Angular Distributions for Multi-body Semileptonic Charmed Baryon Decays

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 $B_1^{\prime }={\Omega }_c^{-}$ 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: $\mathcal{B}({\Lambda }_c^{+}\to p{\pi }^{-}{e}^{+}{\nu }_e)=2.48(15)\%$, $\mathcal{B}({\Lambda }_c^{+}\to p{\pi }^{-}{\mu }^{+}{\nu }_{\mu })=2.50(14)\%$, $\mathcal{B}({\Xi }_c\to \Lambda {\pi }^{-}{e}^{+}{\nu }_e)=2.40(30)\%$, $\mathcal{B}({\Xi }_c\to \Lambda {\pi }^{-}{\mu }^{+}{\nu }_{\nu })=2.41(30)\%$, $\mathcal{B}({\Omega }_c\to \Lambda K^{-}{e}^{+}{\nu }_e)=0.362(14)\%$, $\mathcal{B}({\Omega }_c\to \Lambda K^{-}{\mu }^{+}{\nu }_{\nu })=0.350(14)\%$. Besides, we also predict the $q^2$-dependence and angular distributions of these processes, in particular the coefficients for the $\cos n{\theta }_{\ell }$ ($\cos n{\theta }_h$, $\cos n\varphi$) $(n=0,1,2,\cdots )$ terms. This work can provide a theoretical basis for the ongoing experiments at BESIII, LHCb and BELLE-II.

Comments: 24 pages, 5 figures