[Paper Review] $B o\pi\ell u$ and $B o\pi\ell^+\ell^-$ semileptonic form factors from unquenched lattice QCD

Daping Du, Bailey, Jon A.+12 more|arXiv (Cornell University)|Nov 26, 2013

Quantum Chromodynamics and Particle Interactions11 references4 citations

TL;DR

This paper presents a new lattice QCD calculation of B →πℓν and B →πℓ+ℓ− semileptonic form factors using unquenched Nf = 2+1 asqtad fermions across multiple lattice spacings and light quark masses. Employing SU(2) staggered chiral perturbation theory in the hard-pion limit and a novel functional z-expansion method, it achieves a robust, model-independent extrapolation to the physical and continuum limits, yielding precise form factors for |Vub| and rare B-meson decay studies.

ABSTRACT

Abstract Not Provided

Motivation & Objective

• To improve the theoretical determination of the CKM matrix element |Vub| by calculating B →π semileptonic form factors with higher precision than previous lattice studies.
• To address the long-standing tension between exclusive and inclusive determinations of |Vub| through improved lattice QCD methods and finer control over systematic uncertainties.
• To provide accurate form factors for the rare B →πℓ+ℓ− decay, which is sensitive to new physics beyond the Standard Model.
• To develop and apply a functional z-expansion method that robustly extends lattice form factors to the full kinematic range while preserving analyticity and unitarity constraints.
• To perform a combined chiral and continuum extrapolation using SU(2) hard-pion staggered chiral perturbation theory, accounting for taste-breaking effects in the staggered fermion formulation.

Proposed method

• Utilizes MILC asqtad ensembles with Nf = 2+1 dynamical quarks and lattice spacings ranging from ≈0.045 to 0.12 fm, including light quark masses down to ml/ms ≈ 0.05.
• Employs the Sheikholeslami-Wohlert clover action for the b quark and non-perturbative renormalization of vector and tensor currents via ZhlΓ = ρhlΓ / √(ZhhΓ ZllΓ), with ρhlΓ blinded by a constant factor.
• Extracts form factors f∥, f⊥, fT from ratios of three-point to two-point correlation functions, using a fit ansatz that includes ground and first excited states of the B and π mesons.
• Performs a combined chiral and continuum extrapolation using SU(2) heavy meson staggered chiral perturbation theory in the hard-pion limit, including NNLO analytic terms.
• Applies a functional z-expansion method based on kernel-based functional regression to extrapolate form factors to the full kinematic range, minimizing a functional chi-squared statistic over the χPT-continuum extrapolated form factors.
• Truncates the z-expansion at N = 4, finding stable results for central values and uncertainties, with analyticity and unitarity constraints enforced on the coefficients.

Experimental results

Research questions

• RQ1 How can lattice QCD form factors for B →πℓν be improved in precision and systematic control to resolve the |Vub| tension?
• RQ2 What is the impact of using SU(2) hard-pion staggered chiral perturbation theory on the chiral extrapolation of form factors compared to standard HMSχPT?
• RQ3 Can a functional z-expansion method based on statistical kernel regression provide a more robust and model-independent extrapolation of lattice form factors to the full kinematic range than synthetic data fitting?
• RQ4 How do the vector, scalar, and tensor form factors f+, f0, fT behave in the physical and continuum limit, and what are their correlations?
• RQ5 What are the dominant sources of uncertainty in the final form factor results, and how can they be quantified with full error budgets?

Key findings

• The chiral and continuum extrapolation using SU(2) hard-pion staggered chiral perturbation theory with NNLO analytic terms provides a good fit to the lattice data, with χ²/dof ≈ 1.1 for all form factors.
• The functional z-expansion method successfully extends the form factors f+, f0, and fT to the full kinematic range with stable results for truncation order N ≥ 4.
• The form factor f+ is found to be highly correlated with fT, consistent with their shared heavy quark limit, and both exhibit a pole-dominant structure.
• The scalar form factor f0 is constrained by the weaker unitarity condition and shows a smooth, monotonic behavior across the kinematic range.
• The results are robust against unphysical behavior in the large-Eπ region where chiral perturbation theory breaks down, due to the functional nature of the z-expansion.
• The analysis is currently blinded by a constant factor multiplying the ρhlΓ renormalization factor, which will be unblinded upon finalization of the error budget and publication of the full results.