$B\to K^{\ast }{\ell }^{+}{\ell }^{-}$ 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

References in corpus (38)

• Big Bang Nucleosynthesis (in "The Review of Particle Properties" 2004)
• An effective field theory for collinear and soft gluons: heavy to light decays
• Heavy Quark Symmetry
• Soft-Collinear Factorization in Effective Field Theory
• QCD Factorization for $B\to \pi \pi$ Decays: Strong Phases and CP Violation in the Heavy Quark Limit
• Summing Sudakov logarithms in B -> X_s + gamma in effective field theory
• Invariant Operators in Collinear Effective Theory
• Soft-collinear effective theory and heavy-to-light currents beyond leading power
• B_{d,s}->rho, omega, K*, phi Decay Form Factors from Light-Cone Sum Rules Revisited
• Systematic approach to exclusive B ->V l^+l^-, V gamma decays
• Weak Radiative B-Meson Decay Beyond Leading Logarithms
• A Comparative Study of the Decays $B\to (K,K^{\ast }){\ell }^{+}{\ell }^{-}$ in Standard Model and Supersymmetric Theories
• Asymptotics of Heavy-Meson Form Factors
• Effective Hamiltonian for Non-Leptonic |Delta F| = 1 Decays at NNLO in QCD
• Lepton Polarization in the Decays $B\to X_s{\mu }^{+}{\mu }^{-}$ and $B\to X_s{\tau }^{+}{\tau }^{-}$
• Factorization of heavy-to-light form factors in soft-collinear effective theory
• Factorization and Endpoint Singularities in Heavy-to-Light decays
• Anomalous Dimension Matrix for Radiative and Rare Semileptonic B Decays up to Three Loops
• The Radiative Decays B -> V gamma at Next-to-Leading Order in QCD
• Improved Measurement of the Electroweak Penguin Process B->Xsll
• Measurement of the B -> Xs l+ l- branching fraction with a sum over exclusive modes
• Spectator Interactions in Soft-Collinear Effective Theory
• Branching Ratios for $B\to K^{\ast }\gamma$ and $B\to \rho \gamma$ Decays in Next-to-Leading Order in the Large Eneregy Effective Theory
• Two-loop virtual corrections to B --> X_s l^+ l^- in the standard model
• Sudakov Resummation for Subleading SCET Currents and Heavy-to-Light Form Factors
• Model-Independent Properties of the B-Meson Distribution Amplitude
• SU(3) Breaking of Leading--Twist K and K* Distribution Amplitudes - a Reprise
• Heavy-to-light B meson form factors at large recoil energy -- spectator-scattering corrections
• A Complete Basis for Power Suppressed Collinear-Ultrasoft Operators
• Effects of new physics in the rare decays $B\to K{\ell }^{+}{\ell }^{-}$ and $B\to K^{\ast }{\ell }^{+}{\ell }^{-}$
• Short Distance Coefficients and the Vanishing of the Lepton Asymmetry in $B\to V{\ell }^{+}{\ell }^{-}$
• Factorization and the Soft Overlap Contribution to Heavy-to-Light Form Factors
• Loop corrections to sub-leading heavy quark currents in SCET
• Measurement of the Electroweak Penguin Process B --> X(s) l+ l-
• Factorization in B->V gamma Decays
• Rare decays B -> (K, K*) (l+ l-, nu bar{nu}) in the quark model
• Rare radiative exclusive B decays in soft-collinear effective theory
• Helicity analysis of the decays B --> K^* ell^+ ell^- and B --> rho ell nu_ell in the large Energy Effective Theory

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• Complementarity of Semileptonic $B$ to $K_2^{\ast }(1430)$ and $K^{\ast }(892)$ Decays in the Standard Model with Fourth Generation
• $B\to K^{\ast }{l}^{+}{l}^{-}$: Zeroes of angular observables as test of standard model
• Rare B-Meson Decays at the Crossroads
• Rare Decays as a Probe for New Physics
• Experimental constraints from flavour changing processes and physics beyond the Standard Model
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• What We've Learned from Heavy Flavour Experiments Since CKM2010
• Radiative B to tensor meson decays at NLO in SCET