Semileptonic decays of spin-entangled baryon-antibaryon pairs

A modular representation for the semileptonic decays of baryons originating from spin polarized and correlated baryon-antibaryon pairs is derived. The complete spin information of the decaying baryon is propagated to the daughter baryon via a real-valued matrix. It allows to obtain joint differential distributions in sequential processes involving the semileptonic decay in a straightforward way. The formalism is suitable for extraction of the semileptonic formfactors in experiments where strange-baryon-antibaryon pairs are produced in electron-positron annihilation or in charmonia decays. We give examples such as the complete angular distributions in the $e^+e^-\to \Lambda\bar\Lambda$ process, where $\Lambda\to pe^-\bar{\nu}_e$ and $\bar\Lambda\to\bar{p}\pi^+$. The formalism can also be used to describe the distributions in semileptonic decays of charm and bottom baryons. Using the same principles, the modules to describe electromagnetic and neutral current weak baryon decay processes involving a charged lepton-antilepton pair can be obtained. As an example, we provide the decay matrix for the Dalitz transition between two spin-1/2 baryons.