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

We study the rare B decay B→K*ℓ+ℓ- using soft-collinear effective theory (SCET). At leading power in 1/mb, a factorization formula is obtained valid to all orders in αs. For phenomenological application, we calculate the decay amplitude including order αs corrections, and resum the logarithms by evolving the matching coefficients from the hard scale \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{O}(m_b)$\end{document} down to the scale \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\sqrt{m_{b}\Lambda_{h}}$\end{document}. The branching ratio for B→K*ℓ+ℓ- is uncertain due to the imprecise knowledge of the soft form factors ζ⊥(q2) and ζ∥(q2). Constraining the soft form factor ζ⊥(q2=0) from data on B→K*γ yields ζ⊥(q2=0)=0.32±0.02. Using this input, together with the light-cone sum rules to determine the q2-dependence of ζ⊥(q2) and the other soft form factor ζ∥(q2), we estimate the partially integrated branching ratio in the range 1 GeV2≤q2≤7 GeV2 to be (2.92+0.67-0.61)×10-7. We discuss how to reduce the form factor related uncertainty by combining data on B→ρ(→ππ)ℓνℓ and B→K*(→Kπ)ℓ+ℓ-. The forward-backward asymmetry is less sensitive to the input parameters. In particular, for the zero-point of the forward-backward asymmetry in the standard model, we get q02=(4.07+0.16-0.13) GeV2. The scale dependence of q02 is discussed in detail.