BrokenŨ(8)andpp¯Annihilation at Rest

The problem of $p\overline{p}$ annihilation at rest into two mesons, pseudoscalar-pseudoscalar ($\mathrm{PP}$), pseudoscalar-vector ($\mathrm{PV}$), and vector-vector ($\mathrm{VV}$) mesons, is treated in detail in the framework of covariant $\tilde{U}\mathrm{}\left(8\right)\mathrm{}$ theory. Second-order spurions of the form q≈q, ${\sigma }_{\mu \nu }\times {\sigma }_{\mu \nu }$ are inserted into the $\tilde{U}\mathrm{}\left(8\right)\mathrm{}$-invariant annihilation amplitude, breaking further the intrinsically broken $\tilde{U}\mathrm{}\left(8\right)\mathrm{}$. The highlights of our predictions obtained from the input data (i) $A\left({\pi }^{+}{\pi }^{-}\right):A\left(K^{+}{K}^{-}\right)=9:5\mathrm{}$, (ii) $A\left(K^{+}{K}^{-}\right):A\left(K^0{\overline{K}}^0\right)=7:5\mathrm{}$, and (iii) $A\left({\rho }^0{\pi }^0\right):A\left({\rho }^0{\eta }^0\right)=5:2\mathrm{}$ are: (a) $A\left(K^{+}{K}^{*-}\right):A\left(K^0{\overline{K}}^{*0\mathrm{}}\right)=4:-5\mathrm{}$; (b) $A\left({\rho }^0{\pi }^0\right):A\left(K^{+}{K}^{*-}\right)=3:1\mathrm{}$; (c) $A\left({\rho }^{\pm ,0\mathrm{}}{\rho }^{\mp ,0\mathrm{}}\right):A\left(K^{*+}{K}^{*-}\right)=2:1\mathrm{}$; and (d) the nonexistence of sum rules hitherto predicted by $\tilde{U}\mathrm{}\left(12\right)\mathrm{}$. These results are in good agreement with experiments. We conclude from our results that $\tilde{U}\mathrm{}\left(8\right)\mathrm{}$ may be a better approximate symmetry for reactions than $\tilde{U}\mathrm{}\left(12\right)\mathrm{}$.