K1(1270)-K1(1400) Mixing Angle and New-Physics Effects in B to K1 l+ l- Decays

We study semileptonic B meson decays B to K_1(1270) l^+ l^- and K_1(1400) l^+ l^- (l=e, mu, tau), where the strange P-wave mesons, K_1(1270) and K_1(1400), are the mixtures of the K_{1A} and K_{1B}, which are the 1^3P_1 and 1^1P_1 states, respectively. We show that the ratio R_l = Br(B to K_1(1400) l^+ l^-)/Br(B to K_1(1270) l^+ l^-), insensitive to new-physics parameters, is suitable for determining the K_1(1270)-K_1(1400) mixing angle, theta_{K_1}. The forward-backward asymmetry shows a weak theta_{K_1}-dependence for B to K_1(1270) mu^+ mu^-, but relatively strong for B to K_1(1400) mu^+ mu^-. We investigate model-independent new-physics corrections to operators relevant to the b to s l^+ l^- electroweak-penguin and weak-box diagrams. Furthermore, for the B to K_1(1270) mu^+ mu^- decay the position of the forward-backward asymmetry zero, which is almost independent of the value of theta_{K_1}, can be dramatically changed under variation of new-physics parameters.