$(g-2)_μ$, Lepton Flavour Violation and $Z$ Decays with Leptoquarks: Correlations and Future Prospects

Abstract: 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 flavour 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 $B\to K^{(\star)}\nu\bar\nu$, 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.