$\omega$-meson transverse twist-2 light-cone distribution amplitudes

TL;DR

This paper studies the semileptonic decay of D+ mesons to omega mesons using QCD light-cone sum rules, focusing on twist-2 distribution amplitudes, and provides theoretical predictions consistent with experimental data.

Contribution

It introduces a light-cone harmonic oscillator model for transverse twist-2 LCDA and applies it to calculate form factors and decay observables in D+ to omega semileptonic decays.

Findings

Calculated form factors at zero recoil with uncertainties.

Predicted branching fractions consistent with experimental results.

Provided predictions for polarization and asymmetry observables.

Abstract

In this work, we investigate semileptonic decay $D^+\to \omega \ell^+\nu_{\ell}$ within the framework of QCD light-cone sum rule. By constructing correlation function with right-handed chiral current, the transverse twist-2 light-cone distribution amplitudes (LCDA) $\phi^{\perp}_{2;\omega}(x,\mu)$ dominates the contribution in TFFs. We study the properties of twist-2 LCDA $\phi^{\perp}_{2;\omega}(x,\mu)$ by constructing a light-cone harmonic oscillator model. By applying it to the TFFs, we obtained $A_1(0)=0.537^{+0.053}_{-0.053}$, $A_2(0)=0.540^{+0.068}_{-0.068}$, $V(0)=0.754^{+0.079}_{-0.079}$, and $A_0(0)=0.553^{+0.044}_{-0.043}$ at large recoil point. Two TFF ratios are $r_V=1.40^{+0.21}_{-0.19}$ and $r_2=1.01^{+0.17}_{-0.16}$. After extrapolating those TFFs to the whole physical $q^2$ region by using the simplified $z(q^2,t)$ series expansion, the ratio of longitudinal and transverse decay widths is $\Gamma_{\rm{L}}/\Gamma_{\rm{T}}=0.987^{+0.107}_{-0.121}$. Then, we get branching fraction $\mathcal{B}(D^+\to \omega e^+\nu_e)=(1.84^{+0.36}_{-0.33})\times 10^{-3}$ and $\mathcal{B}(D^+\to \omega \mu^+\nu_{\mu})=(1.78^{+0.33}_{-0.30})\times 10^{-3}$, which is in good agreement with BESIII and CLEO Collaborations. Finally, we predict the forward-backward asymmetry $A_{\rm{FB}}^{\ell}$, lepton-side convexity parameter $C^{\ell}_{\rm{F}}$, longitudinal (transverse) polarization $P_{\rm{L}(\rm{T})}^{\ell}$, as well as longitudinal polarization fraction $F_{\rm{L}}^{\ell}$.