# ${{\boldsymbol Z}}$ AXIAL-VECTOR COUPLINGS

These quantities are the effective axial-vector couplings of the ${{\mathit Z}}$ to charged leptons. Their magnitude is derived from a measurement of the ${{\mathit Z}}$ lineshape and the forward-backward lepton asymmetries as a function of energy around the ${{\mathit Z}}$ mass. The relative sign among the vector to axial-vector couplings is obtained from a measurement of the ${{\mathit Z}}$ asymmetry parameters, ${{\mathit A}_{{e}}}$, ${{\mathit A}_{{\mu}}}$, and ${{\mathit A}_{{\tau}}}$. By convention the sign of $\mathit g{}^{{{\mathit e}}}_{\mathit A}$ is fixed to be negative (and opposite to that of $\mathit g{}^{{{\mathit \nu}_{{e}}}}$ obtained using ${{\mathit \nu}_{{e}}}$ scattering measurements). For the light quarks, the sign of the couplings is assigned consistently with this assumption. The fit values quoted below correspond to global nine- or five-parameter fits to lineshape, lepton forward-backward asymmetry, and ${{\mathit A}_{{e}}}$, ${{\mathit A}_{{\mu}}}$, and ${{\mathit A}_{{\tau}}}$ measurements. See the note The ${{\mathit Z}}$ boson'' and ref. LEP-SLC 2006 for details. Where ${{\mathit p}}{{\overline{\mathit p}}}$ and ${{\mathit e}}{{\mathit p}}$ data is quoted, OUR FIT value corresponds to a weighted average of this with the LEP/SLD fit result.

# $\boldsymbol g{}^{{{\boldsymbol u}}}_{\boldsymbol A}$ INSPIRE search

VALUE EVTS DOCUMENT ID TECN  COMMENT
$\bf{ 0.50 {}^{+0.04}_{-0.05}}$ OUR AVERAGE
$0.532$ ${}^{+0.107}_{-0.063}$ 1
 2016
$0.501$ $\pm0.110$ 156k 2
 2011 D
D0 ${\it{}E}^{\it{}p\overline{\it{}p}}_{\rm{}cm}$ = 1.97 TeV
$0.47$ ${}^{+0.05}_{-0.33}$ 3
 2006
${\it{}E}^{\it{}ee}_{\rm{}cm}$ = $88 - 94$ GeV
$0.441$ ${}^{+0.207}_{-0.173}$ $\pm0.067$ 5026 4
 2005 M
CDF ${\it{}E}^{\it{}p\overline{\it{}p}}_{\rm{}cm}$= 1.96~TeV
• • • We do not use the following data for averages, fits, limits, etc. • • •
$0.50$ ${}^{+0.12}_{-0.05}$ 5
 2016 A
ZEUS
$0.57$ $\pm0.08$ 1500 6
 2006
H1 ${{\mathit e}^{\pm}}$ ${{\mathit p}}$ $\rightarrow$ ${{\overline{\mathit \nu}}_{{e}}}$ (${{\mathit \nu}_{{e}}}){{\mathit X}}$, $\sqrt {s }\approx{}$300 GeV
1  ABT 2016 determine the ${{\mathit Z}^{0}}$ couplings to ${{\mathit u}}$- and ${{\mathit d}}$-quarks using the same techniques and data as ABRAMOWICZ 2016A but additionally use the published H1 polarised data.
2  ABAZOV 2011D study ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit Z}}$ /${{\mathit \gamma}^{*}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ events using 5 fb${}^{-1}$ data at $\sqrt {s }$ = 1.96 TeV. The candidate events are selected by requiring two isolated electromagnetic showers with $\mathit E_{T}>$ 25 GeV, at least one electron in the central region and the di-electron mass in the range $50 - 1000$ GeV. From the forward-backward asymmetry, determined as a function of the di-electron mass, they derive the axial and vector couplings of the ${{\mathit u}}$- and ${{\mathit d}}$- quarks and the value of sin$^2\theta {}^{{{\mathit \ell}}}_{eff}$ = $0.2309$ $\pm0.0008$(stat)$\pm0.0006$(syst).
3  LEP-SLC 2006 is a combination of the results from LEP and SLC experiments using light quark tagging. s- and d-quark couplings are assumed to be identical.
4  ACOSTA 2005M determine the forward-backward asymmetry of ${{\mathit e}^{+}}{{\mathit e}^{-}}$ pairs produced via ${{\mathit q}}$ ${{\overline{\mathit q}}}$ $\rightarrow$ ${{\mathit Z}}$ $/$ ${{\mathit \gamma}^{*}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ in 15 M( ${{\mathit e}^{+}}{{\mathit e}^{-}}$ ) effective mass bins ranging from 40 GeV to 600 GeV. These results are used to obtain the vector and axial-vector couplings of the ${{\mathit Z}}$ to the light quarks, assuming the electron couplings are as predicted by the Standard Model. Higher order radiative corrections have not been taken into account.
5  ABRAMOWICZ 2016A determine the ${{\mathit Z}^{0}}$ couplings to ${{\mathit u}}$- and ${{\mathit d}}$-quarks using the ZEUS polarised data from Run II together with the unpolarised data from both ZEUS and H1 Collaborations for Run I and unpolarised H1 data from Run II.
6  AKTAS 2006 fit the neutral current (1.5${}\leq{}Q{}^{2}{}\leq{}$30,000 GeV${}^{2}$) and charged current (1.5${}\leq{}Q{}^{2}{}\leq{}$15,000 GeV${}^{2}$) differential cross sections. In the determination of the ${{\mathit u}}$-quark couplings the electron and ${{\mathit d}}$-quark couplings are fixed to their standard model values.
References:
 ABRAMOWICZ 2016A
PR D93 092002 Combined QCD and Electroweak Analysis of HERA Data
 ABT 2016
PR D94 052007 Combined Electroweak and QCD Fit to HERA Data
 ABAZOV 2011D
PR D84 012007 Measurement of sin${}^{2}\theta {}^{{{\mathit \ell}}}_{eff}$ and $\mathit Z$-Light Quark Couplings using the Forward-Backward Charge Asymmetry in ${{\mathit p}}$ ${{\overline{\mathit p}}}$ $\rightarrow$ ${{\mathit Z}}$ $/$ ${{\mathit \gamma}^{*}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ events with L=5.0 fb${}^{-1}$ at $\sqrt {s }$ = 1.96 TeV
 AKTAS 2006
PL B632 35 A Determination of Electroweak Parameters at HERA
 LEP-SLC 2006
PRPL 427 257 Precision Electroweak Measurements on the ${{\mathit Z}}$ Resonance
 ACOSTA 2005M
PR D71 052002 Measurement of the Forward-Backward Charge Asymmetry of Electron-Positron Pairs in ${{\overline{\mathit p}}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 1.96 TeV