A discrepancy between the standard model (SM) prediction and the experimental value of muon anomalous magnetic moment (muon g-2) has been reported. If this is due to the new
physics contributions, it can be a very good hint for the new physics. Since the size of the discrepancy is almost the same as the one of the electroweak contribution in the SM, we naively expect that the mass scale of new physics is close to the electroweak scale. However, the new physics close to the electroweak scale is now strongly constrained by the direct search
experiment at the LHC.
In this talk, we consider the S1 leptoquark (LQ) scenario where the LQ contribution to the muon g-2 has a large enhancement so that the TeV scale LQ can still give a sizable correction to the muon g-2, while it can escape from the LHC constraint. In the S_1 LQ scenario, we study processes such as ”b→c τ ν” and ”b → s μ+ μ-” where discrepancies between the SM predictions and the experimental results have been reported as well, and we show how large deviations from the SM predictions are possible and whether the S1 LQ can accommodate some of the discrepancies simultaneously.