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We study the potential of the measurement of the transverse muon polarizationP_T in the K->mu nu gamma decay with the sensitivity of \delta P_T ~ 10^{-4}.It is shown that the forthcoming experiment can measure the contribution of theelectromagnetic final state interactions to P_T that gives a possibility tounambiguously determine the signs of the sum of the kaon form factors F_V andF_A even without fixing their difference. We also estimate the sensitivity ofthis experiment to the new physics, which could give rise to T-violation:multi-Higgs doublet models, supersymmetric extensions of the Standard Model,left-right symmetric model and leptoquark models.Comment: 10 pages, 6 figure

Transverse muon polarization in $K^+\to\mu^+\nu_\mu\gamma$ : scanning over the Dalitz plot