Semileptonic decays of $Λ^{+}_{c}$ in light-front quark model with nonvalence contributions

TL;DR

This study addresses the SM prediction of exclusive semileptonic decays of $\Lambda^{+}_{c}$ to $\Lambda$ or neutron by employing a light-front quark model with a diquark picture to compute baryonic form factors across the time-like region. Nonvalence (zero-mode) contributions are incorporated via an effective Bethe-Salpeter framework, enabling direct calculation in the time-like regime and extraction of the baryon distribution amplitude parameter $\beta$ from data. The authors compute the $q^2$-dependent form factors $f_i(q^2)$ and $g_i(q^2)$, fit them with a double-pole form, and determine $\beta$ values $\beta_{\Lambda_c}=0.58\pm0.08$, $\beta_{\Lambda}=0.52\pm0.08$, and $\beta_{n}=0.44\pm0.04$; they then predict branching ratios for $\Lambda_c\to\Lambda\ell\nu_\ell$ and $\Lambda_c\to n\ell\nu_\ell$ with and without nonvalence contributions, finding that nonvalence effects increase the rates by about 10% and improve agreement with BESIII measurements. The results are compatible with lattice and other LFQM studies, and the framework offers a robust approach for testing SM baryonic dynamics and extending to other heavy-baryon semileptonic decays.

Abstract

We investigate the exclusive semilpetonic decays of $Λ^{+}_{c}\to (Λ/n) \ell^{+} ν_{\ell}~(\ell=e,μ)$ within the standard model by using the light-front quark model (LFQM). The form factor behaviors are obtained from the effective treatment of nonvalence contributions in addition to the valence ones in the Drell-Yan-West frame due to the Bethe-Salpeter formalism. Based on these form factors, we find that the decay branching ratios of $Λ^{+}_{c}\to (Λe^{+} ν_{e},\,Λμ^{+} ν_{e} ,\, n e^{+} ν_{e},\, n μ^{+} ν_{e})$ are about $ (3.39,\,3.21,\,0.36,\,0.35)\%$ with the non-valence contributions, which are consistent with the recent experimental measurements at BESIII. Furthermore, we use the experimental data to fit the $β$ parameters in the baryonic distribution amplitudes under the LFQM, resulting in ($β_{Λ_{c}},β_Λ, β_{n})= (0.58\pm0.08, 0.52\pm0.08,0.44\pm0.04)$.

Figures (6)

• Figure 1: The effective treatment of the LF amplitude (a) can be displayed into the LF valence part (b) in $0 < x <\alpha$ and the nonvalence one (c) in $\alpha < x < 1$, where the small and big dots of the mediator-quark vertices in (b) and (c) represent the LF ordinary and nonvalence wavefunction vertices, respectively.
• Figure 2: Nonvalence vertex (small black dot) linked to an ordinary light-front wave function (big black dot) through a relevant operator ${\cal K}$ (big white dot).
• Figure 3: Form factors of $\Lambda_{c} \to \Lambda$, where the gray bands represent the uncertainties.
• Figure 4: Form factors of $\Lambda_{c} \to n$, where the gray bands show the uncertainties.
• Figure 5: Differential decay widths of $\Lambda_{c} \to \Lambda\,\ell \,\nu_\ell~(\ell=e,\,\mu)$, where the gray bands show the total uncertainties.