A study of B → πℓν and Bs → Kℓν form factors using dispersive constraints

Abstract

This thesis presents several approaches to improve the extrapolation of form factors for the exclusive semileptonic decays $B \rightarrow \pi \ell \nu$ and $B_s \rightarrow K \ell \nu$. These decays are of interest for testing the predictions of the Standard Model.

These form factors cannot be calculated perturbatively, and so we rely on techniques such as Lattice QCD (Quantum Chromodynamics) to make theoretical predictions. For these heavy-to-light decays, Lattice QCD gives form factor information in a limited region of phase space and the results must be extrapolated to cover the entire kinematically-allowed region. Model-independent approaches based on dispersion relations are now widely used. The most common is Z-fits, but recently interest has been revived in what will here be called the Dispersive matrix (DM) approach.

The z-fit approach parametrizes the dispersion relations for these decays and uses lattice information to find optimal coefficients for the resulting curves. Approaches to improving the precision of this technique are explored, such as an alternative parametrization, and making use of information from multiple decays simultaneously.

The Dispersive Matrix method does not require parametrizing the form factor results (and so avoids any issues with truncation of the $z$ expansion). This method finds the minimum and maximum values of the form factors allowed by unitarity using known form factor points. Modifications to the method are trialled, including using information from multiple decays simultaneously, improving numerical stability when computing the bounds, and optimising the implementation of a kinematic constraint relating the form factors.

A novel method to generating form factor curves using the Dispersive matrix method is introduced, alongside several optimisations to improve computation time. This new method is tested, and the results, namely for the Cabibbo–Kobayashi–Maskawa matrix element, $|V_{ub}|$, are compared to those from the Z-fit approach.

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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 Andreas Juttner: orcid.org/0000-0002-3978-0927

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