$Ξ_c \to Ξ$ Semileptonic Decays: An LCSR View on the Experiment-Lattice Tension

TL;DR

The paper addresses the nonperturbative challenge of describing semileptonic decays $\\Xi_c \to \\Xi \\ell^+ \\nu_{\\ell}$ by computing the hadronic transition form factors with light-cone QCD sum rules (LCSR) using the distribution amplitudes of the initial $\\Xi_c$ baryon within HQET. It derives sum rules for the six form factors $f_i(q^2), g_i(q^2)$ through a correlator between the final-state baryon current and the weak current, and then extrapolates the low-$q^2$ predictions to the full kinematic range using a $z$-series (BGL) parametrization with explicit pole masses. Numerical analysis uses $\\Xi_c$ DAs from Ref. Ali:2012pn, with $s_0=(3.5\pm0.5)$ GeV$^2$, $M^2 \in [2.0,3.0]$ GeV$^2$, and the Ioffe current ($\\beta=-1$), yielding $f_i(0)$ and $g_i(0)$ and predicting branching fractions such as $\\mathcal{B}(\\Xi_c^0 \to \\Xi^- e^+ \\nu_e)=(3.73\pm1.04)\%$ and $\\mathcal{B}(\\Xi_c^+ \to \\Xi^0 e^+ \\nu_e)=(11.20\pm3.25)\%$. The results agree with recent lattice QCD calculations but exceed current experimental measurements, highlighting a tension that motivates improved experimental determinations and refinement of heavy-baryon distribution amplitudes. These findings advance the nonperturbative understanding of charmed-baryon decays and provide a benchmark for future lattice and experimental studies.

Abstract

We present a light-cone QCD sum rule analysis of the semileptonic decays of $Ξ_c$ baryons, focusing on the channels $Ξ_c^0 \to Ξ^- \ell^+ ν_\ell$, and $Ξ_c^+ \to Ξ^0 \ell^+ ν_\ell$. The transition form factors are calculated within the light-cone QCD sum rules framework, using the distribution amplitudes of the heavy $Ξ_c$ baryons. The obtained form factors are then used to compute the differential and total decay widths, as well as the branching fractions. Our numerical results for the branching fractions are $\mathcal{B}(Ξ_c^0 \to Ξ^- \ell^+ ν_\ell) = (3.73 \pm 1.04)~\%$ , $\mathcal{B}(Ξ_c^0 \to Ξ^- μ^+ ν_μ) = (3.59 \pm 1.01)~\%$, $\mathcal{B}(Ξ_c^+ \to Ξ^0 \ell^+ ν_\ell) = (11.2 \pm 3.25)~\%$, and $\mathcal{B}(Ξ_c^+ \to Ξ^0 μ^+ ν_μ) = (10.8 \pm 3.13)~\%$. These results are in good agreement with recent lattice QCD calculations, while being larger than the current experimental measurements and differing from the predictions of other theoretical approaches.

Figures (1)

• Figure 1: Normalized distributions of the $\Xi_c^0 \to \Xi^- \ell^+ \nu$ 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.