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We study the rare B decay $B \to K^* \ell^+ \ell^-$ using soft-collineareffective theory (SCET). At leading power in $1/m_b$, a factorization formulais obtained valid to all orders in $\alpha_s$. For phenomenologicalapplication, we calculate the decay amplitude including order $\alpha_s$corrections, and resum the logarithms by evolving the matching coefficientsfrom the hard scale ${\cal O}(m_b)$ down to the scale $\sqrt{m_b \Lambda_h}$.The branching ratio for $B \to K^* \ell^+ \ell^-$ is uncertain due to theimprecise knowledge of the soft form factors $\zeta_\perp (q^2)$ and$\zeta_\parallel (q^2)$. Constraining the soft form factor $\zeta_\perp(q^2=0)$ from data on $B \to K^* \gamma$ yields $\zeta_\perp (q^2=0)=0.32 \pm0.02$. Using this input, together with the light-cone sum rules to determinethe $q^2$dependence of $\zeta_\perp (q^2)$ and the other soft form factor$\zeta_\parallel (q^2)$, we eastimate the partially integrated branching ratioin the range $1~{GeV}^2 \le q^2 \le 7~{GeV}^2$ to be $(2.92^{+0.67}_{-0.61})\times 10^{-7}$. We discuss how to reduce the form factor related uncertaintyby combining data on $B \to \rho (\to \pi \pi) \ell \nu_\ell$ and $B\to K^*(\to K\pi) \ell^+\ell^-$. The forward-backward asymmetry is less sensitive tothe input parameters. In particular, for the zero-point of the forward backwardasymmetry in the standard model, we get $q_0^2=(4.07^{+0.13}_{-0.12})~{GeV}^2$.The scale dependence of $q_0^2$ is discussed in detail.Comment: 34 pages, 7 figures; typos corrected, several references added, and  discussion of the scale dependence of the forward-backward asymmetry  zero-point enlarge

B→K*ℓ+ℓ- decay in soft-collinear effective theory