Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 1-a: Subleading electron and muon ${p_{\mathrm {T}}}$ distributions used as inputs for the binned likelihood fits for the $\mathrm{e} \mathrm{e}$ (upper) and $\mu \mu$ (lower) categories, respectively, with the requirement of one (left) or more than one (right) b-tagged jets. The lower subpanels show the ratio of data over pre-fit (dotted line) and post-fit (black circles) expectations, with associated MC statistical uncertainties (hatched area) and post-fit systematic uncertainties (shaded gray). Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 1-b: Subleading electron and muon ${p_{\mathrm {T}}}$ distributions used as inputs for the binned likelihood fits for the $\mathrm{e} \mathrm{e}$ (upper) and $\mu \mu$ (lower) categories, respectively, with the requirement of one (left) or more than one (right) b-tagged jets. The lower subpanels show the ratio of data over pre-fit (dotted line) and post-fit (black circles) expectations, with associated MC statistical uncertainties (hatched area) and post-fit systematic uncertainties (shaded gray). Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 1-c: Subleading electron and muon ${p_{\mathrm {T}}}$ distributions used as inputs for the binned likelihood fits for the $\mathrm{e} \mathrm{e}$ (upper) and $\mu \mu$ (lower) categories, respectively, with the requirement of one (left) or more than one (right) b-tagged jets. The lower subpanels show the ratio of data over pre-fit (dotted line) and post-fit (black circles) expectations, with associated MC statistical uncertainties (hatched area) and post-fit systematic uncertainties (shaded gray). Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 1-d: Subleading electron and muon ${p_{\mathrm {T}}}$ distributions used as inputs for the binned likelihood fits for the $\mathrm{e} \mathrm{e}$ (upper) and $\mu \mu$ (lower) categories, respectively, with the requirement of one (left) or more than one (right) b-tagged jets. The lower subpanels show the ratio of data over pre-fit (dotted line) and post-fit (black circles) expectations, with associated MC statistical uncertainties (hatched area) and post-fit systematic uncertainties (shaded gray). Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 2: Subleading lepton, electron or muon, ${p_{\mathrm {T}}}$ distributions used as inputs for the binned likelihood fits for the $\mathrm{e} \mu$ categories. The different panels are obtained with the listed selection criteria on the number of jets ( $N_{{\text {j}}}$ ) and of b-tagged jets ( $N_{\mathrm{b}}$ ) required. The lower subpanels show the ratio of data over pre-fit expectations, with the gray histograms (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 2-a: Subleading lepton, electron or muon, ${p_{\mathrm {T}}}$ distributions used as inputs for the binned likelihood fits for the $\mathrm{e} \mu$ categories. The different panels are obtained with the listed selection criteria on the number of jets ( $N_{{\text {j}}}$ ) and of b-tagged jets ( $N_{\mathrm{b}}$ ) required. The lower subpanels show the ratio of data over pre-fit expectations, with the gray histograms (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 2-b: Subleading lepton, electron or muon, ${p_{\mathrm {T}}}$ distributions used as inputs for the binned likelihood fits for the $\mathrm{e} \mu$ categories. The different panels are obtained with the listed selection criteria on the number of jets ( $N_{{\text {j}}}$ ) and of b-tagged jets ( $N_{\mathrm{b}}$ ) required. The lower subpanels show the ratio of data over pre-fit expectations, with the gray histograms (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 2-c: Subleading lepton, electron or muon, ${p_{\mathrm {T}}}$ distributions used as inputs for the binned likelihood fits for the $\mathrm{e} \mu$ categories. The different panels are obtained with the listed selection criteria on the number of jets ( $N_{{\text {j}}}$ ) and of b-tagged jets ( $N_{\mathrm{b}}$ ) required. The lower subpanels show the ratio of data over pre-fit expectations, with the gray histograms (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 2-d: Subleading lepton, electron or muon, ${p_{\mathrm {T}}}$ distributions used as inputs for the binned likelihood fits for the $\mathrm{e} \mu$ categories. The different panels are obtained with the listed selection criteria on the number of jets ( $N_{{\text {j}}}$ ) and of b-tagged jets ( $N_{\mathrm{b}}$ ) required. The lower subpanels show the ratio of data over pre-fit expectations, with the gray histograms (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 2-e: Subleading lepton, electron or muon, ${p_{\mathrm {T}}}$ distributions used as inputs for the binned likelihood fits for the $\mathrm{e} \mu$ categories. The different panels are obtained with the listed selection criteria on the number of jets ( $N_{{\text {j}}}$ ) and of b-tagged jets ( $N_{\mathrm{b}}$ ) required. The lower subpanels show the ratio of data over pre-fit expectations, with the gray histograms (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 2-f: Subleading lepton, electron or muon, ${p_{\mathrm {T}}}$ distributions used as inputs for the binned likelihood fits for the $\mathrm{e} \mu$ categories. The different panels are obtained with the listed selection criteria on the number of jets ( $N_{{\text {j}}}$ ) and of b-tagged jets ( $N_{\mathrm{b}}$ ) required. The lower subpanels show the ratio of data over pre-fit expectations, with the gray histograms (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 3: Distributions of ${\tau _\mathrm {h}}$ ${p_{\mathrm {T}}}$ used as inputs for the binned likelihood fits for the $\mathrm{e} \tau$ categories. The different panels list the varying selections on the number of jets ( $N_{{\text {j}}}$ ) and of b-tagged jets ( $N_{\mathrm{b}}$ ) required in each case. The lower subpanels show the ratio of data over pre-fit expectations, with the gray band (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 3-a: Distributions of ${\tau _\mathrm {h}}$ ${p_{\mathrm {T}}}$ used as inputs for the binned likelihood fits for the $\mathrm{e} \tau$ categories. The different panels list the varying selections on the number of jets ( $N_{{\text {j}}}$ ) and of b-tagged jets ( $N_{\mathrm{b}}$ ) required in each case. The lower subpanels show the ratio of data over pre-fit expectations, with the gray band (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 3-b: Distributions of ${\tau _\mathrm {h}}$ ${p_{\mathrm {T}}}$ used as inputs for the binned likelihood fits for the $\mathrm{e} \tau$ categories. The different panels list the varying selections on the number of jets ( $N_{{\text {j}}}$ ) and of b-tagged jets ( $N_{\mathrm{b}}$ ) required in each case. The lower subpanels show the ratio of data over pre-fit expectations, with the gray band (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 3-c: Distributions of ${\tau _\mathrm {h}}$ ${p_{\mathrm {T}}}$ used as inputs for the binned likelihood fits for the $\mathrm{e} \tau$ categories. The different panels list the varying selections on the number of jets ( $N_{{\text {j}}}$ ) and of b-tagged jets ( $N_{\mathrm{b}}$ ) required in each case. The lower subpanels show the ratio of data over pre-fit expectations, with the gray band (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 3-d: Distributions of ${\tau _\mathrm {h}}$ ${p_{\mathrm {T}}}$ used as inputs for the binned likelihood fits for the $\mathrm{e} \tau$ categories. The different panels list the varying selections on the number of jets ( $N_{{\text {j}}}$ ) and of b-tagged jets ( $N_{\mathrm{b}}$ ) required in each case. The lower subpanels show the ratio of data over pre-fit expectations, with the gray band (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 3-e: Distributions of ${\tau _\mathrm {h}}$ ${p_{\mathrm {T}}}$ used as inputs for the binned likelihood fits for the $\mathrm{e} \tau$ categories. The different panels list the varying selections on the number of jets ( $N_{{\text {j}}}$ ) and of b-tagged jets ( $N_{\mathrm{b}}$ ) required in each case. The lower subpanels show the ratio of data over pre-fit expectations, with the gray band (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 3-f: Distributions of ${\tau _\mathrm {h}}$ ${p_{\mathrm {T}}}$ used as inputs for the binned likelihood fits for the $\mathrm{e} \tau$ categories. The different panels list the varying selections on the number of jets ( $N_{{\text {j}}}$ ) and of b-tagged jets ( $N_{\mathrm{b}}$ ) required in each case. The lower subpanels show the ratio of data over pre-fit expectations, with the gray band (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 3-g: Distributions of ${\tau _\mathrm {h}}$ ${p_{\mathrm {T}}}$ used as inputs for the binned likelihood fits for the $\mathrm{e} \tau$ categories. The different panels list the varying selections on the number of jets ( $N_{{\text {j}}}$ ) and of b-tagged jets ( $N_{\mathrm{b}}$ ) required in each case. The lower subpanels show the ratio of data over pre-fit expectations, with the gray band (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 3-h: Distributions of ${\tau _\mathrm {h}}$ ${p_{\mathrm {T}}}$ used as inputs for the binned likelihood fits for the $\mathrm{e} \tau$ categories. The different panels list the varying selections on the number of jets ( $N_{{\text {j}}}$ ) and of b-tagged jets ( $N_{\mathrm{b}}$ ) required in each case. The lower subpanels show the ratio of data over pre-fit expectations, with the gray band (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 4: Distributions of ${\tau _\mathrm {h}}$ ${p_{\mathrm {T}}}$ 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 ( $N_{{\text {j}}}$ ) and of b-tagged jets ( $N_{\mathrm{b}}$ ) required in each case. The lower subpanels show the ratio of data over pre-fit expectations, with the gray histograms (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 4-a: Distributions of ${\tau _\mathrm {h}}$ ${p_{\mathrm {T}}}$ 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 ( $N_{{\text {j}}}$ ) and of b-tagged jets ( $N_{\mathrm{b}}$ ) required in each case. The lower subpanels show the ratio of data over pre-fit expectations, with the gray histograms (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 4-b: Distributions of ${\tau _\mathrm {h}}$ ${p_{\mathrm {T}}}$ 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 ( $N_{{\text {j}}}$ ) and of b-tagged jets ( $N_{\mathrm{b}}$ ) required in each case. The lower subpanels show the ratio of data over pre-fit expectations, with the gray histograms (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 4-c: Distributions of ${\tau _\mathrm {h}}$ ${p_{\mathrm {T}}}$ 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 ( $N_{{\text {j}}}$ ) and of b-tagged jets ( $N_{\mathrm{b}}$ ) required in each case. The lower subpanels show the ratio of data over pre-fit expectations, with the gray histograms (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 4-d: Distributions of ${\tau _\mathrm {h}}$ ${p_{\mathrm {T}}}$ 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 ( $N_{{\text {j}}}$ ) and of b-tagged jets ( $N_{\mathrm{b}}$ ) required in each case. The lower subpanels show the ratio of data over pre-fit expectations, with the gray histograms (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 4-e: Distributions of ${\tau _\mathrm {h}}$ ${p_{\mathrm {T}}}$ 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 ( $N_{{\text {j}}}$ ) and of b-tagged jets ( $N_{\mathrm{b}}$ ) required in each case. The lower subpanels show the ratio of data over pre-fit expectations, with the gray histograms (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 4-f: Distributions of ${\tau _\mathrm {h}}$ ${p_{\mathrm {T}}}$ 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 ( $N_{{\text {j}}}$ ) and of b-tagged jets ( $N_{\mathrm{b}}$ ) required in each case. The lower subpanels show the ratio of data over pre-fit expectations, with the gray histograms (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 4-g: Distributions of ${\tau _\mathrm {h}}$ ${p_{\mathrm {T}}}$ 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 ( $N_{{\text {j}}}$ ) and of b-tagged jets ( $N_{\mathrm{b}}$ ) required in each case. The lower subpanels show the ratio of data over pre-fit expectations, with the gray histograms (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 4-h: Distributions of ${\tau _\mathrm {h}}$ ${p_{\mathrm {T}}}$ 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 ( $N_{{\text {j}}}$ ) and of b-tagged jets ( $N_{\mathrm{b}}$ ) required in each case. The lower subpanels show the ratio of data over pre-fit expectations, with the gray histograms (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 5: Distributions of electron or muon ${p_{\mathrm {T}}}$ used as inputs for the binned likelihood fits for the $\mathrm{e} {\text {h}}$ (upper) and $\mu {\text {h}}$ (lower) categories, respectively, with the requirement of one (left) or more than one (right) b-tagged jets. The lower subpanels show the ratio of data over pre-fit expectations, with the gray histograms (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 5-a: Distributions of electron or muon ${p_{\mathrm {T}}}$ used as inputs for the binned likelihood fits for the $\mathrm{e} {\text {h}}$ (upper) and $\mu {\text {h}}$ (lower) categories, respectively, with the requirement of one (left) or more than one (right) b-tagged jets. The lower subpanels show the ratio of data over pre-fit expectations, with the gray histograms (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 5-b: Distributions of electron or muon ${p_{\mathrm {T}}}$ used as inputs for the binned likelihood fits for the $\mathrm{e} {\text {h}}$ (upper) and $\mu {\text {h}}$ (lower) categories, respectively, with the requirement of one (left) or more than one (right) b-tagged jets. The lower subpanels show the ratio of data over pre-fit expectations, with the gray histograms (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 5-c: Distributions of electron or muon ${p_{\mathrm {T}}}$ used as inputs for the binned likelihood fits for the $\mathrm{e} {\text {h}}$ (upper) and $\mu {\text {h}}$ (lower) categories, respectively, with the requirement of one (left) or more than one (right) b-tagged jets. The lower subpanels show the ratio of data over pre-fit expectations, with the gray histograms (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 5-d: Distributions of electron or muon ${p_{\mathrm {T}}}$ used as inputs for the binned likelihood fits for the $\mathrm{e} {\text {h}}$ (upper) and $\mu {\text {h}}$ (lower) categories, respectively, with the requirement of one (left) or more than one (right) b-tagged jets. The lower subpanels show the ratio of data over pre-fit expectations, with the gray histograms (hatched area) indicating MC statistical (post-fit systematic) uncertainties. Vertical bars on the data markers indicate statistical uncertainties.
png pdf	Figure 6: Summary of the measured values of the W leptonic branching fractions compared with the corresponding LEP results [8,9]. The vertical green-yellow band shows the extracted W leptonic branching fraction assuming LFU (the hatched band shows the corresponding LEP result). The horizontal error bars on the data points indicate their total uncertainty.
png pdf	Figure 7: Two-dimensional distributions of pairs of W leptonic branching fractions derived here compared with the corresponding LEP results [8,9] and to the SM expectation. The green (darker) and yellow (lighter) bands (dashed lines for the LEP results) correspond to the 68% and 95% CL, respectively, for the resulting two-dimensional Gaussian distribution.
png pdf	Figure 8: Correlation matrix between the four W boson decay branching fraction components extracted in this work.
png pdf	Figure 9: Two-dimensional distribution of the ratio ${R_{\tau /\mathrm{e}}}$ versus ${R_{\tau /\mu}}$ , compared with the corresponding LEP [8,9] and ATLAS [13] results and with the SM expectation. The green and yellow bands (dashed lines for the LEP results) correspond to the 68% and 95% CL, respectively, for the resulting two-dimensional Gaussian distribution. The corresponding 68% CL one-dimensional projections (black error bars) are also overlaid for a better visual comparison with the ATLAS ${R_{\tau /\mu}}$ result.

Tables
png pdf	Table 1: Categorization of events based on the triggering lepton, the number of reconstructed and selected leptons ( $N_{\mathrm{e}}$ , $N_{\mu}$ , $N_{{\tau _\mathrm {h}}}$ ), number of jets ( $N_ {\text {j}}$ ), and number of b-tagged jets ( $N_{\mathrm{b}}$ ). Kinematic requirements of the leptons and jets are listed in the fourth column. Categories with two leptons in the final state require the selected leptons to have opposite signs. The second-to-last column lists the targeted W boson branching fractions, and the last column provides the approximate number of W decays collected in each category.
png pdf	Table 2: Categorization of events with electrons, muons, and ${\tau _\mathrm {h}}$ passing the reconstruction criteria, based on their jet and b-tagged jet multiplicities, used to define signal-enriched and control regions. Events in the $\mathrm{e} {\tau _\mathrm {h}}$ and $\mu {\tau _\mathrm {h}}$ categories with at least one jet that is not b-tagged are additionally required to satisfy 40 $\leq m_{\ell {\tau _\mathrm {h}}} \leq$ 100 GeV, $\Delta \phi (\ell, {\tau _\mathrm {h}}) >$ 2.5, and ${m_{\mathrm {T}}} ^\ell <$ 60 GeV.
png pdf	Table 3: Summary of the impacts of each source of uncertainty (quoted as a percent of the total systematic uncertainty) for each W branching fraction. Whenever multiple NPs impact a common source of systematic uncertainty, each component is varied independently and the range of impacts is given.
png pdf	Table 4: Values of the W boson decay branching fractions measured here compared with the corresponding LEP measurements [8,9]. The lower rows list the average leptonic and inclusive hadronic W branching fractions derived assuming LFU. The first and second uncertainties quoted for each branching fraction correspond to statistical and systematic sources, respectively.
png pdf	Table 5: Ratios of different leptonic branching fractions, $R_{\mu /\mathrm{e}} = \mathcal {B}(\mathrm{W} \to \mu \overline{\nu}_{\mu})/\mathcal {B}(\mathrm{W} \to \mathrm{e} \overline{\nu}_{\mathrm{e}})$ , $R_{\tau /\mathrm{e}} = \mathcal {B}(\mathrm{W} \to \tau \overline{\nu}_{\tau})/\mathcal {B}(\mathrm{W} \to \mathrm{e} \overline{\nu}_{\mathrm{e}})$ , and $R_{\tau /\mu} = \mathcal {B}(\mathrm{W} \to \tau \overline{\nu}_{\tau})/\mathcal {B}(\mathrm{W} \to \mu \overline{\nu}_{\mu})$ , measured here compared with the values obtained by other LEP [8], LHC [16,17,13], and Tevatron [14,15] experiments.
png pdf	Table 6: Values of the QCD coupling constant at the W mass, the charm-strange CKM mixing element, and the squared sum of the first two rows of the CKM matrix, derived in this work.

Summary

A precise measurement of the three leptonic decay branching fractions of the W boson has been presented, as well as the average leptonic and inclusive hadronic branching fractions assuming lepton flavor universality (LFU). The analysis is based on a data sample of pp collisions at a center-of-mass energy of 13 TeV corresponding to an integrated luminosity of 35.9 fb

$^{-1}$ recorded by the CMS experiment. Events with one or two W bosons produced are collected using single-charged-lepton triggers that require at least one prompt electron or muon with large transverse momentum. The extraction of the W boson leptonic branching fractions is performed through a binned maximum likelihood fit of events split into multiple categories defined based on the multiplicity and flavor of reconstructed leptons, the number of jets, and the number of jets identified as originating from the hadronization of b quarks. The measured branching fractions for the decay of the W boson into electrons, muons, tau leptons, and hadrons are (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 LFU hypothesis for the weak interaction, and are more precise than previous measurements based on data collected by the LEP experiments.

Fitting the data assuming LFU provides values of (10.89

$\pm$ 0.08)% and (67.32

$\pm$ 0.23)%, respectively, for the average leptonic and inclusive hadronic branching fractions of the W boson. The comparison of the ratio of hadronic-to-leptonic branching fractions to the theoretical prediction is used to derive other standard model quantities. A value of the strong coupling constant at the W boson mass scale of

${\alpha_S}(m^{2}_\mathrm{W}) =$ 0.095

$\pm$ 0.033 is obtained which, although not competitive compared with the current world average, confirms the usefulness of the W boson decays to constrain this fundamental standard model parameter at future colliders. Using the world average value of

${\alpha_S}(m^{2}_\mathrm{W})$ , the sum of the square of the elements in the first two rows of the Cabibbo-Kobayashi-Maskawa (CKM) matrix is

$\sum_{ij}|V_{{ij}}|^{2} =$ 1.984

$\pm$ 0.021, providing a precise check of CKM unitarity. From this sum and using the world-average values of the other relevant CKM matrix elements, a value of

$|V_{{\mathrm{c}\mathrm{s}}}| =$ 0.967

$\pm$ 0.011 is determined, which is as precise as the current

$|V_{{\mathrm{c}\mathrm{s}}}| =$ 0.987

$\pm$ 0.011 result obtained from direct D meson decay data.

References
1	BaBar Collaboration	Evidence for an excess of $\bar{\mathrm{B}} \to \mathrm{D}^{(*)} \tau^-\bar{\nu}_\tau$ decays	PRL 109 (2012) 101802	1205.5442
2	BaBar Collaboration	Measurement of an excess of $\bar{B} \to D^{(*)}\tau^- \bar{\nu}_\tau$ decays and implications for charged Higgs bosons	PRD 88 (2013) 072012	1303.0571
3	LHCb Collaboration	Measurement of the ratio of branching fractions $\mathcal{B}(\bar{\mathrm{B}}^0 \to \mathrm{D}^{+}\tau^{-}\bar{\nu}_{\tau})/\mathcal{B}(\bar{\mathrm{B}}^0 \to \mathrm{D}^{+}\mu^{-}\bar{\nu}_{\mu})$	PRL 115 (2015) 111803	1506.08614
4	Belle Collaboration	Measurement of the branching ratio of $\bar{B}^0 \to D^{+} \tau^- \bar{\nu}_{\tau}$ relative to $\bar{B}^0 \to D^{+} \ell^- \bar{\nu}_{\ell}$ decays with a semileptonic tagging method	PRD 94 (2016) 072007	1607.07923
5	LHCb Collaboration	Measurement of the ratio of branching fractions $\mathcal{B}(\mathrm{B}_\mathrm{c}^+ \to \mathrm{J}/\psi\tau^+\nu_\tau)$ / $\mathcal{B}(\mathrm{B}_\mathrm{c}^+ \to \mathrm{J}/\psi\mu^+\nu_\mu)$	PRL 120 (2018) 121801	1711.05623
6	LHCb Collaboration	Search for lepton-universality violation in $\mathrm{B ^+\to K ^+\ell^+\ell^-}$ decays	PRL 122 (2019) 191801	1903.09252
7	LHCb Collaboration	Test of lepton universality in beauty-quark decays	2021	2103.11769
8	ALEPH, DELPHI, L3, OPAL, LEP Electroweak Collaboration	Electroweak measurements in electron-positron collisions at W-boson-pair energies at LEP	PR 532 (2013) 119	1302.3415
9	Particle Data Group, P. A. Zyla et al.	Review of particle physics	Prog. Theor. Exp. Phys. 2020 (2020) 083C01
10	A. Denner	Techniques for calculation of electroweak radiative corrections at the one loop level and results for W physics at LEP-200	Fortsch. Phys. 41 (1993) 307	0709.1075
11	B. A. Kniehl, F. Madricardo, and M. Steinhauser	Gauge independent W boson partial decay widths	PRD 62 (2000) 073010	hep-ph/0005060
12	D. d'Enterria and V. Jacobsen	Improved strong coupling determinations from hadronic decays of electroweak bosons at N $^3$ LO accuracy	2020. Submitted to PLB	2005.04545
13	ATLAS Collaboration	Test of the universality of $\tau$ and $\mu$ lepton couplings in W-boson decays from $\mathrm{t\bar{t}}$ events with the ATLAS detector	NP 17 (2021) 813	2007.14040
14	D0 Collaboration	W and Z boson production in ${{\mathrm{p}}}\bar{{\mathrm{p}}}$ collisions at $\sqrt{s} =$ 1.8 TeV	PRL 75 (1995) 1456	hep-ex/9505013
15	CDF Collaboration	Measurements of inclusive W and Z cross sections in ${{\mathrm{p}}}\bar{{\mathrm{p}}}$ collisions at $\sqrt{s} =$ 1.96 TeV	JPG 34 (2007) 2457	hep-ex/0508029
16	ATLAS Collaboration	Precision measurement and interpretation of inclusive W $^+$ , W $^-$ and Z/ $\gamma^*$ production cross sections with the ATLAS detector	EPJC 77 (2017) 367	1612.03016
17	LHCb Collaboration	Measurement of forward W $\to$ e $\nu$ production in pp collisions at $\sqrt{s}=$ 8 TeV	JHEP 10 (2016) 030	1608.01484
18	P. A. Baikov, K. G. Chetyrkin, and J. H. Kuhn	Order $\alpha_s^4$ QCD corrections to Z and tau decays	PRL 101 (2008) 012002	0801.1821
19	D. Kara	Corrections of order $\alpha \alpha_s$ to W boson decays	NPB 877 (2013) 683	1307.7190
20	D. d'Enterria and M. Srebre	$\alpha_s$ and $V_{\rm cs}$ determination, and CKM unitarity test, from W decays at NNLO	PLB 763 (2016) 465	1603.06501
21	CMS Collaboration	Precision luminosity measurement in proton-proton collisions at $\sqrt{s} =$ 13 TeV in 2015 and 2016 at CMS	EPJC 81 (2021) 800	CMS-LUM-17-003 2104.01927
22	CMS Collaboration	The CMS experiment at the CERN LHC	JINST 3 (2008) S08004	CMS-00-001
23	S. Alioli, P. Nason, C. Oleari, and E. Re	A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX	JHEP 06 (2010) 043	1002.2581
24	A. Kardos, P. Nason, and C. Oleari	Three-jet production in POWHEG	JHEP 04 (2014) 043	1402.4001
25	S. Frixione and B. R. Webber	Matching NLO QCD computations and parton shower simulations	JHEP 06 (2002) 029	hep-ph/0204244
26	P. Nason	A new method for combining NLO QCD with shower Monte Carlo algorithm	JHEP 11 (2004) 040	hep-ph/0409146
27	E. Re	Single-top Wt-channel production matched with parton showers using the POWHEG method	EPJC 71 (2011) 1547	1009.2450
28	J. Alwall et al.	MadGraph 5: going beyond	JHEP 06 (2011) 128	1106.0522
29	J. Alwall et al.	The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations	JHEP 07 (2014) 079	1405.0301
30	S. Frixione, P. Nason, and C. Oleari	Matching NLO QCD computations with parton shower simulations: the POWHEG method	JHEP 11 (2007) 070	0709.2092
31	T. Sjostrand et al.	An introduction to PYTHIA 8.2	CPC 191 (2015) 159	1410.3012
32	P. Skands, S. Carrazza, and J. Rojo	Tuning PYTHIA 8.1: the Monash 2013 tune	EPJC 74 (2014) 3024	1404.5630
33	CMS Collaboration	Event generator tunes obtained from underlying event and multiparton scattering measurements	EPJC 76 (2016) 155	CMS-GEN-14-001 1512.00815
34	CMS Collaboration	Investigations of the impact of the parton shower tuning in PYTHIA 8 in the modelling of $\mathrm{t\overline{t}}$ at $\sqrt{s}=$ 8 and 13 TeV	CMS-PAS-TOP-16-021	CMS-PAS-TOP-16-021
35	GEANT4 Collaboration	GEANT4--a simulation toolkit	NIMA 506 (2003) 250
36	CMS Collaboration	Pileup mitigation at CMS in 13 TeV data	JINST 15 (2020) P09018	CMS-JME-18-001 2003.00503
37	CMS Collaboration	Performance of the CMS Level-1 trigger in proton-proton collisions at $\sqrt{s} =$ 13 TeV	JINST 15 (2020) P10017	CMS-TRG-17-001 2006.10165
38	CMS Collaboration	The CMS trigger system	JINST 12 (2017) P01020	CMS-TRG-12-001 1609.02366
39	CMS Collaboration	Particle-flow reconstruction and global event description with the CMS detector	JINST 12 (2017) P10003	CMS-PRF-14-001 1706.04965
40	M. Cacciari, G. P. Salam, and G. Soyez	The anti- ${k_{\mathrm{T}}}$ jet clustering algorithm	JHEP 04 (2008) 063	0802.1189
41	M. Cacciari, G. P. Salam, and G. Soyez	FastJet user manual	EPJC 72 (2012) 1896	1111.6097
42	CMS Collaboration	Description and performance of track and primary-vertex reconstruction with the CMS tracker	JINST 9 (2014) P10009	CMS-TRK-11-001 1405.6569
43	S. Baffioni et al.	Electron reconstruction in CMS	EPJC 49 (2007) 1099
44	CMS Collaboration	Performance of electron reconstruction and selection with the CMS detector in proton-proton collisions at $\sqrt{s} =$ 8 TeV	JINST 10 (2015) P06005	CMS-EGM-13-001 1502.02701
45	CMS Collaboration	Performance of CMS muon reconstruction in pp collision events at $\sqrt{s}=$ 7 TeV	JINST 7 (2012) P10002	CMS-MUO-10-004 1206.4071
46	CMS Collaboration	Performance of the CMS muon detector and muon reconstruction with proton-proton collisions at $\sqrt{s}=$ 13 TeV	JINST 13 (2018) P06015	CMS-MUO-16-001 1804.04528
47	CMS Collaboration	Performance of reconstruction and identification of $\tau$ leptons decaying to hadrons and $\nu_\tau$ in pp collisions at $\sqrt{s}=$ 13 TeV	JINST 13 (2018) P10005	CMS-TAU-16-003 1809.02816
48	CMS Collaboration	Determination of jet energy calibration and transverse momentum resolution in CMS	JINST 6 (2011) 11002	CMS-JME-10-011 1107.4277
49	CMS Collaboration	Identification of heavy-flavour jets with the CMS detector in pp collisions at 13 TeV	JINST 13 (2018) P05011	CMS-BTV-16-002 1712.07158
50	B. Pollack, S. Bhattacharya, and M. Schmitt	Bayesian blocks in high energy physics: Better binning made easy!	2017	1708.00810
51	J. S. Conway	Incorporating nuisance parameters in likelihoods for multisource spectra	in Proceedings, PHYSTAT 2011 Workshop on Statistical Issues Related to Discovery Claims in Search Experiments and Unfolding, CERN 2011	1103.0354
52	CMS Collaboration	Measurement of the inelastic proton-proton cross section at $\sqrt{s}=$ 13 TeV	JHEP 07 (2018) 161	CMS-FSQ-15-005 1802.02613
53	CMS Collaboration	Measurement of the production cross section for single top quarks in association with W bosons in proton-proton collisions at $\sqrt{s}=$ 13 TeV	JHEP 10 (2018) 117	CMS-TOP-17-018 1805.07399
54	ATLAS Collaboration	Measurement of the cross section for isolated-photon plus jet production in pp collisions at $\sqrt s=$ 13 TeV using the ATLAS detector	PLB 780 (2018) 578	1801.00112
55	CMS Collaboration	Measurements of the pp $\to$ WZ inclusive and differential production cross section and constraints on charged anomalous triple gauge couplings at $\sqrt{s} =$ 13 TeV	JHEP 04 (2019) 122	CMS-SMP-18-002 1901.03428
56	CMS Collaboration	Measurements of pp $\to$ ZZ production cross sections and constraints on anomalous triple gauge couplings at $\sqrt{s} =$ 13TeV	EPJC 81 (2021), no. 3, 200	CMS-SMP-19-001 2009.01186
57	CMS Collaboration	Measurements of inclusive W and Z cross sections in pp collisions at $\sqrt{s}=$ 7 TeV	JHEP 01 (2011) 080	CMS-EWK-10-002 1012.2466
58	CMS Collaboration	Jet energy scale and resolution in the CMS experiment in pp collisions at 8 TeV	JINST 12 (2017) P02014	CMS-JME-13-004 1607.03663
59	CMS Collaboration	Extraction and validation of a new set of CMS PYTHIA8 tunes from underlying-event measurements	EPJC 80 (2020) 4	CMS-GEN-17-001 1903.12179
60	CMS Collaboration	Measurement of the top quark polarization and $\mathrm{t\bar{t}}$ spin correlations using dilepton final states in proton-proton collisions at $\sqrt{s} =$ 13 TeV	PRD 100 (2019) 072002	CMS-TOP-18-006 1907.03729
61	CMS Collaboration	Measurement of normalized differential $\mathrm{t}\overline{\mathrm{t}}$ cross sections in the dilepton channel from pp collisions at $\sqrt{s}=$ 13 TeV	JHEP 04 (2018) 060	CMS-TOP-16-007 1708.07638
62	CMS Collaboration	Measurement of differential cross sections for top quark pair production using the lepton+jets final state in proton-proton collisions at 13 TeV	PRD 95 (2017) 092001	CMS-TOP-16-008 1610.04191
63	M. Grazzini, S. Kallweit, D. Rathlev, and M. Wiesemann	Transverse-momentum resummation for vector-boson pair production at NNLL+NNLO	JHEP 08 (2015) 154	1507.02565
64	P. Meade, H. Ramani, and M. Zeng	Transverse momentum resummation effects in W $^+$ W $^-$ measurements	PRD 90 (2014) 114006	1407.4481
65	D. V. Hinkley	On the ratio of two correlated normal random variables	Biometrika 56 (1969) 635
66	FCC Collaboration	FCC-ee: The lepton collider: Future Circular Collider conceptual design report volume 2	EPJST 228 (2019) 261
67	CMS Collaboration	HEPData record for this analysis	link