Letter
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QCD analysis of $B \to π π$ form factors and the $| V_{u b} |$ extraction from $B_{l 4}$ decays

School of Physics and Electronics, Hunan University, 410082 Changsha, China; School for Theoretical Physics, Hunan University, 410082, Changsha, China; and Hunan Provincial Key Laboratory of High-Energy Scale Physics and Applications, 410082 Changsha, China

^*Contact author: scheng@hnu.edu.cn

Phys. Rev. D 112, L111301 – Published 2 December, 2025Erratum Phys. Rev. D 114, 059903 (2026)

DOI: https://doi.org/10.1103/gghb-bwfp

Abstract

We present a comprehensive QCD analysis of the $B \to π π$ form factors within the framework of light-cone sum rules, employing two-pion light-cone distribution amplitudes ( $2 π DA$ s). For the first time, we derive the twist-three $2 π DA$ s explicitly by exploiting the conformal symmetry of massless QCD. This breakthrough enables the first systematic calculation of higher-power corrections to the $B \to π π$ -type transitions. Leveraging the recently measured partial decay fractions of $B^{+} \to π^{+} π^{-} l^{+} ν_{l}$ by the Belle detector, we obtain $| V_{u b} | = (4.27 \pm 0.49 |_{data} \pm 0.55 |_{LCSRs}) \times 10^{- 3}$ within the dominant region of the $ρ$ resonance. We clarify that the relatively small value of $| V_{u b} |$ extracted from $B \to ρ l ν$ , when compared to the golden channel $B \to π l ν$ , arises due to the finite width and nonresonant effects. We anticipate future measurements of purely isovector and isoscalar $B_{l 4}$ decays, which will aid in reducing uncertainties by enhancing our understanding of the $π π$ phase shifts in the two-pion distribution amplitudes through heavy flavor decays.

Physics Subject Headings (PhySH)

Erratum

Erratum: QCD analysis of $B \to π π$ form factors and the $| V_{u b} |$ extraction from $B_{l 4}$ decays [Phys. Rev. D 112, L111301 (2025)]

Shan Cheng

Phys. Rev. D 114, 059903 (2026)

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Phys. Rev. D 112, L111301– Published 2 December, 2025

Vol. 112, Iss. 11 — 1 December 2025

Received 25 March 2025
Accepted 3 November 2025

DOI: https://doi.org/10.1103/gghb-bwfp

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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QCD analysis of $B \to π π$ form factors and the $| V_{u b} |$ extraction from $B_{l 4}$ decays

Abstract

Physics Subject Headings (PhySH)

Erratum

Erratum: QCD analysis of $B \to π π$ form factors and the $| V_{u b} |$ extraction from $B_{l 4}$ decays [Phys. Rev. D 112, L111301 (2025)]

Article Text

Supplemental Material

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QCD analysis of B→ππ form factors and the |Vub| extraction from Bl4 decays

Abstract

Physics Subject Headings (PhySH)

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Erratum: QCD analysis of B→ππ form factors and the |Vub| extraction from Bl4 decays [Phys. Rev. D 112, L111301 (2025)]

Article Text

Supplemental Material

References (67)

QCD analysis of $B \to π π$ form factors and the $| V_{u b} |$ extraction from $B_{l 4}$ decays

Erratum: QCD analysis of $B \to π π$ form factors and the $| V_{u b} |$ extraction from $B_{l 4}$ decays [Phys. Rev. D 112, L111301 (2025)]