Probing $D_s^+ \to η^{(\prime)} \ell^+ν_\ell$ semileptonic decay within LCSR under chiral heavy quark effective field theory

Abstract

Motivated by the successful application of Heavy Quark Effective Field Theory in describing decays from heavy to light mesons, this work explores its applicability to the semileptonic decays of charmed mesons. So in this paper we investigate the $D_s^+\to η^{(\prime)} \ell^+ ν_\ell$ transition form factors using the light-cone sum rules approach within the framework of heavy-quark effective field theory. To address the large uncertainties arsing from the $η^{(\prime)}$-meson twist-3 distribution amplitudes, we employ the right-handed chiral correlation function. By applying the converging simplified series expansion method, we extrapolate the form factors to the entire physical $q^2$-region. Our analysis yields the branching fractions precise predictions for semi-leptonic decays $D_s^+\to η^{(\prime)}\ell^+ν_\ell$ with : $\mathcal{B}(D_s^+\toη\ell^+ν_\ell)=2.300^{+0.230}_{-0.227}\%$ ($\ell = e$) and $2.249_{-0.206}^{+0.209}\%$ ($\ell = μ$); $\mathcal{B}(D_s^+\toη^\prime \ell^+ν_\ell)=0.861^{+0.095}_{-0.093}\%$ ($\ell = e$) and $0.821^{+0.082}_{-0.080}\%$ ($\ell = μ$). The derived lepton flavor universality ratios $R^η_{μ,e}=0.977^{+0.008}_{-0.006}$ and $R^{η^{\prime}}_{μ,e} = 0.953^{+0.011}_{-0.009}$ are consistent with lasted BESIII experimental measurements. Additionally, the forward-backward asymmetry parameters $\langle \mathcal{A}^η_{\rm FB}\rangle=-0.034^{+0.003}_{-0.003}$ and $\langle \mathcal{A}^{η^\prime}_{\rm FB}\rangle=-0.073^{+0.007}_{-0.008}$ suggest that no significant violation of lepton flavor universality in this decay process.

Figures (5)

• Figure 1: The BHL model for the leading twist LCDA $\phi_{2;\eta}(x,\mu_0 = 1~{\rm GeV})$. For comparison, the predictions from the LCSR method Duplancic:2015zna, as well as the asymptotic form, the CLEO fit CLEO:1997fho, BABAR fit BaBar:2011nrp, and the results from P. Ball Ball:2004ye are also presented.
• Figure 2: The behavior of the $D_s \to \eta^{(\prime)} \ell^+ \nu_l$ TFFs $f_{+}^{D_s \eta^{(\prime)}}(q^2)$ with respect to the transfer momentum $q^2$ is shown in the figure. For comparison, this figure displays theoretical predictions obtained from different approaches (LCSR-2013 Offen:2013nma, LCSR-2015 Duplancic:2015zna, CCQM Ivanov:2019nqd) along with the most recent experimental measurements by the BESIII Collaboration BESIII:2023ajrBESIII:2023gbn.
• Figure 3: The behavior of the TFFs $f_{0}^{D_s \eta^{(\prime)}}(q^2)$ is shown in the figure. The data points with error bars in the figure are consistent with those in Fig. \ref{['fp']}.
• Figure 4: The differential decay widths of $D_s \to \eta^{(\prime)} \ell^+ \nu_\ell$, where the uncertainties are squared averages of those from all the mentioned error sources. The other lines and the data points with error bars in the figure are consistent with those in Fig. \ref{['fp']}.
• Figure 5: The relationship between the forward-backward asymmetry $\mathcal{A}_{\rm FB}(q^2)$ and the square of the momentum transfer $q^2$ in the semi-leptonic decay of $D_s \to \eta^{(\prime)} \mu^+\nu_\mu$ is presented. For comparison, data from the BESIII experimental BESIII:2023gbn are also illustrated.