Combination of the CDF and D0 effective leptonic electroweak mixing angles

02 Aug 2016


Drell-Yan lepton pairs are produced in the process pp → γ*/Z + X, with the subsequent decay of the γ*/Z into lepton pairs. The angular distribution of decay leptons provides information on the electroweak-mixing parameter sin2θW via the observable effective-leptonic sin2θW (sin2θefflept) mixing parameter. Measurements of sin2θefflept based on the observed the lepton asymmetry (Afb) as a function of lepton-pair mass from the following measurements are combined:

With the aid of ZFITTER standard model calculations, sin2θW (or equivalently MW) is inferred. The combination of results yields For details, see:



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Brief summary of D0 and CDF sin2θefflept results

The D0 and CDF combined result for sin2θefflept are derived from the following references.

The numbers used from these references are reproduced in this section.

D0 result summary

Result type sin2θefflept
Raw 0.23139 ± 0.00043 (stat.) ± 0.00008 (syst.) ± 0.00017 (PDF)
Final 0.23147 ± 0.00043 (stat.) ± 0.00008 (syst.) ± 0.00017 (PDF)

The raw result is obtained directly from the Afb distributions of electron pairs. Both the central (CC) and end cap (EC) calorimeters are used, and there are three pair topoplgies, CC-CC, CC-EC, and EC-EC, which are combined for the results above. The mixing angle sin2θefflept is extracted from background subtracted Afb distributions. The Afb templates used for the extraction of sin2θefflept are based on PYTHIA and NNPDF 2.3 (NLO) PDFs. They include D0 detector simulation. The PDF uncertainty is obtained using the 100 equally probable ensemble PDFs of NNPDF 2.3.

The Afb templates based on PYTHIA use the same real value for the effective couplings at the lepton, u-quark, and d-quark vertices. However, radiative corrections to the Born level couplings from ZFITTER used by CDF, and ZGRAD used by D0 are complex valued and differ for the different fermions. The real part of the effective couplings for the u- and d-quark vertices are shifted relative to the leptonic vertex by −0.0001 and −0.0002, respectively. These real shifts are incorporated into a version of RESBOS with CTEQ6.6 PDFs. Relative to this modified version of RESBOS, the sin2θefflept from PYTHIA is shifted by −0.00008 with no change in uncertainties. Applying this correction to the raw value gives the final measurement central value without any change of uncertainties.

The uncertainties of sin2θefflept are summarized in the following table.
Category Uncertainty
Statistical 0.00043
Total systematic 0.00008
Energy calibration 0.00001
Energy smearing 0.00002
Background 0.00001
Charge misidentification 0.00003
Electron identification 0.00007
Fiducial asymmetry 0.00001
NNPDF 2.3 0.00017

CDF result summary

Result type sin2θefflept
Muon Afb 0.2315 ± 0.0009 (stat.) ± 0.0002 (syst.) ± 0.0004 (PDF)
Electron Afb 0.23248 ± 0.00049 (stat.) ± 0.00004 (syst.) ± 0.00019 (PDF)
Combined 0.23221 ± 0.00043 (stat.) ± 0.00007 (syst.) ± 0.00016 (PDF)

Afb is measured using the event-weighting method [Eur. Phys. J. C 67, 321 (2010)], and is fully corrected. The effects of detector resolution and QED FSR are removed using the simulation. For the simulation, PYTHIA generates the Drell-Yan event, PHOTOS 2.0 applies QED FSR, and CDF detector simulation is applied. The Afb templates for the extraction of sin2θefflept are calculated with the POWHEG-BOX NLO framework for Drell-Yan events, and the NNPDF 3.0 ensemble PDFs for NNLO and αs(MZ2) = 0.118. PYTHIA 6.4 parton showering follows the event generation. The ensemble consists of 100 equally probable PDFs, which are used to predict the value of observables and their uncertainties. Standard model electroweak radiative corrections calculated by ZFITTER are implemented in the template calculations. This includes the photon propagator correction, whose real part is usually called the running αem.

The muon Afb result in the table above uses templates calculated with RESBOS with CTEQ6.6 PDFs, and with uncertainties estimated with POWHEG-BOX and CT10 NLO PDFs. For the combination of the muon- and electron-channel results, the muon Afb measurement is unchanged but the templates are calculated with the POWHEG-BOX framework with NNPDF 3.0 PDFs described above. The corresponding muon-channel result with templates calculated using POWHEG-BOX and NNPDF 3.0 PDFs is sin2θefflept = 0.23141±0.00086, where the uncertainty is statistical only.

The uncertainties of sin2θefflept for the combination of the muon- and electron-channels are summarized in the following table.
Category Uncertainty
Statistical 0.00043
Total systematic 0.00007
Energy scale and resolution 0.00002
Background 0.00003
QCD scale 0.00006
NNPDF 3.0 0.00016

Combination of CDF and D0 results

Standardization corrections

The CDF and D0 implementations of Afb templates differ in these aspects: the PDFs and a slight variance in the method of radiative corrections. Adjustments that standardize results to NNPDF 3.0 PDFs and ZFITTER radiative corrections are calculated and implemented. The NNPDF 3.0 PDF set is preferred as it includes LHC data and the PDF implementation is more robust. The ZFITTER implementation of electroweak radiative corrections is a precision package used for standard model fits by LEP-1 and SLD.

The CDF results already use the standardization framework of NNPDF 3.0 PDFs and ZFITTER electroweak radiative corrections. The D0 results are corrected for consistency with this framework. There are two standardization corrections

which correct the D0 value of sin2θefflept to the NNPDF 3.0 and ZFITTER framework.

The PDF standardization correction is determined as follows. A pseudodata Afb distribution is calculated using the default PDFs of NNPDF 3.0 and NNPDF 2.3. The NNPDF 3.0 Afb distribution is fit to the templates to obtain the best-fit value of sin2θefflept for NNPDF 2.3. The difference between the fixed value of sin2θefflept of the NNPDF 3.0 Afb distribution and the best fit value is Δsin2θefflept(PDF), and its value is −0.00024±0.00004, where the uncertainty is statistical.

For the radiative correction standardization offset, the CDF ZFITTER based framework is used. The CDF Afb templates include ZFITTER radiative correction form factors, and this implementation is denoted as EBA (Enhanced Born Approximation). The form factors to the Born level vertex couplings are

where ρ and κ are the complex valued form factors which depend on the fermion flavor (f) at the vertex and a mass scale (Mff). The analog to the D0 PYTHIA templates with a single real-valued weak-mixing angle parameter is obtained by setting all form factors to unity, and retaining only the running αem part of the photon propagator correction. In this case, "sin2θW" becomes the single effective leptonic weak mixing angle parameter, and this implementation is denoted by nonEBA. To convert the value of sin2θefflept derived using PYTHIA templates to one derived using ZFITTER form factors, the following additive correction is used. It is calculated using the fits to the combination of the CDF muon- and electron-channel asymmetries using EBA and nonEBA templates for 23 ensemble PDFs of NNPDF 3.0, whose extracted values of the weak mixing angle are near the full ensemble average value. The D0 value of sin2θefflept includes a correction of +0.00008 to account for value extracted from PYTHIA based templates to one that includes corrections accounting for the difference between with effective leptonic weak mixing angle and effective u- and d-quark mixing angles. Thus Δsin2θefflept(RadCor) = Δefflept − 0.00008, or 0.00014 ± 0.00004.

To update the D0 central value of sin2θefflept (0.23147) to one based on templates calculated with NNPDF 3.0 PDFs and ZFITTER-based radiatiive corrections, the two additive adjustments are applied:

The net correction is −0.00010 ± 0.00005, and its uncertainty is denoted as the "correction" uncertainty.

Combination of sin2θefflept results

The input values of the CDF and D0 results, and their combination via the Best Linear Unbiased Estimator (BLUE) are

The D0 value includes the −0.00010±0.00005 correction described in the section above. The uncertainties for the combination are listed below, and they are derived using the individual D0 and CDF uncertainties listed in the tables of the previous section. For the combination, four categories of uncertainties are used: statistical, PDF, uncorrelated, and correction. These categories and their treatment in the combination are summarized below. The input PDF uncertainties are treated as 100% correlated. All other input systematic uncertainties are uncorrelated, and combined into a single combination category denoted as "uncorrelated". The correction uncertainty only applies to the D0 measurement, and is uncorrelated from the other systematic uncertainties. The following table gives the combination uncertainties from BLUE.
Category Uncertainty
Statistical ±0.00030
Uncorrelated ±0.00005
Correction ±0.00003
NNPDF PDF ±0.00017

Inference of sin2θW

The observed asymmetry is directly sensitive to the effective couplings κfsin2θW. The standard model is used to infer the value of sin2θW and values of κf that correspond to the effective couplings. The effective leptonic weak mixing angle in terms of the ZFITTER lepton-vertex form factor κe [PRD 93 112016 (2016)] is

The inference of sin2θW from the D0 value of sin2θefflept uses this relationship. CDF Afb templates use effective couplings κfsin2θW, with sin2θW as the template parameter, so it is obtained from template fits. In either case, there is a corresponding form factor, which depends on standard model inputs and sin2θW. The top-quark mass input is 173.2 ± 0.9 GeV/c2, and the measurement uncertainty propagates to an uncertainty of ±0.00008 for the inferred value of sin2θW. This uncertainty, denoted as the "form factor" uncertainty, only applies to sin2θW.

The inference of sin2θW using ZFITTER implies the inference of MW because of its use of the on-shell renormalization scheme where sin2θW = 1 − (MW/MZ)2 holds to all orders. The inferences for sin2θW (MW) based on the updated D0 value of sin2θefflept and the combination of CDF and D0 values are

where the first uncertainty is statistical, and the second is the systematic uncertainty which includes the PDF and form factor uncertainties.

Comparisons with other measurments

Comparisons of sin2θefflept that includes latest LHC results from CMS [ Phys. Rev. D84 112002, 2011 ], ATLAS [ J. High Energy Phys. 09 (2015) 049 ], and LHCb [ J. High Energy Phys. 11 (2015) 190 ]. LEP-1+SLD [ Phys. Rept. 428, 257 (2006), Phys. Rept. 532, 119 (2013) ]: Z-pole entry is the standard model analysis using all Z-pole measurements, AFB0,b is the b-quark asymmetry based measurement, and Al measurement corresponds to pure leptonic couplings. The entries with D0 are based on the updated results of the previous section, and are preliminary.

The inferred value of sin2θW from on-shell renormalization scheme frameworks is also expressed as an indirect W-boson mass. There are other indirect W-boson mass results, including those from LEP-1 and SLD which are from standard model fits to Z-pole measurements with the top quark mass, and there are direct W-mass measurements from the Tevatron and LEP-2 [Phys. Rev. D86, 010001 (2012): PDG W mass review, 2015 update].
All measurements except for 'TeV and LEP-2' are indirect W-mass measurements that use the standard model (on-shell scheme). The LEP-1 and SLD (mt) result, except for the top mass constraint, only uses LEP-1 and SLD data to constrain the ZFITTER standard model input parameters. NuTeV is the neutrino neutral current measurement [ PRL 88, 091802 (2002); PRL 90, 239902(E) (2003) ] from the Tevatron. The entries with D0 are based on the updated results of the previous section, and are preliminary.