${{\mathit Z}_{{\chi}}}$ is the extra neutral boson in SO(10) $\rightarrow$ SU(5) ${\times }$ U(1)$_{{{\mathit \chi}} }$. ${{\mathit g}_{{\chi}}}$ = ${{\mathit e}}$ /cos $\theta _{\mathit W}$ is assumed unless otherwise stated. We list limits with the assumption $\rho ~=~$1 but with no further constraints on the Higgs sector. Values in parentheses assume stronger constraint on the Higgs sector motivated by superstring models. Values in brackets are from cosmological and astrophysical considerations and assume a light right-handed neutrino.

VALUE (GeV) CL% DOCUMENT ID TECN  COMMENT $\bf{ > 4800}$ OUR LIMIT $\bf{\text{none 250 - 4800}}$ 95 1 AAD 2019 L ATLS ${{\mathit p}}{{\mathit p}}$ ; ${{\mathit Z}_{{\chi}}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ $> 4100$ 95 2 AABOUD 2017 AT ATLS ${{\mathit p}}{{\mathit p}}$ ; ${{\mathit Z}_{{\chi}}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ • • We do not use the following data for averages, fits, limits, etc. • • 3 BOBOVNIKOV 2018 RVUE ${{\mathit p}}{{\mathit p}}$ , ${{\mathit Z}_{{\chi}}^{\,'}}$ $\rightarrow$ ${{\mathit W}^{+}}{{\mathit W}^{-}}$ $> 3050$ 95 4 AABOUD 2016 U ATLS ${{\mathit p}}{{\mathit p}}$ ; ${{\mathit Z}_{{\chi}}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ $> 2620$ 95 5 AAD 2014 V ATLS ${{\mathit p}}{{\mathit p}}$ , ${{\mathit Z}_{{\chi}}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ $> 1970$ 95 6 AAD 2012 CC ATLS ${{\mathit p}}{{\mathit p}}$ , ${{\mathit Z}_{{\chi}}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ $> 930$ 95 7 AALTONEN 2011 I CDF ${{\mathit p}}{{\overline{\mathit p}}}$ ; ${{\mathit Z}_{{\chi}}^{\,'}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ $> 903$ 95 8 ABAZOV 2011 A D0 ${{\mathit p}}{{\overline{\mathit p}}}$ , ${{\mathit Z}_{{\chi}}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $> 1022$ 95 9 DEL-AGUILA 2010 RVUE Electroweak $> 862$ 95 8 AALTONEN 2009 T CDF ${{\mathit p}}{{\overline{\mathit p}}}$ , ${{\mathit Z}_{{\chi}}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $> 892$ 95 10 AALTONEN 2009 V CDF Repl. by AALTONEN 2011I $> 1141$ 95 11 ERLER 2009 RVUE Electroweak $> 822$ 95 8 AALTONEN 2007 H CDF Repl. by AALTONEN 2009T $> 680$ 95 SCHAEL 2007 A ALEP ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $> 545$ 95 12 ABDALLAH 2006 C DLPH ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $> 740$ 8 ABULENCIA 2006 L CDF Repl. by AALTONEN 2007H $> 690$ 95 13 ABULENCIA 2005 A CDF ${{\mathit p}}{{\overline{\mathit p}}}$ ; ${{\mathit Z}_{{\chi}}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ $>781$ 95 14 ABBIENDI 2004 G OPAL ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $>2100$ 15 BARGER 2003 B COSM Nucleosynthesis; light ${{\mathit \nu}_{{R}}}$ $>680$ 95 16 CHEUNG 2001 B RVUE Electroweak $>440$ 95 17 ABREU 2000 S DLPH ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $>533$ 95 18 BARATE 2000 I ALEP Repl. by SCHAEL 2007A $>554$ 95 19 CHO 2000 RVUE Electroweak 20 ERLER 2000 RVUE ${}^{}\mathrm {Cs}$ 21 ROSNER 2000 RVUE ${}^{}\mathrm {Cs}$ $>545$ 95 22 ERLER 1999 RVUE Electroweak $\text{(>1368)}$ 95 23 ERLER 1999 RVUE Electroweak $>215$ 95 24 CONRAD 1998 RVUE ${{\mathit \nu}_{{\mu}}}{{\mathit N}}$ scattering $>595$ 95 25 ABE 1997 S CDF ${{\mathit p}}{{\overline{\mathit p}}}$ ; ${{\mathit Z}}{}^{′}_{\chi }$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ $>190$ 95 26 ARIMA 1997 VNS Bhabha scattering $>262$ 95 27 VILAIN 1994 B CHM2 ${{\mathit \nu}_{{\mu}}}$ ${{\mathit e}}$ $\rightarrow$ ${{\mathit \nu}_{{\mu}}}{{\mathit e}}$ ; ${{\overline{\mathit \nu}}_{{\mu}}}$ ${{\mathit e}}$ $\rightarrow$ ${{\overline{\mathit \nu}}_{{\mu}}}{{\mathit e}}$ $\text{[>1470]}$ 28 FARAGGI 1991 COSM Nucleosynthesis; light ${{\mathit \nu}_{{R}}}$ $>231$ 90 29 ABE 1990 F VNS ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $\text{[> 1140]}$ 30 GONZALEZ-GARC.. 1990 D COSM Nucleosynthesis; light ${{\mathit \nu}_{{R}}}$ $\text{[> 2100]}$ 31 GRIFOLS 1990 ASTR SN 1987A; light ${{\mathit \nu}_{{R}}}$ 1  AAD 2019L search for resonances decaying to ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV. 2  AABOUD 2017AT search for resonances decaying to ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV. 3  BOBOVNIKOV 2018 use the ATLAS limits on $\sigma $( ${{\mathit p}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit Z}^{\,'}}$ )$\cdot{}$B( ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit W}^{+}}{{\mathit W}^{-}}$ ) to constrain the ${{\mathit Z}}-{{\mathit Z}^{\,'}}$ mixing parameter $\xi $. See their Fig. 9 for limits in $\mathit M_{{{\mathit Z}^{\,'}} }−\xi $ plane. 4  AABOUD 2016U search for resonances decaying to ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV. 5  AAD 2014V search for resonances decaying to ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8 TeV. 6  AAD 2012CC search for resonances decaying to ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 7 TeV. 7  AALTONEN 2011I search for resonances decaying to ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ in ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at $\sqrt {s }$ = 1.96 TeV. 8  ABAZOV 2011A, AALTONEN 2009T, AALTONEN 2007H, and ABULENCIA 2006L search for resonances decaying to ${{\mathit e}^{+}}{{\mathit e}^{-}}$ in ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at $\sqrt {s }$ = 1.96$~$TeV. 9  DEL-AGUILA 2010 give 95$\%$ CL limit on the ${{\mathit Z}}-{{\mathit Z}^{\,'}}$ mixing $-0.0011<\theta <$ 0.0007. 10  AALTONEN 2009V search for resonances decaying to ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ in ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at $\sqrt {s }$ = 1.96$~$TeV. 11  ERLER 2009 give 95$\%$ CL limit on the ${{\mathit Z}}$ -${{\mathit Z}^{\,'}}$ mixing $-0.0016<\theta <$ 0.0006. 12  ABDALLAH 2006C give 95$\%$ CL limit $\vert \theta \vert <$ 0.0031. See their Fig. 14 for limit contours in the mass-mixing plane. 13  ABULENCIA 2005A search for resonances decaying to electron or muon pairs in ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at $\sqrt {s }$ = 1.96 TeV. 14  ABBIENDI 2004G give 95$\%$ CL limit on ${{\mathit Z}}-{{\mathit Z}^{\,'}}$ mixing $−$0.00099 $<\theta <$ 0.00194. See their Fig. 20 for the limit contour in the mass-mixing plane. $\sqrt {s }$ = 91 to 207$~$GeV. 15  BARGER 2003B limit is from the nucleosynthesis bound on the effective number of light neutrino $\delta \mathit N_{{{\mathit \nu}} }<$1. The quark-hadron transition temperature $\mathit T_{\mathit c}$=150 MeV is assumed. The limit with $\mathit T_{\mathit c}$=400 MeV is $>$4300 GeV. 16  CHEUNG 2001B limit is derived from bounds on contact interactions in a global electroweak analysis. 17  ABREU 2000S give 95$\%$ CL limit on ${{\mathit Z}}-{{\mathit Z}^{\,'}}$ mixing $\vert \theta \vert <0.0017$. See their Fig.$~$6 for the limit contour in the mass-mixing plane. $\sqrt {\mathit s }$=90 to 189 GeV. 18  BARATE 2000I search for deviations in cross section and asymmetries in ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ fermions at $\sqrt {\mathit s }$=90 to 183 GeV. Assume $\theta $=0. Bounds in the mass-mixing plane are shown in their Figure$~$18. 19  CHO 2000 use various electroweak data to constrain ${{\mathit Z}^{\,'}}$ models assuming ${\mathit m}_{{{\mathit H}}}$=100 GeV. See Fig.$~$3 for limits in the mass-mixing plane. 20  ERLER 2000 discuss the possibility that a discrepancy between the observed and predicted values of ${{\mathit Q}_{{W}}}$ (${}^{}\mathrm {Cs}$) is due to the exchange of ${{\mathit Z}^{\,'}}$ . The data are better described in a certain class of the ${{\mathit Z}^{\,'}}$ models including ${{\mathit Z}_{{LR}}}$ and ${{\mathit Z}_{{\chi}}}$ . 21  ROSNER 2000 discusses the possibility that a discrepancy between the observed and predicted values of ${{\mathit Q}_{{W}}}$ (${}^{}\mathrm {Cs}$) is due to the exchange of ${{\mathit Z}^{\,'}}$ . The data are better described in a certain class of the ${{\mathit Z}^{\,'}}$ models including ${{\mathit Z}_{{\chi}}}$ . 22  ERLER 1999 give 90$\%$ CL limit on the ${{\mathit Z}}-{{\mathit Z}^{\,'}}$ mixing $-0.0020<\theta <0.0015$. 23  ERLER 1999 assumes 2 Higgs doublets, transforming as 10 of SO(10), embedded in $\mathit E_{6}$. 24  CONRAD 1998 limit is from measurements at CCFR, assuming no ${{\mathit Z}}-{{\mathit Z}^{\,'}}$ mixing. 25  ABE 1997S find $\sigma\mathrm {({{\mathit Z}^{\,'}} )}{\times }$B( ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ )$<40~$fb for ${\mathit m}_{{{\mathit Z}^{\,'}}}>600$ GeV at $\sqrt {\mathit s }$= 1.8 TeV. 26  ${{\mathit Z}}-{{\mathit Z}^{\,'}}$ mixing is assumed to be zero. $\sqrt {\mathit s }$= $57.77$ GeV. 27  VILAIN 1994B assume ${\mathit m}_{{{\mathit t}}}$ = 150 GeV and $\theta $=0. See Fig.$~$2 for limit contours in the mass-mixing plane. 28  FARAGGI 1991 limit assumes the nucleosynthesis bound on the effective number of neutrinos $\Delta {{\mathit N}_{{\nu}}}$ $<$ $0.5$ and is valid for ${\mathit m}_{{{\mathit \nu}_{{R}}}}$ $<$ 1 MeV. 29  ABE 1990F use data for $\mathit R$, $\mathit R_{ {{\mathit \ell}} {{\mathit \ell}} }$, and $\mathit A_{ {{\mathit \ell}} {{\mathit \ell}} }$. ABE 1990F fix ${\mathit m}_{{{\mathit W}}}$ = $80.49$ $\pm0.43$ $\pm0.24$ GeV and ${\mathit m}_{{{\mathit Z}}}$ = $91.13$ $\pm0.03$ GeV. 30  Assumes the nucleosynthesis bound on the effective number of light neutrinos ($\delta \mathit N_{{{\mathit \nu}} }$ $<~$1) and that ${{\mathit \nu}_{{R}}}$ is light (${ {}\lesssim{} }~$1 MeV). 31  GRIFOLS 1990 limit holds for ${\mathit m}_{{{\mathit \nu}_{{R}}}}{ {}\lesssim{} }~$1 MeV. See also GRIFOLS 1990D, RIZZO 1991 .

References:

AAD 2019L PL B796 68 Search for high-mass dilepton resonances using 139 fb$^{-1}$ of $pp$ collision data collected at $\\sqrt{s}=$13 TeV with the ATLAS detector BOBOVNIKOV 2018 PR D98 095029 Improved constraints on the mixing and mass of $Z'$ bosons from resonant diboson searches at the LHC at $\sqrt{s}=13$ TeV and predictions for Run II AABOUD 2017AT JHEP 1710 182 Search for New High-Mass Phenomena in the Dilepton Final State using 36 ${\mathrm {fb}}{}^{-1}$ of Proton-Proton Collision Data at $\sqrt {s }$ = 13 TeV with the ATLAS Detector AABOUD 2016U PL B761 372 Search for High-Mass New Phenomena in the Dilepton Final State using Proton-Proton Collisions at $\sqrt {s }$ = 13 TeV with the ATLAS Detector AAD 2014V PR D90 052005 Search for High-Mass Dilepton Resonances in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 8 TeV with the ATLAS Detector AAD 2012CC JHEP 1211 138 Search for High-Mass Resonances Decaying to Dilepton Final States in ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 7 TeV with the ATLAS Detector AALTONEN 2011I PRL 106 121801 Search for High Mass Resonances Decaying to Muon Pairs in $\sqrt {s }$ = 1.96 TeV ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions ABAZOV 2011A PL B695 88 Search for a Heavy Neutral Gauge Boson in the Dielectron Channel with 5.4 fb${}^{-1}$ of ${{\mathit p}}{{\mathit p}}$ Collisions at $\sqrt {s }$ = 1.96$~$TeV DEL-AGUILA 2010 JHEP 1009 033 Electroweak Limits on General New Vector Bosons AALTONEN 2009T PRL 102 031801 Search for High-Mass ${{\mathit e}^{+}}{{\mathit e}^{-}}$ Resonances in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.96$~$TeV AALTONEN 2009V PRL 102 091805 Search for High-Mass Resonances Decaying to Dimuons at CDF ERLER 2009 JHEP 0908 017 Improved Constraints on ${{\mathit Z}^{\,'}}$ Bosons from Electroweak Precision Data AALTONEN 2007H PRL 99 171802 Search for New Physics in High-Mass Electron-Positron Events in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ = 1.96 TeV SCHAEL 2007A EPJ C49 411 Fermion Pair Production in ${{\mathit e}^{+}}{{\mathit e}^{-}}$ Collisions at $189 - 209$ GeV and Constraints on Physics Beyond the Standard Model ABDALLAH 2006C EPJ C45 589 Measurement and Interpretation of Fermion-Pair Production at LEP Energies above the ${{\mathit Z}}$ Resonance ABULENCIA 2006L PRL 96 211801 Search for ${{\mathit Z}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ using Dielectron Mass and Angular Distribution ABULENCIA 2005A PRL 95 252001 Search for New High-Mass Particles Decaying to Lepton Pairs in ${{\mathit p}}{{\overline{\mathit p}}}$ Collisions at $\sqrt {s }$ =1.96 TeV 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 BARGER 2003B PR D67 075009 Primordial Nucleosynthesis Constraints on ${{\mathit Z}^{\,'}}$ Properties CHEUNG 2001B PL B517 167 Constraints on Electron Quark Contact Interactions and Implications to Models of Leptoquarks and Extra ${{\mathit Z}}$ Bosons ABREU 2000S PL B485 45 Measurement and Interpretation of Fermion-Pair Production at LEP Energies of 183 and 189 GeV BARATE 2000I EPJ C12 183 Study of Fermion Pair Production in ${{\mathit e}^{+}}{{\mathit e}^{-}}$ Collisions at $130 - 183$ GeV CHO 2000 MPL A15 311 Looking for ${{\mathit Z}^{\,'}}$ Bosons in Supersymmetric E(6) Models Through Electroweak Precision Data ERLER 2000 PRL 84 212 Indications for an Extra Neutral Gauge Boson in Electroweak Precision Data ROSNER 2000 PR D61 016006 Atomic Parity Violation and Precision Electroweak Physics: An Updated Analysis ERLER 1999 PL B456 68 Constraints on Extended Neutral Gauge Structures CONRAD 1998 RMP 70 1341 Precision Measurements with High Energy Neutrino Beams ABE 1997S PRL 79 2192 Search for New Gauge Bosons Decaying into Dileptons in ${{\overline{\mathit p}}}$ ${{\mathit p}}$ Collisions at $\sqrt {s }$ = 1.8 TeV ARIMA 1997 PR D55 19 Precise Measurement of Bhabha Scattering at a Center-of-Mass Energy of 57.77 GeV VILAIN 1994B PL B332 465 Constraints on Additional ${{\mathit Z}}$ Bosons Derived from Neutrino Electron Scattering Measurements FARAGGI 1991 MPL A6 61 A Superstring ${{\mathit Z}^{\,'}}$ at O(1 TeV)? ABE 1990F PL B246 297 Experimental Limits on Extra ${{\mathit Z}}$ Bosons from ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ Annihilation Data with the VENUS Detector at $\sqrt {s }$ = 50-64 GeV GONZALEZ-GARCIA 1990D PL B240 163 Cosmological Constraints on Additional Light Neutrinos and Neutral Gauge Bosons GRIFOLS 1990 NP B331 244 Implications from SN1987a on Supersymmetric, Left-Right and E(6) Particle Masses