${{\mathit Z}_{{\chi}}}$ 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:

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