Theoretical study of the $\Delta^{++}-\Delta^-$ configuration in the deuteron using antiproton beam

TL;DR

This paper provides a theoretical analysis of the $^{++}-^-$ configuration in the deuteron using light-cone formalism to account for relativistic effects, predicting observable momentum distributions in antiproton-deuteron reactions.

Contribution

It introduces a relativistic light-cone wave function approach to study the $^{++}-^-$ component, highlighting its importance in experimental signal-background separation.

Findings

Large differences between LC and NR wave function calculations.

Predicted characteristic momentum distribution shape of the $-$ system.

Visibility of the meson-exchange model's momentum distribution at 10-15 GeV/c.

Abstract

We study the manifestation of the $\Delta^{++}-\Delta^-$ component of the deuteron wave function in the exclusive reaction $\bar p d \to \pi^- \pi^- \Delta^{++}$. Due to the large binding energy the internal motion in the $\Delta-\Delta$ system is relativistic. We take this into account within the light-cone (LC) wave function formalism and, indeed, found large differences between calculations based on the LC and non-relativistic (NR) wave functions. We demonstrate, that the consistent LC treatment of the $\Delta-\Delta$ system plays the key role in the separation of the signal and background. Within the LC approach, the characteristic shape of the momentum distribution of the $\Delta-\Delta$ bound system predicted by the meson-exchange model is well visible on the background of usual annihilations at beam momenta between 10 and 15 GeV/c.