Amplitude reconstruction in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>NN</mml:mi></mml:math>scattering at 6 GeV/<i>c</i>: Where do we stand and what measurements should be done?

Abstract

We study the problem of amplitude reconstruction at a fixed $t (\ensuremath{-}t\ensuremath{\sim}0.3$ ${\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c}}^{2}$). The five amplitudes are reconstructed, up to an overall phase, by 9 observables $\ensuremath{\sigma}$, ${P}_{0}$, ${C}_{\mathrm{nn}}$, ${K}_{\mathrm{nn}}$, ${D}_{\mathrm{nn}}$, ${C}_{\mathrm{ss}}$, ${C}_{\mathrm{sl}}$, ${C}_{\mathrm{ll}}$, and $I(\mathrm{sn}0s)$. This set includes all possible single-scattering measurements. The status of the amplitude reconstruction is discussed. To study both discrete ambiguities and the effects of the measurement errors, we employ a Monte Carlo method. We find that ${D}_{\mathrm{ls}}$ and $I(\mathrm{ns}0s)$ remove the prominent ambiguities. In addition, given the current precision, $R$ and $I(\mathrm{ls}0n)$ will significantly improve the amplitude determination.