Eur. Phys. J. C (2006) 47: 625-641
https://doi.org/10.1140/epjc/s2006-02596-4

Theoretical Physics

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

¹ Theory Group, Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22603, Hamburg, Germany
² II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, 22761, Hamburg, Germany

^* e-mail: ahmed.ali@desy.de

Received: 7 March 2006
Revised: 20 April 2006
Published online: 18 July 2006

Abstract

We study the rare B decay B→K^*ℓ⁺ℓ^- using soft-collinear effective theory (SCET). At leading power in 1/m_b, a factorization formula is obtained valid to all orders in α_s. For phenomenological application, we calculate the decay amplitude including order α_s corrections, and resum the logarithms by evolving the matching coefficients from the hard scale down to the scale . 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)ℓν_ℓ 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 q₀ ²=(4.07^+0.16 _-0.13) GeV². The scale dependence of q₀ ² is discussed in detail.