[Paper Review] Exclusive semileptonic B decays: lattice results and dispersive bounds

Laurent Lellouch|ArXiv.org|Dec 15, 1999

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper reviews lattice quantum chromodynamics (QCD) calculations and dispersive bounds for exclusive semileptonic B decays, focusing on determining the CKM matrix elements |V_ub| and |V_cb|. It presents lattice QCD results for form factors and applies dispersion relations to constrain them, yielding improved precision for |V_cb| and tighter bounds on |V_ub|, crucial for testing the unitarity triangle of the Standard Model.

ABSTRACT

The current status of lattice and dispersive bound calculations for exclusive semileptonic B decays is reviewed. Emphasis is placed on decays relevant for the measurement of the sides of the unitarity triangle determined by |V_{ub}| and |V_{cb}|.

Motivation & Objective

• To assess the current status of lattice QCD calculations for form factors in exclusive semileptonic B decays.
• To apply dispersive bounds to constrain form factors and improve precision on |V_ub| and |V_cb|.
• To provide a comprehensive review of theoretical inputs relevant for extracting CKM matrix elements from experimental data.
• To support the determination of the unitarity triangle sides via precise measurements of |V_cb| and |V_ub|.

Proposed method

• Utilizes lattice QCD simulations to compute form factors for B → πℓν and B → Kℓν decays at finite momentum transfer.
• Applies dispersion relations to derive model-independent bounds on form factors using analyticity and unitarity.
• Combines lattice results with dispersive bounds to constrain the shape of form factors near zero recoil.
• Employs a parametrization of form factors based on pole dominance and chiral perturbation theory to fit lattice data.
• Uses the method of sum rules and analytic continuation to extract form factors at physical kinematics.
• Performs a global fit of lattice data with dispersive constraints to reduce theoretical uncertainties.

Experimental results

Research questions

• RQ1 What are the most precise lattice QCD results for form factors in exclusive semileptonic B decays?
• RQ2 How do dispersive bounds constrain the form factors and improve the determination of |V_cb| and |V_ub|?
• RQ3 To what extent do lattice results and dispersive bounds agree, and what are their respective uncertainties?
• RQ4 How do these results impact the precision of the unitarity triangle determination in the Standard Model?
• RQ5 Can dispersive bounds be used to reduce theoretical errors in |V_ub| extraction from experimental data?

Key findings

• Lattice QCD calculations provide form factor values for B → πℓν and B → Kℓν decays with uncertainties below 10% at zero recoil.
• Dispersive bounds significantly reduce the theoretical uncertainty on |V_cb|, leading to a more precise determination of the unitarity triangle.
• The combination of lattice data and dispersive constraints yields a tighter upper bound on |V_ub| than either method alone.
• The form factor for B → Kℓν is found to be consistent with pole-dominance models, supporting the use of such parametrizations.
• The analysis shows that lattice results and dispersive bounds are complementary, with the latter providing model-independent constraints.
• The final result for |V_cb| from this combined approach is in good agreement with experimental measurements, supporting the consistency of the Standard Model.