Weak $B^-\rightarrow D^0, \pi^0$ and $D^-\rightarrow {K}^0, \pi^0$ transition form factors are described in both the space- and time-like momentum transfer regions, within a constituent-quark model. Neutrino-meson scattering and semileptonic weak decays are formulated within the point form of 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 space-like momentum transfers, form factors depend on the frame in which the $W M M^\prime$ vertex is considered. Such a frame dependence is expected from a pure valence-quark picture, since a complete, frame independent description of form factors is supposed to include non-valence contributions. The most important of such contributions are the $Z$-graphs, which are, however, suppressed in the infinite-momentum frame ($q^2<0$). On the other hand, they can play a significant role in the Breit frame ($q^2<0$) and in the direct decay calculation ($q^2>0$), as a comparison with the infinite-momentum-frame form factors (analytically continued to $q^2>0$) reveals. Numerical results for the analytically continued infinite-momentum-frame form factors agree very well with lattice data in the time-like momentum transfer region and the experimental value for the slope of the $F^+_{B\rightarrow D}$ transition form factor at zero recoil is reproduced satisfactorily. These predictions satisfy heavy-quark-symmetry constraints and their $q^2$ dependence is well approximated by a pole fit, reminiscent of a vector-meson-dominance-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 non-valence component in the meson wave functions. We also address the question of wrong cluster properties inherent in the Bakamjian-Thomas formulation.


  • We have investigated weak B → D; π and D → K; π transition form factors for space- and timelike momentum transfers, as can be measured in neutrino scattering and semileptonic weak decays

  • We have used the point form of relativistic quantum mechanics in connection with the Bakamjian-Thomas construction to describe these systems in a relativistic invariant way by means of a constituent-quark model

  • The same observation was already made in previous work on electromagnetic form factors [1,10,11], where it was suspected that the origin of this s dependence are wrong clusterseparability properties inherent in the Bakamjian-Thomas construction

Read more



This paper continues previous work in which semileptonic weak B → D; π and D → K; π decays [1–4] have been investigated within a constituent-quark model making use. These analyses make use of front-form dynamics, and the main conclusion is that the construction of a frame independent covariant meson (transition) current requires the inclusion of the, so-called, “Z-graph” contribution In a constituent-quark model, the direct diagram (a) corresponds to the usual valence-quark contribution, whereas the other diagrams, in particular the Z graph

B Mcuobnνfe
Infinite-momentum frame
Frame dependence of spacelike transition form factors
Timelike transition form factors—analytic continuation of BF results
Timelike transition form factors—analytic continuation of IMF results
Z graph and meson pole

Full Text

Published Version
Open DOI Link

Get access to 115M+ research papers

Discover from 40M+ Open access, 2M+ Pre-prints, 9.5M Topics and 32K+ Journals.

Sign Up Now! It's FREE

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call