${{\mathit Z}_{{{\psi}}}}$ is the extra neutral boson in E$_{6}$ $\rightarrow$ SO(10) ${\times }$ U(1)$_{{{\mathit \psi}}}$. ${{\mathit g}_{{{\psi}}}}$ = ${{\mathit e}}$/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 brackets are from cosmological and astrophysical considerations and assume a light right-handed neutrino.

VALUE (GeV) CL% DOCUMENT ID TECN  COMMENT $\bf{ > 4560}$ OUR LIMIT $\bf{> 4560}$ 95 1 SIRUNYAN 2021 N CMS ${{\mathit p}}{{\mathit p}}$; ${{\mathit Z}_{{{\psi}}}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ $\text{none 250 - 4500}$ 95 2 AAD 2019 L ATLS ${{\mathit p}}{{\mathit p}}$; ${{\mathit Z}_{{{\psi}}}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ $\text{none 200 - 3900}$ 95 3 SIRUNYAN 2018 BB CMS ${{\mathit p}}{{\mathit p}}$; ${{\mathit Z}_{{{\psi}}}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ $> 3800$ 95 4 AABOUD 2017 AT ATLS ${{\mathit p}}{{\mathit p}}$; ${{\mathit Z}_{{{\psi}}}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$, ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ $> 2820$ 95 5 KHACHATRYAN 2017 T CMS ${{\mathit p}}{{\mathit p}}$; ${{\mathit Z}_{{{\psi}}}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$, ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ $>1100$ 95 6 CHATRCHYAN 2012 O CMS ${{\mathit p}}{{\mathit p}}$, ${{\mathit Z}_{{{\psi}}}^{\,'}}$ $\rightarrow$ ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ • • We do not use the following data for averages, fits, limits, etc. • • 7 BOBOVNIKOV 2018 RVUE ${{\mathit p}}{{\mathit p}}$, ${{\mathit Z}_{{{\psi}}}^{\,'}}$ $\rightarrow$ ${{\mathit W}^{+}}{{\mathit W}^{-}}$ $> 2740$ 95 8 AABOUD 2016 U ATLS ${{\mathit p}}{{\mathit p}}$; ${{\mathit Z}_{{{\psi}}}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$, ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ $>2570$ 95 9 KHACHATRYAN 2015 AE CMS ${{\mathit p}}{{\mathit p}}$; ${{\mathit Z}_{{{\psi}}}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$, ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ $> 2510$ 95 10 AAD 2014 V ATLS ${{\mathit p}}{{\mathit p}}$, ${{\mathit Z}_{{{\psi}}}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$, ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ $> 2260$ 95 11 CHATRCHYAN 2013 AF CMS ${{\mathit p}}{{\mathit p}}$, ${{\mathit Z}_{{{\psi}}}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$, ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ $> 1790$ 95 12 AAD 2012 CC ATLS ${{\mathit p}}{{\mathit p}}$, ${{\mathit Z}_{{{\psi}}}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$, ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ $>2000$ 95 13 CHATRCHYAN 2012 M CMS Repl. by CHATRCHYAN 2013AF $> 917$ 95 14 AALTONEN 2011 I CDF ${{\mathit p}}{{\overline{\mathit p}}}$; ${{\mathit Z}_{{{\psi}}}^{\,'}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ $> 891$ 95 15 ABAZOV 2011 A D0 ${{\mathit p}}{{\overline{\mathit p}}}$, ${{\mathit Z}_{{{\psi}}}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $> 476$ 95 16 DEL-AGUILA 2010 RVUE Electroweak $> 851$ 95 15 AALTONEN 2009 T CDF ${{\mathit p}}{{\overline{\mathit p}}}$, ${{\mathit Z}_{{{\psi}}}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $> 878$ 95 17 AALTONEN 2009 V CDF Repl. by AALTONEN 2011I $> 147$ 95 18 ERLER 2009 RVUE Electroweak $> 822$ 95 15 AALTONEN 2007 H CDF Repl. by AALTONEN 2009T $> 410$ 95 SCHAEL 2007 A ALEP ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $> 475$ 95 19 ABDALLAH 2006 C DLPH ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $> 725$ 15 ABULENCIA 2006 L CDF Repl. by AALTONEN 2007H $> 675$ 95 20 ABULENCIA 2005 A CDF Repl. by AALTONEN 2011I and AALTONEN 2009T $>366$ 95 21 ABBIENDI 2004 G OPAL ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $>600$ 22 BARGER 2003 B COSM Nucleosynthesis; light ${{\mathit \nu}_{{{R}}}}$ $>350$ 95 23 ABREU 2000 S DLPH ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $>294$ 95 24 BARATE 2000 I ALEP Repl. by SCHAEL 2007A $>137$ 95 25 CHO 2000 RVUE Electroweak $>146$ 95 26 ERLER 1999 RVUE Electroweak $>54$ 95 27 CONRAD 1998 RVUE ${{\mathit \nu}_{{{\mu}}}}{{\mathit N}}$ scattering $>590$ 95 28 ABE 1997 S CDF ${{\mathit p}}{{\overline{\mathit p}}}$; ${{\mathit Z}_{{{\psi}}}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ $>135$ 95 29 VILAIN 1994 B CHM2 ${{\mathit \nu}_{{{\mu}}}}$ ${{\mathit e}}$ $\rightarrow$ ${{\mathit \nu}_{{{\mu}}}}{{\mathit e}}$; ${{\overline{\mathit \nu}}_{{{\mu}}}}$ ${{\mathit e}}$ $\rightarrow$ ${{\overline{\mathit \nu}}_{{{\mu}}}}{{\mathit e}}$ $>105$ 90 30 ABE 1990 F VNS ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $\text{[> 160]}$ 31 GONZALEZ-GARC.. 1990 D COSM Nucleosynthesis; light ${{\mathit \nu}_{{{R}}}}$ $\text{[> 2000]}$ 32 GRIFOLS 1990 D ASTR SN 1987A; light ${{\mathit \nu}_{{{R}}}}$ 1  SIRUNYAN 2021N search for resonance decaying to ${{\mathit e}^{+}}{{\mathit e}^{-}}$, ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV. 2  AAD 2019L search for resonances decaying to ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV. 3  SIRUNYAN 2018BB search for resonances decaying to ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV. 4  AABOUD 2017AT search for resonances decaying to ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV. 5  KHACHATRYAN 2017T search for resonances decaying to ${{\mathit e}^{+}}{{\mathit e}^{-}}$, ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8, 13 TeV. 6  CHATRCHYAN 2012O search for resonances decaying to ${{\mathit \tau}^{+}}{{\mathit \tau}^{-}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 7 TeV. 7  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. 10 for limits in $\mathit M_{{{\mathit Z}^{\,'}}}−\xi $ plane. 8  AABOUD 2016U search for resonances decaying to ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 13 TeV. 9  KHACHATRYAN 2015AE search for resonances decaying to ${{\mathit e}^{+}}{{\mathit e}^{-}}$, ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 8 TeV. 10  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. 11  CHATRCHYAN 2013AF search for resonances decaying to ${{\mathit e}^{+}}{{\mathit e}^{-}}$, ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 7 TeV and 8 TeV. 12  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. 13  CHATRCHYAN 2012M search for resonances decaying to ${{\mathit e}^{+}}{{\mathit e}^{-}}$ or ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ in ${{\mathit p}}{{\mathit p}}$ collisions at $\sqrt {s }$ = 7 TeV. 14  AALTONEN 2011I search for resonances decaying to ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ in ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at $\sqrt {s }$ = 1.96 TeV. 15  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. 16  DEL-AGUILA 2010 give 95$\%$ CL limit on the ${{\mathit Z}}-{{\mathit Z}^{\,'}}$ mixing $-0.0019<\theta <$ 0.0007. 17  AALTONEN 2009V search for resonances decaying to ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ in ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at $\sqrt {s }$ = 1.96$~$TeV. 18  ERLER 2009 give 95$\%$ CL limit on the ${{\mathit Z}}-{{\mathit Z}^{\,'}}$ mixing $-0.0018<\theta <$ 0.0009. 19  ABDALLAH 2006C give 95$\%$ CL limit $\vert \theta \vert <$ 0.0027. See their Fig. 14 for limit contours in the mass-mixing plane. 20  ABULENCIA 2005A search for resonances decaying to electron or muon pairs in ${{\mathit p}}{{\overline{\mathit p}}}$ collisions at $\sqrt {s }$ = 1.96 TeV. 21  ABBIENDI 2004G give 95$\%$ CL limit on ${{\mathit Z}}-{{\mathit Z}^{\,'}}$ mixing $−$0.00129 $<\theta <$ 0.00258. See their Fig. 20 for the limit contour in the mass-mixing plane. $\sqrt {s }$ = 91 to 207$~$GeV. 22  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 $>$1100 GeV. 23  ABREU 2000S give 95$\%$ CL limit on ${{\mathit Z}}-{{\mathit Z}^{\,'}}$ mixing $\vert \theta \vert <0.0018$. See their Fig.$~$6 for the limit contour in the mass-mixing plane. $\sqrt {\mathit s }$=90 to 189 GeV. 24  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. 25  CHO 2000 use various electroweak data to constrain ${{\mathit Z}^{\,'}}$ models assuming ${\mathit m}_{{{\mathit H}}}$=100 GeV. See Fig.$~$3 for limits in the mass-mixing plane. 26  ERLER 1999 give 90$\%$ CL limit on the ${{\mathit Z}}-{{\mathit Z}^{\,'}}$ mixing $-0.0013<\theta <0.0024$. 27  CONRAD 1998 limit is from measurements at CCFR, assuming no ${{\mathit Z}}-{{\mathit Z}^{\,'}}$ mixing. 28  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. 29  VILAIN 1994B assume ${\mathit m}_{{{\mathit t}}}$ = 150 GeV and $\theta $=0. See Fig.$~$2 for limit contours in the mass-mixing plane. 30  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. 31  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). 32  GRIFOLS 1990D limit holds for ${\mathit m}_{{{\mathit \nu}_{{{R}}}}}{ {}\lesssim{} }~$1 MeV. See also RIZZO 1991.

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