High-statistics study of the reactions ${\pi }^{-}p\to K^{-}{K}^{+}n$ and ${\pi }^{+}n\to K^{-}{K}^{+}p$ at 6 GeV/c

The Argonne Effective Mass Spectrometer has been used for a high-precision study of the reactions ${\pi }^{-}p\to K^{-}{K}^{+}n$ (110000 events) and ${\pi }^{+}n\to K^{-}{K}^{+}p$ (50000 events) at 6 GeV/c for $K^{-}{K}^{+}$ masses below 1750 MeV and momentum transfers $-t<\mathrm{}0.40\mathrm{}$ Ge${\mathrm{V}}^2$. Comparison of the two reactions isolates interferences between isospin-0 and isospin-1 $K^{-}{K}^{+}$ states. We observe $f-A_2^0$, $f^{\prime }-A_2^0$, and $f-f^{\prime }$ interferences in the $Y_4^0$ moment and find $f^{\prime }$ production to have a substantial contribution from some mechanism other than pion exchange. We present values for the $f^{\prime }$ mass (1506 ± 5 MeV), width (66 ± 10 MeV), and branching ratio [$(f^{\prime }\to \frac{\pi \pi }{f^{\prime }}\to \mathrm{all})=(1.2\mathrm{}\pm 0.4)\%$]. The relative $f-f^{\prime }$ production phase is found to be 170 ± 10°; the $2^{++}$ nonet mixing angle is determined to be 32.5 ± 0.5°, which is less than the ideal value. The measured relative $f-A_2^0$ production phase of (${63}_{-15\mathrm{}}^{+11\mathrm{}}$)° confirms a prediction of Irving and Michael based on duality and vectormeson production studies. The $\overline{K}K$ branching ratio of the $f$ meson is measured to be $(f\to \frac{\overline{K}K}{f}\to \mathrm{all})=(3.8\mathrm{}\pm 0.4)\%$. An SU(3) prediction for the ratio of the $\rho \mathrm{KK}$ to the $\rho \pi \pi$ coupling is found to agree with the data. In addition to the isospin-0 $S^{*}$, substantial isospin-1 $S$-wave production is observed near the $K^{-}{K}^{+}$ threshold and the effects of the recently reported $S$-wave enhancement of mass ∼1300 MeV are observed. Our results show that the enhancement has isospin 0, with a slow variation of phase.