Nucleon-Antinucleon Annhiliation at Large Nc

TL;DR

This paper analyzes nucleon-antinucleon annihilation at large $N_c$ in QCD, revealing spin-flavor symmetry constraints and predicting equality of proton-antiproton and proton-antineutron annihilation cross-sections, consistent with experimental data.

Contribution

It demonstrates how large $N_c$ QCD imposes symmetry restrictions on annihilation cross-sections and derives identities relating different spin-isospin channels.

Findings

Proton-antiproton and proton-antineutron annihilation cross-sections are approximately equal at large $N_c$.

Spin-flavor symmetry constrains the dependence of the cross-section to three key terms.

Experimental data supports the predicted equality of unpolarized annihilation cross-sections.

Abstract

Nucleon-antinucleon annihilation in the large $N_c$ limit of QCD in the Witten regime of fixed velocity is considered with a focus on the spin and isospin dependence of the annihilation cross-section. In general, time-reversal and isospin invariance restricts the annihilation cross-section to depend on 6 independent energy-dependent terms. At large $N_c$, a spin-flavor symmetry emerges in the theory that acts to further restrict the dependence of the annihilation cross-section to three of these terms; the other terms amount to $1/N_c$ corrections. Assuming dominance of the leading order terms, several identities are derived that relate annihilation in different spin-isospin channels. A key prediction is that for unpolarized nucleons in Witten kinematics, the proton-antiproton annihilation cross-section should be equal to the proton-antineutron annihilation cross-section up to corrections of relative order $1/N_c$. Unpolarized nucleon-antinucleon annihilation data appears to be consistent with this expectation.