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Properties of the $\eta_q$ leading-twist distribution amplitude and its effects to the $B/D^+ \to\eta^{(\prime)}\ell^+ \nu_\ell$ decays

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arxiv 2307.04640 v2 pith:W3MTTVY6 submitted 2023-07-10 hep-ph

classification hep-ph
keywords amplitudedistributionleading-twistprimeranglerulescalculatedecay
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

The $\eta^{(\prime)}$-mesons in the quark-flavor basis are mixtures of two mesonic states $|\eta_{q}\rangle=|\bar u u+\bar d d\rangle/\sqrt 2$ and $|\eta_{s}\rangle=|\bar s s\rangle$. In the previous work, we have made a detailed study on the $\eta_{s}$ leading-twist distribution amplitude. As a sequential work, in the present paper, we fix the $\eta_q$ leading-twist distribution amplitude by using the light-cone harmonic oscillator model for its wave function and by using the QCD sum rules within the QCD background field to calculate its moments. The input parameters of $\eta_q$ leading-twist distribution amplitude $\phi_{2;\eta_q}$ at an initial scale $\mu_0\sim 1$ GeV are then fixed by using those moments. The sum rules for the $0_{\rm th}$-order moment can also be used to fix the magnitude of $\eta_q$ decay constant, which gives $f_{\eta_q}=0.141\pm0.005$ GeV. As an application of the present derived $\phi_{2;\eta_q}$, we calculate the transition form factors $B(D)^+ \to\eta^{(\prime)}$ by using the QCD light-cone sum rules up to twist-4 accuracy and by including the next-to-leading order QCD corrections to the twist-2 part, and then fix the related CKM matrix element and the decay width for the semi-leptonic decays $B(D)^+ \to\eta^{(\prime)}\ell^+ \nu_\ell$.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Non-perturbaitve effects for the isoscalar light vector $\omega$-meson in charmed meson semileptonic decays

    hep-ph 2025-11 conditional novelty 5.0 of 10

    With a new harmonic-oscillator model for the omega's transverse light-cone distribution amplitude, QCD light-cone sum rules reproduce the measured D+→ωℓν branching fractions and predict angular observables.

  2. Form factors and phenomenology of $\boldsymbol{B_{(s)}}$ and $\boldsymbol{D_{(s)}}$ semileptonic decays to $\boldsymbol{\eta}$ and $\boldsymbol{\eta^\prime}$

    hep-ph 2025-07 conditional novelty 5.0 of 10

    Updated light-cone sum rule form factors for B(s), D(s) to eta(eta') are fitted across the full q^2 range and used to extract V_ub, V_cs and V_cd with precision the authors call comparable to standard analyses.

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