Quark-binding effects in inclusive decays of heavy mesons

We present a new approach to the analysis of quark-binding effects in inclusive decays of heavy mesons within the relativistic dispersion quark model. Various differential distributions, such as electron energy spectrum, $q^2$- and $M_X$-distributions, are calculated in terms of the $B$ meson soft wave function which also determines long-distance effects in exclusive transition form factors. Using the quark-model parameters and the $B$ meson wave function previously determined from the description of the exclusive $b \to u$ transitions within the same dispersion approach, we provide numerical results on various distributions in the inclusive $B \to X_c l\nu$ decays.Comment: revtex, 18 pages, preprint HD-THEP-99-50 (Heidelberg) and RM3-TH/99-13 (Roma

Heavy-to-light form factors: sum rules on the light cone and beyond

We report the first systematic analysis of the off-light-cone effects in sum rules for heavy-to-light form factors. These effects are investigated in a model based on scalar constituents, which allows a technically rather simple analysis but has the essential features of the analogous QCD calculation. The correlator relevant for the extraction of the heavy-to-light form factor is calculated in two different ways: first, by adopting the full Bethe-Salpeter amplitude of the light meson and, second, by performing the expansion of this amplitude near the light cone $x^2=0$. We demonstrate that the contributions to the correlator from the light-cone term $x^2=0$ and the off-light-cone terms $x^2\ne 0$ have the same order in the $1/m_Q$ expansion. The light-cone correlator, corresponding to $x^2=0$, is shown to systematically overestimate the full correlator, the difference being $\sim \Lambda_{\rm QCD}/\delta$, with $\delta$ the continuum subtraction parameter of order 1 GeV. Numerically, this difference is found to be 10-20%.Comment: revtex 14 pages, version to be published in Phys. Rev. D (discussion in Sect. 3 extended, example in Sect. 4 added

End-point singularities of Feynman graphs on the light cone

We show that some Lorentz components of the Feynman integrals calculated in terms of the light-cone variables may contain end-point singularities which originate from the contribution of the big-circle integral in the complex k_ plane. These singularities appear in various types of diagrams (two-point functions, three-point functions, etc) and provide the covariance of the Feynman integrals on the light-cone. We propose a procedure for calculating Feynman integrals which guarantees that the end-point singularities do not appear in the light-cone representations of the invariant amplitudes.Comment: final version to appear in PLB; few references adde

Electromagnetic form factors in the light-front formalism and the Feynman triangle diagram: spin-0 and spin-1 two-fermion systems

The connection between the Feynman triangle diagram and the light-front formalism for spin-0 and spin-1 two-fermion systems is analyzed. It is shown that in the limit q+ = 0 the form factors for both spin-0 and spin-1 systems can be uniquely determined using only the good amplitudes, which are not affected by spurious effects related to the loss of rotational covariance present in the light-front formalism. At the same time, the unique feature of the suppression of the pair creation process is maintained. Therefore, a physically meaningful one-body approximation, in which all the constituents are on their mass-shells, can be consistently formulated in the limit q+ = 0. Moreover, it is shown that the effects of the contact term arising from the instantaneous propagation of the active constituent can be canceled out from the triangle diagram by means of an appropriate choice of the off-shell behavior of the bound state vertexes; this implies that in case of good amplitudes the Feynman triangle diagram and the one-body light-front result match exactly. The application of our covariant light-front approach to the evaluation of the rho-meson elastic form factors is presented.Comment: corrected typos in the reference

Lepton asymmetries in exclusive b→sℓ+ℓ−b \to s\ell^+\ell^- decays as a test of the Standard Model

We argue that the longitudinal lepton polarization and the forward-backward asymmetries in exclusive $B\to (K,K^*)\ell^+\ell^-$ decays are largely unaffected by the theoretical uncertainties in the long-distance contributions both induced by the long-range charming penguins in the $\ell^+\ell^-$ channel and those in the meson channels encoded in the meson transition form factors, and are mainly determined by the short-distance Wilson coefficients at the low-energy scale $\mu\simeq m_b$. Thus, the above mentioned asymmetries provide a powerful probe of the Standard Model and its extensions.Comment: revtex, 9 pages, 5 figure