Speaker
Description
We discuss a method to generate form factor curves across the entire
kinematic range for semileptonic (SL) pseudoscalar to pseudoscalar
decays, for example $B \rightarrow \pi \mu \nu$ and $B_s \rightarrow K
\mu \nu$.
The work builds upon the Dispersive Matrix (DM) method. Using known
form factor information at specific discrete $q^2$ points as input,
the DM method allows model-independent extrapolation to any desired
$q^2$ value in the SL physical region. Here $q$ is the outgoing
lepton-pair 4-momentum. The main obstacle in using DM results to
determine phenomenological predictions, such as forward-backward
asymmetry, is that it is not obvious how to exploit the bounds over
continuous ranges of $q^2$ when integrating, for example, the
differential decay rate over the physical $q^2$ range or over bins in
$q^2$.
Using this method, we can generate a family of curves, each consistent
with unitarity constraints, that can be used in the same way as a set
generated from a parametrized fit (e.g. a $z$-fit). This allows
integration over any desired bins. We further show some techniques to
increase the computational efficiency of the method.
We demonstrate the application to determining $V_{ub}$.
