Semileptonic $Λ_c \to Λ\ell ν_\ell$ Decays in Light-Cone QCD Sum Rules with $Λ_c$ Distribution Amplitudes

TL;DR

This work addresses the hadronic input uncertainties in the semileptonic decay $\Lambda_c^+ \to \Lambda \ell^+ \nu_\ell$ by applying light-cone QCD sum rules with $\Lambda_c$ distribution amplitudes. The authors derive sum rules for the six form factors $f_i(q^2)$ and $g_i(q^2)$ by matching hadronic and QCD representations of a correlator involving the interpolating current for $\Lambda$ and the weak current, and they incorporate two sets of $\Lambda_c$ LCDAs in a heavy-baryon framework, using a Borel transform and quark-hadron duality with a continuum threshold $s_0$. The form factors are extended from the LCSR-valid region to the full physical $q^2$ range via a $z$-series expansion with appropriate pole masses, and their uncertainties are assessed through a Monte Carlo analysis. From the extracted form factors, the differential and total decay widths are computed, yielding branching fractions $\mathcal{B}(\Lambda_c^+ \to \Lambda e^+ \nu_e) \approx 3.56$–$3.90\%$ and $\mathcal{B}(\Lambda_c^+ \to \Lambda \mu^+ \nu_\mu) \approx 3.51$–$3.88\%$, in good agreement with BESIII measurements and lattice-QCD calculations. The results reinforce SM expectations for this channel, show consistency across form-factor determinations using heavy-baryon LCDAs, and highlight potential refinements from radiative and subleading $1/m_c$ corrections in future work.

Abstract

We study the semileptonic decay of its SU(3) partner, the $Λ_c \to Λ\ell^+ ν_\ell$ ($\ell = e, μ$) transition, within the framework of light-cone QCD sum rules (LCSR) by using the distribution amplitudes of heavy $Λ_c$ baryon. The numerical analysis is performed using two different sets of $Λ_c$ baryon light-cone distribution amplitudes. The resulting form factors are parametrized by a model-independent $z$-series expansion and used to compute the differential and total decay widths. Our predictions for the branching fractions are in good agreement with the latest BESIII measurements and with lattice-QCD results.

Figures (1)

• Figure 1: Normalized distributions of the $\Lambda_c^+ \to \Lambda^0 \ell^+ \nu$ form factors $f_i$ and $g_i$ at $q^2 = 0$ obtained from LCSR. The solid lines represent Gaussian fits to the Monte Carlo distributions. For illustration, only the results corresponding to the DA set-I are shown.