Form factor curves consistent with unitarity for semileptonic decays

Abstract

We discuss a method to generate form factor curves consistent with dispersive constraints across the entire kinematic range for exclusive semileptonic (SL) pseudoscalar to pseudoscalar decays, for example B→πℓνB→πℓν and B_s \rightarrowK \ell \nu. The work builds on the Dispersive Matrix (DM) method which allows model-independent extrapolation to any desired q2q2value in the SL physical region using known form factor information at specific discrete q2q2 points as input. Here qq is the outgoing lepton-pair 4-momentum. An obstacle in using DM results for phenomenological predictions, such as forward-backward asymmetries,is that it is not obvious how to use the bounds over continuous ranges of q2q2 when integrating, for example, the differential decay rate over the physical q2q2 range or over bins in q2q2. We describe a method to generate a family of curves, each consistent with unitarity constraints, that can be used in the same way as aset generated from a parametrized fit (e.g. a zz-fit). This allows integration over any desired bins. We further show some techniques to increase the computational efficiency of the method. We emonstrate the application to determining ∣Vub∣∣Vub​∣.

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Identifiers

ORCID for Callum James Radley-Scott: orcid.org/0009-0009-3869-6238

ORCID for Jonathan Flynn: orcid.org/0000-0002-6280-1677

ORCID for Nikolai Husung: orcid.org/0000-0003-4253-1443

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