Angular distribution of $\hat{I}{›}_c^{+}\to \hat{I}{›}_{1405/1520}^{\ast }(\to \hat{I}\pounds \ddot{I}€){\ell }^{+}\hat{I}{½}_{\ell }$ and implications for form factors

Abstract

We study the cascade semileptonic decay $\hat{I}{›}_c^{+}\to \hat{I}{›}_{1405/1520}^{\ast }(\to \hat{I}\pounds \ddot{I}€){\ell }^{+}\hat{I}{½}_{\ell }$ using the helicity amplitude formalism, and derive the full four-body angular distribution. The contributions from the spin-$1/2$ and spin-$3/2$ intermediate resonances, their interference effects, and the corresponding angular coefficients are obtained explicitly. Using available form-factor inputs, we provide numerical predictions for the invariant-mass distribution, helicity-angle distributions, and angular asymmetries. Based on these observables, we discuss strategies for extracting the relevant form factors and analyze the sensitivity of the angular observables to variations in the form factors. Finally, we investigate the strong phases in the $\hat{I}{›}_c^{+}\to \hat{I}{›}^{\ast }$ form factors and discuss how the strong-phase difference can be extracted from the angular distribution. Our results offer useful theoretical guidance for future experimental analyses.

32 pages, 7 figures

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