Weak transition form factors of heavy-light pseudoscalar mesons for space- and timelike momentum transfers

Abstract

This paper deals with the description of weak B− → D0; π0 and D− → K0; π0 transition form factors in both the space- and timelike momentum transfer regions, within a constituent-quark model. To this aim, neutrino-meson scattering and semileptonic weak decays are formulated within the framework of pointform relativistic quantum mechanics to end up with relativistic invariant process amplitudes from which meson transition currents and form factors are extracted in an unambiguous way. For spacelike momentum transfers, these form factors depend on the frame in which the WMM0 vertex is considered. On physical grounds, such a frame dependence is expected from a pure valence-quark picture, since a complete, frame independent description of form factors is supposed to require valence as well as nonvalence contributions. Nonvalence contributions, the most important being the Z graphs, are, however, suppressed in the infinitemomentum frame (q2 < 0). On the other hand, they can play a significant role in the Breit frame (q2 < 0) and in the direct decay calculation (q2 > 0), as a comparison with the infinite-momentum-frame form factors (analytically continued to q2 > 0) reveals. Numerical results for the analytically continued infinitemomentum- frame form factors are found to agree very well with lattice data in the timelike momentum transfer region, and also, the experimental value for the slope of the Fþ B→D transition form factor at zero recoil is reproduced satisfactorily. Furthermore, these predictions satisfy heavy-quark-symmetry constraints, and their q2 dependence is well approximated by a pole fit, reminiscent of a vector-mesondominance- like decay mechanism.We discuss how such a decay mechanism can be accommodated within an extension of our constituent-quark model, by allowing for a nonvalence component in the meson wave functions, and we also address the question of wrong cluster properties inherent in the formulation of relativistic quantum mechanics employed in this article.