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Probing Neutral Triple Gauge Couplings at the LHC and Future Hadron Colliders - Ellis, John et al - arXiv:2206.11676KCL-PH-TH/2022-35CERN-TH-2022-089
 
\small {\it Unitarity bounds on new physics cutoff scales for the nTGC operators $(\OGP,\OBW,\OGM,$ $\OCP)$ in plot\,(a) and for the nTGC form factors $(|h_4^{}|,|h_3^Z|,|h_3^{\ga}|)$ in plot\,(b).\ These bounds are derived from the $p$-wave amplitudes of the reaction $\hs f\bar{f}\ito Z\ga\hs$, where $\hs f\bar{f}\!=\!q\bar{q},e^+e^-$ with $q$ being the light quarks.\ }
\small {\it Unitarity bounds on new physics cutoff scales for the nTGC operators $(\OGP,\OBW,\OGM,$ $\OCP)$ in plot\,(a) and for the nTGC form factors $(|h_4^{}|,|h_3^Z|,|h_3^{\ga}|)$ in plot\,(b).\ These bounds are derived from the $p$-wave amplitudes of the reaction $\hs f\bar{f}\ito Z\ga\hs$, where $\hs f\bar{f}\!=\!q\bar{q},e^+e^-$ with $q$ being the light quarks.\ }
\small{ \it Normalized distributions in the azimuthal angle $\phi_*^{}$ for the reaction $\hs p{\hs}p{\hs}(q{\hs}\bar{q})\ito Z\gamma\hs$ followed by $Z\!\to \ell\hs\bar{\ell}\hs$ decays, as generated by the dimension-8 nTGC operator $\,\mO_{G+}^{}$\! at the LHC}\,(13\,TeV). {\it The angular distribution $\,f_{\phi_*^{}}^{1}$ of the interference contribution of $\hs O(\cut^{-4})\hs$ is shown as a red curve; the angular distribution $\hs f_{\phi_*^{}}^{2}\hs$ of the squared contribution of $\hs{\cal O}(\cut^{-8})$ is shown as the blue curve that is flat like the SM distribution $\hs f_{\phi_*^{}}^0\hs$ (black curve).}
\small{\it\hspace*{-2mm} Photon transverse momentum $P_T$ distributions at the azimuthal angle $\,\phi_*^{}\hsm\!=\hsmx 0\,$ for the reaction $\hs p{\hs}p{\hs}(q{\hs}\bar{q})\ito Z\gamma\hs$ followed by $\hs Z\!\to \ell\hs \bar\ell\hs$ decays, as contributed by the SM (black curve) and by the nTGC operator $\OGP$ at $O(\cut^{-4})$ (colored curves for the indicated values of $\Lambda\hs$) at the LHC}\,(13\,TeV) {\it in the upper panel and at the} 100\,TeV $pp$ {\it collider in the lower panel.}
\small{ \it Photon transverse momentum $P_T^{}$ distributions at the azimuthal angle $\phi_*^{}\!=\!0$ for the reaction $\hs p{\hs}p{\hs}(q{\hs}\bar{q})\ito Z\gamma\hs$ followed by $\hs Z\!\to \ell\bar\ell\hs$ decays, as contributed by the SM (black curve) and by the nTGC operator $\OGP$ up to $\hs{O}(\cut^{-4})$ and $\hs{O}(\cut^{-8})$ (colored curves) at the LHC}\,(13\,TeV) {\it and the} $pp$\,(100\,TeV) {\it collider in the lower panel.}
\small{\it\hspace*{-2mm} Photon transverse momentum $P_T$ distributions at the azimuthal angle $\,\phi_*^{}\hsm\!=\hsmx 0\,$ for the reaction $\hs p{\hs}p{\hs}(q{\hs}\bar{q})\ito Z\gamma\hs$ followed by $\hs Z\!\to \ell\hs \bar\ell\hs$ decays, as contributed by the SM (black curve) and by the nTGC operator $\OGP$ at $O(\cut^{-4})$ (colored curves for the indicated values of $\Lambda\hs$) at the LHC}\,(13\,TeV) {\it in the upper panel and at the} 100\,TeV $pp$ {\it collider in the lower panel.}
\small{ \it Photon transverse momentum $P_T^{}$ distributions at the azimuthal angle $\phi_*^{}\!=\!0$ for the reaction $\hs p{\hs}p{\hs}(q{\hs}\bar{q})\ito Z\gamma\hs$ followed by $\hs Z\!\to \ell\bar\ell\hs$ decays, as contributed by the SM (black curve) and by the nTGC operator $\OGP$ up to $\hs{O}(\cut^{-4})$ and $\hs{O}(\cut^{-8})$ (colored curves) at the LHC}\,(13\,TeV) {\it and the} $pp$\,(100\,TeV) {\it collider in the lower panel.}
\small{ \it Normalized distributions in the azimuthal angle $\phi_*^{}$ for the reaction $\hs p{\hs}p{\hs}(q{\hs}\bar{q})\ito Z\gamma\hs$ followed by $Z\!\to \ell\hs\bar{\ell}\hs$ decays, as generated by the dimension-8 nTGC operator $\,\mO_{G+}^{}$\! at the LHC}\,(13\,TeV). {\it The angular distribution $\,f_{\phi_*^{}}^{1}$ of the interference contribution of $\hs O(\cut^{-4})\hs$ is shown as a red curve; the angular distribution $\hs f_{\phi_*^{}}^{2}\hs$ of the squared contribution of $\hs{\cal O}(\cut^{-8})$ is shown as the blue curve that is flat like the SM distribution $\hs f_{\phi_*^{}}^0\hs$ (black curve).}
\small{ \it Photon transverse momentum $P_T^{}$ distributions at the azimuthal angle $\phi_*^{}\!=\!0$ for the reaction $\hs p{\hs}p{\hs}(q{\hs}\bar{q})\ito Z\gamma\hs$ followed by $\hs Z\!\to \ell\bar\ell\hs$ decays, as contributed by the SM (black curve) and by the nTGC operator $\OGP$ up to $\hs{O}(\cut^{-4})$ and $\hs{O}(\cut^{-8})$ (colored curves) at the LHC}\,(13\,TeV) {\it and the} $pp$\,(100\,TeV) {\it collider in the lower panel.}
\small{ \it Photon transverse momentum $P_T^{}$ distributions at the azimuthal angle $\phi_*^{}\!=\!0$ for the reaction $\hs p{\hs}p{\hs}(q{\hs}\bar{q})\ito Z\gamma\hs$ followed by $\hs Z\!\to \ell\bar\ell\hs$ decays, as contributed by the SM (black curve) and by the nTGC operator $\OGP$ up to $\hs{O}(\cut^{-4})$ and $\hs{O}(\cut^{-8})$ (colored curves) at the LHC}\,(13\,TeV) {\it and the} $pp$\,(100\,TeV) {\it collider in the lower panel.}
\small\hspace*{-2mm} {\it Correlation contours of the sensitivity reaches (95\%\,C.L.) for the indicated pairs of nTGC form factors at the LHC}\,(13\,TeV) {\it [\,panels\,$(a)$ and $(c)$] and a} 100\,TeV {\it $pp$ collider [\,panels\,$(b)$ and $(d)$].\ Panels\,(a) and (b) show the correlation contours of $(h_4^{},\,h_3^Z)$ (solid curves) and $(h_4^{},\,h_3^\gamma)$ (dashed curves), and panels\,(c) and (d) depict the correlation contours of $(h_3^Z,\,h_3^\gamma)$.\ }
\small\hspace*{-2mm} {\it Correlation contours of the sensitivity reaches (95\%\,C.L.) for the indicated pairs of nTGC form factors at the LHC}\,(13\,TeV) {\it [\,panels\,$(a)$ and $(c)$] and a} 100\,TeV {\it $pp$ collider [\,panels\,$(b)$ and $(d)$].\ Panels\,(a) and (b) show the correlation contours of $(h_4^{},\,h_3^Z)$ (solid curves) and $(h_4^{},\,h_3^\gamma)$ (dashed curves), and panels\,(c) and (d) depict the correlation contours of $(h_3^Z,\,h_3^\gamma)$.\ }
\small\hspace*{-2mm} {\it Correlation contours of the sensitivity reaches (95\%\,C.L.) for the indicated pairs of nTGC form factors at the LHC}\,(13\,TeV) {\it [\,panels\,$(a)$ and $(c)$] and a} 100\,TeV {\it $pp$ collider [\,panels\,$(b)$ and $(d)$].\ Panels\,(a) and (b) show the correlation contours of $(h_4^{},\,h_3^Z)$ (solid curves) and $(h_4^{},\,h_3^\gamma)$ (dashed curves), and panels\,(c) and (d) depict the correlation contours of $(h_3^Z,\,h_3^\gamma)$.\ }
\small\hspace*{-2mm} {\it Correlation contours of the sensitivity reaches (95\%\,C.L.) for the indicated pairs of nTGC form factors at the LHC}\,(13\,TeV) {\it [\,panels\,$(a)$ and $(c)$] and a} 100\,TeV {\it $pp$ collider [\,panels\,$(b)$ and $(d)$].\ Panels\,(a) and (b) show the correlation contours of $(h_4^{},\,h_3^Z)$ (solid curves) and $(h_4^{},\,h_3^\gamma)$ (dashed curves), and panels\,(c) and (d) depict the correlation contours of $(h_3^Z,\,h_3^\gamma)$.\ }
\small\hspace*{-2mm} {\it Correlation contours of the sensitivity reaches (95\%\,C.L.) for the indicated pairs of nTGC form factors at the LHC}\,(13\,TeV) {\it [\,panels\,$(a)$ and $(c)$] and a} 100\,TeV {\it $pp$ collider [\,panels\,$(b)$ and $(d)$].\ Panels\,(a) and (b) show the correlation contours of $(h_4^{},\,h_3^Z)$ (solid curves) and $(h_4^{},\,h_3^\gamma)$ (dashed curves), and panels\,(c) and (d) depict the correlation contours of $(h_3^Z,\,h_3^\gamma)$.\ }
\small\hspace*{-2mm} {\it Correlation contours of the sensitivity reaches (95\%\,C.L.) for the indicated pairs of nTGC form factors at the LHC}\,(13\,TeV) {\it [\,panels\,$(a)$ and $(c)$] and a} 100\,TeV {\it $pp$ collider [\,panels\,$(b)$ and $(d)$].\ Panels\,(a) and (b) show the correlation contours of $(h_4^{},\,h_3^Z)$ (solid curves) and $(h_4^{},\,h_3^\gamma)$ (dashed curves), and panels\,(c) and (d) depict the correlation contours of $(h_3^Z,\,h_3^\gamma)$.\ }
\small\hspace*{-2mm} {\it Correlation contours of the sensitivity reaches (95\%\,C.L.) for the indicated pairs of nTGC operators at the LHC}\,(13\,TeV) {\it [\,panel $(a)$] and a} 100\,TeV {\it $pp$ {collider} [\,panel $(b)$].\ Panels\,(a) and (b) show the correlation contours of $(\OGP,\,\OBW)$ (solid curves) and $(\OGP,\,\OGM)$ (dashed curves).\ }
\small\hspace*{-2mm} {\it Correlation contours of the sensitivity reaches (95\%\,C.L.) for the indicated pairs of nTGC operators at the LHC}\,(13\,TeV) {\it [\,panel $(a)$] and a} 100\,TeV {\it $pp$ {collider} [\,panel $(b)$].\ Panels\,(a) and (b) show the correlation contours of $(\OGP,\,\OBW)$ (solid curves) and $(\OGP,\,\OGM)$ (dashed curves).\ }
\small\hspace*{-2mm} {\it Correlation contours of sensitivity reaches (95\%\,C.L.) for the indicated pairs of nTGC operators at the LHC}\,(13\,TeV) {\it [\,panels $(a)$ and $(c)$] and the} 100\,TeV {\it $pp$ collider [\,panels $(b)$ and $(d)$].\ Panels\,(a) and (b) show the correlation contours of $(\OBW,\,\OGM)$, whereas panels\,(c) and (d) depict the correlation contours of $(\OCP,\,\OBW)$ (solid curves) and $(\OCP,\,\OGM)$ (dashed curves). }
\small\hspace*{-2mm} {\it Correlation contours of sensitivity reaches (95\%\,C.L.) for the indicated pairs of nTGC operators at the LHC}\,(13\,TeV) {\it [\,panels $(a)$ and $(c)$] and the} 100\,TeV {\it $pp$ collider [\,panels $(b)$ and $(d)$].\ Panels\,(a) and (b) show the correlation contours of $(\OBW,\,\OGM)$, whereas panels\,(c) and (d) depict the correlation contours of $(\OCP,\,\OBW)$ (solid curves) and $(\OCP,\,\OGM)$ (dashed curves). }
\small\hspace*{-2mm} {\it Correlation contours of sensitivity reaches (95\%\,C.L.) for the indicated pairs of nTGC operators at the LHC}\,(13\,TeV) {\it [\,panels $(a)$ and $(c)$] and the} 100\,TeV {\it $pp$ collider [\,panels $(b)$ and $(d)$].\ Panels\,(a) and (b) show the correlation contours of $(\OBW,\,\OGM)$, whereas panels\,(c) and (d) depict the correlation contours of $(\OCP,\,\OBW)$ (solid curves) and $(\OCP,\,\OGM)$ (dashed curves). }
\small\hspace*{-2mm} {\it Correlation contours of sensitivity reaches (95\%\,C.L.) for the indicated pairs of nTGC operators at the LHC}\,(13\,TeV) {\it [\,panels $(a)$ and $(c)$] and the} 100\,TeV {\it $pp$ collider [\,panels $(b)$ and $(d)$].\ Panels\,(a) and (b) show the correlation contours of $(\OBW,\,\OGM)$, whereas panels\,(c) and (d) depict the correlation contours of $(\OCP,\,\OBW)$ (solid curves) and $(\OCP,\,\OGM)$ (dashed curves). }
\small\hspace*{-2mm} {\it Correlation contours of sensitivity reaches (95\%\,C.L.) for the indicated pairs of nTGC operators at the LHC}\,(13\,TeV) {\it [\,panels $(a)$ and $(c)$] and the} 100\,TeV {\it $pp$ collider [\,panels $(b)$ and $(d)$].\ Panels\,(a) and (b) show the correlation contours of $(\OBW,\,\OGM)$, whereas panels\,(c) and (d) depict the correlation contours of $(\OCP,\,\OBW)$ (solid curves) and $(\OCP,\,\OGM)$ (dashed curves). }
\small\hspace*{-2mm} {\it Correlation contours of sensitivity reaches (95\%\,C.L.) for the indicated pairs of nTGC operators at the LHC}\,(13\,TeV) {\it [\,panels $(a)$ and $(c)$] and the} 100\,TeV {\it $pp$ collider [\,panels $(b)$ and $(d)$].\ Panels\,(a) and (b) show the correlation contours of $(\OBW,\,\OGM)$, whereas panels\,(c) and (d) depict the correlation contours of $(\OCP,\,\OBW)$ (solid curves) and $(\OCP,\,\OGM)$ (dashed curves). }
\small\hspace*{-2mm} {\it Correlation contours of the sensitivity reaches} (95\%\,C.L.) {\it for the indicated pairs of nTGC form factors at the LHC}\,(13\,TeV).\ {\it Panels\,(a) and (b) present the correlation contours for $(h_3^\ga ,\,h_4^\ga)$ and $(h_3^Z,\,h_4^Z)$ respectively, by using our SMEFT form factor formula \eqref{eq:FF2-nTGC}, where in each panel the red contour inputs the full integrated luminosity} 140\,fb$^{-1}\!\!$ {\it of Run-2 and the blue contour inputs a partial integrated luminosity} 36.1\,fb$^{-1}\!$ {\it as in the ATLAS analysis\,\cite{Atlas2018nTGC-FF}.}\ {\it Panels\,(c) and (d) compare the theoretical correlation contours (red and blue colors) with the experimental contours (black color) from the ATLAS analysis\,\cite{Atlas2018nTGC-FF}, where we derived the red and blue contours by using the conventional form factor formula \eqref{eq:FF0-nTGC} and by assuming an ideal detection efficiency $\ep\!=\!100\%$ (for red contours) or a reduced detection efficiency $\hs\ep\!=\!75\%$ (for blue contours).\ The ATLAS contours are shown by the black solid curves (observed) and the black dashed curves (expected). }
\small\hspace*{-2mm} {\it Correlation contours of the sensitivity reaches} (95\%\,C.L.) {\it for the indicated pairs of nTGC form factors at the LHC}\,(13\,TeV).\ {\it Panels\,(a) and (b) present the correlation contours for $(h_3^\ga ,\,h_4^\ga)$ and $(h_3^Z,\,h_4^Z)$ respectively, by using our SMEFT form factor formula \eqref{eq:FF2-nTGC}, where in each panel the red contour inputs the full integrated luminosity} 140\,fb$^{-1}\!\!$ {\it of Run-2 and the blue contour inputs a partial integrated luminosity} 36.1\,fb$^{-1}\!$ {\it as in the ATLAS analysis\,\cite{Atlas2018nTGC-FF}.}\ {\it Panels\,(c) and (d) compare the theoretical correlation contours (red and blue colors) with the experimental contours (black color) from the ATLAS analysis\,\cite{Atlas2018nTGC-FF}, where we derived the red and blue contours by using the conventional form factor formula \eqref{eq:FF0-nTGC} and by assuming an ideal detection efficiency $\ep\!=\!100\%$ (for red contours) or a reduced detection efficiency $\hs\ep\!=\!75\%$ (for blue contours).\ The ATLAS contours are shown by the black solid curves (observed) and the black dashed curves (expected). }
\small\hspace*{-2mm} {\it Correlation contours of the sensitivity reaches} (95\%\,C.L.) {\it for the indicated pairs of nTGC form factors at the LHC}\,(13\,TeV).\ {\it Panels\,(a) and (b) present the correlation contours for $(h_3^\ga ,\,h_4^\ga)$ and $(h_3^Z,\,h_4^Z)$ respectively, by using our SMEFT form factor formula \eqref{eq:FF2-nTGC}, where in each panel the red contour inputs the full integrated luminosity} 140\,fb$^{-1}\!\!$ {\it of Run-2 and the blue contour inputs a partial integrated luminosity} 36.1\,fb$^{-1}\!$ {\it as in the ATLAS analysis\,\cite{Atlas2018nTGC-FF}.}\ {\it Panels\,(c) and (d) compare the theoretical correlation contours (red and blue colors) with the experimental contours (black color) from the ATLAS analysis\,\cite{Atlas2018nTGC-FF}, where we derived the red and blue contours by using the conventional form factor formula \eqref{eq:FF0-nTGC} and by assuming an ideal detection efficiency $\ep\!=\!100\%$ (for red contours) or a reduced detection efficiency $\hs\ep\!=\!75\%$ (for blue contours).\ The ATLAS contours are shown by the black solid curves (observed) and the black dashed curves (expected). }
\small\hspace*{-2mm} {\it Correlation contours of the sensitivity reaches} (95\%\,C.L.) {\it for the indicated pairs of nTGC form factors at the LHC}\,(13\,TeV).\ {\it Panels\,(a) and (b) present the correlation contours for $(h_3^\ga ,\,h_4^\ga)$ and $(h_3^Z,\,h_4^Z)$ respectively, by using our SMEFT form factor formula \eqref{eq:FF2-nTGC}, where in each panel the red contour inputs the full integrated luminosity} 140\,fb$^{-1}\!\!$ {\it of Run-2 and the blue contour inputs a partial integrated luminosity} 36.1\,fb$^{-1}\!$ {\it as in the ATLAS analysis\,\cite{Atlas2018nTGC-FF}.}\ {\it Panels\,(c) and (d) compare the theoretical correlation contours (red and blue colors) with the experimental contours (black color) from the ATLAS analysis\,\cite{Atlas2018nTGC-FF}, where we derived the red and blue contours by using the conventional form factor formula \eqref{eq:FF0-nTGC} and by assuming an ideal detection efficiency $\ep\!=\!100\%$ (for red contours) or a reduced detection efficiency $\hs\ep\!=\!75\%$ (for blue contours).\ The ATLAS contours are shown by the black solid curves (observed) and the black dashed curves (expected). }
\small{\hspace*{-1mm} \it Normalized angular distributions in $\phi_*^{}$ for $\hs e^+\hs e^{-}\!\ito Z\ga\hs$ with $Z\!\ito d\hs\bar{d}\hs$, as generated by $h_4^{}$ in our form factor formulation \eqref{eq:FF2-nTGC} in panels $(a)$ and $(b)$, and as generated by $(h_4^Z,\hs h_4^\gamma)$ in the conventional form factor formulation \eqref{eq:FF0-nTGC} with $h_5^V\hsmx\!=\hsm 0\hs$ in panels $(c)$ and $(d)$.\ The panels $(a)$ and $(c)$ correspond to the $e^+e^-$ colliders with} $\sqrt{s}\!=\!250\,$GeV {\it and the panels $(b)$ and $(d)$ correspond to} $\sqrt{s}=3\,$TeV.
\small{\hspace*{-1mm} \it Normalized angular distributions in $\phi_*^{}$ for $\hs e^+\hs e^{-}\!\ito Z\ga\hs$ with $Z\!\ito d\hs\bar{d}\hs$, as generated by $h_4^{}$ in our form factor formulation \eqref{eq:FF2-nTGC} in panels $(a)$ and $(b)$, and as generated by $(h_4^Z,\hs h_4^\gamma)$ in the conventional form factor formulation \eqref{eq:FF0-nTGC} with $h_5^V\hsmx\!=\hsm 0\hs$ in panels $(c)$ and $(d)$.\ The panels $(a)$ and $(c)$ correspond to the $e^+e^-$ colliders with} $\sqrt{s}\!=\!250\,$GeV {\it and the panels $(b)$ and $(d)$ correspond to} $\sqrt{s}=3\,$TeV.
\small{\hspace*{-1mm} \it Normalized angular distributions in $\phi_*^{}$ for $\hs e^+\hs e^{-}\!\ito Z\ga\hs$ with $Z\!\ito d\hs\bar{d}\hs$, as generated by $h_4^{}$ in our form factor formulation \eqref{eq:FF2-nTGC} in panels $(a)$ and $(b)$, and as generated by $(h_4^Z,\hs h_4^\gamma)$ in the conventional form factor formulation \eqref{eq:FF0-nTGC} with $h_5^V\hsmx\!=\hsm 0\hs$ in panels $(c)$ and $(d)$.\ The panels $(a)$ and $(c)$ correspond to the $e^+e^-$ colliders with} $\sqrt{s}\!=\!250\,$GeV {\it and the panels $(b)$ and $(d)$ correspond to} $\sqrt{s}=3\,$TeV.
\small{\hspace*{-1mm} \it Normalized angular distributions in $\phi_*^{}$ for $\hs e^+\hs e^{-}\!\ito Z\ga\hs$ with $Z\!\ito d\hs\bar{d}\hs$, as generated by $h_4^{}$ in our form factor formulation \eqref{eq:FF2-nTGC} in panels $(a)$ and $(b)$, and as generated by $(h_4^Z,\hs h_4^\gamma)$ in the conventional form factor formulation \eqref{eq:FF0-nTGC} with $h_5^V\hsmx\!=\hsm 0\hs$ in panels $(c)$ and $(d)$.\ The panels $(a)$ and $(c)$ correspond to the $e^+e^-$ colliders with} $\sqrt{s}\!=\!250\,$GeV {\it and the panels $(b)$ and $(d)$ correspond to} $\sqrt{s}=3\,$TeV.
\hspace*{-1mm}\small{\it Sensitivity reaches for the new physics scale $\cut$ of the nTGC operators at the hadron colliders LHC}\,(13\,TeV) {\it and} $pp$\,(100\,TeV) {\it in plot (a) and $e^+e^-$\! colliders with collision energies $\sqrt{s\,}\!=\!(0.25,\,0.5,\,1,\,3,\,5)$}\,TeV {\it in plot (b). In each plot, the (${\hsx}2{\hs}\sigma,\,5{\hs}\sigma$) sensitivities are shown in (light,\,heavy) colors, respectively.}
\hspace*{-1mm}\small{\it Sensitivity reaches for the new physics scale $\cut$ of the nTGC operators at the hadron colliders LHC}\,(13\,TeV) {\it and} $pp$\,(100\,TeV) {\it in plot (a) and $e^+e^-$\! colliders with collision energies $\sqrt{s\,}\!=\!(0.25,\,0.5,\,1,\,3,\,5)$}\,TeV {\it in plot (b). In each plot, the (${\hsx}2{\hs}\sigma,\,5{\hs}\sigma$) sensitivities are shown in (light,\,heavy) colors, respectively.}
\small\hspace*{-3mm} {\it Sensitivity reaches for the nTGC form factors $(h_4^{},\,h_3^Z,\,h_3^\gamma)$ at the hadron colliders LHC} (13\,TeV) {\it and} $pp$\,(100\,TeV) {\it in plot\,(a) and at $e^+e^-$\! colliders with collision energies} $\sqrt{s\,}\!=\!(0.25,\,0.5,$ $\,1,\,3,\,5)$\,TeV {\it in plot\,(b).\ In each plot, the {($\,2{\hs}\sigma,\,5{\hs}\sigma$)} sensitivities are shown in (heavy,\,light) colors, respectively.}
\small\hspace*{-3mm} {\it Sensitivity reaches for the nTGC form factors $(h_4^{},\,h_3^Z,\,h_3^\gamma)$ at the hadron colliders LHC} (13\,TeV) {\it and} $pp$\,(100\,TeV) {\it in plot\,(a) and at $e^+e^-$\! colliders with collision energies} $\sqrt{s\,}\!=\!(0.25,\,0.5,$ $\,1,\,3,\,5)$\,TeV {\it in plot\,(b).\ In each plot, the {($\,2{\hs}\sigma,\,5{\hs}\sigma$)} sensitivities are shown in (heavy,\,light) colors, respectively.}