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Tau $g-2$ at $e^-e^+$ colliders with momentum dependent form factor

The deviation between the standard model prediction and the measurement of the muon g-2 is currently at 3-4 sigma (can be up to 7 sigma in the upcoming experiment E989). If new physics is responsible for such discrepancy, it is expected that the new contributions to tau g-2 are even larger than that for muon due to its large mass. In spite of that, the tau g-2 is much more difficult to be directly measured because of its short lifetime. In this paper, we consider the effect of the tau g-2 at $e^-e^+$ colliders in a model independent way. Using the tau pair production channel at the Large Electron Position Collider (LEP), we have found the allowed range for the new physics contribution of the tau g-2 assuming a $q^2$-dependence ansatz for the magnetic form factor. In our analysis, we take into account the standard model one-loop correction as well as the initial state photon radiation. We have also investigated the prospect at future $e^-e^+$ colliders, and determine the expected allowed range for the new physics contribution to the tau g-2. Given the proposed beam polarization configuration at the International Linear Collider (ILC), we have analyzed the dependence of this allowed range on the integrated luminosity as well as the relative systematic error.