Lepton polarization in $B\to K_1{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ Decays

We study the single and double lepton polarization asymmetries in the semileptonic $B$ meson decays $B\to K_1(1270){\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ $\mathrm{\ell }\equiv e$, $\mu$, $\tau$), where the strange $P$-wave meson, $K_1(1270)$, is the mixtures of the $K_{1A}$ and $K_{1B}$, which are the $1^3{P}_1$ and $1^1{P}_1$ states, respectively. The lepton polarization asymmetries show relatively strong dependency in the various region of dileptonic invariant mass. The lepton polarization asymmetries can also be used for determining the $K_1(1270)$–$K_1(1400)$ mixing angle, ${\theta }_{K_1}$ and new physics effects. Furthermore, it is shown that these asymmetries in $B\to K_1(1270){\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ decay compared with those of $B\to K^{\ast }{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ decay are more sensitive to the dileptonic invariant mass.