$ω$-meson transverse twist-2 light-cone distribution amplitudes

TL;DR

The paper tackles the problem of precise theoretical predictions for the semileptonic decay $D^+\to \omega \ell^+ \nu_\ell$ by employing QCD light-cone sum rules with a right-handed chiral current to emphasize the chiral-odd, transverse twist-2 LCDA $\phi^{\perp}_{2;\omega}(x,\mu)$. It introduces a light-cone harmonic oscillator (LCHO) model for $\phi^{\perp}_{2;\omega}(x,\mu)$, parameterized by $A^{\perp}_{2;\omega}$, $b^{\perp}_{2;\omega}$, $B^{\perp}_{2;\omega}$, and guided by the Gegenbauer moment $a^{\perp}_{2;\omega}(\mu)$, evolved from $\mu_0$ to $\mu_k$. The four vector-meson form factors $A_1(q^2)$, $A_2(q^2)$, $A_0(q^2)$ and $V(q^2)$ are computed at low $q^2$ via LCSR, yielding $A_1(0)=0.537^{+0.053}_{-0.053}$, $A_2(0)=0.540^{+0.068}_{-0.068}$, $V(0)=0.754^{+0.079}_{-0.079}$, $A_0(0)=0.553^{+0.044}_{-0.043}$, with ratios $r_V$ and $r_2$ around unity. Extrapolations to the full $q^2$ range using the SSE allow predictions of branching fractions, differential widths, and polarization/asymmetry observables, which are in good agreement with BESIII and CLEO data. The results provide a robust test bed for the transverse LCDA and offer precise SM predictions for current and future experiments. Overall, the work advances the understanding of vector-meson LCDAs and demonstrates the viability of the LCHO approach in heavy-to-light semileptonic decays.

Abstract

In this work, we investigate semileptonic decay $D^+\to ω\ell^+ν_{\ell}$ 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) $φ^{\perp}_{2;ω}(x,μ)$ dominates the contribution in TFFs. We study the properties of twist-2 LCDA $φ^{\perp}_{2;ω}(x,μ)$ 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 $Γ_{\rm{L}}/Γ_{\rm{T}}=0.987^{+0.107}_{-0.121}$. Then, we get branching fraction $\mathcal{B}(D^+\to ωe^+ν_e)=(1.84^{+0.36}_{-0.33})\times 10^{-3}$ and $\mathcal{B}(D^+\to ωμ^+ν_μ)=(1.78^{+0.33}_{-0.30})\times 10^{-3}$, 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 $F_{\rm{L}}^{\ell}$.

Figures (4)

• Figure 1: The comparison of $\phi _{2;\omega}^{\bot} (x,\mu_0)$ with QCDSR Ball:1998sk and DL Dimou:2012un at $\mu_0=1~\rm{GeV}$, where the shaded band represents the uncertainty.
• Figure 2: The behavior of TFFs (a) $A_1(q^2)$, (b) $A_2(q^2)$, (c) $V(q^2)$, and (d) $A_0(q^2)$. For comparison, the predictions from HQEFT Wu:2006rd, $\rm{HM}\chi\rm{T}$Fajfer:2005ug, LFQM Verma:2011yw, RQM Faustov:2019mqr and CCQM Ivanov:2019nqd are also presented.
• Figure 3: The differential decay width $1/|V_{cd}|^2d\Gamma(D^+\to \omega\ell^+\nu_{\ell})/dq^2$ as a function of $q^2$, where (a) denotes the central values of longitudinal, transverse and total CKM-independent differential decay width, (b) denotes the comparison of various experimental and theoretical results for total CKM-independent differential decay width.
• Figure 4: The polarization and asymmetry observables as a function of $q^2$, where (a), (b), (c), (d), and (e) denotes forward-backward asymmetry $A_{\rm{FB}}^{\ell}$, lepton-side convexity parameter $C^{\ell}_{\rm{F}}$, longitudinal polarization $P_{\rm{L}}^{\ell}$, transverse polarization $P_{\rm{T}}^{\ell}$ and longitudinal polarization fraction $F_{\rm{L}}^{\ell}$, respectively.