Scalar Leptoquarks in Leptonic Processes
- Crivellin, Andreas et al
- arXiv:2010.06593CERN-TH-2020-167PSI-20-17ZU-TH 38/20
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 | : LQ effects in $Z\ell\ell$ , $Z\nu\nu$ and $W\ell\nu$ couplings for the scalar LQ representations which give rise to $m_{t}^2$ effects ($\Phi_1$, $\Phi_2$ and $\Phi_3$) as a function of the LQ mass. We neglected LQ mixing and considered only the couplings of third generation quarks to a single lepton flavor with unit strength, i.e. $\lambda_{3\ell}=1$. Here, $\Delta_{L,R}$, $\Theta$ and $\Lambda$ stand for the corrections in $Z\ell\ell$, $Z\nu\nu$ and $W\ell\nu$ couplings, respectively (see Sec.~\ref{sec:Zll}). The solid (dashed) lines refer to the couplings entering on-shell decays (effective couplings at $q^2=0$). The green region is excluded by LEP data~\cite{ALEPH:2005ab} from $Z\to \nu\bar{\nu}$ decays. The blue region is excluded by $Z\to\tau^{+}\tau^{-}$ {which is more constraining than $Z\to\mu^{+}\mu^{-}$ (not shown explicitly). Note that we also do not show $Z\to e^{+}e^{-}$ exclusions here for the sake of clarity since couplings to electrons are usually much smaller in setups motivated by the $B$ anomalies, leading to suppressed effects.} : Caption not extracted |
 | : LQ effects in $Z\ell\ell$ , $Z\nu\nu$ and $W\ell\nu$ couplings for the scalar LQ representations which give rise to $m_{t}^2$ effects ($\Phi_1$, $\Phi_2$ and $\Phi_3$) as a function of the LQ mass. We neglected LQ mixing and considered only the couplings of third generation quarks to a single lepton flavor with unit strength, i.e. $\lambda_{3\ell}=1$. Here, $\Delta_{L,R}$, $\Theta$ and $\Lambda$ stand for the corrections in $Z\ell\ell$, $Z\nu\nu$ and $W\ell\nu$ couplings, respectively (see Sec.~\ref{sec:Zll}). The solid (dashed) lines refer to the couplings entering on-shell decays (effective couplings at $q^2=0$). The green region is excluded by LEP data~\cite{ALEPH:2005ab} from $Z\to \nu\bar{\nu}$ decays. The blue region is excluded by $Z\to\tau^{+}\tau^{-}$ {which is more constraining than $Z\to\mu^{+}\mu^{-}$ (not shown explicitly). Note that we also do not show $Z\to e^{+}e^{-}$ exclusions here for the sake of clarity since couplings to electrons are usually much smaller in setups motivated by the $B$ anomalies, leading to suppressed effects.} : Caption not extracted |
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 | Modified $Z\ell\ell$, $Z\nu\nu$ and $W\ell\nu$ couplings in the $A_{\tilde{2}1}$-$A_{\tilde{2}3}$ plane (in units of GeV) for $\tilde{m}_{2}=m_1=m_3=1\,$TeV and $|\tilde{\lambda}_{3\ell}^{2}|=1$. |
 | Modified $Z\ell\ell$, $Z\nu\nu$ and $W\ell\nu$ couplings in the $A_{\tilde{2}1}$-$A_{\tilde{2}3}$ plane (in units of GeV) for $\tilde{m}_{2}=m_1=m_3=1\,$TeV and $|\tilde{\lambda}_{3\ell}^{2}|=1$. |
 | Correlations between ${\rm Br}[h\to\mu^+\mu^-]$, normalized to its SM value, and the NP contribution to the AMM of the muon ($\delta a_\mu$) for scenario $\Phi_1$ (left) and $\Phi_2$ (right) with \mbox{$m_{1,2}=1.5\,$TeV}. The predictions for different values of the LQ couplings to the Higgs are shown, where for $\Phi_1$ $Y=Y_1$ while for $\Phi_2$ $Y=Y_2+Y_{22}$. Even though the current ATLAS and CMS results are not yet constraining this model, sizeable effects are predicted, which can be tested at future colliders. Furthermore, $\Phi_1$ yields a constructive effect in $h\to\mu^+\mu^-$ while the one of $\Phi_2$ is destructive such that they can be clearly distinguished with increasing experimental precision. |
 | Correlations between ${\rm Br}[h\to\mu^+\mu^-]$, normalized to its SM value, and the NP contribution to the AMM of the muon ($\delta a_\mu$) for scenario $\Phi_1$ (left) and $\Phi_2$ (right) with \mbox{$m_{1,2}=1.5\,$TeV}. The predictions for different values of the LQ couplings to the Higgs are shown, where for $\Phi_1$ $Y=Y_1$ while for $\Phi_2$ $Y=Y_2+Y_{22}$. Even though the current ATLAS and CMS results are not yet constraining this model, sizeable effects are predicted, which can be tested at future colliders. Furthermore, $\Phi_1$ yields a constructive effect in $h\to\mu^+\mu^-$ while the one of $\Phi_2$ is destructive such that they can be clearly distinguished with increasing experimental precision. |
 | Correlations between ${\rm Br}[h\to\mu^+\mu^-]$, normalized to its SM value, and the NP contribution to the AMM of the muon ($\delta a_\mu$) for scenario $\Phi_1$ (left) and $\Phi_2$ (right) with \mbox{$m_{1,2}=1.5\,$TeV}. The predictions for different values of the LQ couplings to the Higgs are shown, where for $\Phi_1$ $Y=Y_1$ while for $\Phi_2$ $Y=Y_2+Y_{22}$. Even though the current ATLAS and CMS results are not yet constraining this model, sizeable effects are predicted, which can be tested at future colliders. Furthermore, $\Phi_1$ yields a constructive effect in $h\to\mu^+\mu^-$ while the one of $\Phi_2$ is destructive such that they can be clearly distinguished with increasing experimental precision. |
 | Correlations between ${\rm Br}[h\to\mu^+\mu^-]$, normalized to its SM value, and the NP contribution to the AMM of the muon ($\delta a_\mu$) for scenario $\Phi_1$ (left) and $\Phi_2$ (right) with \mbox{$m_{1,2}=1.5\,$TeV}. The predictions for different values of the LQ couplings to the Higgs are shown, where for $\Phi_1$ $Y=Y_1$ while for $\Phi_2$ $Y=Y_2+Y_{22}$. Even though the current ATLAS and CMS results are not yet constraining this model, sizeable effects are predicted, which can be tested at future colliders. Furthermore, $\Phi_1$ yields a constructive effect in $h\to\mu^+\mu^-$ while the one of $\Phi_2$ is destructive such that they can be clearly distinguished with increasing experimental precision. |
 | Allowed parameter space by LEP \cite{ALEPH:2005ab} (light green) for the couplings to left- and right-handed muons. In addition, we give the expected sensitivities of future collider experiments, see Tab.~\ref{tab:experimental_limits_Z}. The finite renormalization of $g_{2}$, induced by the effect in the Fermi constant, yields a LFU effect which is depicted by the blue lines in the plot on the left. |
 | Allowed parameter space by LEP \cite{ALEPH:2005ab} (light green) for the couplings to left- and right-handed muons. In addition, we give the expected sensitivities of future collider experiments, see Tab.~\ref{tab:experimental_limits_Z}. The finite renormalization of $g_{2}$, induced by the effect in the Fermi constant, yields a LFU effect which is depicted by the blue lines in the plot on the left. |
 | Allowed parameter space by LEP \cite{ALEPH:2005ab} (light green) for the couplings to left- and right-handed muons. In addition, we give the expected sensitivities of future collider experiments, see Tab.~\ref{tab:experimental_limits_Z}. The finite renormalization of $g_{2}$, induced by the effect in the Fermi constant, yields a LFU effect which is depicted by the blue lines in the plot on the left. |
 | Allowed parameter space by LEP \cite{ALEPH:2005ab} (light green) for the couplings to left- and right-handed muons. In addition, we give the expected sensitivities of future collider experiments, see Tab.~\ref{tab:experimental_limits_Z}. The finite renormalization of $g_{2}$, induced by the effect in the Fermi constant, yields a LFU effect which is depicted by the blue lines in the plot on the left. |
 | Correlations between $\tau\to\mu\gamma$ and $Z\to\tau\mu$ for the three LQ representations which generate an $m_{t}^2/m_{\rm LQ}^2$ effect in $Z\ell\ell$ couplings. We assume that $\Phi_1$ and $\Phi_2$ couple either to left or to right-handed leptons only such that chirally enhanced effects (which would result in dominant effects in $\tau\to\mu\gamma$) are absent. |
 | Correlations between $\tau\to\mu\gamma$ and $Z\to\tau\mu$ for the three LQ representations which generate an $m_{t}^2/m_{\rm LQ}^2$ effect in $Z\ell\ell$ couplings. We assume that $\Phi_1$ and $\Phi_2$ couple either to left or to right-handed leptons only such that chirally enhanced effects (which would result in dominant effects in $\tau\to\mu\gamma$) are absent. |
 | The correlations between $\tau\to\mu\gamma$ and $\tau\to 3\mu$ for a LQ mass of 1.5 TeV where we scanned $\lambda_{33}$ and $\lambda_{32}$ in the range $[-1.5,1.5]$. The gray regions are currently excluded by experiment. The dashed (solid) lines show the projected sensitivities for the HL-LHC (Belle II), see Tab.~\ref{tab:experimental_limits} for the numerical values. |
 | The correlations between $\tau\to\mu\gamma$ and $\tau\to 3\mu$ for a LQ mass of 1.5 TeV where we scanned $\lambda_{33}$ and $\lambda_{32}$ in the range $[-1.5,1.5]$. The gray regions are currently excluded by experiment. The dashed (solid) lines show the projected sensitivities for the HL-LHC (Belle II), see Tab.~\ref{tab:experimental_limits} for the numerical values. |
 | The correlations between $\tau\to\mu\gamma$ and $\tau\to 3\mu$ for a LQ mass of 1.5 TeV where we scanned $\lambda_{33}$ and $\lambda_{32}$ in the range $[-1.5,1.5]$. The gray regions are currently excluded by experiment. The dashed (solid) lines show the projected sensitivities for the HL-LHC (Belle II), see Tab.~\ref{tab:experimental_limits} for the numerical values. |
 | The correlations between $\tau\to\mu\gamma$ and $\tau\to 3\mu$ for a LQ mass of 1.5 TeV where we scanned $\lambda_{33}$ and $\lambda_{32}$ in the range $[-1.5,1.5]$. The gray regions are currently excluded by experiment. The dashed (solid) lines show the projected sensitivities for the HL-LHC (Belle II), see Tab.~\ref{tab:experimental_limits} for the numerical values. |
 | The correlations between $\tau\to\mu\gamma$ and $\tau\to 3\mu$ for a LQ mass of 1.5 TeV where we scanned $\lambda_{33}$ and $\lambda_{32}$ in the range $[-1.5,1.5]$. The gray regions are currently excluded by experiment. The dashed (solid) lines show the projected sensitivities for the HL-LHC (Belle II), see Tab.~\ref{tab:experimental_limits} for the numerical values. |
 | The correlations between $\tau\to\mu\gamma$ and $\tau\to 3\mu$ for a LQ mass of 1.5 TeV where we scanned $\lambda_{33}$ and $\lambda_{32}$ in the range $[-1.5,1.5]$. The gray regions are currently excluded by experiment. The dashed (solid) lines show the projected sensitivities for the HL-LHC (Belle II), see Tab.~\ref{tab:experimental_limits} for the numerical values. |
 | The correlations between $\tau\to\mu\gamma$ and $\tau\to 3\mu$ for a LQ mass of 1.5 TeV where we scanned $\lambda_{33}$ and $\lambda_{32}$ in the range $[-1.5,1.5]$. The gray regions are currently excluded by experiment. The dashed (solid) lines show the projected sensitivities for the HL-LHC (Belle II), see Tab.~\ref{tab:experimental_limits} for the numerical values. |
 | The correlations between $\tau\to\mu\gamma$ and $\tau\to 3\mu$ for a LQ mass of 1.5 TeV where we scanned $\lambda_{33}$ and $\lambda_{32}$ in the range $[-1.5,1.5]$. The gray regions are currently excluded by experiment. The dashed (solid) lines show the projected sensitivities for the HL-LHC (Belle II), see Tab.~\ref{tab:experimental_limits} for the numerical values. |
 | The correlations between $\tau\to\mu\gamma$ and $\tau\to 3\mu$ for a LQ mass of 1.5 TeV where we scanned $\lambda_{33}$ and $\lambda_{32}$ in the range $[-1.5,1.5]$. The gray regions are currently excluded by experiment. The dashed (solid) lines show the projected sensitivities for the HL-LHC (Belle II), see Tab.~\ref{tab:experimental_limits} for the numerical values. |
 | The correlations between $\tau\to\mu\gamma$ and $\tau\to 3\mu$ for a LQ mass of 1.5 TeV where we scanned $\lambda_{33}$ and $\lambda_{32}$ in the range $[-1.5,1.5]$. The gray regions are currently excluded by experiment. The dashed (solid) lines show the projected sensitivities for the HL-LHC (Belle II), see Tab.~\ref{tab:experimental_limits} for the numerical values. |
 | The correlations between $\tau\to\mu\gamma$ and $\tau\to 3\mu$ for a LQ mass of 1.5 TeV where we scanned $\lambda_{33}$ and $\lambda_{32}$ in the range $[-1.5,1.5]$. The gray regions are currently excluded by experiment. The dashed (solid) lines show the projected sensitivities for the HL-LHC (Belle II), see Tab.~\ref{tab:experimental_limits} for the numerical values. |
 | The correlations between $\tau\to\mu\gamma$ and $\tau\to 3\mu$ for a LQ mass of 1.5 TeV where we scanned $\lambda_{33}$ and $\lambda_{32}$ in the range $[-1.5,1.5]$. The gray regions are currently excluded by experiment. The dashed (solid) lines show the projected sensitivities for the HL-LHC (Belle II), see Tab.~\ref{tab:experimental_limits} for the numerical values. |
 | The analogue to the plots above for the $\mu\to e$ transition. The dashed lines depict the expected sensitivity from MEG II \cite{Baldini:2018nnn} and the solid line the one of Mu3e \cite{Berger:2014vba}. {Note that the color scaling shows the product of two couplings, as can be seen from the legend in the bottom-right.} |
 | The analogue to the plots above for the $\mu\to e$ transition. The dashed lines depict the expected sensitivity from MEG II \cite{Baldini:2018nnn} and the solid line the one of Mu3e \cite{Berger:2014vba}. {Note that the color scaling shows the product of two couplings, as can be seen from the legend in the bottom-right.} |
 | The analogue to the plots above for the $\mu\to e$ transition. The dashed lines depict the expected sensitivity from MEG II \cite{Baldini:2018nnn} and the solid line the one of Mu3e \cite{Berger:2014vba}. {Note that the color scaling shows the product of two couplings, as can be seen from the legend in the bottom-right.} |
 | The analogue to the plots above for the $\mu\to e$ transition. The dashed lines depict the expected sensitivity from MEG II \cite{Baldini:2018nnn} and the solid line the one of Mu3e \cite{Berger:2014vba}. {Note that the color scaling shows the product of two couplings, as can be seen from the legend in the bottom-right.} |
 | The analogue to the plots above for the $\mu\to e$ transition. The dashed lines depict the expected sensitivity from MEG II \cite{Baldini:2018nnn} and the solid line the one of Mu3e \cite{Berger:2014vba}. {Note that the color scaling shows the product of two couplings, as can be seen from the legend in the bottom-right.} |
 | The analogue to the plots above for the $\mu\to e$ transition. The dashed lines depict the expected sensitivity from MEG II \cite{Baldini:2018nnn} and the solid line the one of Mu3e \cite{Berger:2014vba}. {Note that the color scaling shows the product of two couplings, as can be seen from the legend in the bottom-right.} |
 | The analogue to the plots above for the $\mu\to e$ transition. The dashed lines depict the expected sensitivity from MEG II \cite{Baldini:2018nnn} and the solid line the one of Mu3e \cite{Berger:2014vba}. {Note that the color scaling shows the product of two couplings, as can be seen from the legend in the bottom-right.} |
 | The analogue to the plots above for the $\mu\to e$ transition. The dashed lines depict the expected sensitivity from MEG II \cite{Baldini:2018nnn} and the solid line the one of Mu3e \cite{Berger:2014vba}. {Note that the color scaling shows the product of two couplings, as can be seen from the legend in the bottom-right.} |
 | The analogue to the plots above for the $\mu\to e$ transition. The dashed lines depict the expected sensitivity from MEG II \cite{Baldini:2018nnn} and the solid line the one of Mu3e \cite{Berger:2014vba}. {Note that the color scaling shows the product of two couplings, as can be seen from the legend in the bottom-right.} |
 | The analogue to the plots above for the $\mu\to e$ transition. The dashed lines depict the expected sensitivity from MEG II \cite{Baldini:2018nnn} and the solid line the one of Mu3e \cite{Berger:2014vba}. {Note that the color scaling shows the product of two couplings, as can be seen from the legend in the bottom-right.} |
 | The analogue to the plots above for the $\mu\to e$ transition. The dashed lines depict the expected sensitivity from MEG II \cite{Baldini:2018nnn} and the solid line the one of Mu3e \cite{Berger:2014vba}. {Note that the color scaling shows the product of two couplings, as can be seen from the legend in the bottom-right.} |
 | The analogue to the plots above for the $\mu\to e$ transition. The dashed lines depict the expected sensitivity from MEG II \cite{Baldini:2018nnn} and the solid line the one of Mu3e \cite{Berger:2014vba}. {Note that the color scaling shows the product of two couplings, as can be seen from the legend in the bottom-right.} |