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In the paper, we apply the $k_T$ factorization approach to deal with the$B\to K$ transition form factor with tensor current in the large recoilregions. Main uncertainties for the estimation are discussed and we obtain$F_T^{B\to K}(0)=0.25\pm0.01\pm0.02$, where the first error is caused by theuncertainties from the pionic wave functions and the second is from that of theB-meson wave functions. This result is consistent with the light-cone sum ruleresults obtained in the literature.

$B\to K$ Transition Form Factor with Tensor Current within the $k_T$ Factorization Approach