[Paper Review] The B -> pi l nu form factor from unquenched lattice QCD with domain-wall light quarks and relativistic b-quarks

Taichi Kawanai, Oliver Witzel+1 more|arXiv (Cornell University)|Jan 1, 2012

Quantum Chromodynamics and Particle Interactions1 references8 citations

TL;DR

This paper presents a first lattice QCD calculation of the B →πlν form factor using unquenched 2+1 flavor domain-wall fermions for light quarks and relativistic b-quarks on RBC/UKQCD ensembles. Employing domain-wall valence quarks and relativistic heavy quark actions, the study computes form factors f∥ and f⊥ via three-point correlation functions, with nonperturbative renormalization and O(αSa) improvement. The key result is a new, independent determination of f+(q²) using a different gauge action, providing a critical check on existing calculations and addressing the persistent |Vub| puzzle.

ABSTRACT

We report on a lattice-QCD calculation of the B to pi l nu form factor with domain-wall light quarks and relativistic b-quarks using the 2 + 1 flavor domain-wall fermion and Iwasaki gauge-field ensembles generated by the RBC and UKQCD Collaborations. We present initial results obtained from the coarser (a ~ 0.11 fm) 24^3 lattices and some of the finer (a ~ 0.086 fm) 32^3 lattices.

Motivation & Objective

• To compute the B →πlν form factor f+(q²) with unquenched lattice QCD using domain-wall fermions for light quarks and a relativistic b-quark action.
• To provide an independent lattice QCD determination of f+(q²) using a different gauge action (Iwasaki) than previous calculations (e.g., MILC), to test consistency and address the |Vub| puzzle.
• To enable precise extraction of |Vub| by computing form factors with nonperturbative renormalization and O(αSa) improvement, reducing systematic uncertainties.
• To perform chiral extrapolation and continuum limit extrapolation using partially quenched valence quark masses and multiple lattice spacings.

Proposed method

• Uses 2+1 flavor domain-wall fermion and Iwasaki gauge-field ensembles from the RBC/UKQCD collaboration at two lattice spacings (a ≈ 0.11 fm and a ≈ 0.086 fm).
• Employs relativistic heavy quark (RHQ) action for the b quark to suppress discretization errors from its large mass.
• Computes the B →πlν matrix element via three-point correlation functions involving gauge-invariant Gaussian-smeared sources for the B meson and point sinks for the pion.
• Applies nonperturbative renormalization using the mostly nonperturbative method, with Zbb_V and Zll_V computed nonperturbatively and ρ computed at one-loop in mean-field improved perturbation theory.
• Implements O(αSa) improvement for the b →u vector current by computing one additional matrix element with a single-derivative operator at one-loop in mean-field improved perturbation theory.
• Uses the z-parameterization to extrapolate form factors over the full kinematic range down to q² = 0, enabling a model-independent determination of f+(q²).

Experimental results

Research questions

• RQ1 Can a lattice QCD calculation of the B →πlν form factor be performed with domain-wall valence quarks and a relativistic b-quark action on Iwasaki gauge ensembles?
• RQ2 How do the form factors f∥ and f⊥ computed with this method compare to previous results from MILC or HPQCD using staggered fermions?
• RQ3 What is the impact of using a different gauge action (Iwasaki) on the extracted value of f+(q²) and the resulting |Vub|?
• RQ4 To what extent can the form factor be extrapolated to the physical point using partially quenched valence quarks and chiral perturbation theory?
• RQ5 How well do the results agree with the experimental measurement of the differential decay rate, and what is the resulting |Vub| value?

Key findings

• The study reports initial results from coarser (a ≈ 0.11 fm) 24³ lattices and a subset of finer (a ≈ 0.086 fm) 32³ lattices, with form factors f∥ and f⊥ computed at multiple partially quenched valence quark masses.
• The nonperturbative renormalization factor Zbb_V is determined via a plateau fit to the Bs →Bs correlator, yielding Zbb_V = 10.037(34) on the coarser ensemble, in good agreement with the tree-level perturbative estimate of 10.606.
• The ratios RB→π_3,μ(t,tsnk) for the three-point functions show clear plateaus in the region 0 ≪ t ≪ tsnk, indicating suppression of excited-state contamination and enabling reliable extraction of f∥ and f⊥.
• The form factors f∥ and f⊥ are presented in lattice units as functions of the pion energy, showing consistent behavior across different valence quark masses and lattice ensembles.
• The results are preliminary and not yet extrapolated to the physical point or continuum limit; however, the methodology is validated on the coarser and selected finer ensembles.
• The authors plan to include the ρ-factor and O(a) improvement terms and perform full chiral and continuum extrapolations using z-parameterization to obtain f+(q²) over the full kinematic range.