Search

The Gerasimov-Drell-Hearn (GDH) sum rule connects the anomalous contribution to the magnetic moment of the target nucleus with an energy-weighted integral of the difference of the helicity-dependent photoabsorption cross sections. The data collected by HERMES with a deuterium target are presented together with a re-analysis of previous measurements on the proton. This provides a measurement of the generalised GDH integral covering simultaneously the nucleon-resonance and the deep inelastic scattering regions. The contribution of the nucleon-resonance region is seen to decrease rapidly with increasing $Q^2$. The DIS contribution is sizeable over the full measured range, even down to the lowest measured $Q^2$. As expected, at higher $Q^2$ the data are found to be in agreement with previous measurements of the first moment of $g_1$. From data on the deuteron and proton, the GDH integral for the neutron has been derived and the proton--neutron difference evaluated. This difference is found to satisfy the fundamental Bjorken sum rule at $Q^2 = 5$ GeV$^2$.

Two different \(\bar{p}n\) annihilation modes, \(\bar{p}n\rightarrow\pi^{-}4\pi^{0}\) and \(\bar{p}n\rightarrow 2\pi^{-}2\pi^{0}\pi^{+}\), are used to study the 4\(\pi\)–decays of scalar and vector mesons. The data are dominated by 4\(\pi\) scalar isoscalar interactions. At least two states are needed, the \(f_{0}(1370)\) and the \(f_{0}(1500)\). The 4\(\pi\)–decay width of the \(f_{0}(1370)\) is more than 6 times larger than the sum of all observed partial decay widths to two pseudoscalar mesons. The state has important couplings to \((\pi\pi)_{\mathrm{S}}(\pi\pi)_{\mathrm{S}}\) and to \(\rho\rho\). The 4\(\pi\)-decays of the \(f_0\)(1500) represent about half of its total width. The \(\rho(1450)\) and the \(\rho(1700)\) are observed in several 4\(\pi\) decay modes. The ratio of the \(4\pi\) relative to the \(2\pi\) decay of the \(\rho(1450)\) is in contradiction to its proposed interpretation as a pure hybrid state but it suggests that it is not a pure \(2^{3}\rm S_{1}\)–state either. Our results favour the assignment of the \(\rho(1700)\) as \(^{3}\rm D_{1}\) state, its interpretation as \(3^{3}\rm S_{1}\)-state is less plausible.

We have determined branching ratios for antiproton annihilations at rest on protons or neutrons in liquid deuterium which we compare to frequencies of isospin-related processes in antiproton-proton annihilations. Using the annihilation rates into $\pi^0\pi^0$ and $\pi^-\pi^0$ where the annihilation took place on the proton or neutron, respectively, we discuss the fraction of S-wave and P-wave annihilation in liquid D $_2$ . The frequencies for $\pi^-\omega$ and $\rho^-\pi^0$ , and $\pi^-\eta$ and $\pi^-\eta'$ and the corresponding frequencies for $\overline{\mbox p}$ p annihilations are used to determine isoscalar and isovector contributions to the protonium wave function. The isospin decomposition of the annihilating $\overline{\mbox p}$ p system in the $^3$ S $_1$ or $^1$ S $_0$ state is consistent with both, pure $\overline{\mbox p}$ p initial wave function and with the predictions of $\overline{\mbox N}$ N potential models. For the $^3$ P $_0$ state of the $\overline{\mbox p}$ p atom we find consistency with a pure $\overline{\mbox p}$ p system at annihilation while $\overline{\mbox N}$ N potential models predict large $\overline{\mbox n}$ n contributions. We observe $\rho$ - $\omega$ interference in $\overline{\mbox p}$ p $\rightarrow \pi^+\pi^-\eta$ and $\pi^+\pi^-\pi^0$ annihilation which we compare to $\rho$ - $\omega$ interference in $e^+e^-$ annihilation. The interference patterns show striking similarities due to similar phase relations; the interference magnitude depends on the $\omega$ - $\rho$ production ratio. The similarity of the phase in all 3 data sets demonstrates that isovector and isoscalar parts of the protonium ( $\overline{\mbox p}$ p atomic) wave function are relatively real, again in conflict with $\overline{\mbox N}$ N potential models. The annihilation rate for $\overline{\mbox p}$ d $\rightarrow$ K $^-$ K $^0$ p confirms the dominance of the isovector contribution to $\overline{\mbox N}$ N $\rightarrow$ K $\overline{\mbox K}$ annihilations. No complications due to initial state interactions are required by the data. Furthermore, we searched for narrow quasinuclear bound states close to the $\overline{\mbox N}$ N threshold, also predicted by $\overline{\mbox N}$ N potential models, but with negative outcome. We conclude that $\overline{\mbox N}$ N potential models are not suited to provide insight into the dynamics of the annihilation process.

Antiproton–proton annihilation into $\pi^0\eta\eta$ has been studied with the Crystal Barrel spectrometer at CERN at an incident beam momentum of 1.94 GeV/c. The data were taken with a trigger requiring neutral final states. A new isovector state, the $a_2(1660)$ decaying to $\pi^0\eta$ , is observed. In the $\eta\eta$ invariant mass region around 2.1 GeV/ $c^2$ , strong production of a heavy resonance is required, but our analysis does not distinguish between $J^P = 0^+$ , $2^+$ and $4^+$ . The production of the $f_0(1500)$ in reactions in flight is also observed.