Isospin mixing in protonium and annihilation dynamics

We have explored the sensitivity of pp¯-nn¯ isospin mixing in L=0,1 atomic states of protonium to changes in the multipion-exchange contribution to the nucleon-antinucleon (NN¯) potential. The resulting annihilation probabilities ${\gamma }_{\mathit{I}}^{\mathrm{\alpha }}$ for isospin I=0,1 and state α${=}^{2\mathit{S}+1\mathrm{}}$ ${\mathit{L}}_{\mathit{J}}$ are combined with the spin-flavor weights for transitions NN¯→${\mathit{M}}_1$ ${\mathit{M}}_2$ in the ${}_{}{}^3{}_{}{}^{}$ ${\mathit{P}}_0$ model, and confronted with selected measured branching ratios. Some problems with the phenomenology of the ${}_{}{}^3{}_{}{}^{}$ ${\mathit{P}}_0$ model are identified. We compare the ${}_{}{}^3{}_{}{}^{}$ ${\mathit{P}}_0$ model with a phenomenological ansatz suggested by Klempt, in which branching ratios are written as a product of spin, isospin, and orbital factors, multiplified by ${\gamma }_{\mathit{I}}^{\mathrm{\alpha }}$.