The leptonic effective electroweak mixing angle, sin$^2\theta {}^{{\mathrm {lept}}}_{{\mathrm {eff}}}$, is given in terms of the ratio of leptonic vector and axial-vector coupling constants, ${{\mathit r}}$ = ${{\mathit g}}{}^{V}_{{{\mathit \ell}}}/{{\mathit g}}{}^{A}_{{{\mathit \ell}}}$ for ${{\mathit \ell}}$ = ${{\mathit e}}$ , ${{\mathit \mu}}$ , ${{\mathit \tau}}$, with sin$^2\theta {}^{{\mathrm {lept}}}_{{\mathrm {eff}}}$ = (1$−{{\mathit r}}$)/4. It can be extracted directly from the leptonic asymmetry parameter, ${{\mathit A}_{{{{{\mathit \ell}}}}}}$ = 2${{\mathit r}}/(1+{{\mathit r}^{2}}$). See note "The ${{\mathit Z}}$ boson" and ref. LEP-SLC 2006.

VALUE DOCUMENT ID TECN  COMMENT $\bf{ 0.23148 \pm0.00013}$ OUR AVERAGE $0.23147$ $\pm0.00050$ 1 AAIJ 2024 AL LHCB ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 13 TeV $0.2319$ $\pm0.0019$ 2 HAYRAPETYAN 2024 T CMS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 13 TeV $0.23148$ $\pm0.00033$ 3 AALTONEN 2018 B TEVA ${\it{}E}^{\it{}p\overline{\it{}p}}_{\rm{}cm}$ = 1.96 TeV $0.23101$ $\pm0.00053$ 4 SIRUNYAN 2018 CY CMS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 8 TeV $0.2308$ $\pm0.0012$ 5 AAD 2015 BT ATLS ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 7 TeV $0.2314$ $\pm0.0011$ 6 AAIJ 2015 BF LHCB ${\it{}E}^{\it{}pp}_{\rm{}cm}$ = 7+8 TeV $0.23153$ $\pm0.00016$ 7 LEP-SLC 2006 ${\it{}E}^{\it{}ee}_{\rm{}cm}$ = $88 - 94$ GeV • • We do not use the following data for averages, fits, limits, etc. • • $0.23016$ $\pm0.00064$ 8 ABAZOV 2018 D0 ${\it{}E}^{\it{}p\overline{\it{}p}}_{\rm{}cm}$ = 1.96 TeV $0.23248$ $\pm0.00053$ 9 AALTONEN 2016 D CDF2 ${\it{}E}^{\it{}p\overline{\it{}p}}_{\rm{}cm}$ = 1.96 TeV $0.23147$ $\pm0.00047$ 10 ABAZOV 2015 C D0 ${\it{}E}^{\it{}p\overline{\it{}p}}_{\rm{}cm}$ = 1.96 TeV $0.2315$ $\pm0.0010$ 11 AALTONEN 2014 C CDF2 ${\it{}E}^{\it{}p\overline{\it{}p}}_{\rm{}cm}$ = 1.96 TeV $0.23099$ $\pm0.00053$ 12 LEP-SLC 2006 LEP ${\it{}E}^{\it{}ee}_{\rm{}cm}$ = $88 - 94$ GeV $0.23159$ $\pm0.00041$ 13 LEP-SLC 2006 LEP ${\it{}E}^{\it{}ee}_{\rm{}cm}$ = $88 - 94$ GeV $0.23098$ $\pm0.00026$ 14 LEP-SLC 2006 SLD ${\it{}E}^{\it{}ee}_{\rm{}cm}$ = $88 - 94$ GeV $0.23221$ $\pm0.00029$ 15 LEP-SLC 2006 ${\it{}E}^{\it{}ee}_{\rm{}cm}$ = $88 - 94$ GeV $0.23220$ $\pm0.00081$ 16 LEP-SLC 2006 ${\it{}E}^{\it{}ee}_{\rm{}cm}$ = $88 - 94$ GeV $0.2324$ $\pm0.0012$ 17 LEP-SLC 2006 LEP ${\it{}E}^{\it{}ee}_{\rm{}cm}$ = $88 - 94$ GeV 1  AAIJ 2024AL analyse the forward-backward asymmetry in Drell-Yan production of ${{\mathit Z}}$ bosons decaying to muon pairs. 2  HAYRAPETYAN 2024T analyse the polarisation of tau leptons in ${{\mathit Z}}$ bosons decaying to tau pairs. 3  AALTONEN 2018B is a combination of the the results from the Tevatron experiments CDF and D0 in the electron and muon channels, AALTONEN 2014C, AALTONEN 2016D, ABAZOV 2015C, ABAZOV 2018, averaging the combined value from CDF and from D0 as also provided by the experiments in AALTONEN 2016D and ABAZOV 2018, respectively. The average of the two results takes correlations into account and has a ${{\mathit \chi}^{2}}$ probability of 2.6$\%$. 4  SIRUNYAN 2018CY analyse the forward-backward asymmetry in Drell-Yan production of ${{\mathit Z}}$ bosons decaying to muon or electron pairs. 5  AAD 2015BT analyse the forward-backward asymmetry in Drell-Yan production of Z bosons decaying to muon or electron pairs. 6  AAIJ 2015BF analyse the forward-backward asymmetry in Drell-Yan production of ${{\mathit Z}}$ bosons decaying to muon pairs. 7  This result combines the six individual results from LEP and SLC. The average, described in LEP-SLC 2006, has a ${{\mathit \chi}^{2}}$ probability of 3.7$\%$. 8  ABAZOV 2018 analyse the forward-backward asymmetry in Drell-Yan production of ${{\mathit Z}}$ bosons decaying to muon pairs. Combining this result with the one from ABAZOV 2015C, a value of $0.23095$ $\pm0.00040$ is obtained. 9  AALTONEN 2016D analyse the forward-backward asymmetry in Drell-Yan production of ${{\mathit Z}}$ bosons decaying to electron pairs. Combining this result with the one from AALTONEN 2014C, a value of $0.23221$ $\pm0.00046$ is obtained. 10  ABAZOV 2015C analyse the forward-backward asymmetry in Drell-Yan production of ${{\mathit Z}}$ bosons decaying to electron pairs. 11  AALTONEN 2014C analyse the forward-backward asymmetry in Drell-Yan production of ${{\mathit Z}}$ bosons decaying to muon pairs. 12  The result is based on the forward-backward asymmetry measured in leptonic ${{\mathit Z}}$ decays (electrons, muons, taus). It combines the results of the LEP experiments, ALEPH, DELPHI, L3 and OPAL, taking correlations into account, see LEP-SLC 2006. 13  The result is based on the polarisation of tau leptons measured in ${{\mathit Z}}$ decays to tau-lepton pairs. It combines the results of the LEP experiments, ALEPH, DELPHI, L3 and OPAL, taking correlations into account, see LEP-SLC 2006. 14  The result is based on the left-right and forward-backward left-right asymmetry measured in leptonic ${{\mathit Z}}$ decays (electrons, muons, taus). It combines the results of the SLC experiment, SLD, taking correlations into account, see LEP-SLC 2006. 15  The result is based on the forward-backward asymmetry measured at LEP and the forward-backward left-right asymmetry measured at SLC, in both cases using ${{\mathit Z}}$ decays to ${\mathit {\mathit b}}$-quarks. It combines the results of the LEP and SLC experiments, ALEPH, DELPHI, L3, OPAL and SLD, taking correlations into account, see LEP-SLC 2006. 16  The result is based on the forward-backward asymmetry measured at LEP and the forward-backward left-right asymmetry measured at SLC, in both cases using ${{\mathit Z}}$ decays to ${\mathit {\mathit c}}$-quarks. It combines the results of the LEP and SLC experiments ALEPH, DELPHI, L3, OPAL and SLD, taking correlations into account, see LEP-SLC 2006. 17  The result is based on the inclusive hadronic charge asymmetry measured in hadronic ${{\mathit Z}}$ decays. It combines the results of the LEP experiments, ALEPH, DELPHI, L3 and OPAL, taking correlations into account, see LEP-SLC 2006.

References