Measurement of the ratio B(t→Wb)/B(t→Wq) in pp collisions at s√ = 8 TeV

The ratio of the top-quark branching fractions R=B(t→Wb)/B(t→Wq)R=B(t→Wb)/B(t→Wq), where the denominator includes the sum over all down-type quarks (q=b,s,dq=b,s,d), is measured in the tt¯ dilepton final state with proton–proton collision data at s=8 TeV from an integrated luminosity of 19.7 fb−1, collected with the CMS detector. In order to quantify the purity of the signal sample, the cross section is measured by fitting the observed jet multiplicity, thereby constraining the signal and background contributions. By counting the number of b jets per event, an unconstrained value of R=1.014±0.003(stat.)±0.032(syst.) is measured, in a good agreement with current precision measurements in electroweak and flavour sectors. A lower limit R>0.955R>0.955 at the 95% confidence level is obtained after requiring R≤1R≤1, and a lower limit on the Cabibbo–Kobayashi–Maskawa matrix element |Vtb|>0.975|Vtb|>0.975 is set at 95% confidence level. The result is combined with a previous CMS measurement of the t  -channel single-top-quark cross section to determine the top-quark total decay width, Γt=1.36±0.02(stat.)−0.11+0.14(syst.) GeV.


Introduction
Because of its large mass [1], the top quark decays before fragmenting or forming a hadronic bound state [2]. According to the standard model (SM), the top quark decays through an electroweak interaction almost exclusively to an on-shell W boson and a b quark. The magnitude of the top-bottom charged current is proportional to |V tb |, an element of the Cabibbo-Kobayashi-Maskawa (CKM) matrix. Under the assumption that the CKM matrix is unitary and given the measured values for V ub and V cb (or V ts and V td ), |V tb | is expected to be close to unity and dominate over the off-diagonal elements, i.e. |V tb | |V ts |, |V td |. Thus, the decay modes of the top quark to lighter down-type quarks (d or s) are allowed, but highly suppressed. The indirect measurement of |V tb |, from the unitarity constraint of the CKM matrix, is |V tb | = 0.999146 +0.000021 −0.000046 [3]. Any deviation from this value or in the partial decay width of the top quark to b quarks, would indicate new physics contributions such as those from new heavy up-and/or down-type quarks or a charged Higgs boson, amongst others [4]. Direct searches at the Large Hadron Collider (LHC) have set lower limits on the mass of these hypothetical new particles [5][6][7][8][9][10][11][12][13][14][15], and the observation of a SM Higgs boson candidate [16][17][18] places stringent constraints on the existence of a fourth sequential generation of quarks. These results support the validity of both the E-mail address: cms-publication-committee-chair@cern.ch. unitarity hypothesis and the 3 × 3 structure of the CKM matrix for the energy scale probed by the LHC experiments. However, other new physics contributions, including those described above, could invalidate the bounds established so far on |V tb | [3].
In this Letter, we present a measurement of R = B(t → Wb)/B(t → Wq), where the denominator includes the sum over the branching fractions of the top quark to a W boson and a down-type quark (q = b, s, d). Under the assumption of the unitarity of the 3 × 3 CKM matrix, R = |V tb | 2 , and thus to indirectly measure |V tb |. In addition, the combination of a determination of R and a measurement of the t-channel single-top cross section can provide an indirect measurement of the top-quark width (Γ t ) [19]. The most recent measurement of Γ t based on this approach [20] is found to be compatible with the SM predictions with a relative uncertainty of approximately 22%. The value of R has been measured at the Tevatron, and the most precise result is obtained by the D0 Collaboration, where R = 0.90 ± 0.04 (stat. + syst.) [21] indicates a tension with the SM prediction. This tension is enhanced for the measurement in the tt dilepton decay channel, where both W bosons decay leptonically and R = 0.86 +0.041 −0.042 (stat.) ± 0.035 (syst.) is obtained. The most recent measurements by the CDF Collaboration are given in [22,23].
Owing to its purity, the tt dilepton channel is chosen for this measurement. Events are selected from the data sample acquired in proton-proton collisions at The selected events are used to measure the tt production cross section by fitting the observed jet multiplicity distribution, constraining the signal and background contributions. The b-quark content of the events is inferred from the distribution of the number of b-tagged jets per event as a function of jet multiplicity for each of the dilepton channels. Data-based strategies are used to constrain the main backgrounds and the contributions of extra jets from gluon radiation in tt events. The R value is measured by fitting the observed b-tagged jet distribution with a parametric model that depends on the observed cross section, correcting for the fraction of jets that cannot be matched to a t → Wq decay. The model also depends on the efficiency for identifying b jets and discriminating them from other jets. Lastly, the measurement of R is combined with a previously published CMS result of the t-channel production cross section of single top quarks in pp collisions [25] to yield an indirect determination of the top-quark total decay width.

The CMS detector
The central feature of the Compact Muon Solenoid (CMS) apparatus is a superconducting solenoid of 6 m internal diameter, providing a magnetic field of 3.8 T. Within the superconducting solenoid volume are a silicon pixel and strip tracker, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass/scintillator hadron calorimeter (HCAL), each composed of a barrel and two endcap sections. Muons are measured in gas-ionisation detectors embedded in the steel flux-return yoke outside the solenoid. Extensive forward calorimetry complements the coverage provided by the barrel and endcap detectors.
The silicon tracker measures charged particles within the pseudorapidity range |η| < 2.5, where the pseudorapidity η is defined as η = −ln[tan(θ/2)] and θ is the polar angle of the trajectory of the particle with respect to the anticlockwise-beam direction. The tracker consists of 1440 silicon pixel and 15 148 silicon strip detector modules and is located in the field of the superconducting solenoid. It provides an impact parameter resolution of ∼15 μm and a transverse momentum (p T ) resolution of about 1.5% for 100 GeV particles. The electron energy is measured by the ECAL and its direction is measured by the tracker. The mass resolution for Z → ee decays is 1.6% when both electrons are in the ECAL barrel, and 2.6% when both electrons are in the ECAL endcap [26]. Matching muons to tracks measured in the silicon tracker results in a p T resolution between 1 and 10%, for p T values up to 1 TeV. The jet energy resolution (JER) amounts typically to 15% at 10 GeV, 8% at 100 GeV, and 4% at 1 TeV [27]. A more detailed description of the detector can be found in Ref. [28].

Simulation of signal and background events
The top-quark pair production cross section has been calculated at next-to-next-to-leading order (NNLO) and next-to-next-toleading logarithmic soft gluon terms (NNLL) [29]. In proton-proton collisions at √ s = 8 TeV, and for a top-quark mass of 172.5 GeV, the expected cross section is σ NNLO+NNLL (tt) = 253 +6 −8 (scale) ± 6 (PDF) pb, where the first uncertainty is from the factorisation and renormalisation scales, and the second is from the parton distribution functions (PDFs  [31], where the τ lepton decays are simulated with the tauola package (v27.121.5) [32]. The CTEQ6L1 PDF set is used in the event generation [33]. Matrix elements describing up to three partons, and including b quarks, in addition to the tt pair are included in the generator used to produce the simulated signal samples. An alternative simulation at next-to-leading order (NLO) based on powheg (v1.0, r1380) [34][35][36], using the CTEQ6M PDF set [33] and interfaced with pythia, is used to evaluate the signal description uncertainty. A correction to the simulated topquark p T is applied, based on the approximate NNLO computation [37]: the events are reweighted at the generator level to match the top-quark p T prediction, and the full difference between the reweighted and unweighted simulations is assigned as a systematic uncertainty. The most relevant background processes for the dilepton channel are from the production of two genuine isolated leptons with large p T . This includes Drell-Yan (DY) production of charged leptons, i.e. from a Z/γ * decay, which is modelled with MadGraph for dilepton invariant masses above 10 GeV, and is normalised to a NNLO cross section of 4.393 nb, computed using fewz [38]. The Z + γ process is also simulated with MadGraph and normalised to the LO predicted cross section of 123.9 pb. Single-top-quark processes are modelled at NLO with powheg [39,40] and normalised to cross sections of 22 ± 2 pb, 86 ± 3 pb, and 5.6 ± 0.2 pb for the tW, t-, and s-channel production, respectively [37]. The theory uncertainties are due to the variation of the PDFs and factorisation and renormalisation scales. Diboson processes are modelled with MadGraph and normalised to the NLO cross section computed with mcfm [41]. The generation of WW, WZ, and ZZ pairs is normalised to inclusive cross sections of 54.8 pb, 33.2 pb, and 17.7 pb, respectively. For WZ and ZZ pairs a minimum dilepton invariant mass of 12 GeV is required. Associated production of W or Z bosons with tt pairs is modelled with MadGraph, and normalised to the LO cross sections of 232 fb and 208 fb, respectively. The production of a W boson in association with jets, which includes misreconstructed and non-prompt leptons, is modelled with Mad-Graph and normalised to a total cross section of 36.3 nb computed with fewz. Multijet processes are also studied in simulation but are found to yield negligible contributions to the selected sample.
A detector simulation based on Geant4 (v.9.4p03) [42,43] is applied after the generator step for both signal and background samples. The presence of multiple interactions (pileup) per bunch crossing is incorporated by simulating additional interactions (both in-time and out-of-time with the collision) with a multiplicity matching that observed in the data. The average number of pileup events in the data is 21 interactions per bunch crossing.

Event selection and background determination
The event selection is optimised for tt dilepton final states that contain two isolated oppositely charged leptons (electrons or muons), missing transverse energy (E miss T ) defined below, and at least two jets. Events in which the electrons or muons are from intermediate τ lepton decays are considered as signal events.
Dilepton triggers are used to acquire the data samples, where a minimum transverse momentum of 8 GeV is required for each of the leptons, and 17 GeV is required for at least one of the leptons. Electron-based triggers include additional isolation requirements, both in the tracker and calorimeter detectors.
All objects in the events are reconstructed with a particle-flow (PF) algorithm [44,45]. Reconstructed electron and muon candidates are required to have p T > 20 GeV and to be in the fiducial region |η| ≤ 2.4 of the detector. A particle-based relative isolation parameter is computed for each lepton and corrected on an event-by-event basis for the contribution from pileup events. We require that the scalar sum of the p T of all particle candidates reconstructed in an isolation cone built around the lepton's momentum vector is less than 15% (12%) of the electron (muon) transverse momentum. The isolation cone is defined using the Table 1 Predicted and observed event yields after the full event selection. The combination of statistical uncertainties with experimental and theoretical systematic uncertainties is reported. Non-dileptonic tt channels, identified using a generator-level matching, as well as associated production with vector bosons (W or Z), is designated as "other tt" and grouped with the expected contribution from single W boson and multijets productions. The expected contribution from vector boson pair processes is designated as "VV".  [3] and M is the invariant mass of the dilepton system. For all dilepton channels it is further required that M > 12 GeV in order to veto low-mass dilepton resonances, and that the leptons have opposite electric charge.
Jets are reconstructed by clustering all the PF candidates using the anti-k T algorithm [46] with a distance parameter of 0.5. Jet momentum is defined as the vector sum of all particle momenta in the jet, and in the simulation it is found to be within 5 to 10% of the hadron-level momentum over the entire p T spectrum and detector acceptance. A correction is applied by subtracting the extra energy clustered in jets due to pileup, following the procedure described in Refs. [47,48]. The energies of charged-particle candidates associated with other reconstructed primary vertices in the event are also subtracted. Jet energy scale (JES) corrections are derived from simulation, and are validated with in-situ measurements of the energy balance of dijet and photon + jet events [27]. Additional selection criteria are applied to events to remove spurious jet-like features originating from isolated noise patterns in certain HCAL regions. In the selection of tt events, at least two jets, each with a corrected transverse momentum p T > 30 GeV and |η| ≤ 2.4, are required. The jets must be separated from the selected leptons by Events with up to four jets, selected under these criteria, are used.
The magnitude of the vector sum of the transverse momenta of all particles reconstructed in the event is used as the estimator for the momentum imbalance in the transverse plane, E miss T . All JES corrections applied to the event are also propagated into the E miss T estimate. For the ee and μμ channels, E miss T > 40 GeV is required in order to reduce the contamination from lepton pairs produced through the DY mechanism in association with at least two jets.
The DY contribution to the same-flavour dilepton channels is estimated from the data after the full event selection through the modelling of the angle Θ between the two leptons. The Θ distribution discriminates between leptons produced in DY processes and leptons from the top-quark pair decay cascade. In the first case an angular correlation is expected, while in the second case the leptons are nearly uncorrelated. The probability distribution function for Θ is derived from data using a DY-enriched control region selected after inverting the E miss T requirement of the standard selection. Studies of simulated events indicate that the shape of the Θ distribution is well described with this method, and that the contamination from other processes in the control region can be neglected. Compatibility tests performed in simulations using different channels and jet multiplicities are used to estimate an intrinsic 10% uncertainty in the final DY background. The other sources of uncertainty in the method are related to the simulation-based description of the probability distribution function for the Θ distribution from other processes. Uncertainties are estimated either by propagating the uncertainties in pileup or JES and JER, or by trying alternative functions for the tt contribution with varied factorisation/renormalisation scales (μ R /μ F ) with respect to their nominal values given by the momentum transfer in the event, matrix element/parton shower (ME-PS) matching threshold, or generator choice (powheg vs. MadGraph). The shapes of kinematic distributions for DY and other processes are used in a maximum-likelihood fit to estimate the amount of DY background in the selected sample. A total uncertainty of 21% is estimated from the data in the rate of DY events for the same-flavour channels.
For the eμ channel, a similar fit procedure is adopted using a different variable: the transverse mass M T = 2E miss of each lepton, where φ is the difference in azimuthal angle between the lepton and the missing transverse momentum. The distribution of the sum M T is used as the distribution in the fit. In this case the probability distribution function for Z/γ * → τ τ → eμ is derived from simulation. The determination of the uncertainty associated with this method follows a similar prescription to that described above for the same-flavour channels. A total uncertainty of 21% is assigned to the amount of DY contamination in the eμ channel.
The second-largest background contribution is from single-topquark processes (in particular the tW channel) that is relevant for this measurement since the decay products of a single top quark (instead of a pair) are selected. The contribution of this process is estimated from simulation. Other background processes are also estimated from simulation. Uncertainties in the normalisation stemming from instrumental uncertainties in the integrated luminosity, trigger and selection efficiencies, and energy scales, as well as generator-specific uncertainties, are taken into account. Table 1 shows the yields in the data and those predicted for signal and background events after the full event selection. The systematic uncertainties assigned to the predictions of signal and background events include the uncertainties in the JES and JER, pileup modelling, cross section calculations, integrated luminosity, and trigger and selection efficiencies. A conservative uncertainty is assigned to the predicted yields of multijet and W → ν background events since these contributions are from misidentified leptons and have been estimated solely from simulation. Good overall agreement is observed for all three dilepton categories between the yields in data and the sum of expected yields.

Cross section measurement
The selected events are categorised by the dilepton channel and the number of observed jets. Fig. 1 shows the expected composition for each event category. Good agreement is observed between the distributions from the data and the expectations, including the control regions, defined as events with fewer than two or more than four jets. The chosen categorisation not only allows one to study the contamination from initial-and final-state gluon radiation (ISR/FSR) in the sample, but also to constrain some of the uncertainties from the data.
The tt dilepton signal strength, μ, defined as the ratio of the observed to the expected signal rate, is measured from the jet multiplicity distribution by using a profile likelihood method [49]. A likelihood is calculated from the observed number of events in the k dilepton channels and jet multiplicity categories as where P is the Poisson probability density function, N k is the number of events observed in the k-th category, N k is the total number of expected events from signal and background, and θ i are the nuisance parameters, distributed according to a probability density function ρ. The nuisance parameters are used to modify the expected number of events according to the different systematic uncertainty sources, which include instrumental effects (such as integrated luminosity, pileup, energy scale and resolution, lepton trigger and selection efficiencies) and signal modelling (μ R /μ F , ME-PS scale, top-quark mass, leptonic branching fractions of the W boson) amongst others. The PDF uncertainty is estimated using the PDF4LHC prescription [50,51]. The uncertainty from the choice of the tt signal generator is estimated by assigning the difference between the MadGraph-based and the powheg-based predictions as an extra uncertainty in the fit. The nuisance parameters are assumed to be unbiased and distributed according to a log-normal function. Based on the likelihood expressed in Eq. (1), the profile likelihood ratio (PLR) λ is defined as where the denominator has estimators μ and θ that maximise the likelihood, and the numerator has estimators θ that maximise the likelihood for the specified signal strength μ. The signal strength is obtained after maximising λ(μ) in Eq. (2). This approach allows us to parameterise the effect of the systematic uncertainties in the fit.
The signal strength μ is determined independently in each category, i.e. for each dilepton channel and jet multiplicity. For each category, the purity of the selected sample ( f tt ) is defined as the fraction of "true" tt signal events in the selected sample, where N ttexp is the number of expected tt events, and N obs is the total number of observed events. By performing the fit for each category, the purity of the sample is obtained. The results are summarised in Table 2. As expected, the eμ category has the highest purity (≈90%). Because of the contamination from DY events, the same-flavour channels have lower purity (≈70%). Overall, the signal purity increases with higher jet multiplicity.
As a cross-check, a fit including all categories, gives the range 0.909 < μ < 1.043 at the 68% confidence level (CL). This leads to a tt production cross section of in good agreement with NNLO + NNLL expectation [29] and the latest CMS measurement [52]. The result is also found to be consistent with the individual results obtained in each event category. An extra uncertainty is assigned in the extrapolation of the cross section to the full phase space because of the dependence of the  acceptance on μ R /μ F , ME-PS threshold choices, and the top-quark mass.
The relative single-top-quark contribution (k st ), defined as the ratio of the expected number of single-top-quark events to the estimated number of inclusive tt events, is also shown in Table 2 for each category. For this determination we use the expected number of single-top-quark events obtained after maximising the PLR in Eq. (2). The contribution due to single-top-quark events tends to be most significant in the two-jet category (<7% relative to inclusive tt events). Since the estimate is obtained for a specific scenario in which R = 1, an extra linear dependence of k st on R is introduced in order to account for the increase in the tW cross section as |V tb | becomes smaller while |V td | and |V ts | become larger [4]. In this parameterisation, the measured ratio |V td |/|V ts | = 0.211 ± 0.006 is used [3], and the uncertainty is considered as an intrinsic systematic uncertainty in the measurement of R.

Probing the b-flavour content
In this section the b-flavour content of the selected events (both signal and background) is determined from the b-tagged jet multiplicity distribution. The probability of incorrectly assigning a jet must be evaluated (Section 6.1) in order to correctly estimate the heavy-flavour content of top-quark decays (Section 6.2).
The b-tagging algorithm that is used (the combined secondary vertex, CSV method described in Ref. [53]) is a multivariate procedure in which both information on the transverse impact parameter with respect to the primary vertex of the associated tracks, and the reconstructed secondary vertices is used to discriminate b jets from c, light-flavour (u, d, s), and gluon jets. The b-tagging efficiency (ε b ) is measured [54] using multijet events where a muon is reconstructed inside a jet; a data-to-simulation scale factor is derived and is used to correct the predicted ε b value in the tt dilepton sample from simulation. After correction, the expected efficiency in the selected tt sample is ≈84%, and the uncertainty in the scale factor from the data is 1-3%, depending on the kinematics of the jets [54]. The same scale factor is applied to the expected c-tagging efficiency but with a doubled uncertainty with respect to the one assigned to b jets owing to the fact that no direct measurement of the c-tagging efficiency is performed. For jets originating from the hadronisation of light-flavour jets, the misidentification efficiency (ε q ) is evaluated [53] from so-called negative tags in jet samples, which are selected using tracks that have a negative impact parameter or secondary vertices with a negative decay length. The scalar product of the jet direction with the vector pointing from the primary vertex to the point of closest approach of a track with negative impact parameter has the opposite sign of the scalar product taken with respect to the point of closest approach. The data-to-simulation correction factor for the misidentification efficiency is known with an uncertainty of about 11%, and the expected misidentification efficiency in the selected sample is approximately 12% [54]. Fig. 2 shows the number of b-tagged jets in the selected dilepton data sample, compared to the expectations from simulation. The multiplicity is shown separately for each dilepton channel and jet multiplicity. The expected event yields are corrected after the PLR fit for the signal strength (described in the previous section) and also incorporate the data-to-simulation scale factors for ε b and ε q . Data and simulation agree within 5%. The residual differences can be related to the different number of jets selected from top-quark decays in data and simulation, the modelling of gluon radiation (ISR/FSR) and if R is different from unity (which is an assumption used in the simulation).

Jet misassignment
There is a non-negligible probability that at least one jet from a tt decay is missed, either because it falls outside of the detector acceptance or is not reconstructed, and another jet from a radiative process is chosen instead. In the following discussion, this is referred to as a "misassigned jet". Conversely, jets that come from a top-quark decay will be referred to as "correctly assigned". The rate of correct jet assignments is estimated from the data using a combination of three different categories: • events with no jets selected from top-quark decays, which also include background events with no top quarks; • events with only one jet from a top-quark decay, which includes some tt events and single-top-quark events (mainly produced through the tW channel); • events with two jets produced from the two top-quark decays.
In order to avoid model uncertainties, the number of selected jets from top-quark decays is derived from the lepton-jet invariantmass (M j ) distribution, reconstructed by pairing each lepton with all selected jets. For lepton-jet pairs originating from the same top-quark decay, the endpoint of the spectrum occurs at M j ≈ [55], where M t (M W ) is the top-quark (W boson) mass (Fig. 3, top, open histogram). The predicted distribution for correct pairings is obtained after matching the simulated reconstructed jets to the b quarks from t → Wb at the generator level using a cone of radius R = 0.3. The same quantity calculated for a lepton from a top-quark decay paired with a jet from the top antiquark decay and vice versa ("wrong" pairing) shows a distribution with a long tail (Fig. 3, top, filled histogram), which can be used as a discriminating feature. A similar tail is observed for "unmatched" pairings: either background processes without top quarks, or leptons matched to other jets. The combinations with M j > 180 GeV are dominated by incorrectly paired jets, and this control region is used to normalise the contribution from background. In order to model the lepton-jet invariant-mass distribution of the misassigned jets, an empirical method is used based on the assumption of uncorrelated kinematics. The validity of the method has been tested using simulation. For each event in data, the momentum vector of the selected lepton is "randomly rotated" with uniform probability in the (cos(θ), φ) phase space, and the M j is recomputed. This generates a combinatorial distribution that is used to describe the true distribution of M j for misassigned jets. Fig. 3 (bottom) compares the data distribution with the two components of the M j spectrum, i.e. "correct assignments" from simulation and "wrong assignments" modelled from the data. The background model provides a good estimate of the shape of the spectrum of the misassigned lepton-jet pairs. After fitting the fractions of the two components to the data, the "misassigned" contribution is subtracted from the inclusive spectrum, and the result is compared to the expected contribution from the correctly assigned lepton-jet pairs. The result of this procedure is shown in the inset of Fig. 3 (bottom). This method is used to determine the fraction ( f correct ) of selected jets from top-quark decays in the M j spectrum. Consequently, by measuring f correct , we estimate directly The endpoint of the spectrum for correctly assigned pairs is shown by the dashed line. In the bottom plot the observed data is compared with the correct (from simulation) and misassigned (from the data) components for the lepton-jet invariantmass spectra in eμ events with exactly two jets. The lepton-jet mass distribution is shown in the inset, after the misassigned pairs are subtracted.

Table 3
Fraction of lepton-jet pairs correctly assigned in the selected events estimated from the data and predicted from simulation. The last column shows the ratio of the fraction measured in data to the prediction from simulation. The total uncertainty is shown. from the data the number of top-quark decays reconstructed and selected. Notice that f correct cannot be larger than 1/n for events with n jets, as it includes the combinatorial contribution by definition.
In Table 3 the values of f correct found in the data are compared to those predicted from simulation. These include both the contamination from background events as well as the effect of missing one or two jets from top-quark decays after selection. The systematic uncertainties affecting the estimate of f correct can be split into two sources: • distortion of the M j shape due to the JES and JER of the reconstructed objects [27]; • calibration uncertainties (derived in the previous section) owing to the uncertainty in the μ R /μ F scale, the simulation of gluon radiation and the underlying event, the top-quark mass value used in simulation, and the contributions from background processes.
For each case the fit is repeated with different signal probability distribution functions. The systematic uncertainty is estimated to be 3-10%, depending on the jet multiplicity in the event, and is dominated by the ME-PS matching threshold and the μ R /μ F scale uncertainties.
By combining the measured f correct from the data with the fraction of tt and single-top-quark events, a parameterisation of the three classes of events is obtained, i.e. the number of events with 0, 1, or 2 selected top-quark decays. The relative amounts of the three event classes are parameterised by the probabilities α i , where i corresponds to the number of jets from top-quark decays selected in an event. The probabilities α i are constrained to i α i = 1. Fig. 4 summarises the values of α i obtained for the individual event categories, where the differences are dominated by the event selection efficiencies and the background contribution in each category.

Heavy-flavour content
For a given number of correctly reconstructed and selected jets, the expected b-tagged jet multiplicity can be modelled as a function of R and the b-tagging and misidentification efficiencies. In the parameterisation, we distinguish events containing jets from 0, 1, or 2 top-quark decays. The model is an extension of the one proposed in Ref. [56]. For illustration, the most significant case is considered, i.e. modelling the observation of two b-tagged jets in an event with two reconstructed jets. For the case where two jets from top-quark decays are selected in the event, the probability to observe two b-tagged jets can be written as where the subscripts (2j, 2t, 2d) indicate a two-jet event, with two b-tagged jets, and two top-quark decays. If instead, only one jet from a top-quark decay is present in the event, the probability is modified to take the second jet into account in the measurement of R. In this case, the probability of observing two b-tagged jets where ε q * is the effective misidentification rate, and is computed by taking into account the expected flavour composition of the "extra" jets in the events (i.e. those not matched to a top-quark decay). The effective misidentification rate is derived specifically for each event category. From simulation, these extra jets are expected to come mostly from light-flavour jets (≈87%). For completeness, for the case in which no jet from top-quark decay is reconstructed, the probability of observing two b-tagged jets is P 2j,2t,0d = ε 2 q * . (5) For each dilepton channel and jet multiplicity, analogous expressions are derived and combined using the probabilities α i of having i reconstructed jets from top-quark decays. Additional terms are added to extend the model to events with more than two jets. All efficiencies are determined per event category, after convolving the corrections from dijet events in the data with the expected efficiencies (ε q and ε b ) and the simulated jet p T spectrum.
For the measurement of R, a binned-likelihood function is constructed using the model described above and the observed b-tagging multiplicity in events with two, three, or four observed jets in the different dilepton channels. A total of 36 event categories, corresponding to different permutations of three leptonflavour pairs, three jet multiplicities, and up to four observed b-tagged jets are used (see Fig. 2). The likelihood is generically written as  1] interval. The residual difference found from these tests is assigned as a model calibration uncertainty.

Measurement of R
In the fit, R is allowed to vary without constraints. The parameters of the model are all taken from the data: f tt and k st are  taken from Table 2, f correct is taken from Table 3, ε b and ε q from dijet-based measurements [53], and ε q * is derived following the method described in the previous section. For these, we obtain values of R ee = 0.997 ± 0.007 (stat.) ± 0.035 (syst.), R μμ = 0.996 ± 0.007 (stat.) ± 0.034 (syst.), and R eμ = 1.015 ± 0.003 (stat.) ± 0.031 (syst.) for the ee, μμ, and eμ channels, respectively. The measurement in the eμ channel dominates in the final combination since the main systematic uncertainties are fully correlated and this channel has the lowest statistical uncertainty.
The total relative uncertainty in the measurement of R is 3.2%, and is dominated by the systematic uncertainty, whose individual contributions are summarised in Table 4. The largest contribution Table 4 Summary of the systematic uncertainties affecting the measurement of R. The values of the uncertainties are relative to the value of R obtained from the fit. to the systematic uncertainty is from the b-tagging efficiency measurement. Additional sources of uncertainty are related to the determination of the purity of the sample ( f tt ) and the fraction of correct assignments ( f correct ) from the data; these quantities are affected by theoretical uncertainties related to the description of tt events, which have similar impact on the final measurement, such as μ R /μ F , ME-PS, signal generator, top-quark mass, and topquark p T . Instrumental contributions from JES and JER, modelling of the unclustered E miss T component in simulation, and the contribution from the DY and misidentified-lepton backgrounds are each estimated to contribute a relative systematic uncertainty <0.6%.
Another source of uncertainty is due to the contribution from extra sources of heavy-flavour production, either from gluon splitting in radiated jets or from decays in background events such as W → cs. This effect has been estimated in the computation of ε q * by assigning a conservative uncertainty of 100% to the c and b contributions. The effect of the uncertainty in the misidentification efficiency is estimated to be small (<1%), as well as other sources of uncertainty, such as pileup and integrated luminosity. After the fit is performed no nuisance parameter is observed to change by more than 1.5σ . The most relevant systematic uncertainty (ε b ) is moved by ∼0.5σ as a result of the fit.
If the three-generation CKM matrix is assumed to be unitary, then R = |V tb | 2 [4]. By performing the fit in terms of |V tb |, a value of |V tb | = 1.007 ±0.016 (stat.+syst.) is measured. Upper and lower endpoints of the 95% CL interval for R are extracted by using the Feldman-Cousins (FC) frequentist approach [57]. The implementation of the FC method in RooStats [58] is used to compute the interval. All the nuisance parameters (including ε b ) are profiled in order to take into account the corresponding uncertainties (statistical and systematic). If the condition R ≤ 1 is imposed, we obtain R > 0.955 at the 95% CL. Fig. 7 summarises the expected limit bands for 68% CL, 95% CL, and 99.7% CL, obtained from the FC method. The expected limit bands are determined from the distribution of the profile likelihood obtained from simulated pseudoexperiments. The upper and lower acceptance regions constructed in this procedure are used to determine the endpoints on the allowed interval for R. In the pseudo-experiments the expected signal and background yields are varied using Poisson probability distributions for the statistical uncertainties and Gaussian distributions for the systematic uncertainties. By constraining |V tb | ≤ 1, a similar procedure is used to obtain |V tb | > 0.975 at the 95% CL.

Indirect measurement of the top-quark total decay width
The result obtained for R can be combined with a measurement of the single-top-quark production cross section in the t-channel to yield an indirect determination of the top-quark total width Γ t . Assuming that q B(t → Wq) = 1, then R = B(t → Wb) and Γ t = σ t-ch.

t-ch. ) is the measured (theoretical) t-channel
single-top-quark cross section and Γ (t → Wb) is the top-quark partial decay width to Wb. If we assume a top-quark mass of 172.5 GeV, then the theoretical partial width of the top quark decaying to Wb is Γ (t → Wb) = 1.329 GeV [3]. A fit to the b-tagged jet multiplicity distribution in the data is performed, leaving Γ t as a free parameter. In the likelihood function we use the theoretical prediction for the t-channel cross section at √ s = 7 TeV from Ref. [59] and the corresponding CMS measurement from Ref. [25]. The uncertainties in the predicted and measured cross sections are taken into account as extra nuisance parameters in the fit. The uncertainty in the theoretical cross section is parameterised by convolving a Gaussian function for the PDF uncertainty with a uniform prior describing the factorisation and renormalisation scale uncertainties. Some uncertainties in the experimental cross section measurement such as those from JES and JER, b-tagging efficiency, μ R /μ F scales, and ME-PS threshold for tt production are fully correlated with the ones assigned to the measurement of R.
All others are summed in quadrature and assumed to be uncorrelated. After performing the maximum-likelihood fit, we measure Γ t = 1.36 ± 0.02 (stat.) +0.14 −0.11 (syst.) GeV, in good agreement with the theoretical expectation [3]. The dominant uncertainty comes from the measurement of the t-channel cross section, as summarised in Table 5.

Acknowledgements
We congratulate our colleagues in the CERN accelerator departments for the excellent performance of the LHC and thank the technical and administrative staffs at CERN and at other CMS institutes for their contributions to the success of the CMS effort. In addition, we gratefully acknowledge the computing centres and personnel of the Worldwide LHC Computing Grid for delivering so effectively the computing infrastructure essential to our analyses.