QCD analysis of $B \to ππ$ form factors and the $\vert V_{ub} \vert$ extraction from $B_{l4}$ decays
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918197332017152 |
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| author | Cheng, Shan |
| author_facet | Cheng, Shan |
| contents | The $B_{l4}$ decays offer an independent method for determining the Cabibbo-Kobayashi-Maskawa matrix element $\vert V_{ub} \vert$, with a QCD analysis of the underlying $B \to ππ$ form factors serving as a crucial component. We present a comprehensive QCD analysis of the $B \to ππ$ form factors within the framework of light-cone sum rules, employing two-pion light-cone distribution amplitudes. For the first time, we derive the twist-three $2π$DAs explicitly by exploiting the conformal symmetry of massless QCD. This breakthrough enables the first systematic calculation of higher-power corrections to the $B \to ππ$-type transitions. Leveraging the recently measured partial decay fractions of $B^+ \to π^+π^- l^+ ν_l$ by the Belle detector, we obtain $\vert V_{ub} \vert = \left( 4.27 \pm 0.49\vert_{\rm data} \pm 0.55\vert_{\rm LCSRs} \right) \times 10^{-3}$ within the dominant region of the $ρ$ resonance. We clarify that the relatively small value of $\vert V_{ub} \vert$ extracted from $B \to ρl ν$, when compared to the golden channel $B \to πlν$, arises due to the finite width and nonresonant effects. We anticipate future measurements of purely isovector and isoscalar $B_{l4}$ decays, which will aid in reducing uncertainties by enhancing our understanding of the $ππ$ phase shifts in the two-pion distribution amplitudes through heavy flavor decays. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_07333 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | QCD analysis of $B \to ππ$ form factors and the $\vert V_{ub} \vert$ extraction from $B_{l4}$ decays Cheng, Shan High Energy Physics - Phenomenology High Energy Physics - Experiment High Energy Physics - Lattice The $B_{l4}$ decays offer an independent method for determining the Cabibbo-Kobayashi-Maskawa matrix element $\vert V_{ub} \vert$, with a QCD analysis of the underlying $B \to ππ$ form factors serving as a crucial component. We present a comprehensive QCD analysis of the $B \to ππ$ form factors within the framework of light-cone sum rules, employing two-pion light-cone distribution amplitudes. For the first time, we derive the twist-three $2π$DAs explicitly by exploiting the conformal symmetry of massless QCD. This breakthrough enables the first systematic calculation of higher-power corrections to the $B \to ππ$-type transitions. Leveraging the recently measured partial decay fractions of $B^+ \to π^+π^- l^+ ν_l$ by the Belle detector, we obtain $\vert V_{ub} \vert = \left( 4.27 \pm 0.49\vert_{\rm data} \pm 0.55\vert_{\rm LCSRs} \right) \times 10^{-3}$ within the dominant region of the $ρ$ resonance. We clarify that the relatively small value of $\vert V_{ub} \vert$ extracted from $B \to ρl ν$, when compared to the golden channel $B \to πlν$, arises due to the finite width and nonresonant effects. We anticipate future measurements of purely isovector and isoscalar $B_{l4}$ decays, which will aid in reducing uncertainties by enhancing our understanding of the $ππ$ phase shifts in the two-pion distribution amplitudes through heavy flavor decays. |
| title | QCD analysis of $B \to ππ$ form factors and the $\vert V_{ub} \vert$ extraction from $B_{l4}$ decays |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2502.07333 |