Spin asymmetries and correlations in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Λ</mml:mi></mml:math>-pair production through the radiative return method

Abstract

Exclusive baryon pair production through the radiative return is a unique tool to determine the electric and the magnetic form factors in the timelike region over a wide range of energies. The decay of $\ensuremath{\Lambda}$-baryons into $p+{\ensuremath{\pi}}^{\ensuremath{-}}$ can be used to measure their spin and to analyze spin-spin correlations in the $\overline{\ensuremath{\Lambda}}\ensuremath{\Lambda}$ system. We evaluate the spin dependent hadronic tensor, which describes this reaction, calculate the corresponding cross section for ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\Lambda}\overline{\ensuremath{\Lambda}}$ and ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\Lambda}\overline{\ensuremath{\Lambda}}\ensuremath{\gamma}$ with subsequent decays of $\ensuremath{\Lambda}$ and $\overline{\ensuremath{\Lambda}}$ and present a compact formula for the correlated distribution. We demonstrate that the relative phase between the electric and the magnetic form factor can be determined in this analysis by considering single-spin asymmetries and correlated decay distributions. The reaction is implemented in the event generator PHOKHARA. It is demonstrated that the relative phase can be measured with the event sample presently accumulated at $B$- factories.