Probing New Physics in Dimension-8 Neutral Gauge Couplings at $e^+e^-$ Colliders
- Ellis, John et al
- arXiv:2008.04298KCL-PH-TH/2020-28CERN-TH-2020-076
 | \small Kinematical structure of the reaction $\,e^+e^-\!\!\to Z\ga\,$ followed by the hadronic decays $\,Z\!\to q\bar{q}\,$,\, in the $\,e^+e^-$ collision frame. |
 | \small Feynman diagrams that contribute to the reaction $e^-e^+\!\!\to\! \gamma\,q\bar{q}$\,. Type\,(a) provides the signals via the nTGC vertex $Z^*Z\gamma$ or $\gamma^*Z\gamma$, arising from the relevant dimension-8 operator, while types\,(b) and (c) give the SM backgrounds. Diagram\,(b) together with a similar $u$-channel diagram for $\,e^-e^+\!\!\to\! Z\gamma\!\to\!\gamma q \bar q$\, presents an irreducible background. Diagram\,(c) has the $s$-channel gauge-boson exchange and final-state $\gamma$ radiation, providing a reducible background. Diagram\,(d) arises from the contact vertex $eeZ\gamma$ which is generated by the relevant dimension-8 fermion-bilinear operator. |
 | \small Feynman diagrams that contribute to the reaction $e^-e^+\!\!\to\! \gamma\,q\bar{q}$\,. Type\,(a) provides the signals via the nTGC vertex $Z^*Z\gamma$ or $\gamma^*Z\gamma$, arising from the relevant dimension-8 operator, while types\,(b) and (c) give the SM backgrounds. Diagram\,(b) together with a similar $u$-channel diagram for $\,e^-e^+\!\!\to\! Z\gamma\!\to\!\gamma q \bar q$\, presents an irreducible background. Diagram\,(c) has the $s$-channel gauge-boson exchange and final-state $\gamma$ radiation, providing a reducible background. Diagram\,(d) arises from the contact vertex $eeZ\gamma$ which is generated by the relevant dimension-8 fermion-bilinear operator. |
 | \small Feynman diagrams that contribute to the reaction $e^-e^+\!\!\to\! \gamma\,q\bar{q}$\,. Type\,(a) provides the signals via the nTGC vertex $Z^*Z\gamma$ or $\gamma^*Z\gamma$, arising from the relevant dimension-8 operator, while types\,(b) and (c) give the SM backgrounds. Diagram\,(b) together with a similar $u$-channel diagram for $\,e^-e^+\!\!\to\! Z\gamma\!\to\!\gamma q \bar q$\, presents an irreducible background. Diagram\,(c) has the $s$-channel gauge-boson exchange and final-state $\gamma$ radiation, providing a reducible background. Diagram\,(d) arises from the contact vertex $eeZ\gamma$ which is generated by the relevant dimension-8 fermion-bilinear operator. |
 | \small Feynman diagrams that contribute to the reaction $e^-e^+\!\!\to\! \gamma\,q\bar{q}$\,. Type\,(a) provides the signals via the nTGC vertex $Z^*Z\gamma$ or $\gamma^*Z\gamma$, arising from the relevant dimension-8 operator, while types\,(b) and (c) give the SM backgrounds. Diagram\,(b) together with a similar $u$-channel diagram for $\,e^-e^+\!\!\to\! Z\gamma\!\to\!\gamma q \bar q$\, presents an irreducible background. Diagram\,(c) has the $s$-channel gauge-boson exchange and final-state $\gamma$ radiation, providing a reducible background. Diagram\,(d) arises from the contact vertex $eeZ\gamma$ which is generated by the relevant dimension-8 fermion-bilinear operator. |
 | \small{ Normalized angular distributions in the azimuthal angle $\phi_*^{}$ for $e^-e^+\!\!\to Z\ga$ followed by $Z\!\to d\bar d$ decays, as generated by $\,\mO_{G+}^{}$\! at the collision energies} $\sqrt{s}=(0.25,\, 0.5,\, 1,\, 3)$\,TeV, {respectively. In each plot, the black, red, and blue curves denote the contributions from the SM, the interference term of $\,{\cal O}(\cut^{-4})$, and the quadratic term of $\,{\cal O}(\cut^{-8})$, respectively, where we note that the blue and black curves almost coincide. We have imposed a basic cut on the polar scattering angle, $\sin\theta>\sin\delta$, with $\delta=0.2$ for illustration.} |
 | \small{ Normalized angular distributions in the azimuthal angle $\phi_*^{}$ for $e^-e^+\!\!\to Z\ga$ followed by $Z\!\to d\bar d$ decays, as generated by $\,\mO_{G+}^{}$\! at the collision energies} $\sqrt{s}=(0.25,\, 0.5,\, 1,\, 3)$\,TeV, {respectively. In each plot, the black, red, and blue curves denote the contributions from the SM, the interference term of $\,{\cal O}(\cut^{-4})$, and the quadratic term of $\,{\cal O}(\cut^{-8})$, respectively, where we note that the blue and black curves almost coincide. We have imposed a basic cut on the polar scattering angle, $\sin\theta>\sin\delta$, with $\delta=0.2$ for illustration.} |
 | \small{ Normalized angular distributions in the azimuthal angle $\phi_*^{}$ for $e^-e^+\!\!\to Z\ga$ followed by $Z\!\to d\bar d$ decays, as generated by $\,\mO_{G+}^{}$\! at the collision energies} $\sqrt{s}=(0.25,\, 0.5,\, 1,\, 3)$\,TeV, {respectively. In each plot, the black, red, and blue curves denote the contributions from the SM, the interference term of $\,{\cal O}(\cut^{-4})$, and the quadratic term of $\,{\cal O}(\cut^{-8})$, respectively, where we note that the blue and black curves almost coincide. We have imposed a basic cut on the polar scattering angle, $\sin\theta>\sin\delta$, with $\delta=0.2$ for illustration.} |
 | \small{ Normalized angular distributions in the azimuthal angle $\phi_*^{}$ for $e^-e^+\!\!\to Z\ga$ followed by $Z\!\to d\bar d$ decays, as generated by $\,\mO_{G+}^{}$\! at the collision energies} $\sqrt{s}=(0.25,\, 0.5,\, 1,\, 3)$\,TeV, {respectively. In each plot, the black, red, and blue curves denote the contributions from the SM, the interference term of $\,{\cal O}(\cut^{-4})$, and the quadratic term of $\,{\cal O}(\cut^{-8})$, respectively, where we note that the blue and black curves almost coincide. We have imposed a basic cut on the polar scattering angle, $\sin\theta>\sin\delta$, with $\delta=0.2$ for illustration.} |
 | \small{ Normalized angular distributions in the azimuthal angle $\phi_*^{}$ for $e^-e^+\!\!\to Z\ga$ followed by $Z\!\to\! d\bar d$ decays, as generated by $\,\mO_{G-}^{}$\! at collision energies} $\sqrt{s}=(0.25,\, 0.5,\, 1,\, 3)$\,TeV, {respectively. In each plot, the black, red, and blue curves denote the contributions from the SM, the interference term of ${O}(\cut^{-4})$, and the quadratic term of ${O}(\cut^{-8})$, respectively, where we note that the blue and black curves almost coincide. We have imposed a basic cut on the polar scattering angle, $\sin\theta>\sin\delta$, with $\delta=0.2$ for illustration. } |
 | \small{ Normalized angular distributions in the azimuthal angle $\phi_*^{}$ for $e^-e^+\!\!\to Z\ga$ followed by $Z\!\to\! d\bar d$ decays, as generated by $\,\mO_{G-}^{}$\! at collision energies} $\sqrt{s}=(0.25,\, 0.5,\, 1,\, 3)$\,TeV, {respectively. In each plot, the black, red, and blue curves denote the contributions from the SM, the interference term of ${O}(\cut^{-4})$, and the quadratic term of ${O}(\cut^{-8})$, respectively, where we note that the blue and black curves almost coincide. We have imposed a basic cut on the polar scattering angle, $\sin\theta>\sin\delta$, with $\delta=0.2$ for illustration. } |
 | \small{ Normalized angular distributions in the azimuthal angle $\phi_*^{}$ for $e^-e^+\!\!\to Z\ga$ followed by $Z\!\to\! d\bar d$ decays, as generated by $\,\mO_{G-}^{}$\! at collision energies} $\sqrt{s}=(0.25,\, 0.5,\, 1,\, 3)$\,TeV, {respectively. In each plot, the black, red, and blue curves denote the contributions from the SM, the interference term of ${O}(\cut^{-4})$, and the quadratic term of ${O}(\cut^{-8})$, respectively, where we note that the blue and black curves almost coincide. We have imposed a basic cut on the polar scattering angle, $\sin\theta>\sin\delta$, with $\delta=0.2$ for illustration. } |
 | \small{ Normalized angular distributions in the azimuthal angle $\phi_*^{}$ for $e^-e^+\!\!\to Z\ga$ followed by $Z\!\to\! d\bar d$ decays, as generated by $\,\mO_{G-}^{}$\! at collision energies} $\sqrt{s}=(0.25,\, 0.5,\, 1,\, 3)$\,TeV, {respectively. In each plot, the black, red, and blue curves denote the contributions from the SM, the interference term of ${O}(\cut^{-4})$, and the quadratic term of ${O}(\cut^{-8})$, respectively, where we note that the blue and black curves almost coincide. We have imposed a basic cut on the polar scattering angle, $\sin\theta>\sin\delta$, with $\delta=0.2$ for illustration. } |
 | \small{ Normalized angular distributions in the azimuthal angle $\phi_*^{}$ for $e^-e^+\!\!\to\! Z\ga$ followed by $Z\!\to d\bar{d}$\, decays, as generated by $\,\mO_{\widetilde{B}W}^{}$\! at the collision energies} $\sqrt{s}=(0.25,\, 0.5,\, 1,\, 3)$\,TeV, {respectively. In each plot, the black, red, and blue curves denote the contributions from the SM, the interference term of $\,{O}(\cut^{-4})$, and the quadratic term of $\,{O}(\cut^{-8})$, respectively, where we note that the blue and black curves almost coincide. We have imposed a basic cut on the polar scattering angle, $\sin\theta>\sin\delta$, with $\,\delta=0.2\,$ for illustration.} |
 | \small{ Normalized angular distributions in the azimuthal angle $\phi_*^{}$ for $e^-e^+\!\!\to\! Z\ga$ followed by $Z\!\to d\bar{d}$\, decays, as generated by $\,\mO_{\widetilde{B}W}^{}$\! at the collision energies} $\sqrt{s}=(0.25,\, 0.5,\, 1,\, 3)$\,TeV, {respectively. In each plot, the black, red, and blue curves denote the contributions from the SM, the interference term of $\,{O}(\cut^{-4})$, and the quadratic term of $\,{O}(\cut^{-8})$, respectively, where we note that the blue and black curves almost coincide. We have imposed a basic cut on the polar scattering angle, $\sin\theta>\sin\delta$, with $\,\delta=0.2\,$ for illustration.} |
 | \small{ Normalized angular distributions in the azimuthal angle $\phi_*^{}$ for $e^-e^+\!\!\to\! Z\ga$ followed by $Z\!\to d\bar{d}$\, decays, as generated by $\,\mO_{\widetilde{B}W}^{}$\! at the collision energies} $\sqrt{s}=(0.25,\, 0.5,\, 1,\, 3)$\,TeV, {respectively. In each plot, the black, red, and blue curves denote the contributions from the SM, the interference term of $\,{O}(\cut^{-4})$, and the quadratic term of $\,{O}(\cut^{-8})$, respectively, where we note that the blue and black curves almost coincide. We have imposed a basic cut on the polar scattering angle, $\sin\theta>\sin\delta$, with $\,\delta=0.2\,$ for illustration.} |
 | \small{ Normalized angular distributions in the azimuthal angle $\phi_*^{}$ for $e^-e^+\!\!\to\! Z\ga$ followed by $Z\!\to d\bar{d}$\, decays, as generated by $\,\mO_{\widetilde{B}W}^{}$\! at the collision energies} $\sqrt{s}=(0.25,\, 0.5,\, 1,\, 3)$\,TeV, {respectively. In each plot, the black, red, and blue curves denote the contributions from the SM, the interference term of $\,{O}(\cut^{-4})$, and the quadratic term of $\,{O}(\cut^{-8})$, respectively, where we note that the blue and black curves almost coincide. We have imposed a basic cut on the polar scattering angle, $\sin\theta>\sin\delta$, with $\,\delta=0.2\,$ for illustration.} |
 | \small{ Normalized angular distributions in the azimuthal angle $\phi_*^{}$ for $e^-e^+\!\!\to Z\ga$ followed by $Z\to d\bar d$ decays, as generated by $\,\mO_{C+}^{}$\! at the collision energies $\sqrt{s}=(0.25,\, 0.5,\, 1,\, 3)$\,TeV, respectively. In each plot, the black, red, and blue curves denote the contributions from the SM, the interference term of ${\cal O}(\cut^{-4})$, and the quadratic term of ${\cal O}(\cut^{-8})$, respectively, where we note that the blue and black curves almost coincide. We have imposed a simple cut on the scattering angle, $\sin\theta>\sin\delta$, with $\delta=0.2$ for illustration.} |
 | \small{ Normalized angular distributions in the azimuthal angle $\phi_*^{}$ for $e^-e^+\!\!\to Z\ga$ followed by $Z\to d\bar d$ decays, as generated by $\,\mO_{C+}^{}$\! at the collision energies $\sqrt{s}=(0.25,\, 0.5,\, 1,\, 3)$\,TeV, respectively. In each plot, the black, red, and blue curves denote the contributions from the SM, the interference term of ${\cal O}(\cut^{-4})$, and the quadratic term of ${\cal O}(\cut^{-8})$, respectively, where we note that the blue and black curves almost coincide. We have imposed a simple cut on the scattering angle, $\sin\theta>\sin\delta$, with $\delta=0.2$ for illustration.} |
 | \small{ Normalized angular distributions in the azimuthal angle $\phi_*^{}$ for $e^-e^+\!\!\to Z\ga$ followed by $Z\to d\bar d$ decays, as generated by $\,\mO_{C+}^{}$\! at the collision energies $\sqrt{s}=(0.25,\, 0.5,\, 1,\, 3)$\,TeV, respectively. In each plot, the black, red, and blue curves denote the contributions from the SM, the interference term of ${\cal O}(\cut^{-4})$, and the quadratic term of ${\cal O}(\cut^{-8})$, respectively, where we note that the blue and black curves almost coincide. We have imposed a simple cut on the scattering angle, $\sin\theta>\sin\delta$, with $\delta=0.2$ for illustration.} |
 | \small{ Normalized angular distributions in the azimuthal angle $\phi_*^{}$ for $e^-e^+\!\!\to Z\ga$ followed by $Z\to d\bar d$ decays, as generated by $\,\mO_{C+}^{}$\! at the collision energies $\sqrt{s}=(0.25,\, 0.5,\, 1,\, 3)$\,TeV, respectively. In each plot, the black, red, and blue curves denote the contributions from the SM, the interference term of ${\cal O}(\cut^{-4})$, and the quadratic term of ${\cal O}(\cut^{-8})$, respectively, where we note that the blue and black curves almost coincide. We have imposed a simple cut on the scattering angle, $\sin\theta>\sin\delta$, with $\delta=0.2$ for illustration.} |
 | \small{ Comparison between the true value and reconstructed value of the azimuthal angle $\phi_*^{}$ at} $\sqrt{s} = 250$\,GeV {[plot\,(a)]}, $\sqrt{s}=3$\,TeV {[plot\,(b)]}, {and} $\sqrt{s}=5$\,TeV {[plot\,(c)].} |
 | \small{ Comparison between the true value and reconstructed value of the azimuthal angle $\phi_*^{}$ at} $\sqrt{s} = 250$\,GeV {[plot\,(a)]}, $\sqrt{s}=3$\,TeV {[plot\,(b)]}, {and} $\sqrt{s}=5$\,TeV {[plot\,(c)].} |
 | \small{ Comparison between the true value and reconstructed value of the azimuthal angle $\phi_*^{}$ at} $\sqrt{s} = 250$\,GeV {[plot\,(a)]}, $\sqrt{s}=3$\,TeV {[plot\,(b)]}, {and} $\sqrt{s}=5$\,TeV {[plot\,(c)].} |
 | \small Reaches of the new physics scale $\cut$ as functions of the $e^+e^-$ collision energy $\sqrt{s\,}$\,. In each plot, the combined sensitivities are presented at $\,2\sigma$ (solid curves) and $5\sigma$ (dashed curves) levels, and for each individual dimension-8 operator among $(\OGP,\,\OGM,\,\OBW,\OCP)$ which correspond to the (red,\,purple,\,blue,\,black) curves, respectively. Plots\,(a) and (c) are for unpolarized $e^\mp$ beams, whereas plots\,(b) and (d) are for polarized $e^\mp$ beams with $(P_L^e,\, P_R^{\bar e})=(0.9,\,0.65)$. The plots\,(a) and (b) have input a sample integrated luminosity $\,\mL\!=\!2\,\text{ab}^{-1}$, whereas the plots\,(c) and (d) have used as input a sample of $\,\mL\!=\!5\,\text{ab}^{-1}$. |
 | \small Reaches of the new physics scale $\cut$ as functions of the $e^+e^-$ collision energy $\sqrt{s\,}$\,. In each plot, the combined sensitivities are presented at $\,2\sigma$ (solid curves) and $5\sigma$ (dashed curves) levels, and for each individual dimension-8 operator among $(\OGP,\,\OGM,\,\OBW,\OCP)$ which correspond to the (red,\,purple,\,blue,\,black) curves, respectively. Plots\,(a) and (c) are for unpolarized $e^\mp$ beams, whereas plots\,(b) and (d) are for polarized $e^\mp$ beams with $(P_L^e,\, P_R^{\bar e})=(0.9,\,0.65)$. The plots\,(a) and (b) have input a sample integrated luminosity $\,\mL\!=\!2\,\text{ab}^{-1}$, whereas the plots\,(c) and (d) have used as input a sample of $\,\mL\!=\!5\,\text{ab}^{-1}$. |
 | \small Reaches of the new physics scale $\cut$ as functions of the $e^+e^-$ collision energy $\sqrt{s\,}$\,. In each plot, the combined sensitivities are presented at $\,2\sigma$ (solid curves) and $5\sigma$ (dashed curves) levels, and for each individual dimension-8 operator among $(\OGP,\,\OGM,\,\OBW,\OCP)$ which correspond to the (red,\,purple,\,blue,\,black) curves, respectively. Plots\,(a) and (c) are for unpolarized $e^\mp$ beams, whereas plots\,(b) and (d) are for polarized $e^\mp$ beams with $(P_L^e,\, P_R^{\bar e})=(0.9,\,0.65)$. The plots\,(a) and (b) have input a sample integrated luminosity $\,\mL\!=\!2\,\text{ab}^{-1}$, whereas the plots\,(c) and (d) have used as input a sample of $\,\mL\!=\!5\,\text{ab}^{-1}$. |
 | \small Reaches of the new physics scale $\cut$ as functions of the $e^+e^-$ collision energy $\sqrt{s\,}$\,. In each plot, the combined sensitivities are presented at $\,2\sigma$ (solid curves) and $5\sigma$ (dashed curves) levels, and for each individual dimension-8 operator among $(\OGP,\,\OGM,\,\OBW,\OCP)$ which correspond to the (red,\,purple,\,blue,\,black) curves, respectively. Plots\,(a) and (c) are for unpolarized $e^\mp$ beams, whereas plots\,(b) and (d) are for polarized $e^\mp$ beams with $(P_L^e,\, P_R^{\bar e})=(0.9,\,0.65)$. The plots\,(a) and (b) have input a sample integrated luminosity $\,\mL\!=\!2\,\text{ab}^{-1}$, whereas the plots\,(c) and (d) have used as input a sample of $\,\mL\!=\!5\,\text{ab}^{-1}$. |
 | \small{ Sensitivity bounds on the new physics scales $\cut_j^{}$ at $2\sigma$ level for each pair of the operators $(\mO_{G+}^{},\, \mO_{G-}^{})$, \,$(\mO_{G+}^{},\, \mO_{\widetilde{B}W}^{})$,\, and \,$(\mO_{C+}^{},\, \mO_{\widetilde{B}W}^{})$, respectively, for the collider energy} $\sqrt{s\,}\!=\!3$\,TeV. In each plot, the results are shown for an integrated luminosity $\mL\!=\!2\,\text{ab}^{-1}$ (dashed curves) and $\mL\!=\!5\,\text{ab}^{-1}$ (solid curves). The plots\,(a) and (b) are shown for the case of unpolarized $e^\mp$ beams, whereas the plots\,(c) and (d) depict the case with polarized beams $(P_L^e,\,P_R^{\bar{e}})\!=\!(0.9,\,0.65)$\,. Here the $\,\pm\,$ inside each axis label denote the sign of the coefficient $\tilde{c}_j^{}$ of the corresponding operator. |
 | \small{ Sensitivity bounds on the new physics scales $\cut_j^{}$ at $2\sigma$ level for each pair of the operators $(\mO_{G+}^{},\, \mO_{G-}^{})$, \,$(\mO_{G+}^{},\, \mO_{\widetilde{B}W}^{})$,\, and \,$(\mO_{C+}^{},\, \mO_{\widetilde{B}W}^{})$, respectively, for the collider energy} $\sqrt{s\,}\!=\!3$\,TeV. In each plot, the results are shown for an integrated luminosity $\mL\!=\!2\,\text{ab}^{-1}$ (dashed curves) and $\mL\!=\!5\,\text{ab}^{-1}$ (solid curves). The plots\,(a) and (b) are shown for the case of unpolarized $e^\mp$ beams, whereas the plots\,(c) and (d) depict the case with polarized beams $(P_L^e,\,P_R^{\bar{e}})\!=\!(0.9,\,0.65)$\,. Here the $\,\pm\,$ inside each axis label denote the sign of the coefficient $\tilde{c}_j^{}$ of the corresponding operator. |
 | \small{ Sensitivity bounds on the new physics scales $\cut_j^{}$ at $2\sigma$ level for each pair of the operators $(\mO_{G+}^{},\, \mO_{G-}^{})$, \,$(\mO_{G+}^{},\, \mO_{\widetilde{B}W}^{})$,\, and \,$(\mO_{C+}^{},\, \mO_{\widetilde{B}W}^{})$, respectively, for the collider energy} $\sqrt{s\,}\!=\!3$\,TeV. In each plot, the results are shown for an integrated luminosity $\mL\!=\!2\,\text{ab}^{-1}$ (dashed curves) and $\mL\!=\!5\,\text{ab}^{-1}$ (solid curves). The plots\,(a) and (b) are shown for the case of unpolarized $e^\mp$ beams, whereas the plots\,(c) and (d) depict the case with polarized beams $(P_L^e,\,P_R^{\bar{e}})\!=\!(0.9,\,0.65)$\,. Here the $\,\pm\,$ inside each axis label denote the sign of the coefficient $\tilde{c}_j^{}$ of the corresponding operator. |
 | \small{ Sensitivity bounds on the new physics scales $\cut_j^{}$ at $2\sigma$ level for each pair of the operators $(\mO_{G+}^{},\, \mO_{G-}^{})$, \,$(\mO_{G+}^{},\, \mO_{\widetilde{B}W}^{})$,\, and \,$(\mO_{C+}^{},\, \mO_{\widetilde{B}W}^{})$, respectively, for the collider energy} $\sqrt{s\,}\!=\!3$\,TeV. In each plot, the results are shown for an integrated luminosity $\mL\!=\!2\,\text{ab}^{-1}$ (dashed curves) and $\mL\!=\!5\,\text{ab}^{-1}$ (solid curves). The plots\,(a) and (b) are shown for the case of unpolarized $e^\mp$ beams, whereas the plots\,(c) and (d) depict the case with polarized beams $(P_L^e,\,P_R^{\bar{e}})\!=\!(0.9,\,0.65)$\,. Here the $\,\pm\,$ inside each axis label denote the sign of the coefficient $\tilde{c}_j^{}$ of the corresponding operator. |