Analysis of $\bar{p}$p $\to$ $\pi pi$ Data at Low Energy and its Implications

This thesis is a study of data on $\bar{p}$p $\to$ $\pi$$^{-}$$\pi$$^{+}$ in the range 0.36 < P$_{lab}$ < 1.55 GeV/c taken by the PS172 experiment at CERN's LEAR facility. The aim is to elucidate the nature of mesonic states coupling both to baryon-antibaryon and meson-meson channels. The PS172 data are compared with, and found to be consistent with, earlier data on the same channel, and, in a model independent way, the consistency of the PS172 results with BNL data on $\bar{p}$p $\to$ $\pi$$^{0}$$\pi$$^{0}$ is also established. The first amplitude analysis of $\bar{p}$p $\to$ $\pi$$\pi$ to incorporate the PS172 data is performed and it is found that from the hundreds of possible amplitudes, only two are compatible with the BNL \bar{p}$p $\to$ $\pi$$^{0}$$\pi$$^{0}$ data and with threshold conditions. The latter may be applied in a far more rigorous way than has been previously possible since the PS172 momentum range extends so close to threshold. Both of the solutions found exhibit resonances with spins 0—5 and the masses, widths and couplings of these states are deduced. The lowest spin resonances are found to have such large couplings to $\bar{N}#N that they are unlikely to be simple $\bar{q}q$ states.