Status of the $D_s^+\toφ\ell^+ν_\ell$ decay with a chiral-odd $φ$-meson light-cone distribution amplitude

TL;DR

The paper develops a transverse leading-twist LCDA for the $\phi$ meson using a light-cone harmonic oscillator model and employs a right-handed chiral correlator in QCD light-cone sum rules to isolate twist contributions in $D_s^+\to\phi\ell^+\nu_\ell$ decays. It derives LCSR expressions for the form factors $V(q^2)$ and $A_{1,2,0}(q^2)$, connects them to helicity amplitudes, and computes observables across the full $q^2$ range via SSE extrapolation. The results yield branching fractions $\mathcal{B}(D_s^+\to\phi e^+\nu_e)=(2.271^{+0.291}_{-0.243})\times 10^{-2}$ and $\mathcal{B}(D_s^+\to\phi\mu^+\nu_\mu)=(2.250^{+0.287}_{-0.240})\times 10^{-2}$, and a CKM element $|V_{cs}|=0.975^{+0.067}_{-0.066}$, with twist-2 contributions dominating the form factors. The work provides predictions for polarization and asymmetry observables and demonstrates consistency with PDG, BESIII, and LQCD results, while offering a refined nonperturbative input for charm–strange semileptonic decays and tests of the SM.

Abstract

The twist-2 distribution amplitude of the $φ$-meson has attracted considerable interest due to its unique properties. In this work, we construct the transverse leading-twist light-cone distribution amplitude $φ_{2;φ}^\bot(x,μ_0)$ of the $φ$-meson using the light-cone harmonic oscillator model, in which a parameter $B_{2;φ}^\bot$ dominantly control its longitudinal distribution. To explicitly isolate different twist contributions, we employ the right-handed chiral correlator for the QCD light-cone sum rules calculation of $D_s^+\toφ$ decays, and further, we get the branching fraction, $\mathcal{B}(D_s^+ \to φe^+ν_e )= (2.271_{-0.243}^{+0.291})\times 10^{-2}$ and $\mathcal{B}(D_s^+ \to φμ^+ν_μ)=(2.250_{-0.240}^{+0.287})\times 10^{-2}$, where errors are squared average of the mentioned error sources. Furthermore, we have extracted the Cabbibo-Kobayashi-Maskawa (CKM) matrix element $|V_{cs}|=0.975_{-0.066}^{+0.067}$ with improved precision through the analysis. Finally, we calculated the polarization parameter and asymmetry parameter for the $D_s^+\toφ$ decays.

Figures (5)

• Figure 1: The transverse leading-twist LCDA $\phi_{2;\phi}^{\bot}(x,\mu_0)$ at the scale $\mu_0=1.5~\mathrm{GeV}$. As a comparison, the results derived from the SR Ball:2007zt, the DSE Gao:2014bca and LQCD Hua:2020gnw approaches have been presented.
• Figure 2: The chiral-odd high-twist DAs of $\phi$-meson at the scale $\mu_0=1~\mathrm{GeV}$.
• Figure 3: The extrapolated TFFs $A_1(q^2)$, $A_2(q^2)$ and $V(q^2)$ in the whole $q^2$-region, where the solid line are central values the shaded bands are corresponding uncertainties. In addition, it is compared with other predictions.
• Figure 4: The differential decay width $1/|V_{cs}|^2 d\Gamma(D_+^s \to \phi\ell^+\nu_\ell)/dq^2$ as a function of $q^2$, where the solid lines are central values and the shaded bands are corresponding uncertainties. In addition, it is compared with other predictions.
• Figure 5: The polarization and asymmetry parameters of the decay $D_s^+ \to \phi\ell^+\nu_\ell$, including their central values and uncertainties. The solid lines represent the central values, while the shaded regions indicate the corresponding uncertainties.