Determination of the muonic branching ratio of the W boson and its total width via cross-section measurements at the Tevatron and LHC

Abstract

(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image)

The total W-boson decay width ...... is an important observable which allows testing of the standard model. The current world average value is based on direct measurements of final state kinematic properties of W-boson decays, and has a relative uncertainty of 2%. The indirect determination of ...... via the cross-section measurements of vector-boson production can lead to a similar accuracy. The same methodology leads also to a determination of the leptonic branching ratio. This approach has been successfully pursued by the CDF and D0 experiments at the Tevatron collider, as well as by the CMS collaboration at the LHC. In this paper we present for the first time a combination of the available measurements at hadron colliders, accounting for the correlations of the associated systematic uncertainties. Our combination leads to values of ...... and ...... MeV, respectively, both compatible with the current world averages.

Eur. Phys. J. C (2016) 76:613DOI 10.1140/epjc/s10052-016-4461-6

Regular Article - Experimental Physics

http://crossmark.crossref.org/dialog/?doi=10.1140/epjc/s10052-016-4461-6&domain=pdf

Web End = http://crossmark.crossref.org/dialog/?doi=10.1140/epjc/s10052-016-4461-6&domain=pdf

Web End = Determination of the muonic branching ratio of the W boson and its total width via cross-section measurementsat the Tevatron and LHC

Stefano Camarda1,a, Jakub Cuth2, Matthias Schott2

1 CERN, Geneva, Switzerland

2 Johannes Gutenberg University, Mainz, Germany

Received: 25 August 2016 / Accepted: 24 October 2016 / Published online: 9 November 2016 The Author(s) 2016. This article is published with open access at Springerlink.com

Abstract The total W-boson decay width W is an important observable which allows testing of the standard model. The current world average value is based on direct measurements of nal state kinematic properties of W-boson decays, and has a relative uncertainty of 2%. The indirect determination of W via the cross-section measurements of vector-boson production can lead to a similar accuracy. The same methodology leads also to a determination of the leptonic branching ratio. This approach has been successfully pursued by the CDF and D0 experiments at the Tevatron collider, as well as by the CMS collaboration at the LHC. In this paper we present for the rst time a combination of the available measurements at hadron colliders, accounting for the correlations of the associated systematic uncertainties. Our combination leads to values of BR(W ) = (10.72 0.16)% and

W = 2113 31 MeV, respectively, both compatible with

the current world averages.

1 Introduction

Precise measurements of the W-boson properties, such as its mass mW and its decay width W , allows testing of the standard model of particle physics. As a matter of fact, the relation between the W-boson mass, mW , the top-quark mass, mt, and the Higgs-boson mass, mH , via loop corrections, allowed a prediction of the mass of the Higgs boson with an uncertainty smaller than 25 GeV. Models beyond the standard model could alter the relation between mW and mH , since new particles can appear in virtual loops. Similarly, the total decay width of the W boson can be altered by new particles.

Within the standard model, the total decay width of the W boson is predicted to be equal to the sum of the partial widths

a e-mail: mailto:[email protected]

Web End [email protected]

over three generations of lepton doublets and two generations of quark doublets. The partial widths are expressed as

W f f =

|M f f |2 NC GF m3W

62 (1 + radf) (1)

where M f f = 1, NC = 1 for leptonic decays, M f f

corresponds to the CKM matrix elements, and NC = 3

(1 + s(mW )/ + ) is the colour factor for the quark-

decay modes [1]. Radiative corrections are represented by radf. They depend, among other parameters, on the top-quark mass, mt, and the Higgs-boson mass, mH , and are small in the standard model (SM) since a large part of the corrections is absorbed in the measured values of GF =

1.1663787(8)105 GeV2 and mW = 80.3850.015 GeV.

The radiative corrections correspond to rad 0.34% for

leptons and of radq 0.40% for quarks [2]. New particle

candidates that couple to the W boson and are lighter than mW , would open a new decay channel and alter W . One very prominent example is supersymmetric models in which the W boson can decay to the lightest super-partner of the charged gauge bosons and the lightest super-partner of the neutral gauge bosons. Hence a precise measurement of W might reveal physics beyond the standard model. In addition, assuming standard model relations, the dependence of the partial and total widths of the W boson on the strong-coupling constant allows to determine the value of s from the hadronic and leptonic branching ratios of the W boson [3].

The total width of the W boson can be measured directly by kinematic ts to the measured decay lepton spectra, such as the transverse momentum of the charged lepton decay pT or the high-mass tail of the transverse mass mT as was performed at CDF and D0 [46], or via ts to the invariant mass distributions in the qqqq and qql nal states as was done at the LEP experiments [711]. A combination of these

123

613 Page 2 of 7 Eur. Phys. J. C (2016) 76 :613

direct results, based on kinematic measurements, leads to W = 2085 42 MeV, which is currently used as world

average value [12].

An independent determination of the width of the W boson is based on the measurement of the ratio of cross sections of W- and Z-boson production in hadron collisions, dened as

R =

(pp W + X) BR(W ) (pp Z + X) BR(Z )

2 Methodology

The production cross section of W and Z bosons in hadron collisions is described by the DrellYan process [18] and can be experimentally dened as

incl(pp V + X ) =

NCand NBkg [integraltext] Ldt

NCand NBkg

= C A [integraltext] Ldt

,

,

where BR(V ) = V / V denotes the leptonic

branching ratio of the vector-boson (V = W, Z) decays.

The ratio R can be written as

R =

W

Z

,

where the total cross-section ratio W /Z is known theoretically to high accuracy [13]. The ratio Z /Z was pre

cisely measured by the LEP experiments and therefore the leptonic branching ratio of the W boson, BR(W ) =

W / W , can be inferred from the measurement of R.

The advantage of extracting BR(W ) from the cross-

section ratio R lies in the fact that many experimental systematic uncertainties of each vector-boson cross-section measurement, such as the uncertainty on the integrated luminosity, are highly correlated and cancel in the ratio. The leptonic width of the W boson in the SM can be predicted by Eq. (1) and is (W ) = 226.5 0.1 MeV.1 The dominant

uncertainty is due to the accuracy of mW . Using this value, the total width of the W boson can be extracted by a measurement of the leptonic branching ratio. This approach for the determination of the W-boson width was already pursued by the CDF [14], D0 [15], and CMS [16,17] experiments, leading to measurements of W which have an accuracy comparable to the current world average.

In this paper we present a procedure for a rst combination of the individual measurements of the muonic branching ratio of the W boson and of W , accounting for the correlations of the individual systematic uncertainties. We have chosen to focus on the muon decay channel, as it has smaller experimental uncertainties.

The paper is structured as follows: we introduce the basic methodology in Sect. 2 and discuss the selected measurements for the combination in Sect. 3, where we also derive the corresponding ducial cross-section ratios. The theoretical predictions of the cross-section ratios are discussed in Sect. 4 and the nal extraction and combination of W for the different experiments is presented in Sect. 5. The paper concludes with a brief summary and a discussion of the consistency of the results with the direct measurements and with the global electroweak t in Sect. 6.

1 Taken from Ref. [2], with updated values of mW and GF, and s(mW ).

where NCand and NBkg are the number of vector-boson candidates and the expected background events, respectively, and [integraltext] Ldt is the integrated luminosity of the corresponding data sample. The factor is the efciency of the signal events passing the signal selection criteria, which is typically estimated with simulated samples of the signal process, and corrected for differences in the detector response between data and MC simulation. The efciency correction can be decomposed as the product of a ducial acceptance, A, and a detector-induced correction factor, C, i.e. = A C. The ducial

acceptance is the ratio of the number of events that pass the geometrical and kinematic requirements in the analysis at generator level over the total number of generated events in a simulated sample of signal process. The advantage of this decomposition is the separation to a large extent of detector and analysis related uncertainties, which enter the factor C, while all model and theoretical uncertainties, such as QCD scales and parton density function (PDF) uncertainties, enter A. The ducial production cross section d within the detector acceptance volume dened by A, is barely affected by model uncertainties, and is related to the fully inclusive cross section by d = incl A.

The strategy for the combination of several indirect BR(W ) and W measurements from various exper

iments is therefore based on the measured ducial cross-section ratio

Rd =

W W

Z Z

d(pp W + X) BR(W ) d(pp Z + X) BR(Z )

,

which has only negligible model uncertainties and uncorrelated experimental uncertainties between the different experiments. The ducial ratio Rd can be related to the inclusive ratio R, by

R =

[parenleftbigg] AW

AZ

[parenrightbigg]1

Rd,

where the AW and AZ are the acceptance correction factors for the Z- and W-boson analyses, respectively. Some published results only present a value for the inclusive cross-section ratio R, but do not publish a value for Rd. In these cases, we have used the ducial volume denition, the PDF set, and the MC generator of the corresponding analysis that were used to extract the acceptance ratio AW /AZ, in order to

123

Eur. Phys. J. C (2016) 76 :613 Page 3 of 7 613

reconstruct the value of Rd. The uncertainty on the extrapolated values of Rd is estimated by subtracting the published model and PDF uncertainties from the total uncertainty on R.

Once the ducial ratios are determined for each measurement, we can coherently predict the acceptance correction ratios AW /AZ and the inclusive ducial cross-section ratios W /Z, and extract the corresponding branching ratio BR(W ) and decay width W from the measurements

of Rd. Each model variation, e.g. one particular eigenvector variation of a given PDF set, leads to new predictions of AW /AZ and W /Z, thus also to new determined values of

BR(W ) and W for each experiment. The measure

ments are combined treating the experimental uncertainties as uncorrelated, and the PDF and model uncertainties with a correlation model based on a common baseline for the theoretical predictions.

3 Measurements used for the combination

One of the rst precise measurements of the W /Z cross-section ratio was published by the D0 collaboration in proton anti-proton collisions at a centre-of-mass energy of s =

1.8 TeV [15]. However, this measurement was performed only in the electron decay channel and hence is not used for this combination. The most precise measurement at the Tevatron collider was performed by the CDF collaboration at s = 1.96 TeV [14], using the electron and muon decay

channels. Only the inclusive cross-section ratio was published (Table 1), but the clear denition of the ducial volume, as reported in the paper, allows the extrapolation of the value of Rd. The extrapolation factor AW /AZ is estimated using the Pythia 6.2 [19] generator with the CTEQ5L PDF set [20].

Several measurements of R were performed at the LHC by the CMS and ATLAS collaborations in protonproton collisions at s = 7 TeV and s = 8 TeV [16,17,21], which

are all used for the combination. In contrast to the Tevatron experiments, ducial ratios together with a ducial volume denition have also been published by the ATLAS and CMS experiments, as summarised in Table 1. Hence no additional extrapolation to Rd is performed for these measurements.

4 Theoretical predictions and systematic uncertainties

The total W- and Z-boson production cross sections and their ratio, corresponding to the ducial volume denitions of Table 1, are calculated at next-to-next-to-leading order in the perturbative expansion of the strong-coupling constant with FEWZ [22] using the MMHT2014 PDF set [23]. The calculations are based on the G electroweak parameter scheme and the strong-coupling constant at the Z-boson mass is set

to s(mZ ) = 0.118, as used in the MMHT2014 PDF deter

mination.2 The uncertainties of the PDF set are estimated by a reevaluation of the predicted cross-section ratio for each error eigenvector within the MMHT2014 PDF set, as well as the comparison to the central prediction using a second PDF set, which is chosen to be the CT10 [24] in this study. The uncertainties, at 68% CL, include contributions from the strong-coupling constant s as well as variations of the renormalisation scale, R, and factorisation scale, F.

The correct description of the vector-boson transverse momentum, pT (V = W, Z), is essential for the estimation

of AW and AZ. Since xed order perturbative QCD predictions do not provide a sufciently good description of the low pT (V = W, Z) spectrum, we use the Powheg MC

generator interfaced to Pythia8, henceforth referred to as Powheg+Pythia8, to estimate the central values for AW and AZ, using the MMHT2014 PDF set.

The uncertainties due to missing higher order QCD corrections are estimated by varying the renormalisation and factorisation scales, R and F, by a factor of two up and down, as well as by reevaluating the acceptance factors with hdamp set to mV (V = W, Z), instead of the default value

hdamp = [25], in the Powheg generator. The correla

tion of the R and F variations on the W- and Z-boson cross sections and acceptances can be treated according to various prescriptions. In the most conservative approach they are considered as fully uncorrelated, leading to an uncertainty of 0.5% on the predicted inclusive cross-section ratio. The uncertainty reduces by more than a factor of two when assuming a fully correlated behaviour. In the following we adopt an intermediate approach, and assume a correlation of 50%. In addition to these uncertainties, the acceptance factor ratio AW /AZ is also affected by other effects, which change the kinematic distribution of the nal states, but has little effect on the inclusive cross sections. In particular, the uncertainties due to soft non-perturbative effects and initial-state radiation (ISR), which vary the transverse momentum spectrum of the vector boson, pT (V ), have to be estimated. To perform a conservative estimation, we reweight the predicted pT (V )

from Powheg+Pythia8 to corresponding predictions of the Resbos generator [2628]. Resbos is based on a resummed calculation, which is performed at next-to-next-to-leading logarithmic order and matched to approximate NNLO perturbative QCD calculations at large boson momenta. The difference between the nominal Powheg+Pythia8 predictions of AW and AZ and the Resbos reweighted samples, is considered as an ISR and resummation uncertainty. The corresponding uncertainties on AW /AZ vary between 0.1%

(ATLAS) and 0.4% (CMS). This difference can be explained by the larger effect on the W-boson selection for CMS, as it

2 In this study, we used GF = 1.1663787 105 GeV2, mW =

80385 MeV, mZ = 91187.6 MeV, and Z = 2495 MeV.

123

613 Page 4 of 7 Eur. Phys. J. C (2016) 76 :613

Table 1 The collider beams, the corresponding centre-of-mass energy, the ducial volume denitions, the published inclusive cross-section ratio R, as well as the ducial cross-section ratio Rd are given for each

analysis used for the combination. The ducial ratio was not published for the measurements of the CDF experiment and the extrapolated value is shown

Experiment Collider Fiducial volume denition R (published) Rd

CDF [14] p p, s = 1.96 TeV pT > 20 GeV for || < 1.0 10.93 7.46

Z : 66 < mee < 116 GeV 0.27 (stat) 0.18 (stat)

W : pT > 20 GeV 0.18 (sys) 0.12 (sys) (extrapolated)

ATLAS [21] pp, s = 7 TeV p T > 20 GeV 10.91 10.85

| | < 2.5 0.11 (stat) 0.11 (stat)

Z : 66 < mll < 116 GeV 0.17 (sys) 0.17 (sys) (published)

W : pT > 25 GeV, mT > 40 GeVCMS [16] pp, s = 7 TeV Z: pT > 20 GeV for || < 2.1 10.52 11.95

Z: 60 < mee < 120 GeV 0.09 (stat) 0.10 (stat)

W : pT > 25 GeV for || < 2.1 0.10 (sys) 0.20 (sys) (published)

CMS [17] pp, s = 8 TeV Z: pT > 25 GeV for || < 2.1 10.44 13.28

Z : 60 < mee < 120 GeV 0.14 (stat) 0.18 (stat)

W : pT > 25 GeV for || < 2.1 0.30 (sys) 0.23 (sys) (published)

Table 2 Predicted acceptance ratios AW /AZ for the extrapolation from the experimental ducial region to the full phase space and predicted cross-section ratios W /Z for all measurements under consideration.

In addition, the uncertainties due to initial-state radiation modelling

and resummation model (ISR), factorisation and renormalisation scales, PDF, QED nal state radiation uncertainties as well as electroweak corrections are given. It should be noted that the invariant mass requirement of the Z-boson selection is different between the analyses

Experiment Quantity Value Scales (R, F) ISR+ resummation PDF QED FSR + EWK Total CDF AW /AZ 1.884 0.007 0.003 0.006 0.004 0.011

(W /Z )pred 3.391 0.005 0.013 0.014 ATLAS AW /AZ 1.000 0.003 0.002 0.004 0.002 0.006

(W /Z )pred 3.395 0.012 0.020 0.023 CMS (7 TeV) AW /AZ 1.135 0.003 0.006 0.005 0.002 0.008

(W /Z )pred 3.346 0.012 0.019 0.022 CMS (8 TeV) AW /AZ 1.266 0.004 0.007 0.005 0.002 0.009

(W /Z )pred 3.326 0.013 0.020 0.023

requires only a minimum threshold on the pT of the decay muons.

Furthermore, NLO electroweak corrections can be comparable in size to NNLO QCD corrections. We distinguish between the corrections due to QED nal-state radiation (FSR) and loop-induced electroweak corrections (EWK). The QED FSR related uncertainties are estimated by comparing Sherpa [29] and Pythia8 [30], where the acceptances are derived for both generators using dressed and bare lep-tons. The resulting differences in the predicted acceptance ratios are taken as the QED FSR model uncertainty and amount to 0.1%. The uncertainties due to loop-induced electroweak corrections are taken from literature [31] and are accounted for by 0.1% variations on AW /AZ.

We obtain 57 predictions for the cross-section ratios W /Z and the acceptance ratios AW /AZ, accounting for 50

MMHT PDF eigenvector variations, the central prediction of the CT10 PDF set, R and F scale variations, and variations of s. In addition, we have further uncertainties on AW /AZ due to ISR/resummation effects, QED FSR and NLO EWK effects. A summary of the cross-section ratios W /Z and acceptance ratios AW /AZ for each measurement, including the relevant model uncertainties, is given in Table 2. The PDF uncertainties are evaluated with the Hessian method [32].

The uncertainties due to ISR and resummation, QED FSR, and electroweak corrections, as well as the variations of F and R, are symmetrised by taking the average of the positive and negative variations.

123

Eur. Phys. J. C (2016) 76 :613 Page 5 of 7 613

Table 3 Extracted values of BR(W ) (%) for all four measurements and their combination. The associated statistical, experimental, and

model uncertainties are also given

Experiment BR. (%) Stat. Exp. sys. Scales (R, F) ISR+ resummation PDF FSR + EWK Total ATLAS 10.75 0.11 0.17 0.05 0.02 0.10 0.01 0.23

CMS (7 TeV) 10.59 0.09 0.18 0.05 0.05 0.10 0.02 0.23

CMS (8 TeV) 10.69 0.14 0.19 0.06 0.05 0.11 0.02 0.27

CDF 11.06 0.27 0.18 0.04 0.02 0.07 0.02 0.33

Combined 10.72 0.07 0.09 0.04 0.02 0.10 0.02 0.16

5 Extraction of the W-boson width and combination

The total inclusive cross-section ratio for each experiment is estimated by combining the central values of AW /AZ reported in Table 2 and the ducial cross-section ratios Rd from Table 1. It should be noted that these derived values for R will differ from the original published values, as our baseline prediction for the estimation of AW /AZ differs from the approach followed by each experiment. Clearly, the advantage of having a common model for the theoretical predictions lies in the traceability of correlated systematic uncertainties. The published values of R are compared to the values obtained using the newly derived acceptance ratios as a rst sanity check of our extrapolation. The derived values agree with the published values of the experiments within their associated model uncertainties.

In a second step, the expected leptonic branching ratios can be rederived for each experiment individually, using the predicted cross-section ratios, the measured ducial ratios of the experiments reported in Table 2, and the relation

BR(W ) =

W

W = R

Z

Z ,

where a value of the leptonic Z-boson branching ratio of Z/ Z = 0.033658 0.000023 [12] is used. The

results are presented in Table 3. Assuming the validity of the SM, the partial leptonic W-boson width is predicted by Eq. (1), leading to W = 226.5 MeV, where the

(1+rad) corrections are taken from Ref. [2]. Finally, the total

W-boson width can be derived from the measured leptonic branching ratios. The resulting values for W = BR W

for each experimental measurement are illustrated in Fig. 2 and reported in Table 4, together with the associated statistical, experimental systematic, and combined model uncertainties.

For the combination, we use the measured inclusive cross-section ratio R and the corresponding inclusive cross-section prediction for each model systematic variation, thus leading to new values of BR(W ) and W for each measure

ment, respectively. In a second step, we combine the individual measurements following the BLUE method [33], again, separately for all model variations. For the combination of

the four experimental values of BR(W ) and W ,

we treat the statistical and experimental systematic uncertainties as fully uncorrelated. In a last step, we calculate the difference between the combined values of BR(W )

and W for each model variation and their central combined values, and evaluate the theoretical and model systematic uncertainties from these differences. The PDF uncertainties are evaluated with the MMHT2014 PDF set using the Hessian method [32]. The other model systematic uncertainties are added in quadrature.

The results of the combination are

BR(W ) = (10.72 0.07 0.09 0.11)% = (10.72 0.16)%

and

W = 2113 13 18 22 MeV

= 2113 31 MeV,where the rst uncertainty is statistical, the second is the experimental systematic uncertainty, and the third is the modelling systematic uncertainty. The results are shown and compared to the current world averages and to the SM predictions in Figs. 1 and 2, respectively. The statistical and systematic uncertainties of the combined measurement of W are 30%

and 45% smaller, respectively, compared to the uncertainties of the most precise single measurement. The model uncertainties on the combined values do not signicantly change and are dominated by PDF uncertainties.

6 Summary and interpretation

In this paper we have presented a combination of measurements of the muonic branching ratio of the W boson and its total decay width, extracted from the cross-section ratios of W- and Z-boson production from the ATLAS, CMS, and CDF experiments at various centre-of-mass energies. Special emphasis was drawn to the correct treatment of the correlations between systematic uncertainties, in particular uncertainties due to the limited knowledge of the parton distribution functions and variations of the renormalisation

Z W

123

613 Page 6 of 7 Eur. Phys. J. C (2016) 76 :613

Table 4 Extracted values of W (MeV) for all four measurements and their combination. The associated statistical, experimental, and model uncertainties are also given

Experiment W (MeV) Stat. Exp. sys. Scales (R, F) ISR+ resummation PDF FSR + EWK Total ATLAS 2108 21 33 10 3 18 4 44

CMS (7 TeV) 2140 18 36 9 11 18 4 46

CMS (8 TeV) 2120 29 37 12 11 19 4 53

CDF 2050 51 34 8 4 13 4 63

Combined 2113 13 18 8 6 19 4 31

Central Value

Exp. Uncertainty

Exp.+Mod. Uncertainty

World Average

CDF

ATLAS

CMS (7 TeV)

CMS (8 TeV)

Combination

SM Predicton

9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.2 11.4

BR(W

) [%]

Fig. 1 Reestimated BR(W ) values of the measurements under

consideration as well as the combined value, the SM prediction, and the current world average

Central Value

Exp. Uncertainty

Exp.+Mod. Uncertainty

World Average

CDF

ATLAS

CMS (7 TeV)

CMS (8 TeV)

Combination

EW-Fit

1800 1850 1900 1950 2000 2050 2100 2150 2200 2250 2300

[MeV]

References

1. J.L. Rosner, M.P. Worah, T. Takeuchi, Oblique corrections to the W width. Phys. Rev. D 49, 13631369 (1994). http://arxiv.org/abs/hep-ph/9309307

Web End =arXiv:hep-ph/9309307

2. P. Renton, Updated SM calculations of W boson width. http://arxiv.org/abs/0804.4779

Web End =arXiv:0804.4779 [hep-ph]

3. D. dEnterria, M. Srebre, s, and CKM unitarity test from W decays at NNLO. http://arxiv.org/abs/1603.06501

Web End =arXiv:1603.06501 [hep-ph]

3 Using s(mW ) = 0.1203, corresponding to the value of s(mZ ) used

for the MMHT2014 PDF set, the SM prediction of BR(W )SM

changes to 10.82%.

Fig. 2 Reestimated W-boson width values of the measurements under consideration as well as the combined value, the result of the global electroweak t, and the current world average

and factorisation scales. The combination yields BR(W

)R = (10.72 0.16)% and RW = 2113 31 MeV. The

results are compatible in value, and similar in accuracy, to the current world averages BR(W )WA = (10.57

0.15)% [11,3437] and WAW = 2085 42 MeV [6,11],

which are based solely on direct measurements.

The total width of the W boson is potentially sensitive to new physics scenarios in the context of the global electroweak t [38]. The indirect determination via the electroweak t yields a value of EWW = 2091 1 MeV [39],

which is in good agreement with our combined value. The relation expressed in Eq. (1) shows that W depends, among other SM parameters, on mW , s, and mH . However, the small uncertainties on the determination of EWW indicates that the sensitivity of W to these parameters of the SM is rather weak.

It should be noted that loop corrections arising from contributions of new physics to the W-boson width would alter the term rad in Eq. (1) independently from the decay channel. As a consequence, the branching ratio is insensitive to effects that could appear in the corresponding loop correction terms. Only new physics effects that directly alter the leptonic branching ratio can be tested with our combined value BR(W )R. We nd a perfect agreement with the

SM prediction BR(W )SM = (10.830.01)% [1,2].3

Acknowledgements We would like to thank M. Boonekamp, A. Glazov, K. Moenig, and S. Webb for the useful comments during the preparation this paper. This work was partly supported by the Volkswagen Foundation and the German Research Foundation (DFG).

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/

Web End =http://creativecomm http://creativecommons.org/licenses/by/4.0/

Web End =ons.org/licenses/by/4.0/ ), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Funded by SCOAP3.

123

Eur. Phys. J. C (2016) 76 :613 Page 7 of 7 613

4. CDF Collaboration, T. Aaltonen et al., A direct measurement of the W boson width in p p collisions at s = 1.96-TeV. Phys. Rev.

Lett. 100, 071801 (2008). http://arxiv.org/abs/0710.4112

Web End =arXiv:0710.4112 [hep-ex]5. D0 Collaboration, V. M. Abazov et al., Direct measurement of the W boson width. Phys. Rev. Lett. 103, 231802 (2009). http://arxiv.org/abs/0909.4814

Web End =arXiv:0909.4814 [hep-ex]

6. T. E. W. Group, Combination of CDF and D0 Results on the Width of the W boson. http://arxiv.org/abs/1003.2826

Web End =arXiv:1003.2826 [hep-ex]

7. ALEPH Collaboration, S. Schael et al., Measurement of the W collisions at LEP. Eur. Phys. J. C 47, 309335 (2006). http://arxiv.org/abs/hep-ex/0605011

Web End =arXiv:hep-ex/0605011

8. DELPHI Collaboration, J. Abdallah et al., Measurement of the mass and width of the W = 161-GeV209-GeV. Eur. Phys. J. C 55, 138 (2008). http://arxiv.org/abs/0803.2534

Web End =arXiv:0803.2534 [hep-ex]

9. L3 Collaboration, P. Achard et al., Measurement of the mass and the width of the W boson at LEP. Eur. Phys. J. C 45, 569587 (2006). http://arxiv.org/abs/hep-ex/0511049

Web End =arXiv:hep-ex/0511049

10. OPAL Collaboration, G. Abbiendi et al., Measurement of the mass and width of the W boson, Eur. Phys. J. C45 (2006) 307335, http://arxiv.org/abs/hep-ex/0508060

Web End =arXiv:hep-ex/0508060 [hep-ex]

11. DELPHI, OPAL, LEP Electroweak, ALEPH, L3 Collaboration,S. Schael et al., Electroweak measurements in electronpositron collisions at W-boson-pair energies at LEP. Phys. Rep. 532, 119 244 (2013). http://arxiv.org/abs/1302.3415

Web End =arXiv:1302.3415 [hep-ex]12. Particle Data Group Collaboration, K. Olive et al., Review of particle physics. Chin. Phys. C 38, 090001 (2014)

13. S. Catani, L. Cieri, G. Ferrera, D. de Florian, M. Grazzini, Vector boson production at hadron colliders: a fully exclusive QCD calculation at NNLO. Phys. Rev. Lett. 103, 082001 (2009). http://arxiv.org/abs/0903.2120

Web End =arXiv:0903.2120 [hep-ph]

14. CDF Collaboration, A. Abulencia et al., Measurements of inclusive W and Z cross sections in p anti-p collisions at s =

1.96 TeV, J. Phys. G 34 (2007) 24572544, http://arxiv.org/abs/hep-ex/0508029

Web End =arXiv:hep-ex/0508029 [hep-ex]15. D0 Collaboration, B. Abbott et al., Extraction of the width of the W and their ratio. Phys. Rev. D 61, 072001 (2000). http://arxiv.org/abs/hep-ex/9906025

Web End =arXiv:hep-ex/9906025

16. CMS Collaboration, S. Chatrchyan et al., Measurement of the inclusive W and Z production cross sections in pp collisions at s = 7 TeV. JHEP 10, 132 (2011). http://arxiv.org/abs/1107.4789

Web End =arXiv:1107.4789 [hep-ex]

17. C.M.S. Collaboration, S. Chatrchyan et al., Measurement of inclusive W and Z boson production cross sections in pp collisions at s = 8 TeV. Phys. Rev. Lett. 112, 191802 (2014). http://arxiv.org/abs/1402.0923

Web End =arXiv:1402.0923 [hep-ex]18. S.D. Drell, T.-M. Yan, Massive lepton pair production in hadron hadron collisions at high-energies. Phys. Rev. Lett. 25, 316320 (1970) (erratum: Phys. Rev. Lett. 25, 902, 1970)

19. T. Sjostrand, L. Lonnblad, S. Mrenna, PYTHIA 6.2: physics and manual. http://arxiv.org/abs/hep-ph/0108264

Web End =arXiv:hep-ph/0108264

20. CTEQ Collaboration, H. Lai et al., Global QCD analysis of parton structure of the nucleon: CTEQ5 parton distributions. Eur. Phys. J.C 12, 375392 (2000). http://arxiv.org/abs/hep-ph/9903282

Web End =arXiv:hep-ph/9903282

21. ATLAS Collaboration, G. Aad et al., Measurement of the inclusive W TeV with the ATLAS detector. Phys. Rev. D 85, 072004 (2012).

http://arxiv.org/abs/1109.5141

Web End =arXiv:1109.5141 [hep-ex]22. R. Gavin, Y. Li, F. Petriello, S. Quackenbush, FEWZ 2.0: a code for hadronic Z production at next-to-next-to-leading order. Comput.Phys. Commun. 182, 23882403 (2011). http://arxiv.org/abs/1011.3540

Web End =arXiv:1011.3540 [hepph]

23. L.A. Harland-Lang, A.D. Martin, P. Motylinski, R.S. Thorne, Parton distributions in the LHC era: MMHT 2014 PDFs. Eur. Phys. J. C 75(5), 204 (2015). http://arxiv.org/abs/1412.3989

Web End =arXiv:1412.3989 [hep-ph]

24. J. Gao et al., CT10 next-to-next-to-leading order global analysis of QCD. Phys. Rev. D 89(3), 033009 (2014). http://arxiv.org/abs/1302.6246

Web End =arXiv:1302.6246 [hepph]

25. S. Alioli, P. Nason, C. Oleari, E. Re, NLO Higgs boson production via gluon fusion matched with shower in POWHEG. JHEP 04, 002 (2009). http://arxiv.org/abs/0812.0578

Web End =arXiv:0812.0578 [hep-ph]

26. C. Balazs, C.P. Yuan, Soft gluon effects on lepton pairs at hadron colliders. Phys. Rev. D 56, 55585583 (1997). http://arxiv.org/abs/hep-ph/9704258

Web End =arXiv:hep-ph/9704258

27. G.A. Ladinsky, C.P. Yuan, The nonperturbative regime in QCD resummation for gauge boson production at hadron colliders. Phys. Rev. D 50, 4239 (1994). http://arxiv.org/abs/hep-ph/9311341

Web End =arXiv:hep-ph/9311341

28. M. Guzzi, P.M. Nadolsky, B. Wang, Nonperturbative contributions to a resummed leptonic angular distribution in inclusive neutral vector boson production. Phys. Rev. D 90(1), 014030 (2014). http://arxiv.org/abs/1309.1393

Web End =arXiv:1309.1393 [hep-ph]

29. T. Gleisberg, S. Hoeche, F. Krauss, M. Schonherr, S. Schumann,F. Siegert, J. Winter, Event generation with SHERPA 1.1. JHEP 02, 007 (2009). http://arxiv.org/abs/0811.4622

Web End =arXiv:0811.4622 [hep-ph]30. T. Sjostrand, S. Mrenna, P.Z. Skands, A brief introduction to PYTHIA 8.1. Comput. Phys. Commun. 178, 852867 (2008). http://arxiv.org/abs/0710.3820

Web End =arXiv:0710.3820 [hep-ph]

31. G. Balossini, G. Montagna, C.M. Carloni Calame, M. Moretti,M. Treccani, O. Nicrosini, F. Piccinini, A. Vicini, Electroweak & QCD corrections to Drell Yan processes. Acta Phys. Polon. B 39, 1675 (2008). http://arxiv.org/abs/0805.1129

Web End =arXiv:0805.1129 [hep-ph]32. J. Pumplin, D. Stump, R. Brock, D. Casey, J. Huston, J. Kalk, H.L. Lai, W.K. Tung, Uncertainties of predictions from parton distribution functions. 2. The Hessian method. Phys. Rev. D 65, 014013 (2001). http://arxiv.org/abs/hep-ph/0101032

Web End =arXiv:hep-ph/0101032

33. L. Lyons, D. Gibaut, P. Clifford, How to combine correlated estimates of a single physical quantity. Nucl. Instrum. Methods A 270, 110 (1988)

34. ALEPH Collaboration, A. Heister et al., Measurement of W collisions at centre-of-mass energies from 183-GeV to 209-GeV. Eur. Phys. J. C 38, 147160 (2004)

35. DELPHI Collaboration, J. Abdallah et al., Measurement of the W pair production cross-section and W branching ratios in e+ e

collisions at s (1/2) = 161-GeV to 209-GeV. Eur. Phys. J. C

34, 127144 (2004). http://arxiv.org/abs/hep-ex/0403042

Web End =arXiv:hep-ex/0403042 36. L3 Collaboration, P. Achard et al., Measurement of the cross section of W-boson pair production at LEP. Phys. Lett. B 600, 2240 (2004). http://arxiv.org/abs/hep-ex/0409016

Web End =arXiv:hep-ex/0409016

37. OPAL Collaboration, G. Abbiendi et al., Measurement of the e+

decay branching fractions at LEP. Eur. Phys. J. C 52, 767785 (2007). http://arxiv.org/abs/0708.1311

Web End =arXiv:0708.1311 [hep-ex]38. ALEPH, CDF, D0, DELPHI, L3, OPAL, SLD, LEP Electroweak Working Group, Tevatron Electroweak Working Group, SLD Electroweak and Heavy Flavour Groups Collaboration, L. E. W. Group, Precision electroweak measurements and constraints on the standard model. http://arxiv.org/abs/1012.2367

Web End =arXiv:1012.2367 [hep-ex]

39. Gtter Group Collaboration, M. Baak et al., The global electroweak t at NNLO and prospects for the LHC and ILC. Eur. Phys. J. C 74, 3046 (2014). http://arxiv.org/abs/1407.3792

Web End =arXiv:1407.3792 [hep-ph]

123