Muon Anomalous Magnetic Moment and Leptoquark Solutions

The recent measurement on the muon anomalous magnetic moment $a_\mu$ shows a $2.6\sigma$ deviation from the standard model value. We show that it puts an interesting bound on the mass of the second generation leptoquarks. To account for the data the leptoquark must have both the left- and right-handed couplings to the muon. Assuming that the couplings have electromagnetic strength, the mass is restricted in the range $0.7 {\rm TeV} < M_{\rm LQ} < 2.2$ TeV at 95% C.L. We also discuss constraints coming from other low energy and high energy experiments. If the first-second-generation universality is assumed, constraints come from the atomic parity violation and charged-current universality. We show that coexistence with other leptoquarks can satisfy these additional constraints and at the same time do not affect the $a_\mu$.