Angular Distributions for Multi-body Semileptonic Charmed Baryon Decays

TL;DR

This paper analyzes angular distributions in semileptonic decays of charmed baryons, deriving analytic formulas and predicting branching fractions, angular distributions, and $q^2$-dependence to support ongoing experimental efforts.

Contribution

It provides analytic expressions for angular distributions using helicity amplitudes and predicts branching fractions and angular coefficients based on lattice QCD and model calculations.

Findings

Predicted branching fractions for various charmed baryon decays.

Derived analytic formulas for angular distributions.

Predicted $q^2$-dependence and angular coefficients.

Abstract

We perform an analysis of angular distributions in semileptonic decays of charmed baryons $B_1^{(\prime)}\to B_2^{(\prime)}(\to B_3^{(\prime)}B_4^{(\prime)})\ell^+\nu_{\ell}$, where the $B_1=(\Lambda_c^+,\Xi_c^{(0,+)})$ are the SU(3)-antitriplet baryons and $B_1'=\Omega_c^-$ is an SU(3) sextet. We will firstly derive analytic expressions for angular distributions using helicity amplitude technique. Based on the lattice QCD results for $\Lambda_c^+\to\Lambda$ and $\Xi_c^0\to\Xi^-$ form factors and model calculation of the $\Omega_c^0\to\Omega^-$ transition, we predict branching fractions: $\mathcal{B}(\Lambda_{c}^{+} \rightarrow p \pi^{-} e^{+} \nu_{e})=2.48(15)\%$, $\mathcal{B}(\Lambda_{c}^+\rightarrow p \pi^{-}\mu^{+}\nu_{\mu})=2.50(14)\%$, $\mathcal{B}(\Xi_{c}\rightarrow \Lambda \pi^{-}e^{+}\nu_{e})=2.40(30)\%$, $\mathcal{B}(\Xi_{c}\rightarrow \Lambda \pi^{-}\mu^{+}\nu_{\nu})=2.41(30)\%$, $\mathcal{B}(\Omega_{c}\rightarrow \Lambda K^{-}e^{+}\nu_{e})=0.362(14)\%$, $\mathcal{B}(\Omega_{c}\rightarrow \Lambda K^{-}\mu^{+}\nu_{\nu})=0.350(14)\%$. Besides, we also predict the $q^2$-dependence and angular distributions of these processes, in particular the coefficients for the $\cos n\theta_{\ell}$ ($\cos n\theta_{h}$, $\cos n\phi$) $(n=0, 1, 2, \cdots)$ terms. This work can provide a theoretical basis for the ongoing experiments at BESIII, LHCb and BELLE-II.