Semileptonic meson decays in point-form relativistic quantum mechanics: Unambiguous extraction of weak form factors

The point-form version of the Bakamjian-Thomas construction is applied to the description of several semileptonic decays of mesons. Weak form factors are extracted without ambiguity for pseudoscalar-to-pseudoscalar as well as for pseudoscalar-to-vector transitions of mesons from the most general covariant decomposition of the weak current. No manifestation of cluster-separability violation appears in the form of nonphysical contributions to the structure of such a current, in contrast to what happens in the electromagnetic case. Moreover, no frame dependence is observed when we extract the form factors from the most general covariant decomposition of the current, which contrasts with analogous front-form calculations that involve vector mesons in the transition. We present our results for heavy-light meson decays, i.e. $B\to D$, as well as for $B$ and $D$ mesons decaying into $\pi$, $\rho$ and $K^{(*)}$, and perform a numerical comparison with the analogous front-form approach. Differences between point and front forms that are not seen in the heavy-quark limit of $q\overline{Q}$ systems appear. These differences are attributed to the different role that the nonvalence contributions play in the description of hadronic reactions in each form. It is argued how contributions from missing $Z$ graphs can be estimated.

Figure 1

Time-ordered contributions to the semileptonic decay of a meson $\alpha$ to ${\alpha }^{\prime }$.

Figure 2

$B\to D$ and $B\to \pi$ transition form factors in the whole range $0\le q^2\le (M_B-M_{D(\pi )}{)}^2$. Parameters for the quark masses and harmonic-oscillator wave functions are taken from Table 1. For the meson masses the current values given by the Particle Data Group have been taken [44].

Figure 3

Same as in Fig. 2 for $D\to K$ and $D\to \pi$ transition form factors.

Figure 4

$B\to D^{*}$ transition form factors in the whole range $0\le q^2\le (M_B-M_{D^{*}}{)}^2$. Parameters for the quark masses and harmonic-oscillator wave functions are taken from Table 1. For the meson masses the current values given by the Particle Data Group are taken [44].

Figure 5

Same as in Fig. 4 for $D\to K^{*}$ transition form factors.

Figure 6

Same as in Fig. 4 for $B\to \rho$ transition form factors.

Figure 7

Same as in Fig. 4 for $D\to \rho$ transition form factors.