Abstract
We discuss the general properties of the $B$-meson decay form factors $F({q}^{2},{q}^{\ensuremath{'}2})$, describing $B$-meson decays induced by two currents, e.g., $B$ decays into four leptons in the final state. We study the analytic properties of these complicated objects and identify those regions of ${q}^{2}$ and ${q}^{\ensuremath{'}2}$, where perturbative QCD can be applied for obtaining predictions for the physical form factors.
Highlights
The goal of this paper is to study the general properties of the B-meson form factors into two currents
We presented the analysis of the analytic properties of the form factor Fðq2; q02Þ which describes the B decay into two currents
The results obtained above are based on the integral representation for the form factor Fðq2; q02Þ in terms of the B-meson field-theoretic wave function and the quark propagator, for which the Feynman form is used
Summary
The goal of this paper is to study the general properties of the B-meson form factors into two currents. One needs to study the analytic properties of the latter in broad ranges of momentum transfers, including the timelike regions of four-lepton decays, in order to understand where model-independent predictions for such form factors directly from QCD may be obtained. The knowledge of rigorous properties of such form factors from field theory allows one to obtain constraints to be used in building realistic phenomenological models for the amplitudes of various four-lepton decays. For the sake of argument, we omit here the Lorentz and the spinor indices and consider field theory with scalar particles Such an approach allows us to avoid technical complications and to concentrate on the conceptual aspects [23,24,25]. Z Fðq; q02Þ 1⁄4 i dxdkeiðq−kÞxDsðkÞh0jsð0ÞbðxÞjBðpÞi; ð1:3Þ where DsðkÞ is the propagator of the scalar light s“quark.”
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