OUR FIT is obtained using the fit procedure and correlations as determined by the LEP Electroweak Working Group (see the note “The ${{\mathit Z}}$ boson” and ref. LEP-SLC 2006 ). The fit is performed using the ${{\mathit Z}}$ mass and width, the ${{\mathit Z}}$ hadronic pole cross section, the ratios of hadronic to leptonic partial widths, and the ${{\mathit Z}}$ pole forward-backward lepton asymmetries. This set is believed to be most free of correlations.

The ${{\mathit Z}}$ -boson mass listed here corresponds to the mass parameter in a Breit-Wigner distribution with mass dependent width. The value is 34 MeV greater than the real part of the position of the pole (in the energy-squared plane) in the ${{\mathit Z}}$ -boson propagator. Also the LEP experiments have generally assumed a fixed value of the ${{\mathit \gamma}}$ $−$ ${{\mathit Z}}$ interferences term based on the standard model. Keeping this term as free parameter leads to a somewhat larger error on the fitted ${{\mathit Z}}$ mass. See ACCIARRI 2000Q and ABBIENDI 2004G for a detailed investigation of both these issues.

VALUE (GeV) EVTS DOCUMENT ID TECN  COMMENT $\bf{ 91.1876 \pm0.0021}$ OUR FIT $91.1852$ $\pm0.0030$ 4.57M 1 ABBIENDI 2001 A OPAL ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $88 - 94$ GeV $91.1863$ $\pm0.0028$ 4.08M 2 ABREU 2000 F DLPH ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $88 - 94$ GeV $91.1898$ $\pm0.0031$ 3.96M 3 ACCIARRI 2000 C L3 ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $88 - 94$ GeV $91.1885$ $\pm0.0031$ 4.57M 4 BARATE 2000 C ALEP ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $88 - 94$ GeV • • We do not use the following data for averages, fits, limits, etc. • • $91.084$ $\pm0.107$ 5 ANDREEV 2018 A H1 ${{\mathit e}^{\pm}}{{\mathit p}}$ $91.1872$ $\pm0.0033$ 6 ABBIENDI 2004 G OPAL ${\it{}E}^{\it{}ee}_{\rm{}cm}$= LEP1 + $130 - 209$ GeV $91.272$ $\pm0.032$ $\pm0.033$ 7 ACHARD 2004 C L3 ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $183 - 209$ GeV $91.1875$ $\pm0.0039$ 3.97M 8 ACCIARRI 2000 Q L3 ${\it{}E}^{\it{}ee}_{\rm{}cm}$= LEP1 + $130 - 189$ GeV $91.151$ $\pm0.008$ 9 MIYABAYASHI 1995 TOPZ ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $57.8$ GeV $91.74$ $\pm0.28$ $\pm0.93$ 156 10 ALITTI 1992 B UA2 ${\it{}E}^{\it{}p\overline{\it{}p}}_{\rm{}cm}$= 630 GeV $90.9$ $\pm0.3$ $\pm0.2$ 188 11 ABE 1989 C CDF ${\it{}E}^{\it{}p\overline{\it{}p}}_{\rm{}cm}$= $1.8$ TeV $91.14$ $\pm0.12$ 480 12 ABRAMS 1989 B MRK2 ${\it{}E}^{\it{}ee}_{\rm{}cm}$= $89 - 93$ GeV $93.1$ $\pm1.0$ $\pm3.0$ 24 13 ALBAJAR 1989 UA1 ${\it{}E}^{\it{}p\overline{\it{}p}}_{\rm{}cm}$= 546,630 GeV 1  ABBIENDI 2001A error includes approximately $2.3$ MeV due to statistics and $1.8$ MeV due to LEP energy uncertainty. 2  The error includes $1.6$ MeV due to LEP energy uncertainty. 3  The error includes $1.8$ MeV due to LEP energy uncertainty. 4  BARATE 2000C error includes approximately $2.4$ MeV due to statistics, $0.2~$MeV due to experimental systematics, and $1.7~$MeV due to LEP energy uncertainty. 5  ANDREEV 2018A obtain this result in a combined electroweak and QCD analysis using all deep-inelastic ${{\mathit e}^{+}}{{\mathit p}}$ and ${{\mathit e}^{-}}{{\mathit p}}$ neutral current and charged current scattering cross sections published by the H1 Collaboration, including data with longitudinally polarized lepton beams. 6  ABBIENDI 2004G obtain this result using the S$-$matrix formalism for a combined fit to their cross section and asymmetry data at the ${{\mathit Z}}$ peak and their data at $130 - 209$ GeV. The authors have corrected the measurement for the 34 MeV shift with respect to the Breit$-$Wigner fits. 7  ACHARD 2004C select ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit \gamma}}$ events with hard initial$-$state radiation. Z decays to ${{\mathit q}}{{\overline{\mathit q}}}$ and muon pairs are considered. The fit results obtained in the two samples are found consistent to each other and combined considering the uncertainty due to ISR modelling as fully correlated. 8  ACCIARRI 2000Q interpret the $\mathit s$-dependence of the cross sections and lepton forward-backward asymmetries in the framework of the S-matrix formalism. They fit to their cross section and asymmetry data at high energies, using the results of S-matrix fits to ${{\mathit Z}}$ -peak data (ACCIARRI 2000C) as constraints. The $130 - 189$ GeV data constrains the ${{\mathit \gamma}}$ /${{\mathit Z}}$ interference term. The authors have corrected the measurement for the $34.1$ MeV shift with respect to the Breit-Wigner fits. The error contains a contribution of $\pm2.3$ MeV due to the uncertainty on the ${{\mathit \gamma}}{{\mathit Z}}$ interference. 9  MIYABAYASHI 1995 combine their low energy total hadronic cross-section measurement with the ACTON 1993D data and perform a fit using an S-matrix formalism. As expected, this result is below the mass values obtained with the standard Breit-Wigner parametrization. 10  Enters fit through ${{\mathit W}}$ $/{{\mathit Z}}$ mass ratio given in the ${{\mathit W}}$ Particle Listings. The ALITTI 1992B systematic error ($\pm0.93$) has two contributions: one ($\pm0.92$) cancels in ${\mathit m}_{{{\mathit W}}}/{\mathit m}_{{{\mathit Z}}}$ and one ($\pm0.12$) is noncancelling. These were added in quadrature. 11  First error of ABE 1989 is combination of statistical and systematic contributions; second is mass scale uncertainty. 12  ABRAMS 1989B uncertainty includes 35 MeV due to the absolute energy measurement. 13  ALBAJAR 1989 result is from a total sample of 33 ${{\mathit Z}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ events.

References:

ANDREEV 2018A EPJ C78 777 Determination of electroweak parameters in polarised deep-inelastic scattering at HERA ABBIENDI 2004G EPJ C33 173 Tests of the Standard Model and Constraints on New Physics from Measurements of Fermion Pair Production at 189 to 209 GeV at LEP ACHARD 2004C PL B585 42 Measurement of the ${{\mathit Z}}$ Boson Mass using ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit \gamma}}$ Events at Center of Mass Energies above the Z Pole ABBIENDI 2001A EPJ C19 587 Precise Determination of the ${{\mathit Z}}$ Resonance Parameters at LEP: “Zedometry'' ABREU 2000F EPJ C16 371 Cross Sections and Leptonic Forward-Backward Asymmetries from the ${{\mathit Z}^{0}}$ Running of LEP ACCIARRI 2000C EPJ C16 1 Measurements of Cross Sections and Forward Backward Asymmetries at the ${{\mathit Z}}$ Resonance and Determination of Electroweak Parameters ACCIARRI 2000Q PL B489 93 Determination of ${{\mathit \gamma}}$ /${{\mathit Z}}$ Interference in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ Annihilation at LEP BARATE 2000C EPJ C14 1 Measurement of the ${{\mathit Z}}$ Resonance Parameters at LEP MIYABAYASHI 1995 PL B347 171 Measurement of the Total Hadronic Cross Section and Determination of ${{\mathit \gamma}}$ ${{\mathit Z}}$ Interference in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ Annihilation ALITTI 1992B PL B276 354 An Improved Determination of the Ratio of ${{\mathit W}}$ and ${{\mathit Z}}$ Masses at the CERN ${{\overline{\mathit p}}}{{\mathit p}}$ Collider ABE 1989C PRL 63 720 Measurement of the Mass and Width of ${{\mathit Z}^{0}}$ Boson at the Fermilab Tevatron ABRAMS 1989B PRL 63 2173 Measurements of ${{\mathit Z}^{0}}$ -Boson Resonance Parameters in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ Annihilation ALBAJAR 1989 ZPHY C44 15 Studies of Intermediate Vector Boson Production and Decay in UA1 at the CERN Proton-Antiproton Collider