$B\to K^{\ast }{\ell }^{+}{\ell }^{-}$ in soft-collinear effective theory

Abstract

We study the rare B decay $B\to K^{\ast }{\ell }^{+}{\ell }^{-}$ using soft-collinear effective theory (SCET). At leading power in $1/m_b$, a factorization formula is obtained valid to all orders in ${\alpha }_s$. For phenomenological application, we calculate the decay amplitude including order ${\alpha }_s$ corrections, and resum the logarithms by evolving the matching coefficients from the hard scale $\mathcal{O}(m_b)$ down to the scale $\sqrt{m_b{\Lambda }_h}$. The branching ratio for $B\to K^{\ast }{\ell }^{+}{\ell }^{-}$ is uncertain due to the imprecise 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 $B\to K^{\ast }\gamma$ yields ${\zeta }_{\perp }(q^2=0)=0.32\pm 0.02$. Using this input, together with the light-cone sum rules to determine the $q^2$dependence of ${\zeta }_{\perp }(q^2)$ and the other soft form factor ${\zeta }_{\parallel }(q^2)$, we eastimate the partially integrated branching ratio in the range $1{GeV}^2\le q^2\le 7{GeV}^2$ to be $(2.92_{-0.61}^{+0.67})\times 10^{-7}$. We discuss how to reduce the form factor related uncertainty by combining data on $B\to \rho (\to \pi \pi )\ell {\nu }_{\ell }$ and $B\to K^{\ast }(\to K\pi ){\ell }^{+}{\ell }^{-}$. 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 $q_0^2=(4.07_{-0.12}^{+0.13}){GeV}^2$. The scale dependence of $q_0^2$ is discussed in detail.

34 pages, 7 figures; typos corrected, several references added, and discussion of the scale dependence of the forward-backward asymmetry zero-point enlarged

Cited by in corpus (5)

• Angular Distributions of B -> K ll Decays
• Constraints on New Physics in MFV models: a model-independent analysis of Delta F=1 processes
• Extracting short distance information from b -> s l+ l- effectively
• Probe R-parity Violating Supersymmetry Effects in $B\to K^{(\ast )}{\ell }^{+}{\ell }^{-}$ and $B_s\to {\ell }^{+}{\ell }^{-}$ Decays
• Rare Decays as a Probe for New Physics