$(g-2{)}_{\mu }$, lepton flavor violation, and $Z$ decays with leptoquarks: Correlations and future prospects

The long-standing anomaly in the anomalous magnetic moment of the muon indicates the presence of chirality violating new physics contributions. A possible solution involves scalar leptoquarks with left- and right-handed couplings to the top quark. Two such representations of scalar leptoquarks exist for which the contribution to $(g-2{)}_{\mu }$ can possess an $m_t/m_{\mu }$ enhancement compared to the Standard Model. The leptoquarks also induce loop corrections to $Z$ couplings to muons which probe as well new physics contributions which possess sources of $SU(2)$ symmetry breaking and we find that this effect should be observable at future experiments as GigaZ or TLEP. Furthermore, once interactions of the leptoquark with tau leptons and electrons are present, additional correlated effects in anomalous magnetic moments, $Z\to \ell {\ell }^{\prime }$ and $\ell \to {\ell }^{\prime }\gamma$, arise, which can be used to test the model and to determine the flavor structure of the couplings. We find that the two representations of leptoquarks can be distinguished also from low-energy experiments: one representation predicts constructive interference with the Standard Model in $Z$ couplings to leptons and effects in $B\to K^{(\star )}\nu \overline{\nu }$, while the other representation interferes destructively with the Standard Model in $Z$ couplings to leptons and gives a $C_9=C_{10}$-like contribution to $b\to s{\ell }^{+}{\ell }^{-}$ processes.

Figure 1

Left: Feynman diagram showing the $m_t/m_{\mu }$ enhanced leptoquark contribution to the anomalous magnetic moment of the muon. Right: Leading correction to the $Z$ couplings to muons proportional to $m_t^2$.

Figure 2

Left: Allowed regions in the ${\lambda }_{\mu }^L\text{−}{\lambda }_{\mu }^R$ plane from current and future experiments for $SU(2)$ singlet leptoquarks ${\mathrm{\Phi }}_1$ with $M=1\mathrm{TeV}$. Right: Same as the left plot for the $SU(2)$ doublet leptoquark ${\mathrm{\Phi }}_2$.

Figure 3

Left: Allowed regions from $\tau \to \mu \gamma$ in the ${\lambda }_{\tau }^L\text{−}{\lambda }_{\tau }^R$ plane for different couplings to left-handed muons assuming vanishing couplings to electrons for ${\mathrm{\Phi }}_1$ and $M=1\mathrm{TeV}$. The right-handed coupling to muon is fixed by requiring $\delta a_{\mu }={10}^{-9}$. The contour lines denote the predicted branching ratio for $Z\to {\tau }^{\pm }{\mu }^{\mp }$. Right: Same as left plot for the $SU(2)$ doublet leptoquark ${\mathrm{\Phi }}_2$.