Nucleon-antinucleon annihilation at large $N_c$

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 restrict the annihilation cross section so that it depends on six independent energy-dependent terms. At large $N_c$, a spin-flavor symmetry emerges 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 appear to be consistent with this expectation.

Figure 1

The data points represent the total annihilation cross section for unpolarized antineutrons incident on protons with various beam momentum; the data come from Ref. [31] and the errors include both systematic and statistical errors added in quadrature. The solid curve is a phenomenological fit to the total annihilation cross section for unpolarized antiprotons incident on protons as a function of beam momentum from Ref. [32]. This curve accurately fits all of the data points in this range to within a few percent.